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6.5.5.4 BER and message acceptance measurement uncertainty
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Any BER (or message acceptance) uncertainty will influence the total uncertainty by the inverse of the slope of the appropriate BER function at the actual signal-to-noise ratio. As the BER function is very steep, the resulting dependency function is small, and it is sufficient to use the differential coefficient as an approximation. If the signalling is on a sub carrier, the relation between the signal-to-noise ratio of the sub carrier must be dealt with in the same way as with other receiver measurements. See clause 6.6.3.
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6.5.5.5 Other methods of measuring third order intermodulation
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Some test specifications specify other methods of measuring the intermodulation rejection. The measured result is the SINAD, BER, or message acceptance at fixed test signal levels. This is the case with some digital communication equipment like DECT and GSM. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 55 In these measurements the uncertainty must be calculated in 3 steps: 1) the uncertainty of the resulting signal-to-noise ratio is calculated; 2) this uncertainty is then applied to the appropriate SINAD, BER, or message acceptance function; 3) and then combined with the measurement uncertainty of the SINAD, BER, or message acceptance measurement. The uncertainty of the signal-to-noise ratio due to uncertainty of the level of the test signals is: ( ) 2 2 2 2 j w j y j x j SNR u u u = u + + This uncertainty is then transformed to the measured parameter. If the measured value is a SINAD value and the receiver is working beyond the knee point the SINAD uncertainty is identical, but if the receiver is working below the knee point the dependency function is in the order of 3,0. If the measurand is a BER or a message acceptance, the dependency function is too non linear to be regarded as a first order function. The total uncertainty must then be calculated as described in clause 6.6.4.3.
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6.6 Uncertainty in measuring continuous bit streams
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6.6.1 General
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If an EUT is equipped with data facilities, the characteristic used to assess its performance is the Bit Error Ratio (BER). The BER is the ratio of the number of bits in error to the total number of bits in a received signal and is a good measure of receiver performance in digital radio systems just as SINAD is a good measure of receiver performance in analogue radios. BER measurements, therefore, are used in a very similar way to SINAD measurements, particularly in sensitivity and immunity measurements.
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6.6.2 Statistics involved in the measurement
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Data transmissions depend upon a received bit actually being that which was transmitted. As the level of the received signal approaches the noise floor (and therefore the signal to noise ratio decreases), the probability of bit errors (and the BER) increases. The first assumption for this statistical analysis of BER measurements is that each bit received (with or without error) is independent of all other bits received. This is a reasonable assumption for measurements on radio equipment, using binary modulation, when measurements are carried out in steady state conditions. If, for instance, fading is introduced, it is not a reasonable assumption. The measurement of BER is normally carried out by comparing the received data with that which was actually transmitted. The statistics involved in this measurement can be studied using the following population of stones: one black and (1/BER)-1 white stones. If a stone is taken randomly from this population, its colour recorded and the stone replaced N times, the black stone ratio can be defined as the number of occurrences of black stones divided by N. This is equivalent to measuring BER. The statistical distribution for this measurement is the binomial distribution. This is valid for discrete events and gives the probability that x samples out of the N stones sampled are black stones (or x bits out of N received bits are in error) given the BER: ( ) ( ) ( ) x N x x BER BER ! x N x! N! P − − × − = 1 (6.7) ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 56 The mean value of this distribution is BER × N and the standard deviation is: ( ) N BER BER × − × 1 (6.8) and for large values of N the shape of the distribution approximates a Gaussian distribution. Normalizing the mean value and standard uncertainty (by dividing by N) gives: Mean value = BER (6.9) ( ) N BER BER u BER j − = 1 (6.10) From these two formulas it is easy to see that the larger number of bits, the smaller the random uncertainty, and the relation between number of bits and uncertainty is the same as for random uncertainty in general. By means of formula 6.11 it is possible to calculate the number of bits needed to be within a specific uncertainty. For example: A BER in the region of 0,01 is to be measured. a) If the standard uncertainty, due to the random behaviour discussed above, is to be 0,001, then the number of bits to be compared, N, in order to fulfil this demand is calculated from the rearranged formula (6.11). ( ) 900 9 001 0 99 0 01 0 1 2 2 = × = − = , , , u BER BER N jBER b) If the number of bits compared, N, is defined, e.g. 2 500 then the standard uncertainty is given directly by formula (6.11). ( ) 002 0 2500 01 0 1 01 0 , , , u BER j = − = As stated earlier the binomial distribution can be approximated by a Normal distribution. This is not true when the BER is so small that only a few bit errors (< 10) are detected within a number of bits. In this case the binomial distribution is skewed as the p (BER < 0) = 0. Another problem that occurs when only few bit errors are detected, and the statistical uncertainty is the dominant uncertainty (which does not happen in PMR measurements, but it does, due to the method, occur in DECT and GSM tests) is that the distribution of the true value about the measured value can be significantly different from an assumed Normal distribution. 6.6.3 Calculation of uncertainty limits when the distribution characterizing the combined standard uncertainty cannot be assumed to be a Normal distribution In the calculations of uncertainty there is usually no distinction between the distribution of a measured value about the true value, and the distribution of the true value about a measured value. The assumption is that they are identical. This is true in the cases where the standard uncertainty for the distribution of the measured value about the true value is independent of the true value - which usually is the case. But if the standard uncertainty is a function of the true value of the measurand (not the measured value), the resulting distribution of the measurement uncertainty will not be a Normal distribution even if the measured value about the true value is. This is illustrated by the following (exaggerated) example. A DC voltage is to be measured. We assume that there is only one uncertainty contribution which comes from the voltmeter used for the measurement. In the manufacturers data sheet for the voltmeter it is stated that the measured value is within ±25 % of the true value. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 57 If the true value is 1,00 V then the measured value lies between 0,75 V and 1,25 V. However, if the measured value is 0,75 V and the true value is still 1,00 V corresponding to 1,3333 times the measured value. Similarly, If the measured value is 1,25 V and the true value is still 1,0 V this corresponds to 0,8 times the measured value. Therefore the limits are asymmetric for the true value about the measured value (-20 % and +33,33 %). When looking at the standard deviations, the error introduced is small. In the previous example the standard deviation of the measured value about the true value is 14,43 %. The standard deviation of the related true value about the measured value is 15,36 %. As the difference is small, and the distribution of the measured value about the true value is based on an assumption anyway, the present document suggests that it can be used directly. NOTE: The average value, however, is no longer zero, but in this case is approximately 4,4 %. Alternatively, also in this example, xt is the true value and xm is the measured value. Any parameter printed in square brackets, e.g. [xm], is considered to be constant. The distribution of the measured value xm about the true value xt is given by the function p (xm, [xt]). Based on this function the distribution p1 (xt, [xm]) of the true value xt about the measured value xm can be derived. The intermediate function is p (xt, [xm]) which is the same as the previous; the only difference being that xt is the variable and xm is held constant. This function is not a probability distribution as the integral from -∞ to +∞ is not unity. To be converted to the probability function p1 (xt, [xm]) it must be normalized. Therefore: [ ] ( ) [ ] ( ) [ ] ( ) ∫ ∞ ∞ − = dx x x, p x , x p x , x p m m t m t 1 (6.11) As this distribution is not Normal, the uncertainty limits must be found by other means than by multiplication with a coverage factor from Student's t-distribution. How the actual limits are calculated in practise depends on the actual distribution. An example: If the true BER of a radio is 5 × 10-6 and the BER is measured over 106 bits, the probability of detecting 0 bits is 0,674 %. On the other hand if the BER in a measurement is measured as 5 × 10-6 the true value cannot be 0. If the uncertainty calculations are based on the assumption of a Gaussian distribution, the lower uncertainty limit becomes negative (which of course does not reflect reality, and provides the evidence that not all distributions are Normal!). The standard uncertainty based on the measured value 3,0 × 10-6: ( ) 6 6 6 6 10 1,73 10 10 0 3 1 10 0 3 − − − × = × − × = , , u j The expanded uncertainty is ±1,96 × 1,73 × 10-6 = ±3,39 × 10-6 at a 95 % confidence level. The correct distribution p1 (xt) is the continuous function in figure 17. NOTE: The true value is not BER, but number of bit errors, where BER= (bit errors/number of bits tested)). The binomial function p (xm) based on the true value = 3 bit errors (corresponding to BER = 3 × 10-6) is the discrete function shown. The distribution p (xt) (based on the binomial distribution with 3 bit errors and 106 bits tested): ( ) ( ) % x x k x p t t t 3 10 6 3 6 6 10 1 10 100 − − × × × = where ( ) 17 6 6 10 67 1 3 10 3 10 × = − × = , ! ! ! k ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 58 The integral from -∞ to +∞ of p (xt) is very close to 1. Therefore p (xt) is a good approximation to the correct distribution p1 (xt). By means of numerical methods the 95 % error limits are found to be +5,73 and -1,91 corresponding to +5,73 × 10-6 and -1,91 × 10-6. Figure 17 shows the discrete distribution giving the probabilities of measuring from 0 to 14 bit errors when the true value is 3 bit errors corresponding to BER = 3 × 10-6, and the continuous distribution giving the probability function for the true value when the measured value is 3 bit errors corresponding to BER = 3 × 10-6. 0 5 10 15 20 25 % bit errors 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 p (x ) 1 t Figure 17: BER uncertainty
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6.6.4 BER dependency functions
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As in SINAD measurements, the BER of a receiver is a function of the signal to noise ratio of the RF signal at the input of the receiver. Several modulation and demodulation techniques are used in data communication and the dependency functions are related to these techniques. This clause covers the following types of modulation: - coherent modulation/demodulation of the RF signal; - non coherent modulation/demodulation of the RF signal; - FM modulation. The following assumes throughout that the data modulation uncertainty combines linearly to the carrier to noise ratio uncertainty. The uncertainty calculations are based on ideal receivers and demodulators where correctly matched filters are utilized. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 59 The characteristics of practical implementations may differ from the theoretical models thereby having BER dependency functions which are different from the theoretical ones. The actual dependency functions can, of course, be estimated individually for each implementation. This, however, would mean additional measurements. Instead the theoretically deduced dependency functions may be used in uncertainty calculations.
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6.6.4.1 Coherent data communications
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Coherent demodulation techniques are techniques which use absolute phase as part of the information. Therefore the receiver must be able to retrieve the absolute phase from the received signal. This involves very stable oscillators and sophisticated demodulation circuitry, but there is a gain in performance under noise conditions compared to non coherent data communication. Coherent demodulation is used, for example, in the GSM system with Gaussian Minimum Shift Keying (GMSK).
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6.6.4.2 Coherent data communications (direct modulation)
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The BER as a function of SNRb, the signal to noise ratio per bit for coherent binary systems is: BER (SNRb) = 0,5 × erfc (√SNRb) (6.12) where erfc (x) is defined as: dt e erfc(x)= -t x 2 2 ∫ ∞ π (6.13) It is not possible to calculate the integral part of (6.11) analytically, but the BER as a function of the signal to noise ratio is shown in figure 18 together with the function for non coherent binary data communication. There are different types of coherent modulation and the noise dependency of each varies, but the shape of the function remains the same. The slope, however, is easily calculated and, although it is negative, the sign has no meaning for the following uncertainty calculations: ( ) ( ) b SNR b b e SNR SNR d BER d − × × = π 2 1 (6.14) For the purpose of calculating the measurement uncertainty, this can be approximated: ( ) ( ) BER , SNR d BER d b × ≈2 1 (6.15) If the aim is to transform BER uncertainty to level uncertainty - which is the most likely case in PMR measurements, the inverse dependency function must be used (the result is in percentage power terms as it is normalized by division with SNRb*): ( ) ( ) % SNR BER , u % SNR SNR d BER d u u b jBER b b jBER nty uncertai BER to due j level 100 2 1 100 * * × × × ≈ × = (6.16) The SNRb* is a theoretical signal to noise ratio read from figure 19. It may not be the signal to noise ratio at the input of the receiver but the slope of the function is assumed to be correct for the BER measured. For example: The sensitivity of a receiver is measured. The RF input level to the receiver is adjusted to obtain a BER of 10-2. The measured result is the RF level giving this BER. The BER is measured over a series of 25 000 bits. The resulting BER uncertainty is then calculated using formula (6.11): ( ) 4 10 29 6 25000 01 0 1 01 0 − × = − = , , , u j BER ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 60 The uncertainty of the RF signal at the input is 0,7 dB (uj). The signal to noise ratio giving this BER is then read from figure 18: SNRb*(0,01) = 2,7 and the dependency function at this level is: ( ) ( ) ( ) 2 2 10 2 1 10 1 2 1 2 1 7 2 − − × = × × = × = , , BER , SNR d , BER d b The BER uncertainty is then transformed to level uncertainty using formula (6.16): power % 1,95 100 7,2 10 2 1 10 29 6 2 4 = × × × × = − − % , , u j level dB 0,085 dB 0 23 95 1 = ≈ , , .... 085 0 7 0 2 2 + + = , , u level j RF There is an additional uncertainty component due to resolution of the readout of the measured BER. If the RF input level has been adjusted to give a reading of 0,01 and the resolution of the BER meter is 0,001 the correct lies between 0,0095 and 0,0105 with equal probability. The standard deviation is therefore 4 3 10 89 2 3 10 5 0 − − × = × = , , u lution j BER reso This standard deviation is then by means of formula 6.16 converted to level uncertainty: % SNR ) d(SNR d(BER) u u b b lution j BER reso esolution e to BER r j level du 100 × × = dB , dB , , % , % , , , , u esolution e to BER r j level du 004 0 0 23 089 0 089 0 100 7 2 01 0 2 1 10 289 0 4 = ≈ = × × × × = − The total uncertainty of the sensitivity level is then: dB 71 ,0 7,0 004 ,0 085 ,0 2 2 2 2 2 2 = + + = + = j resolution BER to due level j level j level c RF u u u u As can be seen the BER statistical uncertainty and the BER resolution only plays a minor role.
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6.6.4.3 Coherent data communications (sub carrier modulation)
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If a sub carrier frequency modulation is used in the data communication the functions related to direct coherent data communication apply, but in this case they give the relationship between BER and the signal to noise of the sub carrier. To be able to transform BER uncertainty to RF input level uncertainty the relationship between the sub carrier signal to noise ratio and the RF carrier signal to noise ratio must be calculated. If the BER is measured at a RF level much higher than the sensitivity this relation is assumed to be 1:1 as described in clause 6.5. In FM systems, if the BER is measured in the sensitivity region (below the knee point) the relationship as for analogue receivers is assumed and the same value taken from TR 100 028-2 [8], table F.1, 0,375 dB RF i/p level/dB SINAD and standard uncertainty 0,075 dB RF i/p level/dB SINAD. (see clause 6.5). EXAMPLE: The sensitivity of an FM receiver is measured. The RF input level to the receiver is adjusted to obtain a BER of 10-2. The measured result is the RF level giving this BER. The BER is measured over a series of 2 500 bits. The uncertainty of the RF signal at the input is 0,5 dB (uj). ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 61 The resulting BER uncertainty is then calculated using formula (6.11): ( ) 3 10 0 2 2500 01 0 1 01 0 − × = − = , , , u j BER The signal to noise ratio giving this BER is then read from figure 18: SNRb*(0,01) = 2,7. The dependency function at this level is: ( ) ( ) ( ) 2 2 10 2 1 10 0 1 2 1 2 1 7 2 − − × = × × = × = , , , BER , SNR d , BER d b The BER uncertainty is then transformed to level (or SNRb) uncertainty using formula (6.4): % 6,17 % 100 7 2 10 2 1 10 0 2 2 3 = × × × × = − − , , , u b j SNR power, which is equal to (6,17/23,0) = 0,27 dB. This uncertainty is then by means of formula (5.2) and the relationship taken from TR 100 028-2 [8], table F.1 converted to RF input level uncertainty (as SINAD and SNRb is considered to be equivalent in this case). The dependency function is: mean = 0,375 dB RF i/p level/dB SINAD and standard uncertainty 0,075 dB RF i/p level/dB SINAD. ( ) dB 102 0 08 0 38 0 27 0 2 2 2 , , , , u j level = + × = (formula 5.2) This RF level uncertainty is then combined with the uncertainty of the level of the input signal to obtain the total uncertainty of the sensitivity: dB 0,51 10 0 5 0 2 2 = + = , , u ity j sensitiv In this example the uncertainty due to meter resolution is assumed to be negligible.
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6.6.4.4 Non coherent data communication
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Non coherent modulation techniques disregard absolute phase information. Communications based on non coherent modulation tend to be more sensitive to noise, and the techniques used may be much simpler. A typical non coherent demodulation technique is used with FSK, where only the information of the frequency of the signal is required.
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6.6.4.5 Non coherent data communications (direct modulation)
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The BER as a function of the SNRb in this case is: ( ) 2 2 1 b SNR b e SNR BER − = (6.17) provided that the cross correlation coefficient ccross between the two frequencies defining the zeros and the ones is 0. The cross correlation coefficient ccross of two FSK signals with frequency separation fδ and the bit time T is: ( ) δ δ π π f T f T ccross × × × × sin = (6.18) It is assumed that the cross correlation coefficient for land mobile radio systems is so small that the formulas for ccross = 0 apply, and as ccross is 0 the BER, as a function of the SNRb for non coherent modulation is shown in equation 6.15. The slope of the function (in fact the slope is negative, but the sign is of no interest for the uncertainty calculation). The BER (SNRb) function for non coherent data communication is shown in figure 19. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 62 The inverse function is: SNRb (BER) = -2 × ln (2 × BER) (6.19) From (6.17) the slope of SNRb (BER) is: ( ) ( ) BER BER d SNR d b 2 − = (6.20) The slope of the function is the inverse of (6.18): ( ) ( ) 2 BER SNR d BER d b = (6.21) The SNRb can be calculated by means of formula (6.19) or read from the function shown in figure 19. If the aim is to transform BER uncertainty to level uncertainty - which is generally the case in PMR measurements - formula (6.16) is used. ( ) ( ) * b b j BER j level SNR SNR d BER d u u × = Before it can be combined with the other part uncertainties at the input of the receiver it must be transformed to linear voltage terms. EXAMPLE: The sensitivity of a receiver is measured. The RF input level to the receiver is adjusted to obtain a BER of 10-2. The measured result is the RF level giving this BER. The BER is measured over a series of 2 500 bits. The uncertainty of the RF signal at the input is 0,6 dB (uj). The resulting BER uncertainty is then calculated using formula (6.11): 3 10 00 2 2500 99 0 01 0 − × = × = , , , u j BER The signal to noise ratio giving this BER is then calculated using formula (6.19). SNRb (0,01) = -2 × ln (2 × 0,01) = 7,824 The dependency function at this level is (formula (6.21)): ( ) ( ) ( ) 01 0 5 0 824 7 , , SNR d , BER d b × = The BER uncertainty is then transformed to level uncertainty using formula (6.16): power % 5,11 % 100 824 7 10 5 0 10 00 2 2 3 = × × × × = − − , , , u j level which is equal to 5,11/23,0 dB = 0,22 dB (uj) in voltage terms. This RF level uncertainty is then combined with the rest of the uncertainty contribution to give the combined standard uncertainty of the RF level. ( ) ( ) dB 64 0 22 0 6 0 2 2 , , , u level c RF = + = ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 63
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6.6.4.6 Non coherent data communications (sub carrier modulation)
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If a sub carrier modulation is used in the data communication the functions related to direct non coherent data communications apply, but in this case they give the relation between BER and signal to noise ratio of the sub carrier. To be able to transform BER uncertainty to RF input level uncertainty the relationship between the sub carrier signal to noise ratio and the RF carrier signal to noise ratio must be calculated. If the BER is measured at a RF level much higher than the sensitivity this relationship is assumed to be 1:1 as described in clause 6.5. In FM systems, If the BER is measured in the sensitivity region (below the knee point) the relationship as for analogue receivers is assumed and the same value taken from TR 100 028-2 [8], table F.1, 0,375 dBRF i/p level/dBSINAD and standard uncertainty 0,075 dB RF i/p level/dB SINAD (see clause 6.5). EXAMPLE: The sensitivity of an FM receiver is measured. The RF input level to the receiver is adjusted to obtain a BER of 10-2. The measured result is the RF level giving this BER. The BER is measured over a series of 2 500 bits. The uncertainty of the RF signal at the input is 0,6 dB (uj). The resulting BER uncertainty is then calculated using formula (6.11): 3 10 00 2 2500 99 0 01 0 − × = × = , , , u BER j The signal to noise ratio giving this BER is then calculated using formula (6.19). SNRb*(0,01) = -2 × ln (2 × 0,01) = 7,824 The dependency function at this level is: ( ) ( ) ( ) 2 01 0 824 7 , SNR d , BER d b = This BER uncertainty is then transformed to level uncertainty using formula (6.16): power % 5,11 % 100 824 7 10 5 0 10 00 2 2 3 = × × × × = − − , , , u j level which is equal to 5,11/23,0 = 0,22 dB (uj level). This sub carrier level uncertainty is then transformed to RF level uncertainty. ( ) ( ) ( ) ( ) dB 0,08 075 0 375 0 22 0 2 2 2 = + × = SINAD RF SINAD RF /dB dB /dB dB d transforme level j RF , , , u NOTE: As the uncertainty is small the dependency function can be used directly without transforming to dB. This RF level uncertainty is then combined with the uncertainty of the level of the input signal to obtain the total uncertainty of the sensitivity: ( ) ( ) dB 0,61 08 0 6 0 2 2 = + = , , u ity j sensitiv The uncertainty due to meter resolution is assumed to be negligible.
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6.6.5 Effect of BER on the RF level uncertainty
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The SNRb to BER function is used to transform BER uncertainty to RF input level uncertainty. In the measurements on PMR equipment the RF input level is adjusted to obtain a specified BER. A sufficiently large number of bits are examined to measure the BER, but still there is a (small) measurement uncertainty contribution uj BER. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 64
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6.6.5.1 BER at a specified RF level
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If the purpose is to measure the BER at a specific input level, the transformation is more of a problem. The BER function is so non-linear that the approximation where (dBER)/(dSNRB) is used as the dependency function is no longer sufficient. One approach is to calculate the uncertainty limits of the RF input level at the wanted confidence level, and then apply these limits directly to the BER function. In this case the statistical uncertainty in the BER measurement is ignored, but as the following example shows, the uncertainty due to this is negligible. For example: The BER of a receiver is measured with the RF input level adjusted to the sensitivity limit. A BER of 0,75 × 10-2 is measured over a series of 25 000 bits. The uncertainty of the RF signal at the input is 1,1 dB (uj). The resulting BER uncertainty is then calculated using formula (6.11): ( ) 4 10 45 5 25000 0075 0 1 0075 0 − × = − = , , , u j BER corresponding to 7,3 % The straight forward procedure of calculating the combined standard uncertainty by applying a 1st order dependency function to the standard uncertainty of the RF input level uncertainty does not reflect reality due to the non linearity of the BER function. This is shown in the following calculation. The dependency function is 1,2 × 0,75 × 10-2 = 0,9 × 10-2 found by formula 6.3. The SNRb at BER= 0,0075 is read to be 2,9 from figure 18. The level uncertainty of 1,1 dB corresponds to 1,1 × 23,0 % (p) = 25,5 % (uj).This is transformed to SNRb uncertainty: 0,255 × 2,9 = 0,74 (uj). The level uncertainty is then transformed to BER uncertainty by means of the dependency function. uj BER = 0,74 × 0,9 × 10-2 = 0,666 × 10-2. The expanded uncertainty = ±1,96 × 0,666 × 10-2 = ±1,31 × 10-2 at a 95 % confidence level. This expanded uncertainty would give a negative bit error ratio as the lower limit. The reason is the non-linearity of the BER function (see also the discussion on confidence levels and their relations with the actual distributions, in clause D.5.6.2 of TR 100 028-2 [8]). Therefore another method should be applied. The expanded uncertainty should be expressed at a 95 % confidence level. Therefore the input level uncertainty limits are found to be ±1,96 × 1,1 dB = ±2,16 dB. This corresponds to 1,64 and 0,608 (power values). The values corresponding to the 95 % confidence level is then 2,9 × 1,64 = 4,76 and 2,9 × 0,608 = 1,76. By means of figure 18 the BER uncertainty limits at 95 % confidence level are read to be 3,0 × 10-2 and 1,0 × 10-3 corresponding to +300 % and -87 %. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 65 1 2 3 7 8 9 10 11 12 6 5 4 Signal to noise ratio per bit SNRb (in linear terms) BER(SNRb) for coherent modulation 10-4 10-3 10-2 10-1 1,5 2,0 3,0 4,0 5,0 6,0 8,0 1,5 2,0 3,0 4,0 5,0 6,0 1,5 2,0 3,0 4,0 5,0 6,0 1,5 2,0 3,0 4,0 5,0 6,0 1,5 2,0 3,0 4,0 5,0 6,0 8,0 8,0 8,0 8,0 10-6 10-5 Figure 18: BER (SNRb) against SNRb ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 66 4 6 8 16 18 20 22 24 26 14 12 10 Signal to noise ratio per bit SNRb (in linear terms) BER(SNRb) for noncoherent modulation 10-6 10-5 10-4 10-3 10-2 10-1 1,5 2,0 3,0 4,0 5,0 6,0 8,0 1,5 2,0 3,0 4,0 5,0 6,0 1,5 2,0 3,0 4,0 5,0 6,0 1,5 2,0 3,0 4,0 5,0 6,0 1,5 2,0 3,0 4,0 5,0 6,0 8,0 8,0 8,0 8,0 Figure 19: BER (SNRb) against SNRb ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 67
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6.6.6 Limitations in the applicability of BER uncertainty calculations
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As mentioned earlier the above figures and formulas are not applicable to all BER measurements; the conditions for applicability : - the noise is white Gaussian noise; - the signal-to-noise ratio is constant; - each bit error is statistically independent; - the transmission channel delay is constant. These 4 conditions apply to most normal receiver measurements covered by this document, but the blocking measurement (and any variant where the unwanted signal is un-modulated) does not satisfy the first condition about white Gaussian noise. Therefore the formulas do not apply to this measurement. The receiver is normally not as sensitive to a single frequency component as to a broad band signal with the same power. In some technologies (for instance GSM) data are protected by error correcting signalling schemes. The data are usually transmitted in packets with extra information for the error correction attached to the packet, so that up to a specified number of bit errors within a packet can be corrected. When this limit is exceeded the number of bits will increase dramatically because the error correction procedures will generate more bit errors than actually received. The result is that the BER will be less sensitive to noise at moderate signal-to-noise ratios, but the dependency function will be steeper at lower signal-to-noise ratios. The reception of the data packet also relies on the recognition of the packet's preamble or synchronization pattern. If this is not received and accepted all data are lost. The dependency function depends very much on the error correction algorithm and must be analysed and derived in each case. In some technologies receiver characteristics are measured under fading and multi-path conditions which means that the signal-to-noise ratio is not constant, but the multi-path conditions add other errors like distortion and timing errors of the demodulated signal. Also it causes the bit errors to appear as bursts rather than independent errors. In all the cases above the BER dependency functions derived previously do not apply, as one or more of the conditions are not fulfilled. The dependency functions must then be derived or estimated by other means. A simple approach is to estimate the dependency function by measuring the BER at different signal-to-noise ratios, for instance by changing the level of the wanted signal 1 dB up and down. The problem is that the dependency functions estimated for one receiver do not necessarily apply to the next receiver even within the same technology.
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100 028-1
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6.7 Uncertainty in measuring messages
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100 028-1
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6.7.1 General
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If the EUT is equipped with message facilities the characteristic used to assess the performance of the equipment is the Message acceptance ratio. The Message acceptance ratio is the ratio of the number of Messages accepted to the total number of message sent. Normally it is required to assess the receiver performance at a Message acceptance ratio of 80 %. The Message acceptance ratio is used as a measure of receiver performance in digital radio systems in a similar way that SINAD and BER ratios are used as a measure of receiver performance in analogue and bit stream measurements, particularly in sensitivity and immunity measurements. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 68
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6.7.2 Statistics involved in the measurement
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When considering messages, parameters such as message length (in bits), type of modulation (direct or sub-carrier, coherent or non-coherent), affect the statistics that describe the behaviour of the receiver system. Performance of the receiver is assessed against a message acceptance ratio set by the appropriate standard and/or methodology used. To assess the uncertainty the cumulative probability distribution curves for message acceptance are required, these can be calculated from (6.20). Pe (0) + Pe (1) + Pe (2) + Pe (3) + ... + Pe (n) (6.22) Where: n is the message length: - Pe (0) is the probability of 0 errors; - Pe (1) is the probability of 1 errors; - Pe (2) is the probability of 2 errors; - Pe (3) is the probability of 3 errors; - Pe (n) is the probability of n errors. The individual contribution of each probability Pe (x) in formula (6.22) is calculated using formula (6.8). Curves for a theoretical 50 bit system with 1, 2, 3, 4, 5 and 6 bits of error correction are shown in figure 20. As the number of bits of error correction increase so does the slope of the relevant portion of the cumulative probability density function, and as the slope increases less carrier to noise (or RF input level) variation is required to cause the message acceptance ratio to vary between 0 % and 100 %. This effect is increased in non-linear systems by a factor of approximately 3:1. Due to the increased slope associated with sub-carrier modulation, as a result of this in our theoretical 50 bit system, 6 bits of error correction will result in a very well defined level of 0 % acceptance to 100 % acceptance, (with 1 dB level variation), however, with no error correction, the level variation between 0 % and 100 % acceptance will be several dB. C u m u l a t i v e p r o b a b i l i t y d i s t r i b u t i o n level (dB) 2 3 4 5 6 7 8 0,0 10 20 30 40 50 60 70 80 90 100 9 1 0 1 1 1 2 Probability(%) Figure 20: Cumulative Probability (error correction for Messages) ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 69 As a method of testing receivers the "up-down" method is used. The usage of the up down method will result in a series of transmissions using a limited number of RF levels. 6.7.3 Analysis of the situation where the up down method results in a shift between two levels With some systems (e.g. 6 bits of error correction) the up-down method will typically result in a pattern shifting between two levels, where at the lower level the message acceptance ratio will approach zero and at the higher level (+1 dB) the message acceptance ratio will approach 100 %. In this case the measurement uncertainty is of the simplest form for this contribution. The RF is switching between two levels, the mean value is calculated, usually from 10 or 11 measurements. The measurement uncertainty cannot be calculated as though random, independent sources are involved. The RF is switching between two output levels of the same signal generator, the levels therefore are correlated and only have two values (upper and lower), hence the standard uncertainty for a signal generator with output level uncertainty of ±1 dB is: dB 0,58 3 0 1 = = , u level j output Also there is a quantization uncertainty associated with half of the step size (in this case 1 dB which gives ±0,5 dB). dB 0,29 3 5 0 = = , u ation j quantisi Therefore the combined standard uncertainty of this step will be: dB 0,65 29 0 58 0 2 2 2 2 = + = + = , , u u u tion j quantisa level j output shift level two c For the case of no error correction the pattern of the measured results will spread beyond a single dB step and measurement uncertainty calculations are more complex.
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100 028-1
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6.7.4 Detailed example of uncertainty in measuring messages
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For this example a theoretical system with 50 bit message length and 1 bit error correction will be considered, although the principles can be applied to all practicable message and correction lengths. a) Calculate the message acceptance ratio (formula (6.22)) for the given message length and given number of bit error corrections, using bit error ratios corresponding to a convenient step size (in this case 1 dB) using either formula (6.18) for non-coherent, or, formula (6.12) for coherent, and if sub-carrier modulation is used, use the appropriate SINAD conversion in TR 100 028-2 [8], table F.1. b) Now the probability of being at a given point on the curve must be assessed. For example the probability of being at a particular point (in figure 20) is: - the probability of being below a particular point times the probability of going up from this point; plus - the probability of being above a particular point times the probability of going down from this point. The method requires three successful responses, therefore the probability of going up is: Pp (up) = 1 - (Message Acceptance)3 = 1- (MA)3 (6.23) and the probability of going down is: Pp (down) = (Message Acceptance)3 = (MA)3 (6.24) (Pe (0) + Pe (1)) = Probability of 0 errors + the probability of 1 error (see formula (6.24)). These calculations are shown in table 2. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 70 Table 2: Probability of going up or down from a given position dB Linear BER (Pe(0) + Pe(1))% Pp (up)=1- (MA)3 Pp (down)= (MA)3 +2 12,679 0,8826 × 10-3 99,91 2,698 × 10-3 997,3 × 10-3 +1 10,071 3,251 × 10-3 98,83 34,69 × 10-3 965,3 × 10-3 0 8,000 9,158 × 10-3 92,30 213,7 × 10-3 786,3 × 10-3 -1 6,355 20,84 × 10-3 72,02 626,4 × 10-3 373,6 × 10-3 -2 5,048 40,07 × 10-3 39,95 936,2 × 10-3 63,76 × 10-3 -3 4,010 67,33 × 10-3 14,13 997,2 × 10-3 2,821 × 10-3 -4 3,185 101,7 × 10-3 3,123 1,000 30,46 × 10-6 -5 2,530 141,1 × 10-3 0,459 1,000 96,55 × 10-9 Based on equations (6.21) and (6.22), and the fact that the sum of all probabilities equals 1, the individual probabilities of being at each step of the signal to noise ratio per bit (SNRb) can be calculated. Assuming that at SNRb greater than +1 dB all messages are accepted (therefore can only move down from here) and Assuming that at SNRb less than -4 dB all messages are rejected (therefore can only move up from here), this gives rise to two boundary positions -5 dB and +2 dB. The probability of being at any one of the points -5, -4, -3, -2, -1, 0, +1, +2 is Pp-5, Pp-4, Pp-3, Pp-2, Pp-1, Pp0, Pp + 1, and Pp + 2 respectively. The analysis of the possible transitions between these points provide: - Pp-5 = (Pp-4 + 30,46 × 10-6) + (Pp-6 × 1); - Pp-4 = (Pp-3 × 2,821 × 10-3) + (Pp-5 × 1); - Pp-3 = (Pp-2 × 63,76 × 10-3) + (Pp-4 × 1); - Pp-2 = (Pp-1 × 373,6 × 10-3) + (Pp-3 × 997,2 × 10-3); - Pp-1 = (Pp0 × 786,3 × 10-3) + (Pp-2 × 936,2 × 10-3); - Pp0 = (Pp + 1 × 965,3 × 10-3) + (Pp-1 × 626,4 × 10-3); - Pp + 1 = (Pp + 2 × 1) + (Pp0 × 213,7 × 10-3); - Pp + 2 = (Pp + 3 × 1) + (Pp + 1 × 34,69 × 10-3). NOTE: The probability of being at point Pp-6 or Pp + 3 is zero, hence Pp-6 × 1 and Pp + 3 × 1 are both equal to zero. Based on seven out of these eight equations and the fact that the sum of Pp-5 to Pp + 2 is one, each individual probability Pp-5 to Pp + 2 is calculated as follows. Rearranging the above equations gives: - Pp-6 × 1 - Pp-5 + Pp-4 × 30,46 × 10-6 = 0; - Pp-5 × 1 - Pp-4 + Pp-3 × 2,821 × 10-3 = 0; - Pp-4 × 1 - Pp-3 + Pp-2 × 63,76 × 10-3 = 0; - Pp-3 × 997,3 × 10-3 - Pp-2 + Pp-1 × 373,6 × 10-3 = 0; - Pp-2 × 936,2 × 10-3 - Pp-1 + Pp0 × 786,3 × 10-3 = 0; - Pp-1 × 626,4 × 10-3 - Pp0 + Pp + 1 × 965,3 × 10-3 = 0; ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 71 - Pp0 × 213,7 × 10-3 - Pp + 1 + Pp + 2 × 1 = 0; - Pp + 1 × 34,69 × 10-3 - Pp + 2 + Pp + 3 × 1 = 0; - Pp-5 + Pp-4 + Pp-3 + Pp-2 + Pp-1 + Pp0 + Pp + 1 + Pp + 2 = 1; - Pp-6 = Pp + 3 = 0. Pp-5 Pp-4 Pp-3 Pp-2 Pp-1 Pp0 Pp + 1 Pp + 2 1 1 -1 2,821 × 10-3 2 1 -1 63,76 × 10-3 3 997,3 × 10-3 -1 373,6 × 10-3 4 936,2 × 10-3 -1 786,3 × 10-3 5 626,4 × 10-3 -1 965,3 × 10-3 6 213,7 × 10-3 -1 1 7 34,69 × 10-3 -1 8 1 1 1 1 1 1 1 1 1 Solving this by means of row operations on row 8, gives: 1 1 -1 2,821 ×××× 10-3 2 1 -1 63,76 × 10-3 3 997,3 × 10-3 -1 373,6 × 10-3 4 936,2 × 10-3 -1 786,3 × 10-3 5 626,4 × 10-3 -1 965,3 × 10-3 6 213,7 × 10-3 -1 1 7 34,69 × 10-3 -1 8 392,91 1 From this we have: 392,91 × Pp + 2 = 1; therefore Pp + 2 = 2,545 × 10-3: - this is then used in row 7 to determine Pp + 1: 3 3 3 1 10 36 73 10 69 34 10 545 2 − − − + × = × × = , , , Pp ; - this is used in row 6 to determine Pp0: ( ) 3 3 3 0 10 38 331 10 7 213 1 10 545 2 07336 0 − − − × = × × × − = , , , , Pp ; - this is used in row 5 to determine Pp-1: ( ) 3 3 3 3 3 1 10 97 415 10 4 626 10 3 965 10 36 73 10 38 331 − − − − − − × = × × × × − × = , , , , , Pp ; - this is used in row 4 to determine Pp-2: ( ) 3 3 2 10 0 166 9362 0 7863 0 33138 0 10 97 415 − − − × = × − × = , , , , , Pp ; - this is used in row 3 to determine Pp-3: ( ) 3 3 3 10 622 10 9973 0 3736 0 41597 0 10 00 166 − − − × = × − × = , , , , , Pp ; - this is used in row 2 to determine Pp-4: ( ) 6 3 3 4 10 84 37 1 10 76 63 1660 0 10 622 10 − − − − × = × × − × = , , , , Pp ; - this is used in row 1 to determine Pp-5: ( ) 6 3 3 6 5 10 87 7 1 10 821 2 10 622 10 10 84 37 − − − − − × = × × × − × = , , , , Pp . There are, off course, other ways of solving the equations. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 72 After having calculated the probabilities it should always be checked that the sum of all probabilities is 1. If the sum is not 1 (to within 0,001) it can cause major uncertainties in the calculation of the resulting standard uncertainty of the distribution. Based on these probabilities the standard uncertainty of the distribution is calculated: ∑ = − = − = × = 2 5 70 0 i i i , i Pp X (formula 5.6) ∑ = − = = × = 2 5 2 26 1 i i i , i Pp Y (formula 5.7) then: ( ) dB 0,88 70 0 26 1 2 2 = − − = − = , , X Y u j (formula 5.8) and the standard uncertainty for the measurement (as the result is the average value of 10 samples): dB 0,28 10 88 0 = , (formula 5.9) The expanded uncertainty is ±1,96 × 0,28 = ±0,54 dB at a 95 % confidence level. Therefore the methodology introduces an additional ±0,54 dB of uncertainty to the level. 6.8 Examples of measurement uncertainty analysis (Free Field Test Sites)
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100 028-1
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6.8.1 Introduction
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This clause contains detailed worked examples of the calculation of expanded uncertainty of the radiated tests on Free Field Test Sites i.e. Anechoic Chambers, Anechoic Chamber with a ground plane and Open Area Test Sites. The example tests given are limited to: - a verification procedure; - the measurement of a transmitter parameter (spurious emission); - the measurement of a receiver parameter (sensitivity). All the example tests are assumed to have been carried out in an Anechoic Chamber with a ground plane since this type of test site will contribute virtually all the uncertainty contributions involved in radiated tests on any Free Field Test Site (i.e. all uncertainties associated with absorbing materials and ground planes). NOTE 1: The values given to the uncertainty components in these examples are only to illustrate the uncertainty calculations. In practice, values should be derived by consulting annex A. All radiated tests consist of two stages. For a verification procedure, the first stage is to set a reference level whilst the second stage involves the measurement of path loss between two antennas. For the measurement of a particular parameter from an EUT, the first stage is usually to measure the relevant parameter whilst the second stage compares this measurement against that from a known standard. Within any radiated test there are uncertainty components that are common to both stages of the test. By their different natures some of these common uncertainties will cancel (e.g. the uncertainty of the insertion loss of a cable common to both parts) whilst others may contribute twice (e.g. the level stability of a signal generator in receiver tests). In each of the following uncertainty analyses, uncertainty components common to both stages are shown as shaded areas in the accompanying schematic diagrams. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 73 As shown in the examples, all the individual uncertainty components for any test are combined in the manner described in TR 102 273 [3], part 1, sub-part 1, clauses 4 and 5 in order to derive an expanded uncertainty figure for the measurement. The values of the individual components are either provided in annex A or should be taken from manufacturers' data sheets. Whenever they are obtained from data sheets, worst case figures given over a frequency band should be used. For example, in the case of a signal generator whose absolute level accuracy is quoted as ±1 dB over 30 MHz to 300 MHz, ±2 dB over 300 MHz to 1 000 MHz the figure for the band containing the test frequency should be used. This approach should be adopted for all uncertainty components, taking the uncertainty figures over as broad a band a possible. This is normally satisfactory when the variation with frequency is not large and provides a simple and flexible approach. The resulting expanded uncertainty figure is valid across a broad range of frequencies and measurement conditions and avoids the necessity of repeated calculation for minor frequency changes. NOTE 2: Taking specific frequency values may result in a lower expanded uncertainty value, but this lower value is only valid when that specific set of circumstances apply for which the value was derived.
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6.8.2 Example 1: Verification procedure
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The verification procedure is a process carried out to prove a facility's suitability as a Free Field Test Site. It involves the transmission of a known signal level from one calibrated antenna (usually a dipole) and the measurement of the received signal level in a second calibrated antenna (also usually a dipole). By comparison of the transmitted and received signal levels, an "insertion loss" can be deduced. For the measurement of NSA two stages are involved. The first is a direct attenuation measurement (Vdirect) whilst the second is a radiated attenuation measurement (Vsite). After inclusion of any correction factors relevant to the measurement, the figure of loss which results from the verification procedure is known as "Site Attenuation". NSA is determined from the value of Site Attenuation by subtraction of the antenna factors and mutual coupling effects. The subtraction of the antenna factors and any mutual coupling effects makes NSA independent of antenna type. Symbolically: NSA = Vdirect - Vsite - AFT - AFR - AFTOT where: Vdirect = received voltage using the "in-line" adapter; Vsite = received voltage using the antennas; AFT = antenna factor of the transmitting antenna; AFR = antenna factor of the receiving antenna; AFTOT = mutual coupling correction factor. The verification procedure measures both Vdirect and Vsite and then (after relevant corrections and calculations) compares the measured value of NSA against the theoretical figure calculated for that particular type of facility. The difference between the two values at any specific frequency is a measure of the quality of the facility at that frequency.
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100 028-1
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6.8.2.1 Uncertainty contributions: Stage 1: Direct attenuation measurement
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The first stage of the verification procedure is the direct attenuation measurement. This is carried out with all the items of test equipment connected directly together via an "in line" adapter between the attenuators as shown in figure 21. The components shown shaded are common to both stages of the procedure. "In line" adapter Attenuator 2 10 dB Receiving device Attenuator 1 10 dB Signal generator cable 1 cable 2 ferrite beads ferrite beads Figure 21: Stage 1: Direct attenuation measurement Despite the commonality of most of the components to both stages of this procedure, the mismatch uncertainty contribution for both stages has to be calculated and included in the uncertainty calculations. This is a result of load conditions varying (i.e. antennas replacing the adapter in the second stage). Conversely, as a result of this commonality, the uncertainty contributions of some of the individual components will cancel. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 74 Whereas figure 21 shows, schematically, the test equipment set-up for this stage of the verification procedure, an analysis diagram of the individual components (each of which contributes its own uncertainty) for this stage of the measurement is shown in figure 22. Again, as stated above, the shaded areas represent components common to both stages of the verification procedure.
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100 028-1
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6.8.2.1.1 Contributions from the mismatch components
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Mismatch: direct attenuation measurement: The value of the combined standard uncertainty of the contribution due to the mismatch from the source to the receptor, i.e. between the signal generator and the receiving device, is calculated from the approach described in annex G. All the individual contributions are U-distributed. NOTE 1: In this example the value taken for the signal generator output reflection coefficient is the worst case value over the frequency band of interest. Similarly for the cable, adapter and attenuator VSWRs. NOTE 2: The attenuation values of the cables and attenuators should be obtained from the data sheets/calibration records at the specific frequency of the test, along with the associated uncertainties for these values. Receiving device Cable loss Receiving device Signal generator Cable loss Cable factor Receiving antenna cable 2 Transmitting antenna cable 1 source Transmitting Adaptor Mismatch Attenuator 1 10 dB Mismatch + + + + Attenuator 2 10 dB Cable factor Mismatch Mismatch Mismatch Mismatch + + + + Figure 22: Stage 1: Direct attenuation measurement individual uncertainty components Signal generator: Output reflection coefficient: |ρG| = 0,20 Cable: Input and output reflection coefficients: |S11| = |S22| = 0,07 Attenuation: 1 dB = |S12| = |S21| = 0,891 Attenuator: Input and output reflection coefficients |S11| = |S22| = 0,05 Attenuation = 10 dB |S12| = |S21| = 0,3162 Adapter: Input and output reflection coefficients |S11| = |S22| = 0,02 Attenuation = 0,1 dB |S12| = |S21| = 0,9886 ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 75 Attenuator: Input and output reflection coefficients |S11| = |S22| = 0,05 Attenuation = 10 dB |S12| = |S21| = 0,3162 Cable: Input and output reflection coefficients: |S11| = |S22| = 0,07 Attenuation: 1 dB = |S12| = |S21| = 0,891 Receiving device: Input reflection coefficient: |ρRD| = 0,20 Mismatch uncertainty in the direct attenuation measurement: In the following the transmitting antenna cable is named cable 1, the transmitting antenna attenuator is named attenuator 1, the receiving antenna cable is named cable 2, the receiving attenuator is named attenuator 2. Those components that are constant for both stages 1 and 2 are not calculated as they do not contribute to the overall uncertainty. Mismatch between: - uj generator and cable 1: Constant for both stage 1 and 2. Hence this value does not contribute. - uj cable 1 and attenuator 1: Constant for both stage 1 and 2. Hence this value does not contribute. % 0,071 % 2 100 02 ,0 05 ,0 1 : = × × = adapter and attenuator mismatch j u % 0,071 % 2 100 05 ,0 02 ,0 1 : = × × = attenuator and adapter mismatch j u - uj attenuator 2 and cable 2: Constant for both stage 1 and 2. Hence this value does not contribute. - uj cable 2 and receiving device: Constant for both stage 1 and 2. Hence this value does not contribute. - uj generator and attenuator 1: Constant for both stage 1 and 2. Hence this value does not contribute. % 0,035 % 2 100 316 ,0 07 ,0 07 ,0 2 1 : = × × × = adapter and cable mismatch j u % 0,173 % 2 100 988 ,0 05 ,0 05 ,0 2 2 1 : = × × × = attenuator and attenuator mismatch j u % 0,010 % 2 100 316 ,0 07 ,0 02 ,0 2 2 : = × × × = cable and adapter mismatch j u - uj attenuator 2 and receiving device: Constant for both stage 1 and 2. Hence this value does not contribute. % 0,022 % 2 100 316 ,0 891 ,0 02 ,0 2,0 2 2 : = × × × × = adapter and generator mismatch j u % 0,024 % 2 100 988 ,0 316 ,0 05 ,0 07 ,0 2 2 2 1 : = × × × × = attenuator and cable mismatch j u % 0,024 % 2 100 316 ,0 988 ,0 07 ,0 05 ,0 2 2 2 1 : = × × × × = cable and attenuator mismatch j u % 0,022 % 2 100 891 ,0 316 ,0 2,0 02 ,0 2 2 : = × × × × = device receiving and adapter mismatch j u ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 76 % 0,055 % 2 100 988 ,0 316 ,0 891 ,0 05 ,0 2,0 2 2 2 2 : = × × × × × = attenuator and generator mismatch j u - uj mismatch: cable 1 and cable 2: Less than 0,01 % due to the two attenuators, therefore neglected. % 0,055 % 2 100 891 ,0 316 ,0 988 ,0 2,0 05 ,0 2 2 2 1 : = × × × × × = device receiving and attenuator mismatch j u - uj mismatch: generator and cable 2: Less than 0,01 % due to the two attenuators, therefore neglected. - uj mismatch: cable 1 and receiving device: Less than 0,01 % due to the two attenuators, therefore neglected. - uj mismatch: generator and receiving device: Less than 0,01 % due to the two attenuators, therefore neglected. The combined standard uncertainty of the mismatch is then calculated: % 0,306 055 ,0 055 ,0 ... 071 ,0 071 ,0 2 2 2 2 . : = + + + + = att direct mismatch c u Transforming to logarithmic form (TR 100 028-2 [8], annex E): 0,306 %/11,5 = 0,026 dB. The standard uncertainty of the contribution, due to the mismatch in the direct attenuation measurement, is designated throughout all parts of TR 102 273 [3] as uj35. Its value in this example is 0,026 dB.
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100 028-1
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6.8.2.1.2 Contributions from individual components
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6.8.2.1.2.1 Signal generator Signal generator: absolute output level: In a verification procedure, the signal generator's absolute level uncertainty contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the signal generator absolute output level uncertainty is designated throughout all parts of TR 102 273 [3] as uj38. NOTE 1: In this example case the standard uncertainty of the contribution due to the signal generator absolute output level uncertainty is taken to be 0,00 dB since, once the level has been set in stage one of the procedure, the level is not further adjusted. The uncertainty is therefore assumed to be systematic i.e. it produces the same offset in both stages. Signal generator: output level stability: In any test in which the contribution of the absolute level uncertainty of the signal generator contributes to the combined standard uncertainty of the test i.e. it does not cancel due to the methodology, the contribution from the output level stability is considered to have been included in the signal generator absolute output level, uj38. Conversely, for any level in which the absolute level uncertainty of the signal generator does not contribute to the combined standard uncertainty, the output level stability of the signal generator should be included. The standard uncertainty of the contribution due to the signal generator output level stability is designated throughout all parts of TR 102 273 [3] as uj39. Its value can be derived from manufacturers' data sheet. NOTE 2: In this example case the uncertainty of the contribution due to the signal generator output level stability is obtained from the manufacturers data sheet as ±0,02 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,01155 dB. This is rounded down to 0,01 dB. 6.8.2.1.2.2 Transmitting antenna cable Insertion loss: transmitting antenna cable: The transmitting antenna cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the transmitting antenna cable is designated throughout all parts of TR 102 273 [3] as uj41. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 77 NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the transmitting antenna cable is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. Cable factor: transmitting antenna: Cable factor is defined as the total effect of the antenna cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency, parasitic effects on the transmitting antenna (acting as a director or reflector) and introducing an unbalanced, common mode current into the dipole balun. In a radiated measurement the standard uncertainty of the cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the transmitting antenna cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the transmitting antenna cable is taken as 0,00 dB since there are no external fields involved other than leakage, which is assumed to have a negligible effect on the measurement. 6.8.2.1.2.3 Transmitting antenna attenuator Insertion loss: transmitting antenna attenuator: The transmitting antenna attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution, due to the insertion loss uncertainty of the transmitting antenna attenuator, is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the transmitting antenna attenuator is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. 6.8.2.1.2.4 Adapter Insertion loss: adapter: The adapter has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the adapter is not used outside the manufacturer's specification. The standard uncertainty of the contribution due to the insertion loss uncertainty of the adapter is designated throughout all parts of TR 102 273 [3] as uj42. Its value can be derived from the manufacturer's data sheet. NOTE: In this example case the uncertainty of the contribution due to the insertion loss uncertainty of the adapter is obtained from the manufacturer's data sheet as ±0,10 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,06 dB. 6.8.2.1.2.5 Receiving antenna attenuator Insertion loss: receiving antenna attenuator: The attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the receiving antenna attenuator is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the receiving antenna attenuator is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 78 6.8.2.1.2.6 Receiving antenna cable Insertion loss: receiving antenna cable: The receiving antenna cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution, due to the insertion loss uncertainty of the receiving antenna cable, is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the receiving antenna cable is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. Cable factor: receiving antenna cable: Cable factor is defined as the total effect of the antenna cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency, parasitic effects on the receiving antenna (acting as a director or reflector) and introducing an unbalanced, common mode current into the dipole balun. In a radiated measurement the standard uncertainty of the cable factor, associated with each cable is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of receiving antenna cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the receiving antenna cable is taken as 0,00 dB since there are no external fields involved other than leakage, which is assumed to have a negligible effect on the measurement. 6.8.2.1.2.7 Receiving device In this, the first stage of the verification procedure, a reference level is recorded from the receiving device for a particular output level from the signal generator. In the second stage (where the path loss between the two antennas is measured), a second level is recorded on the receiving device. Only in the second stage do the linearity and absolute level uncertainties of the receiver become involved in the calculation of the combined standard uncertainty of the measurement. Receiving device: absolute level: The standard uncertainty of the contribution due to the absolute level uncertainty of the receiving device is designated throughout all parts of TR 102 273 [3] as uj47. NOTE 1: In this example case the standard uncertainty of the contribution due to the absolute level uncertainty of the receiving device is assumed to be 0,00 dB since, in this part of the measurement, a reference level is recorded. Receiving device: linearity: The standard uncertainty of the contribution due to the receiving device linearity is designated throughout all parts of TR 102 273 [3] as uj48. NOTE 2: In this example case the standard uncertainty of the contribution due to the receiving device linearity is assumed to be 0,00 dB since, in this part of the measurement, a reference level is recorded.
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100 028-1
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6.8.2.1.3 Contribution from the random component
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Random uncertainty: The magnitude can be assessed from multiple measurements of the direct attenuation measurement. The standard uncertainty of the contribution due to the random uncertainty is designated throughout all parts of TR 102 273 [3] as ui01. Its value can then be calculated. The direct attenuation measurement was repeated 10 times. The following results were obtained in dBµV (before correcting for cabling and attenuator network insertion loss): - 106,8; 107,2; 106,7; 107,0; 107,2; 106,7; 107,1; 106,8; 107,1; 107,0. Converting to linear terms: - 0,2188; 0,2291; 0,2163; 0,2239; 0,2291; 0,2163; 0,2265; 0,2188; 0,2265; 0,2239. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 79 The two sums X and Y are calculated: - X = the sum of the measured values = 2,2292 V; - Y = the sum of the squares of the measured values = 0,4972 V2. = − − = − − = 1 10 10 2292 ,2 4972 ,0 1 2 2 n n X Y uc random 5,444 ×10-3 (formula 5.6) As the result is obtained as the mean value of 10 measurements and the standard uncertainty of the random uncertainty is: dB 0,212 5, 11 100 22292 ,0 10 444 ,5 3 = × × = − j random u NOTE: In this example case the standard uncertainty of the contribution due to the random uncertainty is 0,212 dB. See also the note in clause 6.4.7.
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100 028-1
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6.8.2.1.4 Summary table of contributory components
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The uncertainty contributions for stage 1 of the verification procedure are listed in table 3. Table 3: Contributions from the direct attenuation measurement uj or i Description of uncertainty contributions dB uj35 mismatch: direct attenuation measurement 0,03 uj38 signal generator: absolute output level 0,00 uj39 signal generator: output level stability 0,01 uj41 insertion loss: transmitting antenna cable 0,00 uj19 cable factor: transmitting antenna 0,00 uj40 insertion loss: transmitting antenna attenuator 0,00 uj42 insertion loss: adapter 0,06 uj40 insertion loss: receiving antenna attenuator 0,00 uj41 insertion loss: receiving antenna cable 0,00 uj19 cable factor: receiving antenna 0,00 uj47 receiving device: absolute level 0,00 uj48 receiving device: linearity 0,00 ui01 random uncertainty (see note in clause 6.4.7) 0,21 The standard uncertainties from table 3 should be combined by RSS in accordance with TR 102 273 [3], part 1, sub-part 1, clause 5. This gives the combined standard uncertainty (uc direct attenuation measurement) for the direct attenuation measurement in dB. The value of uc direct attenuation measurement is calculated as 0,221 dB.
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100 028-1
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6.8.2.2 Uncertainty contributions: Stage 2: Radiated attenuation measurement
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The second stage of the verification procedure is the radiated attenuation measurement which is carried out by removing the adapter and connecting each attenuator to an antenna as shown in figure 23, and recording the new level on the receiving device. The difference in received levels (after allowance for any correction factors and calculations which may be appropriate), for the same signal generator output level, reveals the NSA. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 80 cable 1 ferrite beads Attenuator 1 10 dB Signal generator cable 2 ferrite beads Receiving device Attenuator 2 10 dB Receiving antenna Transmitting antenna Ground plane Figure 23: Stage 2: Radiated attenuation measurement Whereas figure 23 shows, schematically, the test equipment set-up for this stage of the verification procedure an analysis diagram of the individual components (each of which contributes its own uncertainty) for this stage of the measurement is shown in figure 24. Again, as stated above, the shaded areas represent components common to both stages of the verification procedure.
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100 028-1
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6.8.2.2.1 Contributions from the mismatch components
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Mismatch uncertainty transmitting and receiving parts: The value of the combined standard uncertainty of the contribution due to the mismatch are calculated from the approach described in annex G. For this stage is calculated in two parts. Firstly the standard uncertainty of the contribution due to the mismatch in the transmitting part, i.e. between the signal generator, cable, attenuator and the transmitting antenna and secondly, that for the receiving part, i.e. between the receiving antenna, attenuator, cable and the receiving device. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 81 Transmitting antenna Cable factor Receiving antenna Cable factor Antenna to antenna coupling Mutual image coupling Antenna factor + Cable loss Receiving device Signal generator Cable loss + Antenna factor Mutual image coupling Antenna to antenna coupling Direct path loss Reflected path loss Site Imperfections Receiving antenna cable 2 Transmitting antenna cable 1 Transmitting Receiving device source Mismatch Mismatch Mismatch Mismatch Mismatch Mismatch + + + + + + Attenuator 2 (10 dB) Attenuator 2 (10 dB) Figure 24: Stage 2: Radiated attenuation measurement individual uncertainty components Mismatch: transmitting part: Signal generator: Output reflection coefficient: |ρG| = 0,20 Cable: Input and output reflection coefficients: |S11| and |S22| = 0,07 Attenuation: 1 dB = |S12| = |S21| = 0,891 Attenuator: Input and output reflection coefficients |S11| = |S22| = 0,05 Attenuation = 10 dB |S12| = |S21| = 0,3162 Transmitting antenna: Input reflection coefficient: |ρTA| = 0,333 ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 82 All these contributions are U-distributed. Those components that cancel are not calculated. Other contributions are (see annex G): - uj mismatch: generator and cable 1: Constant for both stage 1 and 2. Hence this value does not contribute. - uj mismatch: cable 1 and attenuator 1: Constant for both stage 1 and 2. Hence this value does not contribute. % ,177 1 % 2 100 333 ,0 05 ,0 1 : = × × = antenna and attenuator mismatch j u - uj generator and attenuator 1: Constant for both stage 1 and 2. Hence this value does not contribute. % 0,165 % 2 100 316 ,0 333 ,0 07 ,0 2 1 : = × × × = antenna and cable mismatch j u % 0,373 % 2 100 316 ,0 891 ,0 333 ,0 2,0 2 2 : = × × × × = antenna and generator mismatch j u The combined standard uncertainty of the mismatch is then calculated: % 25 1 373 ,0 165 ,0 177 ,1 2 2 2 : , u part ng transmitti mismatch c = + + = transforming to the logarithmic form (TR 100 028-2 [8], annex E): 1,25 %/11,5 = 0,11 dB. The standard uncertainty of the contribution due to the mismatch in the transmitting part, is designated throughout all parts of TR 102 273 [3] as uj36. Its value in this example is 0,11 dB. Mismatch: receiving part: Receiving antenna: Input reflection coefficient: |ρRA| = 0,333 Attenuator: Input and output reflection coefficients |S11| = |S22| = 0,05 Attenuation = 10 dB |S12| = |S21| = 0,3162 Cable: Input and output reflection coefficients: |S11| and |S22| = 0,07 Attenuation: 1 dB = |S12| = |S21| = 0,891 Receiving device: Input reflection coefficient: |ρRD| = 0,20 % ,177 1 % 2 100 05 ,0 333 ,0 2 : = × × = attenuator and antenna mismatch j u - uj attenuator 2 and cable 2: Constant for both stage 1 and 2. Hence this value does not contribute. - uj cable 2 and receiving device: Constant for both stage 1 and 2. Hence this value does not contribute. % 0,165 % 2 100 316 ,0 07 ,0 333 ,0 2 2 : = × × × = cable and antenna mismatch j u - uj attenuator 2 and receiving device: Constant for both stage 1 and 2. Hence this value does not contribute. % 0,373 % 2 100 891 ,0 316 ,0 2,0 333 ,0 2 2 : = × × × × = device receiving and antenna mismatch j u ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 83 The combined standard uncertainty of the mismatch is then calculated: % 25 1 373 ,0 165 ,0 177 ,1 2 2 2 : , u part receiving mismatch c = + + = Transforming to the logarithmic form (TR 100 028-2 [8], annex E): 1,25 %/11,5 = 0,11 dB. The standard uncertainty of the contribution due to the mismatch in the receiving part is designated throughout all parts of TR 102 273 [3] as uj37. Its value in this example is 0,11 dB.
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100 028-1
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6.8.2.2.2 Contributions from individual components
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6.8.2.2.2.1 Signal generator Signal generator: absolute output level: In a verification procedure, the signal generator's absolute level uncertainty contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the signal generator absolute output level uncertainty is designated throughout all parts of TR 102 273 [3] as uj38. NOTE 1: In this example case the standard uncertainty of the contribution due to the signal generator absolute output level uncertainty is taken to be 0,00 dB since, once the level has been set in stage one of the procedure, the level is not further adjusted. The uncertainty is therefore assumed to be systematic i.e. it produces the same offset in both stages. Signal generator: output level stability: In any test in which the contribution of the absolute level uncertainty of the signal generator contributes to the combined standard uncertainty of the test i.e. it does not cancel due to the methodology, the contribution from the output level stability is considered to have been included in the signal generator absolute output level, uj38. Conversely, for any level in which the absolute level uncertainty of the signal generator does not contribute to the combined standard uncertainty, the output level stability of the signal generator should be included. The standard uncertainty of the contribution due to the signal generator output level stability is designated throughout all parts of TR 102 273 [3] as uj39. Its value can be derived from manufacturers' data sheet. NOTE 2: In this example case the uncertainty of the contribution due to the signal generator output level stability is obtained from the manufacturers data sheet as ±0,02 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,01155 dB. This is rounded down to 0,01 dB. 6.8.2.2.2.2 Transmitting antenna cable Insertion loss: transmitting antenna cable: The transmitting antenna cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution, due to the insertion loss uncertainty of the transmitting antenna cable, is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the transmitting antenna cable is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. Cable factor: transmitting antenna cable: Cable factor is defined as the total effect of the antenna cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency, parasitic effects on the transmitting antenna (acting as a director or reflector) and introducing an unbalanced, common mode current into the dipole balun. In a radiated measurement the standard uncertainty of the cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the receiving antenna cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the transmitting antenna cable is taken as 0,50 dB since the precautions detailed in the methods are assumed to have been observed. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 84 6.8.2.2.2.3 Transmitting antenna attenuator Insertion loss: transmitting antenna attenuator: The transmitting antenna attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution, due to the insertion loss uncertainty of the transmitting antenna attenuator, is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the transmitting antenna attenuator is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. 6.8.2.2.2.4 Transmitting antenna Antenna: antenna factor of the transmitting antenna: Uncertainty is introduced as a result of the inaccurate knowledge of the antenna factor of the transmitting antenna. The antenna factor contributes only to the radiated part of this procedure. The standard uncertainty of the contribution due to the antenna factor uncertainty of the transmitting antenna is designated throughout all parts of TR 102 273 [3] as uj44. For ANSI dipoles the value should be obtained from table 4. Table 4: Uncertainty contribution of the antenna factor of the transmitting antenna Frequency Standard uncertainty of the contribution 30 MHz ≤ frequency < 80 MHz 1,73 dB 80 MHz ≤ frequency < 180 MHz 0,60 dB frequency ≥ 180 MHz 0,30 dB NOTE 1: For other antenna types the values should be taken from manufacturers' data sheets. If a value is not given the standard uncertainty is 1,0 dB. NOTE 2: In this example case the standard uncertainty of the contribution due to the antenna factor uncertainty of the transmitting antenna is 0,30 dB since ANSI dipoles have been used and the frequency is above 180 MHz. Antenna: tuning of the transmitting antenna: Uncertainty is introduced as a result of the inaccurate tuning of the transmitting antenna. This only occurs in stage two of the measurement and therefore only contributes to this stage. The standard uncertainty of the contribution, due to the tuning uncertainty of the transmitting antenna, is designated throughout all parts of TR 102 273 [3] as uj46. NOTE 3: In this example case the standard uncertainty of the contribution due to the tuning uncertainty of the transmitting antenna is taken as 0,06 dB (see annex A). Position of the phase centre: transmitting antenna: Uncertainty is introduced as a result of the inaccurate positioning of the phase centre of the transmitting antenna. This only occurs in stage two of the measurement. The standard uncertainty of the contribution, due to the uncertainty in the position of the phase centre of the transmitting antenna, is designated throughout all parts of TR 102 273 [3] as uj22. NOTE 4: In this example case the standard uncertainty of the contribution due to the uncertainty in the position of the phase centre of the transmitting antenna has been calculated from (±(the offset from axis of rotation)/(range length) x 100 %). The positioning uncertainty is ±0,01 m and therefore the worst case uncertainty = 0,01/3,0 = 0,333 %. As the offset can be anywhere between these limits, the uncertainty is taken to be rectangularly distributed (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) and the standard uncertainty is calculated as 0,192 %. This is transformed to the logarithmic form (TR 100 028-2 [8], annex E), to be 0,02 dB. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 85 6.8.2.2.2.5 Site factors Ambient effect: Uncertainty is introduced as a result of local ambient signals raising the noise floor at the measurement frequency. The standard uncertainty of the contribution due to the ambient effect is designated throughout all parts of TR 102 273 [3] as uj34. The values of the standard uncertainty should be taken from table 5. Table 5: Uncertainty contribution: Ambient effect Receiving device noise floor (generator OFF) is within: Standard uncertainty of the contribution 3 dB of measurement 1,57 dB 3 dB to 6 dB of measurement 0,80 dB 6 dB to 10 dB of measurement 0,30 dB 10 dB to 20 dB of measurement 0,10 dB 20 dB or more of the measurement 0,00 dB NOTE 1: In this example case the standard uncertainty of the contribution due to the ambient effect is taken as 0,00 dB, since the chamber is assumed to be shielded. Mutual coupling: transmitting antenna to its images in the absorbing material: This uncertainty is the effect of the change produced in the antenna's input impedance and/or gain. The standard uncertainty of the contribution due to the mutual coupling of the transmitting antenna to its images in the absorbing materials is designated throughout all parts of TR 102 273 [3] as uj07. NOTE 2: In this example case the standard uncertainty of the contribution due to the mutual coupling of the transmitting antenna to its images in the absorbing materials is taken as 0,5 dB (see annex A). Mutual coupling: transmitting antenna to its image in the ground plane: This uncertainty is the effect of the change produced in the antenna's input impedance and/or gain. The standard uncertainty of the contribution due to the mutual coupling of the transmitting antenna to its image in the ground plane, designated throughout all parts of TR 102 273 [3] as uj15, has a value of 0,00 dB for ANSI dipoles since it is included, where significant, in the mutual coupling and mismatch loss correction factors (see table A.20). For other dipoles the value can be obtained from table 6. Table 6: Uncertainty contribution of the mutual coupling between the transmitting antenna to its image in the ground plane Spacing between the antenna and the ground plane Standard uncertainty of the contribution For a vertically polarized antenna spacing ≤ 1,25 λ 0,15 dB spacing > 1,25 λ 0,06 dB For a horizontally polarized antenna spacing < λ/2 1,15 dB λ/2 ≤ spacing < 3λ/2 0,58 dB 3λ/2 ≤ spacing < 3λ 0,29 dB spacing ≥ 3λ 0,15 dB NOTE 3: In this example case the standard uncertainty of the contribution due to mutual coupling between the transmitting antenna and its image in the ground plane is taken as 0,00 dB as we are assuming the use of ANSI dipoles. Mutual coupling: transmitting antenna to receiving antenna: This is the effect produced by any change in the gains of the antennas which results from their close spacing. The standard uncertainty of the contribution due to the mutual coupling of the transmitting antenna to receiving antenna, is designated throughout all parts of TR 102 273 [3] as uj10. It has a standard uncertainty of 0,00 dB for ANSI dipoles since it is included, where significant, in the mutual coupling and mismatch loss correction factors. For non-ANSI dipoles the standard uncertainty can be taken from table 7. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 86 Table 7: Uncertainty contribution of the mutual coupling between the transmitting and receiving antenna Frequency Standard uncertainty of the contribution (3 m range) Standard uncertainty of the contribution (10 m range) 30 MHz ≤ frequency < 80 MHz 1,73 dB 0,60 dB 80 MHz ≤ frequency < 180 MHz 0,6 dB 0,00 dB frequency ≥ 180 MHz 0,00 dB 0,00 dB NOTE 4: In this example case the standard uncertainty of the contribution due to mutual coupling between the transmitting and receiving antennas is taken as 0,00 dB as we are using ANSI dipoles. Mutual coupling: interpolation of mutual coupling and mismatch loss correction factors, only for ANSI dipoles: The standard uncertainty of the contribution, due to the interpolation of mutual coupling and mismatch loss correction factors, is designated throughout all parts of TR 102 273 [3] as uj12. It has, for spot frequencies given in table A.20, a value of 0,00 dB. However, for all other frequencies, the standard uncertainty should be obtained from table 8. Table 8: Uncertainty contribution of the interpolation of mutual coupling and mismatch loss correction factors Frequency (MHz) Standard uncertainty of the contribution for a spot frequency given in the table 0,00 dB 30 MHz ≤ frequency < 80 MHz 0,58 dB 80 MHz ≤ frequency < 180 MHz 0,17 dB frequency ≥ 180 MHz 0,00 dB NOTE 5: In this example case the standard uncertainty of the contribution, due to the interpolation of mutual coupling and mismatch loss correction factors, is taken as 0,00 dB as the frequency is above 180 MHz. Range length: This contribution is associated with the curvature of the phase front from the transmitting antenna to the receiving antenna. The standard uncertainty of the contribution, due to range length, is designated throughout all parts of TR 102 273 [3] as uj16. The standard uncertainty is 0,00 dB if ANSI dipoles are used. For other types of antenna the standard uncertainty of the contribution should be obtained from table 9. Table 9: Uncertainty contribution of the range length (verification) Range length (i.e. the horizontal distance between phase centres) Standard uncertainty of the contribution (d1 + d2)2/4λ ≤ range length < (d1 + d2)2/2λ 1,26 dB (d1 + d2)2/2λ ≤ range length < (d1 + d2)2/λ 0,30 dB (d1 + d2)2/λ ≤ range length < 2(d1 + d2)2/λ 0,10 dB range length ≥ 2(d1 + d2)2/λ 0,00 dB NOTE 6: In table 9, d1 and d2 are the maximum dimensions of the antennas. NOTE 7: In this example case the standard uncertainty of the contribution, due to the range length, is taken as 0,00 dB as we are using ANSI dipoles. Reflectivity of absorbing material: transmitting antenna to the receiving antenna: This uncertainty is associated with the magnitude of the reflections occurring from the side walls, end walls and ceiling. These magnitudes are a function of the quality of the absorber at the frequency of test. The standard uncertainty of the contribution, due to reflectivity of the absorber material between the transmitting antenna and the receiving antenna, is designated throughout all parts of TR 102 273 [3] as uj03. The relevant value for this contribution should be taken from table 10. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 87 Table 10: Uncertainty contribution of the reflectivity of absorbing material between the transmitting and receiving antennas Reflectivity of the absorbing material Standard uncertainty of the contribution reflectivity < 10 dB 4,76 dB 10 dB ≤ reflectivity < 15 dB 3,92 dB 15 dB ≤ reflectivity < 20 dB 2,56 dB 20 dB ≤ reflectivity < 30 dB 1,24 dB reflectivity ≥ 30 dB 0,74 dB NOTE 8: In this example case the standard uncertainty of the contribution, due to the reflectivity of absorber material between the transmitting antenna and the receiving antenna, is taken as 2,56 dB since it is assumed that the absorber has a reflectivity in the range 15 dB to 20 dB. Mutual coupling: receiving antenna to its images in the absorbing material: This uncertainty is the effect of the change produced in the antenna's input impedance and/or gain. The standard uncertainty of the contribution, due to the mutual coupling of the receiving antenna to its images in the absorbing material, is designated throughout all parts of TR 102 273 [3] as uj07. NOTE 9: In this example case the standard uncertainty of the contribution due to the mutual coupling of the receiving antenna to its images in the absorbing material is taken as 0,5 dB. Mutual coupling: receiving antenna to its image in the ground plane: This uncertainty is the effect of the change produced in the antenna's input impedance and/or gain. The standard uncertainty of the contribution, due to the mutual coupling of the receiving antenna to its image in the ground plane, is designated throughout all parts of TR 102 273 [3] as uj15. It has a value of 0,00 dB for ANSI dipoles since it is included, where significant, in the mutual coupling and mismatch loss correction factors. For other antennas the value can be obtained from table 11. Table 11: Uncertainty contribution of the mutual coupling between the receiving antenna and its image in the ground plane Spacing between the antenna and the ground plane Standard uncertainty of the contribution For a vertically polarized antenna spacing ≤ 1,25 λ 0,15 dB spacing > 1,25 λ 0,06 dB For a horizontally polarized antenna spacing < λ/2 1,15 dB λ/2 ≤ spacing < 3λ/2 0,58 dB 3λ/2 ≤ spacing < 3λ 0,29 dB spacing ≥ 3λ 0,15 dB NOTE 10: In this example case the standard uncertainty of the contribution due to the mutual coupling between the receiving dipole and its image in the ground plane is taken as 0,00 dB as we are using ANSI dipoles. 6.8.2.2.2.6 Receiving antenna Correction: measurement distance: For verification procedures only one stage involves a radiated measurement and hence no correction can be applied i.e. the uncertainty contribution is 0,00 dB. The standard uncertainty of the contribution, due to the correction for measurement distance, is designated throughout all parts of TR 102 273 [3] as uj18. Correction: off boresight angle in elevation plane: For verification procedures only one stage involves a radiated measurement and hence no correction can be applied i.e. the uncertainty contribution is 0,00 dB. The standard uncertainty of the contribution, due to the correction for off boresight angle in elevation plane is designated throughout all parts of TR 102 273 [3] as uj17. Antenna: antenna factor of the receiving antenna: Uncertainty is introduced as a result of the inaccurate knowledge of the antenna factor of the receiving antenna. The antenna factor contributes only to the radiated part of this procedure. The standard uncertainty of the contribution due to the antenna factor uncertainty of the receiving antenna is designated throughout all parts of TR 102 273 [3] as uj44. For ANSI dipoles the value should be obtained from table 12. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 88 Table 12: Uncertainty contribution of the antenna factor of the receiving antenna Frequency Standard uncertainty of the contribution 30 MHz ≤ frequency < 80 MHz 1,73 dB 80 MHz ≤ frequency < 180 MHz 0,60 dB frequency ≥ 180 MHz 0,30 dB NOTE 1: For other antenna types the figures should be taken from manufacturers data sheets. If a figure is not given the standard uncertainty is 1,0 dB. NOTE 2: In this example case the standard uncertainty of the contribution due to the antenna factor uncertainty of the receiving antenna is 0,30 dB since ANSI dipoles have been used and the frequency is above 180 MHz. Antenna: tuning of the receiving antenna: Uncertainty is introduced as a result of the inaccurate tuning of the receiving antenna. This only occurs in stage two of the measurement and therefore does not cancel. The standard uncertainty of the contribution, due to the tuning uncertainty of the receiving antenna, is designated throughout all parts of TR 102 273 [3] as uj46. NOTE 3: In this example case the standard uncertainty of the contribution due to the tuning uncertainty of the receiving antenna is taken as 0,06 dB (see annex A). Position of the phase centre: receiving antenna: Uncertainty is introduced as a result of the inaccurate positioning of the phase centre of the receiving antenna. This only occurs in stage two of the measurement. The standard uncertainty of the contribution, due to the uncertainty in the position of the phase centre of the receiving antenna, is designated throughout all parts of TR 102 273 [3] as uj22. NOTE 4: In this example case the standard uncertainty of the contribution due to the position of the phase centre of the receiving antenna has been calculated from ± (the offset) / (range length) x100 %). The positioning uncertainty is ±0,01 m and therefore the worst case uncertainty = 0,01/3,0 = 0,333 %. As the offset can be anywhere between these limits, the uncertainty is taken to be rectangularly distributed (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) and the standard uncertainty is calculated as 0,192 %. This is transformed to the logarithmic form (TR 100 028-2 [8], annex E), to be 0,02 dB. 6.8.2.2.2.7 Receiving antenna attenuator Insertion loss: receiving antenna attenuator: The attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the receiving antenna attenuator is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution, due to the insertion loss uncertainty of the transmitting antenna attenuator, is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. 6.8.2.2.2.8 Receiving antenna cable Insertion loss: receiving antenna cable: The receiving antenna cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the receiving antenna cable is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the transmitting antenna cable is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 89 Cable factor: receiving antenna: Cable factor is defined as the total effect of the antenna cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency, parasitic effects on the receiving antenna (acting as a director or reflector) and introducing an unbalanced, common mode current into the dipole balun. In a radiated measurement the standard uncertainty of the cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the receiving antenna cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the receiving antenna cable is taken as 0,50 dB since the precautions detailed in the methods are assumed to have been observed. 6.8.2.2.2.9 Receiving device The first stage of the verification procedure involved setting a reference level on the receiving device for a particular output level from the signal generator. In this the second stage (where the path loss between two antennas is measured), a second level is obtained which results in linearity and absolute level uncertainties becoming involved in the calculation of the combined standard uncertainty for the measurement. Receiving device: absolute level: This uncertainty only contributes during the second stage of the procedure if the input attenuation range setting on the receiving device has been changed from its setting in the first stage. The standard uncertainty of the contribution due to the receiving device absolute level uncertainty is designated throughout all parts of TR 102 273 [3] as uj47. NOTE 1: In this example case the standard uncertainty of the contribution due to the receiving device absolute level uncertainty (a range change is assumed) is obtained from the manufacturers data as ±1,0 dB. This is taken as being rectangularly distributed (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2), so the standard uncertainty is calculated as 0,58 dB. Receiving device: linearity: The standard uncertainty of the contribution due to the receiving device linearity, designated throughout all parts of TR 102 273 [3] as uj48, always contributes during the second stage of the procedure unless there has been a range change in which case it is included in the receiving device absolute level uncertainty uj47. NOTE 2: In this example case a range change has been assumed therefore the contribution is 0,00 dB.
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6.8.2.2.3 Contribution from the random component
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Random uncertainty: The magnitude can be assessed from multiple measurements of the radiated attenuation measurements. The standard uncertainty of the contribution due to the random uncertainty is designated throughout all parts of TR 102 273 [3] as ui01. The radiated attenuation measurement was repeated 10 times. The following results were obtained in dBµV (before correcting for cabling and attenuator network insertion loss): - 65,4; 63,4; 66,0; 65,3; 63,0; 64,9; 65,2; 66,8; 65,5; 63,7. Converting to linear terms: - 1,862 × 10-3; 1,479 × 10-3; 1,995 × 10-3; 1,841 × 10-3; 1,413 × 10-3; 1,758 × 10-3; 1,820 × 10-3; 2,188 × 10-3; 1,884 × 10-3; 1,531 × 10-3. The two sums X and Y are calculated: - X = the sum of the measured values = 17,77 × 10-3; - Y = the sum of the squares of the measured values = 32,10 × 10-6 V2. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 90 ( ) = − × − × = − − = − − 1 10 10 10 77 , 17 10 10 , 32 1 2 3 6 2 n n X Y uc random 238,3 ×10-6 (formula 5.6) As the result is obtained as the mean value of 10 measurements and the standard uncertainty of the random uncertainty is: dB 1,17 5, 11 100 10 777 ,1 10 3, 238 3 6 = × × × = − − j random u NOTE: In this example case the standard uncertainty of the contribution due to the random uncertainty is 1,17 dB. See also the note in clause 6.4.7.
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6.8.2.2.4 Summary table of contributory components
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All the uncertainty contributions to this part of the procedure are listed in table 13. Table 13: Contributions from the radiated attenuation measurement uj or i Description of uncertainty contributions dB uj36 mismatch: transmitting part 0,11 uj37 mismatch: receiving part 0,11 uj38 signal generator: absolute output level 0,00 uj39 signal generator: output level stability 0,01 uj41 insertion loss: transmitting antenna cable 0,00 uj19 cable factor: transmitting antenna 0,50 uj40 insertion loss: transmitting antenna attenuator 0,00 uj44 antenna: antenna factor of the transmitting antenna 0,30 uj46 antenna: tuning of the transmitting antenna 0,06 uj22 position of the phase centre: transmitting antenna 0,02 uj34 ambient effect 0,00 uj07 mutual coupling: transmitting antenna to its images in the absorbing material 0,50 uj15 mutual coupling: transmitting antenna to its image in the ground plane 0,00 uj10 mutual coupling: transmitting antenna to the receiving antenna 0,00 uj12 mutual coupling: interpolation of mutual coupling and mismatch loss correction factors 0,00 uj16 range length 0,00 uj03 reflectivity of absorber material: transmitting antenna to the receiving antenna 2,56 uj07 mutual coupling: receiving antenna to its images in the absorbing material 0,50 uj15 mutual coupling: receiving antenna to its image in the ground plane 0,00 uj18 correction: measurement distance 0,00 uj17 correction: off boresight angle in the elevation plane 0,00 uj44 antenna: antenna factor of the receiving antenna 0,30 uj46 antenna: tuning of the receiving antenna 0,06 uj22 position of the phase centre: receiving antenna 0,02 uj40 insertion loss: receiving antenna attenuator 0,00 uj41 insertion loss: receiving antenna cable 0,00 uj19 cable factor: receiving antenna 0,50 uj47 receiving device: absolute level 0,58 uj48 receiving device: linearity 0,00 ui01 random uncertainty (see note in clause 6.4.7) 1,17 The standard uncertainties from table 13 should be combined by RSS in accordance with TR 102 273 [3], part 1, sub-part 1, clause 5. This gives the combined standard uncertainty (uc NSA measurement) for the NSA measurement in dB. The value of uc NSA measurement is calculated as 3,08 dB. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 91
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6.8.2.2.5 Expanded uncertainty for the verification procedure
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The combined standard uncertainty of the results of the verification procedure is the combination of the components outlined in clauses 6.8.2.1.4 and 6.8.2.2.4. The components to be combined are uc direct attenuation measurement and uc NSA measurement. dB 3,08 = 08 ,3 221 ,0 2 2 + = c u The expanded uncertainty is ±1,96 x 3,08 dB = ±6,04 dB at a 95 % confidence level. 6.8.3 Example 2: Measurement of a transmitter parameter (spurious emission) For the measurement of the effective radiated power in a spurious emission two stages of test are involved. The first stage (the EUT measurement) is to measure on the receiving device, a level from the EUT. The second stage (the substitution) involves replacing the EUT with a substitution antenna and signal source and adjusting the output level of the signal generator until the same level as in stage one is achieved on the receiving device.
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6.8.3.1 Uncertainty contributions: Stage 1: EUT measurement
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The first stage of the spurious emission measurement is to measure on the receiving device, a level from the EUT. This is normally carried out with a broadband antenna and receiver combination as shown in figure 25. The components shown shaded are common to both stages of the test. Test antenna cable 2 Test antenna ferrite beads Attenuator 2 10 dB Receiving device EUT Ground plane Figure 25: Stage 1: EUT measurement Due to the commonality of all of the components from the test antenna to the receiver in both stages of the test, the mismatch uncertainty contributes identically to both stages and hence does not contribute to the combined standard uncertainty of the measurement. Similarly, for the systematic uncertainty contributions (e.g. test antenna cable loss etc.) of the individual components. Whereas figure 25 shows, schematically, the test equipment set-up for this stage of the spurious emission measurement, an analysis diagram of the individual components (each of which contributes its own uncertainty) for this stage of the measurement is shown in figure 26. Again, as stated above, the shaded areas represent components common to both stages of the spurious emissions measurement.
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6.8.3.1.1 Contributions from the mismatch components
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Mismatch: receiving part: The uncertainty contribution due to the mismatch for the receiving part from the test antenna to the receiver, can be calculated from the approach described in annex G. All the individual contributions are U-distributed. NOTE 1: In this example the value taken for the signal generator output reflection coefficient is the worst case value over the frequency band of interest. Similarly for the cable, adapter and attenuator VSWRs. NOTE 2: The attenuation values of the cables and attenuators should be obtained from the data sheets/calibration records at the specific frequency of the test, along with the associated uncertainties for these values. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 92 The mismatch uncertainty between the test antenna and the receiving device however, contributes equally to both stages of the test and therefore has no contribution to the combined standard uncertainty. Therefore it is not calculated. Test antenna Site factors Cable factor Test antenna cable 2 Cable loss Attenuator 2 10 dB Equipment under test Mismatch Mutual image coupling Antenna gain + Antenna to EUT coupling Reflected path loss Direct path loss Site effects EUT + Receiving device device Receiving Mismatch Mismatch + + Figure 26: Stage 1: EUT measurement individual uncertainty components The standard uncertainty of the contribution, due to the mismatch in the receiving part, is designated throughout all parts of TR 102 273 [3] as uj37. NOTE 3: In this example case the standard uncertainty of the contribution due to mismatch in the receiving part is taken as 0,00 dB, since the uncertainty is assumed to be systematic i.e. it is assumed constant and common to both stages of the measurement.
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6.8.3.1.2 Contributions from the individual components
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6.8.3.1.2.1 EUT EUT: influence of setting the power supply on the spurious emission level: This is the resulting uncertainty caused by the uncertainty of setting of the power supply level. In this case normal supply conditions are assumed, not extreme. The supply voltage uncertainty is taken to be ±100 mV so the uncertainty caused by this supply voltage uncertainty is calculated using the dependency function (TR 100 028-2 [8], table C.1: "Equipment under test dependency functions and uncertainties") whose mean value is 10 %/V and whose standard uncertainty is 3 %/V. The standard uncertainty of the spurious emission level uncertainty caused by power supply voltage uncertainty (using formula 5.3) is: % , = ) ) %/V +( ) %/V (( ) V , ( 60 0 3 10 3 1 0 2 2 2 × This is then transformed to logarithmic form: 0,60 %/23,0 % = 0,03 dB (TR 100 028-2 [8], annex E). ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 93 The standard uncertainty of the contribution, due to the influence of setting the power supply on the spurious emission level, is designated throughout all parts of TR 102 273 [3] as uj54. NOTE 1: In this example case the standard uncertainty of the contribution, due to the influence of setting the power supply on the spurious emission level, is calculated above as 0,03 dB. EUT: influence of the ambient temperature on the spurious emissions: This is the uncertainty in the power level of the spurious emission caused by the uncertainty in knowing the ambient temperature. The ambient temperature uncertainty is ±1°C. The uncertainty caused by this temperature uncertainty is calculated using the dependency function (TR 100 028-2 [8], table C.1: "EUT dependency functions and uncertainties") whose mean value is 4 %/°C and whose standard uncertainty is 1,2 %/°C. The standard uncertainty of the spurious emission power level uncertainty caused by ambient temperature uncertainty (using formula 5.3) is: = ) ) C %/ , +( ) C %/ , (( ) C) ( ( 2 2 2 2 1 0 4 3 1 ° ° × ° 2,41 %. This is then transformed to logarithmic form: 2,41/23,0 % = 0,10 dB (TR 100 028-2 [8], annex E). The standard uncertainty of the contribution, due to the influence of the ambient temperature on the spurious emissions, is designated throughout all parts of TR 102 273 [3] as uj51. NOTE 2: In this example case the standard uncertainty of the contribution due to the influence of the ambient temperature on the spurious emissions level is calculated above as 0,10 dB. EUT: mutual coupling to the power leads: This is the uncertainty associated with the influence (reflections, parasitic effects, etc.) of the power leads on the EUT. The standard uncertainty associated with this effect is 0,5 dB provided that the precautions detailed in the methods have been observed. I.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 2,0 dB. The standard uncertainty of the contribution, due to the mutual coupling to the power leads, is designated throughout all parts of TR 102 273 [3] as uj54. NOTE 3: In this example case the standard uncertainty of the contribution due to the mutual coupling to the power leads is taken as 0,5 dB since the precautions detailed in the methods are assumed to have been observed. Position of the phase centre: within the EUT volume: This contribution is associated with the uncertainty with which the actual radiating point within the equipment volume is known. If this point is known exactly the contribution is 0,00 dB. The standard uncertainty of the contribution, due to the position of the phase centre within the EUT volume, is designated throughout all parts of TR 102 273 [3] as uj20. NOTE 4: In this example case the standard uncertainty of the contribution due to the position of the phase centre within the EUT volume has been calculated from (±(the maximum dimension of device)/(2 × range length) × 100 %). In this example the position is not known. Hence, the uncertainty of the position of the phase centre within the EUT of 0,15 m maximum dimension is 0,15/2 m = 0,075 m, and the worst case uncertainty due to this offset is therefore ±(0,075/3,0) × 100 % = ±2,50 %. As the phase centre can be anywhere inside the EUT, the uncertainty is taken as rectangularly distributed and the standard uncertainty is calculated as 1,44 %. This is then transformed to the logarithmic form (1,44/11,5) = 0,12 dB (TR 100 028-2 [8], annex E). Positioning of the phase centre: within the EUT over the axis of rotation of the turntable: This contribution is associated with the uncertainty with which the actual radiating point within the equipment is placed over the centre of the turntable. If the point is placed exactly, the contribution is 0,00 dB. The standard uncertainty of the contribution due to the positioning of the EUT phase centre over the axis of rotation of the turntable, is designated throughout all parts of TR 102 273 [3] as uj21. NOTE 5: In this example case the standard uncertainty of the contribution due to the positioning of the EUT phase centre over the axis of rotation of the turntable is calculated from (± (the estimated offset from the axis of rotation)/(2 × range length) × 100 %). In this case, the uncertainty of the positioning is taken as ±0,01 m, and the worst case uncertainty is ±(0,01/3,0) × 100 = ±0,333 %. As the offset can be anywhere between the limits the uncertainty is rectangularly distributed and the standard uncertainty is calculated as 0,192 %. This is then transformed to the logarithmic form (0,192/11,5) = 0,02 dB (TR 100 028-2 [8], annex E). ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 94 Range length: This contribution is associated with the curvature of the phase front from the EUT to the test antenna. The standard uncertainty of the contribution due to the range length is designated throughout all parts of TR 102 273 [3] as uj16. The standard uncertainty of the contribution should be obtained from table 14. Table 14: Uncertainty contribution of the range length (verification) Range length (i.e. the horizontal distance between phase centres) Standard uncertainty of the contribution (d1 + d2)2/4λ ≤ range length < (d1 + d2)2/2λ 1,26 dB (d1 + d2)2/2λ ≤ range length < (d1 + d2)2/λ 0,30 dB (d1 + d2)2/λ ≤ range length < 2(d1 + d2)2/λ 0,10 dB range length ≥ 2(d1 + d2)2/λ 0,00 dB NOTE 6: In table 14, d1 and d2 are the maximum dimensions of the antennas. NOTE 7: In this example case the standard uncertainty of the contribution due to the range length is taken as 0,00 dB since the range length is ≥ 2 (d1 + d2)2/λ. 6.8.3.1.2.2 Site factors Ambient effect: Ambient effect is the uncertainty caused by local ambient signals raising the noise floor at the measurement frequency. The standard uncertainty of the contribution, due to the ambient effect, is designated throughout all parts of TR 102 273 [3] as uj34. The values of the standard uncertainty should be taken from table 15. Table 15: Uncertainty contribution: Ambient effect Receiving device noise floor (EUT OFF) is within: Standard uncertainty of the contribution 3 dB of measurement 1,57 dB 3 dB to 6 dB of measurement 0,80 dB 6 dB to 10 dB of measurement 0,30 dB 10 dB to 20 dB of measurement 0,10 dB 20 dB or more of the measurement 0,00 dB NOTE 1: In this example case the standard uncertainty of the contribution due to the ambient effect is taken as 0,00 dB, since the chamber is assumed to be shielded. Mutual coupling: amplitude effect of the test antenna on the EUT: This uncertainty results from the interaction between the EUT and the test antenna when placed close together. The standard uncertainty of the contribution due to the amplitude effect of the mutual coupling between the test antenna and the EUT, is designated throughout all parts of TR 102 273 [3] as uj08. The standard uncertainty should be taken from table 16. Table 16: Uncertainty contribution: Mutual coupling: amplitude effect of the test antenna on the EUT Range length Standard uncertainty of the contribution 0,62√((d1 + d2)3/λ)≤ range length < 2(d1 + d2)2/λ 0,50 dB range length ≥ 2(d1 + d2)2/λ 0,00 dB NOTE 2: In this example case the standard uncertainty of the contribution due to the amplitude effect of the mutual coupling between the test antenna and the EUT is 0,00 dB since the distance is ≥ 2 (d1 + d2)2/λ. Mutual coupling: EUT to its images in the absorbing material: This uncertainty is dependant on the quality of the absorbing material and the effect imaging of the EUT in the ceiling, side and end walls has on the input impedance and/or gain of the integral antenna. The standard uncertainty of the contribution, due to the mutual coupling of the EUT to its images in the absorbing material, is designated throughout all parts of TR 102 273 [3] as uj04. NOTE 3: In this example case the standard uncertainty of the contribution due to the mutual coupling amplitude effect of the absorbing material on the EUT is assumed to be 0,5 dB (see annex A). ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 95 Mutual coupling: EUT to its image in the ground plane: This uncertainty results from the change in the EUT spurious emission level as a result of being placed close to the ground plane. The standard uncertainty of the contribution, due to the mutual coupling of the EUT to its image in the ground plane, is designated throughout all parts of TR 102 273 [3] as uj13. Its value can be obtained from table 17. Table 17: Uncertainty contribution of the mutual coupling between the EUT to its image in the ground plane Spacing between the EUT and the ground plane Standard uncertainty of the contribution For a vertically polarized EUT spacing ≤ 1,25 λ 0,15 dB spacing > 1,25 λ 0,06 dB For a horizontally polarized EUT spacing < λ/2 1,15 dB λ/2 ≤ spacing < 3λ/2 0,58 dB 3λ/2 ≤ spacing < 3λ 0,29 dB spacing ≥ 3λ 0,15 dB NOTE 4: In this example case the standard uncertainty of the contribution, due to the mutual coupling of the EUT to its image in the ground plane (assuming the polarization is vertical and the spacing above the ground plane is < 1,25 λ at the test frequency), is taken as 0,15 dB. Reflectivity of absorbing material: EUT to the test antenna. This uncertainty is associated with the magnitudes of the reflections occurring from the side walls, end walls and ceiling. These magnitudes are a function of the quality of the absorber at the frequency of test. The standard uncertainty of the contribution, due to the reflectivity of the absorbing material between the EUT and the test antenna, is designated throughout all parts of TR 102 273 [3] as uj01. The relevant value for this contribution should be taken from table 18. Table 18: Uncertainty contribution of the reflectivity of absorbing material between the EUT and test antenna Reflectivity of the absorbing material Standard uncertainty of the contribution reflectivity <10 dB 4,76 dB 10 ≤ reflectivity < 15 dB 3,92 dB 15 ≤ reflectivity < 20 dB 2,56 dB 20 ≤ reflectivity < 30 dB 1,24 dB reflectivity ≥ 30 dB 0,74 dB NOTE 5: In this example case the standard uncertainty of the contribution due to the reflectivity of the absorbing material between the EUT and the test antenna is taken as 0,00 dB since this is a substitution measurement and the contribution cancels (see annex A). Mutual coupling: test antenna to its images in the absorbing material: This is the uncertainty due to the mutual coupling between the test antenna and its images in the ceiling, side and end walls and is the effect of the change produced in the antenna's input impedance and/or gain. As this is the first stage of a substitution measurement and the uncertainty is common to both stages it will only contribute in the second stage if the test antenna is located at a different height on the antenna mast. The standard uncertainty of the contribution, due to the mutual coupling between the test antenna and its images in the absorbing material, is designated throughout all parts of TR 102 273 [3] as uj06. NOTE 6: In this example case the standard uncertainty of the contribution due to the mutual coupling between the test antenna and its images in the absorbing material is taken as 0,00 dB since this is the reference position. Mutual coupling: test antenna to its image in the ground plane: This is the uncertainty due to the mutual coupling between the test antenna and its image in the ground plane and is the effect of the change produced in the antenna's input impedance and/or gain when placed close to a ground plane. As this is the first stage of a substitution measurement and the uncertainty is common to both stages, it will only contribute in the second stage if the test antenna is located at a different height on the antenna mast. The standard uncertainty of the contribution, due to the mutual coupling between the test antenna and its image in the ground plane, is designated throughout all parts of TR 102 273 [3] as uj14. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 96 NOTE 7: In this example case the standard uncertainty of the contribution due to the mutual coupling between the test antenna and its image in the ground plane is taken as 0,00 dB since this is the reference position. 6.8.3.1.2.3 Test antenna Correction: measurement distance: For those tests in which the test antenna on the mast peaks at different heights in the two stages, a correction for the measurement distance should be made to account for the different measurement distances. The standard uncertainty of the contribution due to the correction for measurement distance is designated throughout all parts of TR 102 273 [3] as uj18. NOTE 1: In this example case the standard uncertainty of the contribution due to the correction for measurement distance is taken as 0,00 dB since, in this, the first stage of the measurement, only a reference height is being set. Correction: off boresight angle in elevation plane: For those tests in which the test antenna on the mast peaks at different heights in the two stages, a correction must be made to account for the different angles subtended by the EUT/substitution antenna. The standard uncertainty of the contribution, due to the correction for off boresight angle in elevation plane, is designated throughout all parts of TR 102 273 [3] as uj17. NOTE 2: In this example case the standard uncertainty of the contribution due to the correction for off boresight angle in elevation plane is taken as 0,00 dB since in this, the first stage of the measurement, only a reference height is being set. Antenna: gain of the test antenna: The gain, and its uncertainty, of the test antenna act as systematic offsets since they are present in both stages of the test. The standard uncertainty of the contribution, due to the uncertainty of the gain of the test antenna, is designated throughout all parts of TR 102 273 [3] as uj45. NOTE 3: In this example case the standard uncertainty of the contribution due to the uncertainty of the gain of the test antenna is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. Antenna: tuning of the test antenna: This uncertainty is introduced as a result of inaccurate tuning of the test antenna. The standard uncertainty of the contribution, due to the tuning of the test antenna, is designated throughout all parts of TR 102 273 [3] as uj46. NOTE 4: In this example case the standard uncertainty of the contribution due to the tuning of the test antenna is taken as 0,00 dB since the uncertainty is systematic i.e. it is assumed constant and common to both stages of the measurement and, provided that once set in stage one of the test it is not subsequently re-tuned, its contribution is the same in both stages. Position of the phase centre: test antenna: The horizontal position of the test antenna defines one end of the range length. The standard uncertainty of the contribution, due to the position of the phase centre of the test antenna, is designated throughout all parts of TR 102 273 [3] as uj22. NOTE 5: In this example case the test antenna is assumed to describe a vertical straight line as its height on the mast is changed. The standard uncertainty of the contribution due to the position of the phase centre of the test antenna is assumed to be 0,00 dB (see annex A). 6.8.3.1.2.4 Test antenna attenuator Insertion loss: test antenna attenuator: The attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss of the test antenna attenuator is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution, due to the insertion loss uncertainty of the test antenna attenuator, is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 97 6.8.3.1.2.5 Test antenna cable Insertion loss: test antenna cable: The test antenna cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution, due to the insertion loss uncertainty of the test antenna cable, is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the test antenna cable is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. Cable factor: test antenna cable: Cable factor is defined as the total effect of the antenna cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency, parasitic effects (acting as a director or reflector) on the test antenna and introducing an unbalanced, common mode current into the dipole balun. In a radiated measurement the standard uncertainty of the cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the test antenna cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the test antenna cable is taken as 0,50 dB since in this measurement, the cable changes position in both stages (the height of the test antenna being optimized in both stages) even though the precautions detailed in the methods have been observed. 6.8.3.1.2.6 Receiving device Whereas the first stage of a spurious emission test is to observe and record the received level from the EUT on the receiving device, the second stage involves the adjustment of the output level of a signal generator to achieve the same received level from a substitution antenna. As a consequence of this methodology, the receiving device contributes neither linearity nor absolute level uncertainty to either stage of the test. Receiving device: absolute level: The standard uncertainty of the contribution, due to the absolute level uncertainty of the receiving device, is designated throughout all parts of TR 102 273 [3] as uj47. NOTE 1: In this example case the standard uncertainty of the contribution, due to the absolute level uncertainty of the receiving device is taken as 0,00 dB. Receiving device: linearity: The standard uncertainty of the contribution, due to the receiving device linearity, is designated throughout all parts of TR 102 273 [3] as uj48. NOTE 2: In this example case the standard uncertainty of the contribution due to the receiving device linearity is taken as 0,00 dB.
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6.8.3.1.3 Contribution from the random component
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Random uncertainty: The magnitude can be assessed from multiple measurements of the spurious emission. The standard uncertainty of the contribution due to the random uncertainty is designated throughout all parts of TR 102 273 [3] as ui01. The EUT measurement was repeated 10 times. The following results were obtained in dBµV (before correcting for cabling and attenuator network insertion loss): - 65,4; 63,4; 66,0; 65,3; 63,0; 64,9; 65,2; 66,8; 65,5; 63,7. Converting to linear terms: - 1,862 × 10-3; 1,479 × 10-3; 1,995 × 10-3; 1,841 × 10-3; 1,413 × 10-3; 1,758 × 10-3; 1,820 × 10-3; 2,188 × 10-3; 1,884 × 10-3; 1,531 × 10-3. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 98 The two sums X and Y are calculated: - X = the sum of the measured values = 17,77 × 10-3; - Y = the sum of the squares of the measured values = 32,10 × 10-6 V2. ( ) = − × − × = − − = − − 1 10 10 10 77 , 17 10 10 , 32 1 2 3 6 2 n n X Y uc random 238,3 ×10-6 (formula 5.6) As the result is obtained as the mean value of 10 measurements and the standard uncertainty of the random uncertainty is: dB 1,17 5, 11 100 10 777 ,1 10 3, 238 3 6 = × × × = − − j random u NOTE: In this example case the standard uncertainty of the contribution due to the random uncertainty is 1,17 dB. See also the note in clause 6.4.7.
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100 028-1
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6.8.3.1.4 Summary table of contributory components
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All the uncertainty contributions for this part of the procedure are listed in table 19. Table 19: Contributions from the EUT measurement uj or i Description of uncertainty contributions dB uj37 mismatch: receiving part 0,00 uj54 EUT: influence of setting the power supply on the spurious emission level 0,03 uj51 EUT: influence of the ambient temperature on the spurious emission level 0,03 uj55 EUT: mutual coupling to the power leads 0,50 uj20 position of the phase centre: within the EUT volume 0,12 uj21 positioning of the phase centre: within the EUT over the axis of rotation of the turntable 0,02 uj16 range length 0,00 uj34 ambient effect 0,00 uj08 mutual coupling: amplitude effect of the test antenna on the EUT 0,00 uj04 Mutual coupling: EUT to its images in the absorbing material 0,50 uj13 mutual coupling: EUT to its image in the ground plane 0,15 uj01 reflectivity of absorbing material: EUT to the test antenna 0,00 uj06 mutual coupling: test antenna to its images in the absorbing material 0,00 uj14 mutual coupling: test antenna to its image in the ground plane 0,00 uj18 correction: measurement distance 0,00 uj17 correction: off boresight angle in elevation plane 0,00 uj45 antenna: gain of the test antenna 0,00 uj46 antenna: tuning of the test antenna 0,00 uj22 position of the phase centre: test antenna 0,00 uj40 insertion loss: test antenna attenuator 0,00 uj41 insertion loss: test antenna cable 0,00 uj19 cable factor: test antenna cable 0,50 uj47 receiving device: absolute level 0,00 uj48 receiving device: linearity 0,00 ui01 random uncertainty (see note in clause 6.4.7) 1,17 The standard uncertainties from table 19 should be combined by RSS in accordance with TR 102 273 [3], part 1, sub-part 1, clause 5. This gives the combined standard uncertainty (uc contribution from the EUT measurement) for the EUT measurement in dB. The value of uc contribution from the EUT measurement is calculated as 1,47 dB. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 99
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6.8.3.2 Uncertainty contributions: Stage 2: Substitution measurement
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The second stage of the spurious emission test (the substitution) involves replacing the EUT with a substitution antenna and signal source as shown in figure 27, and adjusting the output level of the signal generator until the same level as in stage one is achieved on the receiving device. Ground plane Test antenna cable 2 Test antenna ferrite beads Attenuator 2 10 dB Receiving device cable 1 ferrite beads Attenuator 1 10 dB Signal generator Figure 27: Stage two: Typical emission substitution test Whereas figure 27 shows, schematically, the test equipment set-up for this substitution stage of the spurious emission test, figure 28, an analysis diagram, provides a detailed picture of the individual uncertainty components (each of which contributes its own uncertainty) for this stage in the measurement. As stated above, the shaded areas represent components common to both stages of the test method.
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6.8.3.2.1 Contributions from the mismatch components
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Mismatch uncertainty transmitting and receiving parts: The value of the combined standard uncertainty of the contribution due to the mismatch for the substitution measurement are calculated from the approach described in annex G. For this stage it is calculated in two parts. Firstly the standard uncertainty of the contribution due to the mismatch in the transmitting part, i.e. between the signal generator, cable, attenuator and the substitution antenna and secondly, that for the receiving part, i.e. between the test antenna, attenuator, cable and the receiver. However, only the contribution for the transmitting part is actually calculated since the receiving part is common to both stages of the test and its uncertainty contribution therefore largely cancels. Mismatch: transmitting part: Signal generator: Output reflection coefficient: |ρG| = 0,20 Cable: Input and output reflection coefficients: |S11| and |S22| = 0,07 Attenuation: 1 dB = |S12| = |S21| = 0,891 Attenuator: Input and output reflection coefficients |S11| = |S22| = 0,05 Attenuation = 10 dB |S12| = |S21| = 0,3162 Transmitting antenna: Input reflection coefficient: |ρTA| = 0,333 All these contributions are U-distributed. Those components that cancel are not calculated. Other contributions are (see annex G): - uj generator and cable 1: Constant for both stage 1 and 2. Hence this value does not contribute. - uj cable 1 and attenuator 1: Constant for both stage 1 and 2. Hence this value does not contribute. % 177 ,1 % 2 100 333 ,0 05 ,0 1 = × × = antenna and attenuator j u ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 100 - uj generator and attenuator 1: Constant for both stage 1 and 2. Hence this value does not contribute. % 165 ,0 % 2 100 316 ,0 333 ,0 07 ,0 2 1 = × × × = antenna and cable j u % 373 ,0 % 2 100 316 ,0 891 ,0 333 ,0 2,0 2 2 = × × × × = antenna and generator j u Substitution antenna Cable factor Test antenna Cable factor + Antenna to antenna coupling Mutual image coupling Antenna factor Cable loss Direct path loss Reflected path loss Site Imperfections Antenna to antenna coupling Mutual image coupling Antenna factor Mismatch Mismatch + Cable loss Mismatch Signal generator Receiving device Test antenna cable 2 Receiving device Transmitting antenna cable 1 Transmitting source Attenuator 1 10 dB Attenuator 2 10 dB Mismatch Mismatch Mismatch + + + Figure 28: Stage two: Substitution measurement individual uncertainty components The combined standard uncertainty of the mismatch is then calculated: % 25 1 373 ,0 165 ,0 177 ,1 2 2 2 : , u on substituti mismatch c = + + = Transforming to the logarithmic form (TR 100 028-2 [8], annex E): 1,24 %/11,5 = 0,11 dB. The standard uncertainty of the contribution due to the mismatch in the transmitting part, is designated throughout all parts of TR 102 273 [3] as uj36. Its value in this example is 0,11 dB. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 101 Mismatch: Receiving part: The mismatch uncertainty between the test antenna and the receiving device contributes equally to both stages of the test and therefore has no contribution to the combined standard uncertainty. Therefore it is not calculated. The standard uncertainty of the contribution due to mismatch in the receiving part is designated throughout all parts of TR 102 273 [3] as uj37. NOTE: In this example case the standard uncertainty of the contribution due to mismatch in the receiving part is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages.
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6.8.3.2.2 Contributions from the individual components
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6.8.3.2.2.1 Signal generator Signal generator: absolute output level: The signal generator replaces the EUT in the substitution part of this test and, as a result, should be included in the combined standard uncertainty since it does not cancel as a systematic offset. The standard uncertainty of the contribution, due to the signal generator absolute output level, is designated throughout all parts of TR 102 273 [3] as uj38. NOTE 1: In this example case the uncertainty of the contribution due to the signal generator absolute output level uncertainty is obtained from the manufacturers data sheet as ±1,0 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,58 dB. Signal generator: output level stability: In any test in which the contribution of the absolute level uncertainty of the signal generator contributes to the combined standard uncertainty of the test i.e. it does not cancel due to the methodology, the contribution from the output level stability is considered to have been included in the signal generator absolute output level, uj38. Conversely, for any level in which the absolute level uncertainty of the signal generator does not contribute to the combined standard uncertainty, the output level stability of the signal generator should be included. The standard uncertainty of the contribution due to the signal generator output level stability is designated throughout all parts of TR 102 273 [3] as uj39. Its value can be derived from manufacturers' data sheet. NOTE 2: In this example case the standard uncertainty of the contribution due to the signal generator output level stability is taken as 0,00 dB as it is covered by the absolute level uncertainty. 6.8.3.2.2.2 Substitution antenna cable Insertion loss: substitution antenna cable: The substitution antenna cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the substitution antenna cable, is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the uncertainty of the contribution due to the insertion loss uncertainty of the substitution antenna cable is taken from the manufacturers data sheet as ±0,5 dB. As nothing is said about the distribution, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed and the standard uncertainty is calculated as 0,29 dB. Cable factor: substitution antenna cable: Cable factor is defined as the total effect of the antenna cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency, parasitic effects (acting as a director or reflector) and introducing an unbalanced, common mode current into the dipole balun. In a radiated measurement the standard uncertainty of the cable factor, associated with the substitution antenna cable is 0,5 dB provided the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution, due to the cable factor of the substitution antenna cable, is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the substitution antenna cable is taken as 0,50 dB since the precautions detailed in the methods are assumed to have been observed. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 102 6.8.3.2.2.3 Substitution antenna attenuator Insertion loss: substitution antenna attenuator: The attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss is taken from the manufacturer's data sheet since it does not cancel as a systematic offset (it only appears in one stage of the test). The standard uncertainty of the contribution, due to the insertion loss uncertainty of the substitution antenna attenuator, is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the uncertainty of the contribution, due to the insertion loss uncertainty of the substitution antenna attenuator, is obtained from the manufacturer's data sheet as ±0,3 dB. As nothing is said about the distribution, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed and the standard uncertainty is calculated as 0,17 dB. 6.8.3.2.2.4 Substitution antenna Antenna: gain of the substitution antenna: The gain (and its uncertainty) of the substitution antenna is only involved in the second stage of the test. The standard uncertainty of the contribution due to the gain of the substitution antenna is designated throughout all parts of TR 102 273 [3] as uj45. For ANSI dipoles the value should be obtained from table 20. Table 20: Uncertainty contribution: Antenna: gain of the test or substitution antenna Frequency Standard uncertainty of the contribution 30 MHz ≤ frequency ≤ 80 MHz 1,73 dB 80 MHz < frequency ≤ 180 MHz 0,60 dB frequency > 180 MHz 0,30 dB NOTE 1: For other antenna types the figures should be taken from manufacturers data sheets. If a figure is not given the standard uncertainty is 1,0 dB. NOTE 2: In this example case the standard uncertainty of the contribution due to the gain of the substitution antenna is taken as 0,3 dB as an ANSI dipole is used and the frequency is above 180 MHz. Antenna: tuning of the substitution antenna: Uncertainty is introduced as a result of the inaccurate tuning of the substitution antenna. This only occurs in stage two of the measurement. The standard uncertainty of the contribution, due to the tuning of the substitution antenna, is designated throughout all parts of TR 102 273 [3] as uj46. NOTE 3: In this example case the standard uncertainty of the contribution due to the tuning of the substitution antenna is taken as 0,06 dB. Position of the phase centre: substitution antenna: Uncertainty is introduced as a result of the inaccurate positioning of the phase centre of the substitution antenna. This only occurs in stage two of the measurement. The standard uncertainty of the contribution, due to the position of the phase centre of the substitution antenna, is designated throughout all parts of TR 102 273 [3] as uj22. NOTE 4: In this example case the standard uncertainty of the contribution due to the uncertainty in the position of the phase centre of the substitution antenna has been calculated from (±(the offset from axis of rotation)/ (range length) x100 %). The positioning uncertainty is ±0,01 m and therefore the worst case uncertainty = 0,01/3,0 = 0,333 %. As the offset can be anywhere between these limits, the uncertainty is taken to be rectangularly distributed (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) and the standard uncertainty is calculated as 0,192 %. This is transformed to the logarithmic form (TR 100 028-2 [8], annex E), to be 0,02 dB. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 103 6.8.3.2.2.5 Site factors Ambient effect: Uncertainty is introduced as a result of local ambient signals raising the noise floor at the measurement frequency. The standard uncertainty of the contribution due to the ambient effect is designated throughout all parts of TR 102 273 [3] as uj34. The values of the standard uncertainty should be taken from table 21. Table 21: Uncertainty contribution: Ambient effect Receiving device noise floor (generator OFF) is within: Standard uncertainty of the contribution 3 dB of measurement 1,57 dB 3 dB to 6 dB of measurement 0,80 dB 6 dB to 10 dB of measurement 0,30 dB 10 dB to 20 dB of measurement 0,10 dB 20 dB or more of the measurement 0,00 dB NOTE 1: In this example case the standard uncertainty of the contribution due to the ambient effect is taken as 0,00 dB, since the chamber is assumed to be shielded. Mutual coupling: substitution antenna to its images in the absorbing material: This uncertainty is the effect of the change produced in the antenna's input impedance and/or gain. The standard uncertainty of the contribution due to the mutual coupling of the substitution antenna to its images in the absorbing material is designated throughout all parts of TR 102 273 [3] as uj06. NOTE 2: In this example case the standard uncertainty of the contribution due to the mutual coupling of the transmitting antenna to its images in the absorbing materials is taken as 0,5 dB (see annex A). Mutual coupling: substitution antenna to its image in the ground plane: This uncertainty is the effect of the change produced in the antenna's input impedance and/or gain. The standard uncertainty of the contribution due to the mutual coupling of the substitution antenna to its image in the ground plane, designated throughout all parts of TR 102 273 [3] as uj14. has a value of 0,00 dB for ANSI dipoles since it is included, where significant, in the mutual coupling and mismatch loss correction factors (see table A.20). For other dipoles the value can be obtained from table 22. Table 22: Uncertainty contribution of the mutual coupling between the substitution antenna and its image in the ground plane Spacing between the antenna and the ground plane Standard uncertainty of the contribution For a vertically polarized antenna spacing ≤ 1,25 λ 0,15 dB spacing > 1,25 λ 0,06 dB For a horizontally polarized antenna spacing < λ/2 1,15 dB λ/2 ≤ spacing < 3λ/2 0,58 dB 3λ/2 ≤ spacing < 3λ 0,29 dB spacing ≥ 3λ 0,15 dB NOTE 3: In this example case the standard uncertainty of the contribution due to mutual coupling between the substitution antenna and its image in the ground plane is taken as 0,58 dB. Mutual coupling: substitution antenna to the test antenna: This is the effect produced by any change in gain of the antennas which results from their close spacing. The standard uncertainty of the contribution due to the mutual coupling of the substitution antenna to the test antenna, designated throughout all parts of TR 102 273 [3] as uj11. For ANSI dipoles the value of this uncertainty is 0,00 dB as it is included, where significant, in the mutual coupling and mismatch loss correction factors. For non-ANSI dipoles the standard uncertainty for frequencies can be taken from table 23. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 104 Table 23: Uncertainty contribution of the mutual coupling between the substitution and test antennas Frequency Standard uncertainty of the contribution (3 m range) Standard uncertainty of the contribution (10 m range) 30 MHz ≤ frequency < 80 MHz 1,73 dB 0,60 dB 80 MHz ≤ frequency < 180 MHz 0,6 dB 0,00 dB frequency ≥ 180 MHz 0,00 dB 0,00 dB NOTE 4: In this example case the standard uncertainty of the contribution due to mutual coupling between the substitution and test antennas is taken as 0,00 dB as the frequency is above 180 MHz. Mutual coupling: interpolation of mutual coupling and mismatch loss correction factors, only for ANSI dipoles: The standard uncertainty of the contribution due to the interpolation of mutual coupling and mismatch loss correction factors, is designated throughout all parts of TR 102 273 [3] as uj12. For spot frequencies given in table A.20, the value of the contribution is 0,00 dB. However, for all other frequencies, the standard uncertainty should be obtained from table 24. Table 24: Uncertainty contribution of the interpolation of mutual coupling and mismatch loss correction factors Frequency (MHz) Standard uncertainty of the contribution for a spot frequency given in the table 0,00 dB 30 MHz ≤ frequency < 80 MHz 0,58 dB 80 MHz ≤ frequency < 180 MHz 0,17 dB frequency ≥ 180 MHz 0,00 dB NOTE 5: In this example case the standard uncertainty of the contribution due to the interpolation of mutual coupling and mismatch loss correction factors is taken as 0,00 dB as the frequency is above 180 MHz. Range length: This contribution is associated with the curvature of the phase front from the substitution antenna to the test antenna. The standard uncertainty of the contribution, due to range length, is designated throughout all parts of TR 102 273 [3] as uj16. The standard uncertainty is 0,00 dB if ANSI dipoles are used. For other types of antenna the standard uncertainty of the contribution should be obtained from table 25. Table 25: Uncertainty contribution of the range length (verification) Range length (i.e. the horizontal distance between phase centres) Standard uncertainty of the contribution (d1 + d2)2/4λ ≤ range length < (d1 + d2)2/2λ 1,26 dB (d1 + d2)2/2λ ≤ range length < (d1 + d2)2/λ 0,30 dB (d1 + d2)2/λ ≤ range length < 2(d1 + d2)2/λ 0,10 dB range length ≥ 2(d1 + d2)2/λ 0,00 dB NOTE 6: In table 25, d1 and d2 are the maximum dimensions of the antennas. NOTE 7: The standard uncertainty of the contribution due to the range length is taken as 0,00 dB since in this case the range length is ≥ 2 (d1 + d2)2/λ. Reflectivity of absorbing material: substitution antenna to the test antenna: This uncertainty is associated with the magnitude of the reflections occurring from the side walls, end walls and ceiling. These magnitudes are a function of the quality of the absorber at the frequency of test. However, in this, a substitution measurement, the contribution is only concerned with taking into account the possible differences in the antenna patterns (principally in the vertical plane) between the EUT and substitution antenna. The standard uncertainty of the contribution due to the reflectivity of the absorbing material between the substitution and test antenna is designated throughout all parts of TR 102 273 [3] as uj02. NOTE 8: In this example case the standard uncertainty of the contribution due to the reflectivity of the absorbing material between the substitution and test antenna is 0,50 dB (see annex A). ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 105 Mutual coupling: test antenna to its images in the absorbing material: This is the uncertainty due to the mutual coupling between the test antenna and its images in the ceiling, side and end walls and is the effect of the change produced in the antenna's input impedance and/or gain. As this is the second stage of a substitution measurement and the uncertainty is common to both stages it will only contribute in this stage if the test antenna is located at a different height on the antenna mast from the first stage. The standard uncertainty of the contribution, due to the mutual coupling of the test antenna to its images in the absorbing material, is designated throughout all parts of TR 102 273 [3] as uj06. NOTE 9: In this example case the standard uncertainty of the contribution due to the mutual coupling of the test antenna to its images in the absorbing material is taken as 0,50 dB since this is the second stage of a substitution measurement and the test antenna is assumed to be located at a different height to stage one and therefore the contribution does not cancel. Mutual coupling: test antenna to its image in the ground plane: As this is the second stage of a substitution measurement and the uncertainty is common to both stages it will only contribute in this stage if the test antenna is located at a different height on the antenna mast from the first stage. The standard uncertainty of the contribution, due to the mutual coupling of the test antenna to its image in the ground plane, is designated throughout all parts of TR 102 273 [3] as uj14. NOTE 10: In this example case the standard uncertainty of the contribution due to the mutual coupling of the test antenna to its image in the ground plane is taken as 0,50 dB since this is the second stage of a substitution measurement and the test antenna is assumed to be located at a different height to stage one and therefore the contribution does not cancel. 6.8.3.2.2.6 Test antenna Correction: measurement distance: For those tests in which the test antenna on the mast peaks at different heights in the two stages, a correction should be made to account for the different measurement distances. Where a correction is required the standard uncertainty of the correction factor should be taken as 0,10 dB. The standard uncertainty of the contribution due to the correction for measurement distance is designated throughout all parts of TR 102 273 [3] as uj18. NOTE 1: In this example case the standard uncertainty of the contribution due to the correction for measurement distance is taken as 0,10 dB since it is assumed that, in this second stage, a different height of test antenna has been necessary and the correction applied. Correction: off boresight angle in elevation plane: For those tests in which the test antenna on the mast peaks at different heights in the two stages, a correction should be made to account for the different angles subtended by the EUT/substitution antenna. Where a correction is required the standard uncertainty of the correction factor should be taken as 0,10 dB. The standard uncertainty of the contribution due to the correction for off boresight angle in elevation plane is designated throughout all parts of TR 102 273 [3] as uj17. NOTE 2: In this example case the standard uncertainty of the contribution due to the correction for off boresight angle in the elevation plane is taken as 0,10 dB since it is assumed that, in this second stage, a different height of test antenna has been necessary and the correction applied. Antenna: gain of the test antenna: The gain, and its uncertainty, of the test antenna act as systematic offsets since they are present in both stages of the test. The standard uncertainty of the contribution, due to the uncertainty of the gain of the test antenna, is designated throughout all parts of TR 102 273 [3] as uj45. NOTE 3: In this example case the standard uncertainty of the contribution due to the uncertainty of the gain of the test antenna is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. Antenna: tuning of the test antenna: This uncertainty is introduced as a result of inaccurate tuning of the test antenna. The standard uncertainty of the contribution, due to the tuning of the test antenna, is designated throughout all parts of TR 102 273 [3] as uj46. NOTE 4: In this example case the standard uncertainty of the contribution due to the tuning of the test antenna is taken as 0,00 dB since the uncertainty is systematic i.e. it is assumed constant and common to both stages of the measurement and, provided that once set in stage one of the test it is not subsequently re-tuned, its contribution is the same in both stages. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 106 Position of the phase centre: test antenna: The horizontal position of the test antenna defines one end of the range length. The standard uncertainty of the contribution, due to the position of the phase centre of the test antenna, is designated throughout all parts of TR 102 273 [3] as uj22. NOTE 5: In this example case the test antenna is assumed to describe a vertical straight line as its height on the mast is changed. The standard uncertainty of the contribution due to the position of the phase centre of the test antenna is assumed to be 0,00 dB (see annex A). 6.8.3.2.2.7 Test antenna attenuator Insertion loss: test antenna attenuator: The attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss of the test antenna attenuator is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution, due to the insertion loss uncertainty of the test antenna attenuator, is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. 6.8.3.2.2.8 Test antenna cable Insertion loss: test antenna cable: The test antenna cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution, due to the insertion loss uncertainty of the test antenna cable, is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the test antenna cable is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. Cable factor: test antenna cable: Cable factor is defined as the total effect of the antenna cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency, parasitic effects (acting as a director or reflector) on the test antenna and introducing an unbalanced, common mode current into the dipole balun. In a radiated measurement the standard uncertainty of the cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the test antenna cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the test antenna cable is taken as 0,50 dB since in this measurement, the cable changes position in both stages (the height of the test antenna being optimized in both stages) even though the precautions detailed in the methods have been observed. 6.8.3.2.2.9 Receiving device Whereas the first stage of a spurious emission test is to observe and record the received level from the EUT on the receiving device, the second stage involves the adjustment of the output level of a signal generator to achieve the same received level from a substitution antenna. As a consequence of this methodology, the receiving device contributes neither linearity nor absolute level uncertainty to either stage of the test. Receiving device: absolute level: The standard uncertainty of the contribution, due to the absolute level uncertainty of the receiving device, is designated throughout all parts of TR 102 273 [3] as uj47. NOTE 1: In this example case the standard uncertainty of the contribution, due to the absolute level uncertainty of the receiving device is taken as 0,00 dB. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 107 Receiving device: linearity: The standard uncertainty of the contribution, due to the receiving device linearity, is designated throughout all parts of TR 102 273 [3] as uj48. NOTE 2: In this example case the standard uncertainty of the contribution due to the receiving device linearity is taken as 0,00 dB.
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100 028-1
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6.8.3.2.3 Contribution from the random component
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Random uncertainty: The magnitude can be assessed from multiple measurements of the substitution measurement. The standard uncertainty of the contribution due to the random uncertainty is designated throughout all parts of TR 102 273 [3] as ui01. The substitution measurement was repeated 10 times. The following levels were set on the signal generator in dBm (before correcting for cabling and attenuator network insertion loss): - -20,1; -20,1; -20,2; -20,2; -20,1; -20,1; -20,2; -20,3; -20,3; -20,3. Converting to linear terms: - 9,772 × 10-3; 9,772 × 10-3; 9,550 × 10-3; 9,550 × 10-3; 9,772 × 10-3; 9,772 × 10-3; 9,550 × 10-3; 9,333 × 10-3; 9,333 × 10-3; 9,333 × 10-3. The two sums X and Y are calculated: - X = the sum of the measured values = 95,737 × 10-3; - Y = the sum of the squares of the measured values = 916,89 × 10-6 W2. ( ) = − × − × = − − = − − 1 10 10 10 737 , 95 10 89 , 916 1 2 3 6 2 n n X Y uc random 192,3 × 10-6 (formula 5.7) As the result is obtained as the mean value of 10 measurements and the standard uncertainty of the random uncertainty is: dB 0,175 0, 23 100 10 5737 ,9 10 3, 192 3 6 = × × × = − − j random u NOTE: In this example case the standard uncertainty of the contribution due to the random uncertainty is 0,05 dB. See also the note in clause 6.4.7. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 108
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100 028-1
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6.8.3.2.4 Summary table of contributory components
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All the uncertainties contributions for this part of the procedure are listed in table 26. Table 26: Contributions from the substitution uj or i Description of uncertainty contributions dB uj36 mismatch: transmitting part 0,11 uj37 mismatch: receiving part 0,00 uj38 signal generator: absolute output level 0,58 uj39 signal generator: output level stability 0,00 uj41 insertion loss: substitution antenna cable 0,29 uj19 cable factor: substitution antenna cable 0,50 uj40 insertion loss: substitution antenna attenuator 0,17 uj45 antenna: gain of the substitution antenna 0,30 uj46 antenna: tuning of the substitution antenna 0,06 uj22 position of the phase centre: substitution antenna 0,02 uj34 ambient effect 0,00 uj06 mutual coupling: substitution antenna to its images in the absorbing material 0,50 uj14 mutual coupling: substitution antenna to its image in the ground plane 0,58 uj11 mutual coupling: substitution antenna to the test antenna 0,00 uj12 mutual coupling: interpolation of mutual coupling and mismatch loss correction factors 0,00 uj16 range length 0,00 uj02 reflectivity of absorbing material: substitution antenna to the test antenna 0,50 uj06 mutual coupling: test antenna to its images in the absorbing material 0,50 uj14 mutual coupling: test antenna to its image in the ground plane 0,50 uj18 correction: measurement distance 0,10 uj17 correction: off boresight angle in elevation plane 0,10 uj45 antenna: gain of the test antenna 0,00 uj46 antenna: tuning of the test antenna 0,00 uj22 position of the phase centre: test antenna 0,00 uj40 insertion loss: test antenna attenuator 0,00 uj41 insertion loss: test antenna cable 0,00 uj19 cable factor: test antenna cable 0,50 uj47 receiving device: absolute level 0,00 uj48 receiving device: linearity 0,00 ui01 random uncertainty (see note in clause 6.4.7) 0,175 The standard uncertainties from table 26 should be combined by RSS in accordance with TR 102 273 [3], part 1, sub-part 1, clause 5. This gives the combined standard uncertainty (uc substitution measurement) for the NSA measurement in dB. The value of uc substitution measurement is calculated as 1,56 dB.
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6.8.3.2.5 Expanded uncertainty for the spurious emission test
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The combined standard uncertainty of the results of the spurious emissions test is the combination of the components outlined in clauses 6.8.3.1.4 and 6.8.3.2.4. The components to be combined are (uc EUT measurement) and (uc substitution measurement). dB 2,15 = 56 ,1 47 ,1 2 2 + = c u The expanded uncertainty is ±1,96 x 2,15 dB = ±4,21 dB at a 95 % confidence level. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 109
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6.8.4 Example 3: Measurement of a receiver parameter (Sensitivity)
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For the measurement of receiver sensitivity two stages of test are involved. The first stage (determining the Transform Factor of the site) involves measuring the field strength at the point where the receiver will be placed and determining the relationship between the signal generator output power level and the resulting field strength. The second stage (the EUT measurement) involves replacing the measuring antenna with the EUT and adjusting the output level of the signal generator until the required response is obtained on the receiver. The signal generator output power level is then converted to field strength using the Transform Factor.
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6.8.4.1 Uncertainty contributions: Stage 1: Transform Factor measurement
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The first stage of the receiver sensitivity test is to determine the Transform Factor of the site. This is normally carried out by placing a measuring antenna in the volume occupied by the EUT and determining the relationship between the signal generator output power and the resulting field strength. The test equipment configuration is shown in figure 29. The components shown shaded are common to both stages of the test. Attenuator 2 10 dB Test antenna cable 2 Attenuator 1 10 dB Receiving device Measuring antenna cable 1 Measuring antenna Test antenna Signal generator Ground plane Figure 29: Stage 1: Transform Factor measurement Due to the commonality of all of the components from the test antenna to the receiver in both stages of the test, the mismatch uncertainty contributes identically to both stages and hence does not contribute to the combined standard uncertainty of the measurement. Similarly, for the systematic uncertainty contributions (e.g. test antenna cable loss etc.) of the individual components. Whereas figure 29 shows, schematically, the equipment set-up for this stage of the receiver sensitivity test, an analysis diagram of the individual components (each of which contributes its own uncertainty) for this stage of the measurement is shown in figure 30. Again, as stated above, the shaded areas represent components common to both stages of the receiver sensitivity test.
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6.8.4.1.1 Contributions from the mismatch components
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Mismatch in the transmitting and receiving part: The value of the combined standard uncertainty of the contribution due to the mismatch are calculated from the approach described in annex G. For this stage is calculated in two parts. Firstly the standard uncertainty of the contribution due to the mismatch in the transmitting part, i.e. between the signal generator, cable, attenuator and the test antenna and secondly, that for the receiving part, i.e. between the receiving antenna, attenuator, cable and the receiving device. Mismatch: transmitting part: The standard uncertainty of the contribution due to mismatch in the transmitting part is designated throughout all parts of TR 102 273 [3] as uj36. NOTE: In this example case the uncertainty due to mismatch in the receiving part is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 110 Measuring antenna Cable Factor Test antenna Cable Factor Antenna to antenna coupling Mutual image coupling Test source Test source cable 2 Measuring antenna cable 1 Measuring device Direct Path Loss Reflected Path Loss Antenna factor + Cable loss Antenna to antenna coupling Mutual image coupling Antenna factor Mismatch Mismatch Cable loss Mismatch Signal generator Site Imperfections Measuring device Attenuator 2 10 dB Attenuator 1 10 dB Mismatch Mismatch Mismatch + + + Figure 30: Schematic of the Transform Factor measurement Mismatch: receiving part: Measuring antenna: Input reflection coefficient: |ρRA| = 0,333 Attenuator: Input and output reflection coefficients |S11| = |S22| = 0,05 Attenuation = 10 dB |S12| = |S21| = 0,3162 Cable: Input and output reflection coefficients: |S11| and |S22| = 0,07 Attenuation: 1 dB = |S12| = |S21| = 0,891 Measuring device: Input reflection coefficient: |ρRD| = 0,20 % 177 ,1 % 2 100 05 ,0 333 ,0 2 : = × × = attenuator and antenna mismatch j u - uj attenuator 2 and cable 2: Constant for both stage 1 and 2. Hence this value does not contribute. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 111 - uj cable 2 and receiving device: Constant for both stage 1 and 2. Hence this value does not contribute. % 165 ,0 % 2 100 316 ,0 07 ,0 333 ,0 2 1 = × × × = antenna and cable j u - uj attenuator 2 and receiving device: Constant for both stage 1 and 2. Hence this value does not contribute. % 373 ,0 % 2 100 891 ,0 316 ,0 2,0 333 ,0 2 2 = × × × × = device receiving and antenna j u The combined standard uncertainty of the mismatch is then calculated: % , u part measuring mismatch j 25 1 373 ,0 165 ,0 177 ,1 2 2 2 : = + + = Transforming to the logarithmic form (TR 100 028-2 [8], annex E): 1,24 %/11,5 = 0,11 dB. The standard uncertainty of the contribution, due to the mismatch in the direct attenuation measurement, is designated throughout all parts of TR 102 273 [3] as uj37. Its value in this example is 0,11 dB.
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6.8.4.1.2 Contributions from the individual components
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6.8.4.1.2.1 Signal generator Signal generator: absolute output level: There is not necessarily any similarity between the output levels from the signal generator in the two stages of this test. As a result it contributes to both stages. The standard uncertainty of the contribution, due to the signal generator absolute output level, is designated throughout all parts of TR 102 273 [3] as uj38. Its value can be derived from manufacturer's data sheet. NOTE 1: In this example case the uncertainty of the contribution due to the signal generator absolute output level uncertainty is taken from the manufacturers data sheet as ±1,0 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,58 dB. Signal generator: output level stability: In any test in which the contribution of the absolute level uncertainty of the signal generator contributes to the combined standard uncertainty of the test i.e. it does not cancel due to the methodology, the contribution from the output level stability is considered to have been included in the signal generator absolute output level, uj38. Conversely, for any level in which the absolute level uncertainty of the signal generator does not contribute to the combined standard uncertainty, the output level stability of the signal generator should be included. The standard uncertainty of the contribution due to the signal generator output level stability is designated throughout all parts of TR 102 273 [3] as uj39. Its value can be derived from manufacturers' data sheet. NOTE 2: In this example case the standard uncertainty of the contribution due to the signal generator output level stability is taken as 0,0 dB as it is covered by the absolute level uncertainty. 6.8.4.1.2.2 Test antenna cable Insertion loss: test antenna cable: The test antenna cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the test antenna cable, is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the test antenna cable is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 112 Cable factor: test antenna cable: Cable factor is defined as the total effect of the antenna cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency, parasitic effects (acting as a director or reflector) on the test antenna and introducing an unbalanced, common mode current into the dipole balun. In a radiated measurement the standard uncertainty of the cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the test antenna cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the test antenna cable is taken as 0,00 dB since in this measurement, the cable position, once set in this stage is not subsequently changed during the test. 6.8.4.1.2.3 Test antenna attenuator Insertion loss: test antenna attenuator: The attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss of the test antenna attenuator is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution, due to the insertion loss uncertainty of the test antenna attenuator, is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. 6.8.4.1.2.4 Test antenna Correction: measurement distance: For those tests in which the test antenna on the mast peaks at different heights in the two stages, a correction for measurement distance must be made to account for the different measurement distances. In this test, once the position of the test antenna is set in stage one no further adjustment to its position is subsequently made during the test. The standard uncertainty of the contribution due to the correction for measurement distance is designated throughout all parts of TR 102 273 [3] as uj18. NOTE 1: In this example case the standard uncertainty of the contribution due to the correction for measurement distance is taken as 0,00 dB. Correction: off boresight angle in elevation plane: For those tests in which the test antenna on the mast peaks at different heights in the two stages, a correction must be made to account for the different angles subtended by the EUT/substitution antenna. In this test, once the position of the test antenna is set in stage one no further adjustment to its position is subsequently made during the test. The standard uncertainty of the contribution due to the correction for off boresight angle in elevation plane is designated throughout all parts of TR 102 273 [3] as uj17. NOTE 2: In this example case the standard uncertainty of the contribution due to the correction for off boresight angle in elevation plane is taken as 0,00 dB. Antenna: gain of the test antenna: The gain, and its uncertainty, of the test antenna act as systematic offsets since they are present in both stages of the test. The standard uncertainty of the contribution, due to the uncertainty of the gain of the test antenna, is designated throughout all parts of TR 102 273 [3] as uj45. NOTE 3: In this example case the standard uncertainty of the contribution due to the uncertainty of the gain of the test antenna is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. Antenna: tuning of the test antenna: This uncertainty is introduced as a result of inaccurate tuning of the test antenna. The standard uncertainty of the contribution, due to the tuning of the test antenna, is designated throughout all parts of TR 102 273 [3] as uj46. NOTE 4: In this example case the standard uncertainty of the contribution due to the tuning of the test antenna is taken as 0,00 dB since the uncertainty is systematic i.e. it is assumed constant and common to both stages of the measurement and, provided that once set in stage one of the test it is not subsequently re-tuned, its contribution is the same in both stages. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 113 Position of the phase centre: test antenna: The horizontal position of the test antenna defines one end of the range length. The standard uncertainty of the contribution, due to the position of the phase centre of the test antenna, is designated throughout all parts of TR 102 273 [3] as uj22. NOTE 5: In this example case the test antenna is assumed to describe a vertical straight line as its height on the mast is changed. The standard uncertainty of the contribution due to the position of the phase centre of the test antenna is assumed to be 0,00 dB (see annex A). 6.8.4.1.2.5 Site factors Ambient effect: Ambient effect: Ambient effect is the uncertainty caused by local ambient signals raising the noise floor at the measurement frequency. The standard uncertainty of the contribution, due to the ambient effect, is designated throughout all parts of TR 102 273 [3] as uj34. The values of the standard uncertainty should be taken from table 27. Table 27: Uncertainty contribution: Ambient effect Receiving device noise floor (EUT OFF) is within: Standard uncertainty of the contribution 3 dB of measurement 1,57 dB 3 dB to 6 dB of measurement 0,80 dB 6 dB to 10 dB of measurement 0,30 dB 10 dB to 20 dB of measurement 0,10 dB 20 dB or more of the measurement 0,00 dB NOTE 1: In this example case the standard uncertainty of the contribution due to the ambient effect is taken as 0,00 dB, since the chamber is assumed to be shielded. Mutual coupling: test antenna to its images in the absorbing material: This is the uncertainty due to the mutual coupling between the test antenna and its images in the ceiling, side and end walls and is the effect of the change produced in the antenna's input impedance and/or gain. The standard uncertainty of the contribution due to the mutual coupling between the test antenna and its images in the absorbing material is designated throughout all parts of TR 102 273 [3] as uj06. NOTE 2: In this example case the standard uncertainty of the contribution due to the mutual coupling between the test antenna and its images in the absorbing material is taken as 0,00 dB since this is the first stage of a two stage measurement, where, in the second stage, the test antenna is located at the same height on the mast as in this, the first stage. Mutual coupling: test antenna to its image in the ground plane: This is the uncertainty due to the mutual coupling between the test antenna and its image in the ground plane and is the effect of the change produced in the antenna's input impedance and/or gain when placed close to a ground plane. The standard uncertainty of the contribution due to the mutual coupling between the test antenna and its image in the ground plane is designated throughout all parts of TR 102 273 [3] as uj14. NOTE 3: In this example case the standard uncertainty of the contribution due to the mutual coupling between the test antenna and its image in the ground plane is taken as 0,00 dB since this is the first stage of a two stage measurement, where, in the second stage, the test antenna is located at the same height on the mast as in this, the first stage. Mutual coupling: measuring antenna to the test antenna: This is the effect produced by any change in gain of the antennas which results from their close spacing. The standard uncertainty of the contribution due to the mutual coupling of the measuring antenna to the test antenna, designated throughout all parts of TR 102 273 [3] as uj11, It has a standard uncertainty of 0,00 dB for ANSI dipoles since it is included, where significant, in the mutual coupling and mismatch loss correction factors. For non-ANSI dipoles the standard uncertainty can be taken from table 28. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 114 Table 28: Uncertainty contribution of the mutual coupling between the measuring and test antenna Frequency Standard uncertainty of the contribution (3 m range) Standard uncertainty of the contribution (10 m range) 30 MHz ≤ frequency < 80 MHz 1,73 dB 0,60 dB 80 MHz ≤ frequency < 180 MHz 0,6 dB 0,00 dB frequency ≥ 180 MHz 0,00 dB 0,00 dB NOTE 4: In this example case the standard uncertainty of the contribution due to mutual coupling between the measuring and test antennas is taken as 0,00 dB as we are using ANSI dipoles. Mutual coupling: interpolation of mutual coupling and mismatch loss correction factors, only for ANSI dipoles: The standard uncertainty of the contribution, due to the interpolation of mutual coupling and mismatch loss correction factors, is designated throughout all parts of TR 102 273 [3] as uj12. It has, for spot frequencies given in table A.20, a value of 0,00 dB. However, for all other frequencies, the standard uncertainty should be obtained from table 29. Table 29: Uncertainty contribution of the interpolation of mutual coupling and mismatch loss correction factors Frequency (MHz) Standard uncertainty of the contribution for a spot frequency given in the table 0,00 dB 30 MHz ≤ frequency < 80 MHz 0,58 dB 80 MHz ≤ frequency < 180 MHz 0,17 dB frequency ≥ 180 MHz 0,00 dB NOTE 5: In this example case the standard uncertainty of the contribution, due to the interpolation of mutual coupling and mismatch loss correction factors, is taken as 0,00 dB as the frequency is above 180 MHz. Range length: This contribution is associated with the curvature of the phase front from the measuring antenna to the test antenna. The standard uncertainty of the contribution, due to range length, is designated throughout all parts of TR 102 273 [3] as uj16. The standard uncertainty is 0,00 dB if ANSI dipoles are used. For other types of antenna the standard uncertainty of the contribution should be obtained from table 30. Table 30: Uncertainty contribution of the range length (verification) Range length (i.e. the horizontal distance between phase centres) Standard uncertainty of the contribution (d1 + d2)2/4λ ≤ range length < (d1 + d2)2/2λ 1,26 dB (d1 + d2)2/2λ ≤ range length < (d1 + d2)2/λ 0,30 dB (d1 + d2)2/λ ≤ range length < 2(d1 + d2)2/λ 0,10 dB range length ≥ 2(d1 + d2)2/λ 0,00 dB NOTE 6: In table 30, d1 and d2 are the maximum dimensions of the antennas. NOTE 7: In this example case the standard uncertainty of the contribution, due to the range length, is taken as 0,00. Reflectivity of absorbing material: measuring antenna to the test antenna: This uncertainty is the residual effect of the reflections in the absorbing materials which result from the measuring antenna and EUT having different elevation patterns. The standard uncertainty of the contribution due to the reflectivity of absorbing material between the measuring and test antenna is designated throughout all parts of TR 102 273 [3] as uj02. NOTE 8: In this example case the standard uncertainty of the contribution due to the reflectivity of absorbing material between the measuring and test antenna is taken as 0,00 dB since a reference is set. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 115 Mutual coupling: measuring antenna to its images in the absorbing material: This uncertainty is the effect of the change produced in the antenna's input impedance and/or gain. The standard uncertainty of the contribution, due to the mutual coupling between the measuring antenna and its images in the absorbing material, is designated throughout all parts of TR 102 273 [3] as uj06. NOTE 9: In this example case the standard uncertainty of the contribution due to the mutual coupling between the measuring antenna and its images in the absorbing material is taken as 0,5 dB. Mutual coupling: measuring antenna to its image in the ground plane: This uncertainty is the effect of the change produced in the antenna's input impedance and/or gain. The standard uncertainty of the contribution, due to the mutual coupling of the measuring antenna to its image in the ground plane, is designated throughout all parts of TR 102 273 [3] as uj14. Its value can be obtained from table 31. Table 31: Uncertainty contribution of the mutual coupling between the measuring antenna and its image in the ground plane Spacing between the antenna and the ground plane Standard uncertainty of the contribution For a vertically polarized antenna spacing ≤ 1,25 λ 0,15 dB spacing > 1,25 λ 0,06 dB For a horizontally polarized antenna spacing < λ/2 1,15 dB λ/2 ≤ spacing < 3λ/2 0,58 dB 3λ/2 ≤ spacing < 3λ 0,29 dB spacing ≥ 3λ 0,15 dB NOTE 10: In this example case the standard uncertainty of the contribution due to the mutual coupling of the measuring antenna to its image in the ground plane is taken as 0,15 dB since we are assuming vertical polarization and a spacing of < 1,25 λ. 6.8.4.1.2.6 Measuring antenna Antenna: antenna factor of the measuring antenna: Uncertainty is introduced as a result of the inaccurate knowledge of the antenna factor of the measuring antenna. The antenna factor of the measuring antenna is only involved in the second stage of the test and therefore does not act as a systematic offset. The standard uncertainty of the contribution, due to the antenna factor of the measuring antenna, is designated throughout all parts of TR 102 273 [3] as uj44. For ANSI dipoles the value should be obtained from table 32. Table 32: Uncertainty contribution of the antenna factor of the measuring antenna. Frequency Standard uncertainty of the contribution 30 MHz ≤ frequency < 80 MHz 1,73 dB 80 MHz ≤ frequency < 180 MHz 0,60 dB frequency ≥ 180 MHz 0,30 dB NOTE 1: For other antenna types the figures should be taken from manufacturers data sheets. If a figure is not given the standard uncertainty is 1,0 dB. NOTE 2: In this example case the standard uncertainty of the contribution due to the antenna factor uncertainty of the receiving antenna is 0,30 dB since ANSI dipoles have been used and the frequency is above 180 MHz. Antenna: tuning of the measuring antenna Uncertainty is introduced as a result of the inaccurate tuning of the measuring antenna. The standard uncertainty of the contribution due to the tuning of the measuring antenna is designated in the present document by uj46. NOTE 3: In this example case the standard uncertainty of the contribution due to the tuning of the measuring antenna is taken to be 0,06 dB (see annex A) since the tuning of the measuring antenna is only involved in this stage of the test and therefore does not act as a systematic offset. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 116 Position of the phase centre: measuring antenna: Uncertainty is introduced as a result of the inaccurate positioning of the phase centre of the measuring antenna, since it affects the range length i.e. the horizontal distance between itself and the test antenna. The standard uncertainty of the contribution, due to the position of the phase centre of the measuring antenna, is designated throughout all parts of TR 102 273 [3] as uj22. NOTE 4: In this example case the standard uncertainty of the contribution due to the position of the phase centre of the receiving antenna has been calculated from ± (the offset)/(range length) x 100 %). The positioning uncertainty is ±0,01 m and therefore the worst case uncertainty = 0,01/3,0 = 0,333 %. As the offset can be anywhere between these limits, the uncertainty is taken to be rectangularly distributed (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) and the standard uncertainty is calculated as 0,192 %. This is transformed to the logarithmic form (TR 100 028-2 [8], annex E), to be 0,02 dB. 6.8.4.1.2.7 Measuring antenna attenuator Insertion loss: measuring antenna attenuator: The attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss is taken from the manufacturer's data sheet since it does not cancel as a systematic offset (it only appears in one stage of the test). The standard uncertainty of the contribution, due to the insertion loss uncertainty of the measuring antenna attenuator, is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the uncertainty of the contribution, due to the insertion loss uncertainty of the measuring antenna attenuator, is taken from the manufacturer's data sheet as ±0,3 dB as nothing is said about the distribution, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed and the standard uncertainty is calculated as 0,17 dB. 6.8.4.1.2.8 Measuring antenna cable Insertion loss: measuring antenna cable: The measuring antenna cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the measuring antenna cable, is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the uncertainty of the contribution due to the insertion loss uncertainty of the measuring antenna cable is taken from the manufacturer's data sheet as ±0,5 dB. As nothing is said about the distribution, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed and the standard uncertainty is calculated as 0,29 dB. Cable factor: measuring antenna cable: Cable factor is defined as the total effect of the antenna cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency, parasitic effects (acting as a director or reflector) and introducing an unbalanced, common mode current into the dipole balun. In a radiated measurement the standard uncertainty of the cable factor associated with the measuring antenna cable is 0,5 dB provided the precautions detailed in the method have been observed i.e. routing and dressing the cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution, due to the cable factor of the measuring antenna cable, is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In the example case the standard uncertainty of the contribution due to the cable factor of the measuring antenna cable is taken as 0,50 dB since the precautions detailed in the methods are assumed to have been observed. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 117 6.8.4.1.2.9 Receiving device The receiving device is only used in the first stage of this test. Therefore, the absolute level uncertainty contributes fully to this stage although the linearity does not. Receiving device: absolute level: This uncertainty only contributes during the first stage of the measurement. The standard uncertainty of the contribution due to the receiving device absolute level uncertainty is designated throughout all parts of TR 102 273 [3] as uj47. Its value can be derived from manufacturers data. NOTE 1: In this example case the uncertainty of the contribution due to the receiving device absolute level uncertainty) is obtained from the manufacturers data as ±1 dB with a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs. The standard uncertainty of the contribution due to the receiving device absolute level uncertainty is calculated as 0,58 dB. Receiving device: linearity: In any test in which the contribution of the absolute level uncertainty of the receiving device contributes to the combined standard uncertainty of the test i.e. it does not cancel due to the methodology, the contribution from the receiving device linearity is considered to have been included in uj47. Conversely, for any test in which the absolute level uncertainty of the receiving device does not contribute to the combined standard uncertainty the linearity of the receiving device should be included. The standard uncertainty of the contribution due to the receiving device linearity is designated throughout all parts of TR 102 273 [3] as uj48. NOTE 2: In this example case the standard uncertainty of the contribution due to the receiving device linearity is taken as 0,00 dB.
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6.8.4.1.3 Contribution from the random component
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Random uncertainty: The magnitude can be assessed from multiple measurements of the Transform Factor. The standard uncertainty of the contribution due to the random uncertainty is designated throughout all parts of TR 102 273 [3] as ui01. The Transform Factor measurement was repeated 10 times. The following results were obtained in dBµV (before correcting for cabling and attenuator network insertion loss): - 65,4; 63,4; 66,0; 65,3; 63,0; 64,9; 65,2; 66,8; 65,5; 63,7. Converting to linear terms: - 1,862 × 10-3; 1,479 × 10-3; 1,995 × 10-3; 1,841 × 10-3; 1,413 × 10-3; 1,758 × 10-3; 1,820 × 10-3; 2,188 × 10-3; 1,884 × 10-3; 1,531 × 10-3; The two sums X and Y are calculated: - X = the sum of the measured values = 17,77 × 10-3; - Y = the sum of the squares of the measured values = 32,10 × 10-6 V2. ( ) = − × − × = − − = − − 1 10 10 10 77 , 17 10 10 , 32 1 2 3 6 2 n n X Y uc random 238,3 ×10-6 (formula 5.6) As the result is obtained as the mean value of 10 measurements and the standard uncertainty of the random uncertainty is: dB ,17 1 5, 11 100 10 777 ,1 10 3, 238 3 6 = × × × = − − j random u NOTE: In this example case the standard uncertainty of the contribution due to the random uncertainty is 1,17 dB. See also the note in clause 6.4.7. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 118
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6.8.4.1.4 Summary table of contributory components
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All the uncertainties for this part of the procedure are listed in table 33. Table 33: Contributions from the transfer factor measurement uj or i Description of uncertainty contributions dB uj36 mismatch: transmitting part 0,00 uj37 mismatch: receiving part 0,11 uj38 signal generator: absolute output level 0,58 uj39 signal generator: output level stability 0,00 uj41 insertion loss: test antenna cable 0,00 uj19 cable factor: test antenna cable 0,00 uj40 insertion loss: test antenna attenuator 0,00 uj18 correction: measurement distance 0,00 uj17 correction: off boresight angle in elevation plane , 0,00 uj45 antenna: gain of the test antenna 0,00 uj46 antenna: tuning of the test antenna 0,00 uj22 position of the phase centre: test antenna 0,00 uj34 ambient effect 0,00 uj06 mutual coupling: test antenna to its images in the absorbing material 0,00 uj14 mutual coupling: test antenna to its image in the ground plane 0,00 uj11 mutual coupling: measuring antenna to the test antenna 0,00 uj12 mutual coupling: interpolation of mutual coupling and mismatch loss correction factors 0,00 uj16 range length 0,00 uj02 reflectivity of absorber material: measuring antenna to the test antenna 0,00 uj06 mutual coupling: measuring antenna to its images in the absorbing material 0,50 uj14 mutual coupling: measuring antenna to its image in the ground plane 0,15 uj44 antenna: antenna factor of the measuring antenna 0,30 uj46 antenna: tuning of the measuring antenna 0,06 uj22 position of the phase centre: measuring antenna 0,02 uj40 insertion loss: measuring antenna attenuator 0,17 uj41 insertion loss: measuring antenna cable 0,29 uj19 cable factor: measuring antenna cable 0,50 uj47 receiving device: absolute level 0,58 uj48 receiving device: linearity 0,00 ui01 random uncertainty (see note in clause 6.4.7) 1,17 The standard uncertainties from table 33 should be combined by RSS in accordance with TR 102 273 [3], part 1, sub-part 1, clause 5. This gives the combined standard uncertainty (uc Transform Factor) for the Transform Factor measurement in dB. The value of uc Transform Factor is calculated as 1,67 dB.
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100 028-1
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6.8.4.2 Uncertainty contributions: Stage 2: EUT measurement
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The second stage of the measurement (EUT sensitivity measurement) is to determine the minimum signal generator output level which produces the required response from the EUT and converting the output level of the signal generator, to a field strength using the Transform Factor derived in stage one. The test equipment set-up is shown in figure 31. The components shown shaded are common to both stages of the test. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 119 Test antenna cable 2 ferrite beads Test antenna Signal generator Attenuator 2 10 dB EUT Ground plane Figure 31: EUT measurement Whereas figure 31 shows, schematically, the test equipment for the EUT sensitivity measurement, figure 32 an analysis diagram, provides a detailed picture of the individual uncertainty components (each of which contributes its own uncertainty) for this stage in the measurement. As stated above, the shaded areas represent components common to both stages of the test method.
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100 028-1
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6.8.4.2.1 Contributions from the mismatch components
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Mismatch: transmitting part: Only the transmitting part of the test equipment set-up is involved in this stage of the test. The standard uncertainty of the contribution due to mismatch is 0,00 dB since, as stated in clause 6.8.4.1.1 the transmitting part is common to both stages of the test. Signal Test antenna Site factors Cable factor Test antenna cable 2 Cable loss Attenuator 2 10 dB Equipment under test generator Antenna to EUT coupling Mutual image coupling Antenna gain + + SINAD meter EUT Site effects Reflected path loss Direct path loss Signal generator Mismatch Mismatch Mismatch + + Figure 32: Reference for the measurement on the equipment (sensitivity) ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 120 The mismatch uncertainty between the signal generator and the test antenna contributes equally to both stages of the test and therefore it does not contribute to the combined standard uncertainty and is not calculated. The standard uncertainty of the contribution due to mismatch in the transmitting part is designated throughout all parts of TR 102 273 [3] as uj35. NOTE: In this example case the standard uncertainty of the contribution due to mismatch in the transmitting part is taken as 0,00 dB, since the uncertainty is systematic i.e. it produces the same offset in both stages.
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6.8.4.2.2 Contributions from the individual components
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6.8.4.2.2.1 Signal generator Signal generator: absolute output level: There is not necessarily any similarity between the output levels from the signal generator in the two stages of this test. As a result it contributes to both stages. The standard uncertainty of the contribution, due to the signal generator absolute output level, is designated throughout all parts of TR 102 273 [3] as uj38. Its value can be derived from manufacturer's data sheet. NOTE 1: In this example case the uncertainty of the contribution due to the signal generator absolute output level uncertainty is taken from the manufacturers data sheet as ±1,0 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,58 dB. Signal generator: output level stability: In any test in which the contribution of the absolute level uncertainty of the signal generator contributes to the combined standard uncertainty of the test i.e. it does not cancel due to the methodology, the contribution from the output level stability is considered to have been included in the signal generator absolute output level, uj38. Conversely, for any level in which the absolute level uncertainty of the signal generator does not contribute to the combined standard uncertainty, the output level stability of the signal generator should be included. The standard uncertainty of the contribution due to the signal generator output level stability is designated throughout all parts of TR 102 273 [3] as uj39. Its value can be derived from manufacturers' data sheet. NOTE 2: In this example case the standard uncertainty of the contribution due to the signal generator output level stability is taken as 0,00 dB as it is covered by the absolute level uncertainty. 6.8.4.2.2.2 Test antenna cable Insertion loss: test antenna cable: The test antenna cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the test antenna cable is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the test antenna cable is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. Cable factor: test antenna cable: Cable factor is defined as the total effect of the antenna cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency, parasitic effects (acting as a director or reflector) on the test antenna and introducing an unbalanced, common mode current into the dipole balun. In a radiated measurement the standard uncertainty of the cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the test antenna cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the test antenna cable is taken as 0,00 dB since in this measurement, the cable position, once set in stage 1, is not subsequently changed during the test. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 121 6.8.4.2.2.3 Test antenna attenuator Insertion loss: test antenna attenuator: The test antenna attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss of the test antenna attenuator is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution, due to the insertion loss uncertainty of the test antenna attenuator, is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. 6.8.4.2.2.4 Test antenna Correction: measurement distance: For those tests in which the test antenna on the mast peaks at different heights in the two stages, a correction for measurement distance must be made to account for the different measurement distances. In this test, once the position of the test antenna is set in stage one no further adjustment to its position is subsequently made during the test. The standard uncertainty of the contribution due to the correction for measurement distance is designated throughout all parts of TR 102 273 [3] as uj18. NOTE 1: In this example case the standard uncertainty of the contribution due to the correction for measurement distance is taken as 0,00 dB. Correction: off boresight angle in elevation plane: For those tests in which the test antenna on the mast peaks at different heights in the two stages, a correction must be made to account for the different angles subtended by the EUT/substitution antenna. In this test, once the position of the test antenna is set in stage one no further adjustment to its position is subsequently made during the test. The standard uncertainty of the contribution due to the correction for off boresight angle in elevation plane is designated throughout all parts of TR 102 273 [3] as uj17. NOTE 2: In this example case the standard uncertainty of the contribution due to the correction for off boresight angle in elevation plane is taken as 0,00 dB since the uncertainty is assumed to be systematic i.e. it is assumed constant and common to both stages of the measurement. Antenna: gain of the test antenna: The gain of the test antenna acts as a systematic offset since it is present in both stages of the test. The standard uncertainty of the contribution due to the gain of the test antenna is designated throughout all parts of TR 102 273 [3] as uj45. NOTE 3: In this example case the standard uncertainty of the contribution due to the gain of the test antenna is taken as 0,00 dB since the uncertainty is assumed to be systematic i.e. it is assumed constant and common to both stages of the measurement. Antenna: tuning of the test antenna: This uncertainty is introduced as a result of inaccurate tuning of the test antenna. The standard uncertainty of the contribution due to the tuning of the test antenna is designated throughout all parts of TR 102 273 [3] as uj46. NOTE 4: In this example case the standard uncertainty of the contribution due to the tuning of the test antenna is taken as 0,00 dB since the uncertainty is assumed to be systematic i.e. it is assumed constant and common to both stages of the measurement (provided that once set in stage one of the test it is not subsequently re-tuned). Position of the phase centre: test antenna: The horizontal position of the test antenna defines one end of the range length. Since the test antenna position on the mast is not changed after being set in this stage the standard uncertainty of the contribution due to the position of the phase centre of the test antenna is designated throughout all parts of TR 102 273 [3] as uj22. NOTE 5: In this example case the standard uncertainty of the contribution due to the position of the phase centre of the test antenna is taken as 0,00 dB since the uncertainty is assumed to be systematic i.e. it is assumed constant and common to both stages of the measurement. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 122 6.8.4.2.2.5 Site factors Ambient effect: Ambient effect is the uncertainty caused by local ambient signals raising the noise floor at the measurement frequency. The standard uncertainty of the contribution due to the ambient effect is designated throughout all parts of TR 102 273 [3] as uj34. The values of the standard uncertainties for this part of the test should be the same as for stage 1. NOTE 1: In this example case the standard uncertainty of the contribution due to the ambient effect is taken as 0,00 dB as this was the value in stage 1. Range length: This contribution is associated with the curvature of the phase front from the EUT to the test antenna. The standard uncertainty of the contribution, due to range length, is designated throughout all parts of TR 102 273 [3] as uj16. The standard uncertainty is 0,00 dB if ANSI dipoles are used. For other types of antenna the standard uncertainty of the contribution should be obtained from table 34. Table 34: Uncertainty contribution of the range length (verification) Range length (i.e. the horizontal distance between phase centres) Standard uncertainty of the contribution (d1 + d2)2/4λ ≤ range length < (d1 + d2)2/2λ 1,26 dB (d1 + d2)2/2λ ≤ range length < (d1 + d2)2/λ 0,30 dB (d1 + d2)2/λ ≤ range length < 2(d1 + d2)2/λ 0,10 dB range length ≥ 2(d1 + d2)2/λ 0,00 dB NOTE 2: In table 34, d1 and d2 are the maximum dimensions of the antennas. NOTE 3: In this example case the standard uncertainty of the contribution due to the range length is taken as 0,00 dB since the range length is ≥ 2 (d1 + d2)2/λ. Mutual coupling: amplitude effect of the test antenna on the EUT: This uncertainty results from the interaction between the EUT and the test antenna when placed close together. The standard uncertainty of the contribution due to the amplitude effect of the mutual coupling between the test antenna and the EUT, is designated throughout all parts of TR 102 273 [3] as uj08. The standard uncertainty should be taken from table 35. Table 35: Uncertainty contribution: Mutual coupling: amplitude effect of the test antenna on the EUT Range length Standard uncertainty of the contribution 0,62√((d1 + d2)3/λ)≤ range length < 2(d1 + d2)2/λ 0,50 dB range length ≥ 2(d1 + d2)2/λ 0,00 dB NOTE 4: In this example case the standard uncertainty of the contribution due to the amplitude effect of the mutual coupling between the test antenna and the EUT is 0,00 dB since the distance is ≥ 2 (d1 + d2)2/λ. Mutual coupling: EUT to its images in the absorbing material: This uncertainty is dependant on the quality of the absorbing material and the effect imaging of the EUT in the ceiling, side and end walls has on the input impedance and/or gain of the integral antenna. The standard uncertainty of the contribution, due to the mutual coupling of the EUT to its images in the absorbing material, is designated throughout all parts of TR 102 273 [3] as uj04. NOTE 5: In this example case the standard uncertainty of the contribution due to the mutual coupling amplitude effect of the absorbing material on the EUT is assumed to be 0,5 dB (see annex A). Mutual coupling: EUT to its image in the ground plane: This uncertainty results from the change in the EUT spurious emission level as a result of being placed close to the ground plane. The standard uncertainty of the contribution, due to the mutual coupling of the EUT to its image in the ground plane, is designated throughout all parts of TR 102 273 [3] as uj13. Its value can be obtained from table 36. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 123 Table 36: Uncertainty contribution of the mutual coupling between the EUT to its image in the ground plane Spacing between the EUT and the ground plane Standard uncertainty of the contribution For a vertically polarized EUT spacing ≤ 1,25 λ 0,15 dB spacing > 1,25 λ 0,06 dB For a horizontally polarized EUT spacing < λ/2 1,15 dB λ/2 ≤ spacing < 3λ/2 0,58 dB 3λ/2 ≤ spacing < 3λ 0,29 dB spacing ≥ 3λ 0,15 dB NOTE 6: In this example case the standard uncertainty of the contribution, due to the mutual coupling of the EUT to its image in the ground plane, (assuming the polarization is vertical and the spacing above the ground plane is < 1,25 λ at the test frequency) is taken as 0,15 dB. Reflectivity of absorbing material: EUT to the test antenna. This uncertainty is associated with the magnitudes of the reflections occurring from the side walls, end walls and ceiling. These magnitudes are a function of the quality of the absorber at the frequency of test. The standard uncertainty of the contribution, due to the reflectivity of the absorbing material between the EUT and the test antenna, is designated throughout all parts of TR 102 273 [3] as uj01. The relevant value for this contribution should be taken from table 37. Table 37: Uncertainty contribution of the reflectivity of absorbing material between the EUT and test antenna Reflectivity of the absorbing material Standard uncertainty of the contribution reflectivity < 10 dB 4,76 dB 10 ≤ reflectivity < 15 dB 3,92 dB 15 ≤ reflectivity < 20 dB 2,56 dB 20 ≤ reflectivity < 30 dB 1,24 dB reflectivity ≥ 30 dB 0,74 dB NOTE 7: In this example case the standard uncertainty of the contribution due to the reflectivity of the absorbing material between the EUT and the test antenna is taken as 1,24 dB. Mutual coupling: test antenna to its images in the absorbing material: This is the uncertainty due to the mutual coupling between the test antenna and its images in the ceiling, side and end walls and is the effect of the change produced in the antenna's input impedance and/or gain. The standard uncertainty of the contribution, due to the mutual coupling between the test antenna and its images in the absorbing material, is designated throughout all parts of TR 102 273 [3] as uj06. NOTE 8: In this example case the standard uncertainty of the contribution due to the mutual coupling between the test antenna and its images in the absorbing material is taken as 0,00 dB since in this, the second stage of the measurement, the uncertainty will only contribute if the test antenna is located at a different height to the first stage which is not allowed by the methodology hence the uncertainty is assumed to be systematic i.e. it is assumed constant and common to both stages of the measurement. Mutual coupling: test antenna to its image in the ground plane: This is the uncertainty due to the mutual coupling between the test antenna and its image in the ground plane and is the effect of the change produced in the antenna's input impedance and/or gain when placed close to a ground plane. The standard uncertainty of the contribution, due to the mutual coupling of the test antenna to its image in the ground plane, is designated throughout all parts of TR 102 273 [3] as uj14. NOTE 9: In this example case the standard uncertainty of the contribution due to the mutual coupling of the test antenna to its image in the ground plane is taken as 0,00 dB since in this, the second stage of the measurement, the uncertainty will only contribute if the test antenna is located at a different height to the first stage which is not allowed by the methodology hence the uncertainty is assumed to be systematic i.e. it is assumed constant and common to both stages of the measurement. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 124 6.8.4.2.2.6 EUT EUT: mutual coupling to the power leads: This is the uncertainty associated with the influence (reflections, parasitic effects, etc.) of the power leads on the EUT. The standard uncertainty associated with this effect is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 2,0 dB. The standard uncertainty of the contribution, due to the mutual coupling of the EUT to the power leads, is designated throughout all parts of TR 102 273 [3] as uj54. NOTE 1: In this example case the standard uncertainty of the contribution due to the mutual coupling of the EUT to the power leads is taken as 0,5 dB since the precautions detailed in the methods have been observed. Position of the phase centre: within the EUT volume: This contribution is associated with the uncertainty with which the actual radiating point within the equipment volume is known. If this point is known exactly the contribution is 0,00 dB. The standard uncertainty of the contribution due to the position of the phase centre within the EUT volume is designated throughout all parts of TR 102 273 [3] as uj20. NOTE 2: In this example case the standard uncertainty of the contribution due to the position of the phase centre within the EUT volume has been calculated from (±(the maximum dimension of device)/(2 × range length) × 100 %). In this example the position is not known. Hence, the uncertainty of the position of the phase centre within the EUT of 0,15 m maximum dimension is 0,15/2 m = 0,075 m, and the worst case uncertainty due to this offset is therefore (0,075/3,0) × 100 % = ±2,50 %. As the phase centre can be anywhere inside the EUT, the uncertainty is taken as rectangularly distributed and the standard uncertainty is calculated as 1,44 %. This is then transformed to the logarithmic form (1,44/11,5) = 0,12 dB (TR 100 028-2 [8], annex E). Positioning of the phase centre: within the EUT over the axis of rotation of the turntable: This contribution is associated with the uncertainty with which the actual radiating point within the equipment is placed over the centre of the turntable. If the point is placed exactly, the contribution is 0,00 dB. The standard uncertainty of the contribution, due to the positioning of the phase centre within the EUT over the axis of rotation of the turntable, is designated throughout all parts of TR 102 273 [3] as uj21. NOTE 3: In this example case the standard uncertainty of the contribution due to the positioning of the EUT phase centre over the axis of rotation of the turntable is calculated from (±(the estimated offset from the axis of rotation)/(2 × range length) × 100 %). In this case, the uncertainty is taken as ±0,01 m, and the worst case uncertainty is ±(0,01/3,0) × 100 = ±0,333 %. As the offset can be anywhere between the limits the uncertainty is rectangularly distributed and the standard uncertainty is calculated as 0,192 %. This is then transformed to the logarithmic form (0,192/11,5) = 0,02 dB (TR 100 028-2 [8], annex E). EUT: degradation measurement: This contribution is a RF level uncertainty associated with the uncertainty of measuring 20 dB SINAD, 10-2 bit stream or 80 % message acceptance ratio. The standard uncertainty of the contribution, due to the EUT degradation measurement, is designated throughout all parts of TR 102 273 [3] as uj52. Its value can be obtained from TR 100 028 (all parts). NOTE 4: In this example case, the standard uncertainty of the contribution is obtained from TR 100 028 (all parts) and its value is 0,68 dB.
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100 028-1
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6.8.4.2.3 Contribution from the random component
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Random uncertainty: The magnitude can be assessed from multiple measurements of the receiver sensitivity. The standard uncertainty of the contribution due to the random uncertainty is designated throughout all parts of TR 102 273 [3] as ui01. The receiver sensitivity measurement was repeated 10 times. The following results were obtained in dBµV (before correcting for cabling and attenuator network insertion loss): - 65,4; 63,4; 66,0; 65,3; 63,0; 64,9; 65,2; 66,8; 65,5; 63,7. Converting to linear terms: - 1,862 × 10-3; 1,479 × 10-3; 1,995 × 10-3; 1,841 × 10-3; 1,413 × 10-3; 1,758 × 10-3; 1,820 × 10-3; 2,188 × 10-3; 1,884 × 10-3; 1,531 × 10-3. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 125 The two sums X and Y are calculated: - X = the sum of the measured values = 17,77 × 10-3; - Y = the sum of the squares of the measured values = 32,10 × 10-6 V2. ( ) = − × − × = − − = − − 1 10 10 10 77 , 17 10 10 , 32 1 2 3 6 2 n n X Y uc random 238,3 ×10-6 (formula 5.6) As the result is obtained as the mean value of 10 measurements and the standard uncertainty of the random uncertainty is: dB 1,17 5, 11 100 10 777 ,1 10 3, 238 3 6 = × × × = − − j random u NOTE: In this example case the standard uncertainty of the contribution due to the random uncertainty is 1,17 dB. See also the note in clause 6.4.7.
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100 028-1
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6.8.4.2.4 Summary table of contributory components
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All the uncertainty contributions for this part of the procedure are listed in table 38. Table 38: Contributions from the EUT measurement uj or i Description of uncertainty contributions dB uj36 mismatch: transmitting part 0,00 uj38 signal generator: absolute output level 0,58 uj39 signal generator: output level stability 0,00 uj41 insertion loss: test antenna cable 0,00 uj19 cable factor: test antenna cable 0,00 uj40 insertion loss: test antenna attenuator 0,00 uj17 correction: off boresight angle in elevation plane 0,00 uj18 correction: measurement distance 0,00 uj45 antenna: gain of the test antenna 0,00 uj46 antenna: tuning of the test antenna 0,00 uj22 position of the phase centre: test antenna 0,00 uj34 ambient effect 0,00 uj08 mutual coupling: amplitude effect of the test antenna on the EUT 0,00 uj04 Mutual coupling: EUT to its images in the absorbing material 0,50 uj13 mutual coupling: EUT to its image in the ground plane 0,15 uj01 reflectivity of absorber material: EUT to the test antenna 1,24 uj06 mutual coupling: test antenna to its images in the absorbing material 0,00 uj14 mutual coupling: test antenna to its image in the ground plane 0,00 uj55 EUT: mutual coupling to the power leads 0,50 uj20 position of the phase centre: within the EUT volume 0,12 uj22 positioning of the phase centre: within the EUT over the axis of rotation of the turntable 0,02 uj16 range length 0,00 uj52 EUT: degradation measurement 0,68 ui01 random uncertainty (see note in clause 6.4.7) 1,17 The standard uncertainties from table 38 should be combined by RSS in accordance with TR 102 273 [3], part 1, sub-part 1, clause 5. This gives the combined standard uncertainty (uc EUT measurement) for the NSA measurement in dB. The value of uc EUT measurement is calculated as 2,06 dB. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 126
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6.8.4.2.5 Expanded uncertainty for the receiver Sensitivity measurement
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The combined standard uncertainty of the results of the verification procedure is the combination of the components outlined in clauses 6.8.2.1.4 and 6.8.2.2.4. The components to be combined are uc Transform Factor and uc EUT measurement. dB 2,65 = 06 ,2 67 ,1 2 2 + = t measuremen y Sensitivit c u The expanded uncertainty is ±1,96 x 2,65 dB = ±5,19 dB at a 95 % confidence level.
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6.9 Examples of measurement uncertainty analysis (Stripline)
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6.9.1 Introduction
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This clause contains detailed worked examples of the calculation of expanded uncertainty of radiated tests in a Stripline test facility. The example tests given are limited to: - a verification procedure; - the measurement of a receiver parameter (Sensitivity). Both of the example tests are assumed to have been carried out in the 2-plate open Stripline described in CENELEC European Standard EN 55020 [7]. NOTE 1: The values given to all of the uncertainty components in these examples are only to illustrate the uncertainty calculation. In practice, values should be derived by consulting annex A. All radiated tests consist of two stages. For the verification procedure, the first stage is to set a reference level whilst the second stage involves the measurement of path loss/attenuation through the Stripline. For the measurement of the receive sensitivity of an EUT, the first stage is to find the minimum (or average) signal generator output that produces the required receiver response, whilst the second stage determines the field strength in the Stripline corresponding to that generator output level. Within any radiated test there are uncertainty components that are common to both stages of the test. By their different natures some of these common uncertainties will cancel (e.g. the uncertainty of the insertion loss of a cable common to both parts), others will contribute once (e.g. the increase in the field strength caused by a large EUT) whilst others may contribute twice (e.g. the level stability of a signal generator in receiver tests). In each of the following uncertainty analyses, uncertainty components common to both stages are shown as shaded areas in the accompanying schematic diagrams. As shown in the examples, all the individual uncertainty components for any test are combined in the manner described in TR 102 273 [3], part 1, sub-part 1, clauses 4 and 5 in order to derive an expanded uncertainty figure for the measurement. The values of the individual components are either provided in annex A or should be taken from manufacturers' data sheets. Whenever they are obtained from data sheets, worst case figures given over a frequency band should be used. For example, in the case of a signal generator whose absolute level accuracy is quoted as ±1 dB over 30 MHz to 300 MHz, ±2 dB over 300 MHz to 1 000 MHz the figure for the band containing the test frequency should be used. This approach should be adopted for all uncertainty components, taking the uncertainty figures over as broad a band a possible. This is normally satisfactory when the variation with frequency is not large and provides a simple and flexible approach. The resulting expanded uncertainty figure is valid across a broad range of frequencies and measurement conditions and avoids the necessity of repeated calculation for minor frequency changes. NOTE 2: Taking specific frequency values may result in a lower expanded uncertainty value, but this lower value is only valid when that specific set of circumstances apply for which the value was derived.
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6.9.2 Example 1: Verification procedure
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The Stripline verification procedure involves two different measurement stages and it results in values for both the attenuation through the Stripline and its Transform Factor (i.e. the relationship between the input voltage to the Stripline and the resulting field strength between the plates). ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 127
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6.9.2.1 Uncertainty contributions: Stage 1: Direct attenuation measurement
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The first stage of the verification procedure is the direct attenuation measurement. This is carried out with all the items of test equipment connected directly together via an "in line" adapter between the attenuators as shown in figure 33. The components shown shaded are common to both stages of the procedure. "In line" adapter Attenuator 2 10 dB Receiving device Attenuator 1 10 dB Signal generator cable 1 cable 2 ferrite beads ferrite beads Figure 33: Stage 1: Direct attenuation measurement Despite the commonality of most of the components to both stages of this procedure, the mismatch uncertainty contribution for both stages has to be calculated and included in the uncertainty calculations. This is the result of load conditions varying (i.e. the Stripline and monopole replaces the adapter in the second stage). Conversely, as a result of this commonality, the uncertainty contributions of some of the individual components will cancel. Whereas figure 33 shows, schematically, the test equipment set-up for this stage of the verification procedure, an analysis diagram of the individual components (each of which contributes its own uncertainty) for this stage of the measurement is shown in figure 34. Again, as stated above, the shaded areas represent components common to both stages of the verification procedure.
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6.9.2.1.1 Contributions from the mismatch components
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Mismatch: direct attenuation measurement: The value of the combined standard uncertainty of the contribution due to the mismatch from the source to the receptor, i.e. between the signal generator and the receiving device, is calculated from the approach described in annex G. All the individual contributions are U-distributed. NOTE 1: In this example the signal generator output reflection coefficient used is the worst case magnitude over the frequency band of interest, as is the case with the cable, adapter and attenuator VSWRs. NOTE 2: The attenuation values of the cables and attenuators should be obtained from the manufacturers data sheet/calibration records at the specific frequency of the test, along with the associated uncertainties for these values. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 128 Receiving device Cable factor Cable loss Receiving device Signal generator Cable loss Cable factor Receiving antenna cable 2 Transmitting antenna cable 1 source Transmitting Adapter Mismatch Attenuator 1 10 dB Mismatch + + + + Attenuator 2 10 dB Mismatch Mismatch Mismatch Mismatch + + + + Figure 34: Stage 1: Direct attenuation measurement individual uncertainty components Signal generator: Output reflection coefficient: |ρG| = 0,20 Cable: Input and output reflection coefficients: |S11| = |S22| = 0,07 Attenuation: 1 dB = |S12| = |S21| = 0,891 Attenuator: Input and output reflection coefficients |S11| = |S22| = 0,05 Attenuation = 10 dB |S12| = |S21| = 0,3162 Adapter: Input and output reflection coefficients |S11| = |S22| = 0,02 Attenuation = 0,1 dB |S12| = |S21| = 0,9886 Attenuator: Input and output reflection coefficients |S11| = |S22| = 0,05 Attenuation = 10 dB |S12| = |S21| = 0,3162 Cable: Input and output reflection coefficients: |S11| = |S22| = 0,07 Attenuation: 1 dB = |S12| = |S21| = 0,891 Receiving device: Input reflection coefficient: |ρRD| = 0,20 ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 129 Mismatch uncertainty in the direct attenuation measurement: In the following the transmitting antenna cable is named cable 1, the transmitting antenna attenuator is named attenuator 1, the receiving antenna cable is named cable 2, the receiving attenuator is named attenuator 2. Those components that are constant for both stages 1 and 2 are not calculated as they do not contribute to the overall uncertainty. Mismatch between: - uj generator and cable 1: Constant for both stage 1 and 2. Hence this value does not contribute. - uj cable 1 and attenuator 1: Constant for both stage 1 and 2. Hence this value does not contribute. % 0,071 % 2 100 02 ,0 05 ,0 1 : = × × = adapter and attenuator mismatch j u % 0,071 % 2 100 05 ,0 02 ,0 1 : = × × = attenuator and adapter mismatch j u - uj attenuator 2 and cable 2: Constant for both stage 1 and 2. Hence this value does not contribute. - uj cable 2 and receiving device: Constant for both stage 1 and 2. Hence this value does not contribute. - uj generator and attenuator 1: Constant for both stage 1 and 2. Hence this value does not contribute. % 0,035 % 2 100 316 ,0 07 ,0 07 ,0 2 1 : = × × × = adapter and cable mismatch j u % 0,173 % 2 100 988 ,0 05 ,0 05 ,0 2 2 1 : = × × × = attenuator and attenuator mismatch j u % 0,010 % 2 100 316 ,0 07 ,0 02 ,0 2 2 : = × × × = cable and adapter mismatch j u - uj attenuator 2 and receiving device: Constant for both stage 1 and 2. Hence this value does not contribute. % 0,022 % 2 100 316 ,0 891 ,0 02 ,0 2,0 2 2 : = × × × × = adapter and generator mismatch j u % 0,024 % 2 100 988 ,0 316 ,0 05 ,0 07 ,0 2 2 2 1 : = × × × × = attenuator and cable mismatch j u % 0,024 % 2 100 316 ,0 988 ,0 07 ,0 05 ,0 2 2 2 1 : = × × × × = cable and attenuator mismatch j u % 0,022 % 2 100 891 ,0 316 ,0 2,0 02 ,0 2 2 : = × × × × = device receiving and adapter mismatch j u % 0,055 % 2 100 988 ,0 316 ,0 891 ,0 05 ,0 2,0 2 2 2 2 : = × × × × × = attenuator and generator mismatch j u - uj mismatch: cable 1 and cable 2: Less than 0,01 % due to the two attenuators, therefore neglected. % 0,055 % 2 100 891 ,0 316 ,0 988 ,0 2,0 05 ,0 2 2 2 1 : = × × × × × = device receiving and attenuator mismatch j u ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 130 - uj mismatch: generator and cable 2: Less than 0,01 % due to the two attenuators, therefore neglected. - uj mismatch: cable 1 and receiving device: Less than 0,01 % due to the two attenuators, therefore neglected. - uj mismatch: generator and receiving device: Less than 0,01 % due to the two attenuators, therefore neglected. The combined standard uncertainty of the mismatch is then calculated: % 0,306 055 ,0 055 ,0 ... 071 ,0 071 ,0 2 2 2 2 . : = + + + + = att direct mismatch c u Transforming to logarithmic form (TR 100 028-2 [8], annex E): 0,306 %/11,5 = 0,026 dB. The standard uncertainty of the contribution, due to the mismatch in the direct attenuation measurement, is designated throughout all parts of TR 102 273 [3] as uj35. Its value in this example is 0,026 dB.
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100 028-1
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6.9.2.1.2 Contributions from individual components
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6.9.2.1.2.1 Signal generator Signal generator: absolute output level: In a verification procedure, the signal generator's absolute level uncertainty contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the signal generator absolute output level uncertainty is designated throughout all parts of TR 102 273 [3] as uj38. NOTE 1: In this example case the standard uncertainty of the contribution due to the signal generator absolute output level uncertainty is taken to be 0,00 dB since, once the level has been set in stage one of the procedure, the level is not further adjusted. The uncertainty is therefore assumed to be systematic i.e. it produces the same offset in both stages. Signal generator: output level stability: In any test in which the contribution of the absolute level uncertainty of the signal generator contributes to the combined standard uncertainty of the test i.e. it does not cancel due to the methodology, the contribution from the output level stability is considered to have been included in the signal generator absolute output level, uj38. Conversely, for any level in which the absolute level uncertainty of the signal generator does not contribute to the combined standard uncertainty, the output level stability of the signal generator should be included. The standard uncertainty of the contribution due to the signal generator output level stability is designated throughout all parts of TR 102 273 [3] as uj39. Its value can be derived from manufacturers' data sheet. NOTE 2: In this example case the uncertainty of the contribution due to the signal generator output level stability is obtained from the manufacturers data sheet as ±0,02 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,01155 dB. This is rounded down to 0,01 dB. 6.9.2.1.2.2 Signal generator cable Insertion loss: signal generator cable: The signal generator cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator cable is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the transmitting antenna cable is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 131 Cable factor: signal generator cable: Cable factor is defined as the total effect of the signal generator cable's influence on the measuring system including its interaction with the Stripline. It consists of the leakage caused by cable screening inefficiency and introducing an unbalanced current into the Stripline. In a radiated measurement the standard uncertainty of the cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the signal generator cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the signal generator is taken as 0,00 dB since there are no external fields involved other than leakage, which is assumed to have a negligible effect on the measurement. 6.9.2.1.2.3 Signal generator attenuator Insertion loss: signal generator attenuator: The signal generator attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution, due to the insertion loss uncertainty of the signal generator attenuator, is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator attenuator is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. 6.9.2.1.2.4 Adapter Insertion loss: adapter: The adapter has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the adapter is not used outside the manufacturer's specification. The standard uncertainty of the contribution due to the insertion loss uncertainty of the adapter is designated throughout all parts of TR 102 273 [3] as uj42. Its value can be derived from the manufacturer's data sheet. NOTE: In this example case the uncertainty of the contribution due to the insertion loss uncertainty of the adapter is obtained from the manufacturers data sheet as ±0,10 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,06 dB. 6.9.2.1.2.5 Receiving device attenuator Insertion loss: receiving device attenuator: The attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the receiving device attenuator is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the receiving device attenuator is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 132 6.9.2.1.2.6 Receiving device cable Insertion loss: receiving device cable: The receiving device cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution, due to the insertion loss uncertainty of the receiving device cable, is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the receiving device cable is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. Cable factor: receiving device cable: Cable factor is defined as the total effect of the receiving device cable's influence on the measuring system including its interaction with the Stripline. It consists of the leakage caused by cable screening inefficiency and introducing an unbalanced current into the Stripline. In a radiated measurement the standard uncertainty of the cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the receiving device cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the receiving device cable is taken as 0,00 dB since there are no external fields involved other than leakage, which is assumed to have a negligible effect on the measurement. 6.9.2.1.2.7 Receiving device In this, the first stage of the Stripline verification procedure, a reference level is set on the receiving device for a particular output level from the signal generator. In the second stage (where the path loss through the Stripline is measured), a second level is obtained on the receiving device. Only in the second stage do the linearity and absolute level uncertainties of the receiver become involved in the calculation of the combined standard uncertainty for the measurement. Receiving device: absolute level: The standard uncertainty of the contribution due to the receiving device absolute level uncertainty is designated throughout all parts of TR 102 273 [3] as uj47. NOTE 1: In this example case the standard uncertainty of the contribution due to the absolute level uncertainty of the receiving device is assumed to be 0,00 dB since, in this part of the measurement, a reference level is recorded. Receiving device: linearity: The standard uncertainty of the contribution due to the receiving device linearity is designated throughout all parts of TR 102 273 [3] as uj48. NOTE 2: In this example case the standard uncertainty of the contribution due to the receiving device linearity is assumed to be 0,00 dB since, in this part of the measurement, a reference level is recorded.
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100 028-1
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6.9.2.1.3 Contribution from the random component
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Random uncertainty: The magnitude can be assessed from multiple measurements of the direct attenuation measurement. The standard uncertainty of the contribution due to the random uncertainty is designated throughout all parts of TR 102 273 [3] as ui01. Its value can then be calculated. The direct attenuation measurement was repeated 10 times. The following results (dBµV) in were obtained (before correcting for cabling and attenuator network insertion loss): - 106,8; 107,2; 106,7; 107,0; 107,2; 106,7; 107,1; 106,8; 107,1; 107,0. Converting to linear terms: - 0,2188; 0,2291; 0,2163; 0,2239; 0,2291; 0,2163; 0,2265; 0,2188; 0,2265; 0,2239. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 133 The two sums X and Y are calculated: - X = the sum of the measured values = 2,2292 V; - Y = the sum of the squares of the measured values = 0,4972 V2. = − − = − − = 1 10 10 2292 ,2 4972 ,0 1 2 2 n n X Y uc random 5,444 ×10-3 (formula 5.6) As the result is obtained as the mean value of 10 measurements and the standard uncertainty of the random uncertainty is: dB 0,212 5, 11 100 22292 ,0 10 444 ,5 3 = × × = − j random u NOTE: In this example case the standard uncertainty of the contribution due to the random uncertainty is 0,212 dB.
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100 028-1
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6.9.2.1.4 Summary table of contributory components
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A complete list of all the contributions to this part of the verification procedure is given in table 39. Table 39: Contributions from the reference, direct measurement uj or i Description of uncertainty contributions dB uj35 mismatch: direct attenuation measurement 0,03 uj38 signal generator: absolute output level 0,00 uj39 signal generator: output level stability 0,01 uj41 insertion loss: signal generator cable 0,00 uj19 cable factor: signal generator cable 0,00 uj40 insertion loss: signal generator attenuator 0,00 uj42 insertion loss: adapter 0,06 uj40 insertion loss: receiving device attenuator 0,00 uj41 insertion loss: receiving device cable 0,00 uj19 cable factor: receiving device cable 0,00 uj47 receiving device: absolute level 0,00 uj48 receiving device: linearity 0,00 ui01 random uncertainty (see note in clause 6.4.7) 0,21 The standard uncertainties from table 39 should be combined by RSS in accordance with TR 102 273 [3], part 1, sub-part 1, clause 5. This gives the combined standard uncertainty (uc direct attenuation measurement) for the direct attenuation measurement in dB. The value of uc direct attenuation measurement is calculated as 0,223 dB.
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100 028-1
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6.9.2.2 Uncertainty contributions: Stage 2: Radiated attenuation measurement
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The second stage of the verification procedure is the Stripline radiated attenuation measurement. This involves mounting a monopole antenna through a hole in the lower plate of the Stripline, so that the feed point to the monopole is flush with the surface of the lower plate. The radiated attenuation measurement is carried out by removing the adapter and connecting the signal generator attenuator to the Stripline and connecting the receiving device attenuator to the monopole output (figure 35). The difference in received levels (after allowance for any correction factors which may be appropriate), for the same signal generator output level, is the Stripline radiated attenuation. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 134 150 termination Load Central axis of stripline Ferrite beads 10dB attenuator Ω Receiving device Signal generator Figure 35: Stage 2: Radiated attenuation measurement Whereas figure 35 shows, schematically, the test equipment set-up for this stage of the verification procedure, an analysis diagram of the individual components (each of which contributes its own uncertainty) for this stage of the measurement is shown in figure 36. Again, as stated above, the shaded areas represent components common to both stages of the verification procedure. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 135
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100 028-1
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6.9.2.2.1 Contributions from the mismatch components
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Mismatch in the transmitting and receiving parts: The value of the combined standard uncertainty of the contributions due to the mismatch are calculated from the approach described in annex G. It is calculated in two parts. Firstly the standard uncertainty of the contribution due to the mismatch in the transmitting part, i.e. between the signal generator, cable, attenuator and the input to the Stripline and secondly, that for the receiving part, i.e. between the receiving monopole antenna, attenuator, cable and the receiving device. Signal generator Cable loss Cable factor Cable loss Receiving device Stripline Signal generator Signal generator cable 1 Receiving device cable 2 Attenuator 2 10 dB Attenuator 1 10 dB resonances, etc. Cable factor Stripline to monopole coupling Radiated Loss Monopole Site effects + Receiving device + Room Mismatch Mismatch Mismatch Mismatch Mismatch Mismatch + + + + + + Figure 36: Stage 2: Radiated attenuation measurement All the individual contributions are U-distributed. NOTE 1: In this example value taken for the signal generator output reflection coefficient is the worst case over the frequency band of interest, similarly, for the cable, adapter and attenuator VSWRs. NOTE 2: The attenuation values of the cables and attenuators should be obtained from the data sheets/calibration records at the specific frequency of the test, along with the associated uncertainties for these values. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 136 Mismatch: transmitting part: Signal generator: Output reflection coefficient: |ρG| = 0,20 Cable: Input and output reflection coefficients: |S11| and |S22| = 0,07 Attenuation: 1 dB = |S12| = |S21| = 0,891 Attenuator: Input and output reflection coefficients |S11| = |S22| = 0,05 Attenuation = 10 dB |S12| = |S21| = 0,3162 Stripline: Input reflection coefficient: |ρSL| = 0,333 Those components that cancel are not calculated. Other contributions are (see annex G): - uj mismatch: generator and cable 1: Constant for both stage 1 and 2. Hence this value does not contribute. - uj mismatch: cable 1 and attenuator 1: Constant for both stage 1 and 2. Hence this value does not contribute. % ,177 1 % 2 100 333 ,0 05 ,0 1 : = × × = Stripline and attenuator mismatch j u - uj generator and attenuator 1: Constant for both stage 1 and 2. Hence this value does not contribute. % 0,165 % 2 100 316 ,0 333 ,0 07 ,0 2 1 : = × × × = Stripline and cable mismatch j u % 0,373 % 2 100 316 ,0 891 ,0 333 ,0 2,0 2 2 : = × × × × = Stripline and generator mismatch j u The combined standard uncertainty of the mismatch is then calculated: % 25 1 373 ,0 165 ,0 177 ,1 2 2 2 : , u part ng transmitti mismatch c = + + = transforming to the logarithmic form (TR 100 028-2 [8], annex E): 1,25 %/11,5 = 0,11 dB. The standard uncertainty of the contribution due to the mismatch in the transmitting part, is designated throughout all parts of TR 102 273 [3] as uj36. Its value in this example is 0,11 dB. Mismatch: receiving part: Monopole: Input reflection coefficient: |ρM| = 0,333 Attenuator: Input and output reflection coefficients |S11| = |S22| = 0,05 Attenuation = 10 dB |S12| = |S21| = 0,3162 Cable: Input and output reflection coefficients: |S11| and |S22| = 0,07 Attenuation: 1 dB = |S12| = |S21| = 0,891 Receiving device: Output reflection coefficient: |ρRD| = 0,20 % ,177 1 % 2 100 05 ,0 333 ,0 : = × × = attenuator and monopole mismatch j u - uj attenuator 2 and cable 2: Constant for both stage 1 and 2. Hence this value does not contribute. - uj cable 2 and receiving device: Constant for both stage 1 and 2. Hence this value does not contribute. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 137 % 0,165 % 2 100 316 ,0 07 ,0 333 ,0 2 2 : = × × × = cable and monopole mismatch j u - uj attenuator 2 and receiving device: Constant for both stage 1 and 2. Hence this value does not contribute. % 0,373 % 2 100 891 ,0 316 ,0 2,0 333 ,0 2 2 : = × × × × = device receiving and monopole mismatch j u The combined standard uncertainty of the mismatch is then calculated: % 25 1 373 ,0 165 ,0 177 ,1 2 2 2 : , u part receiving mismatch c = + + = Transforming to the logarithmic form (TR 100 028-2 [8], annex E): 1,25 %/11,5 = 0,11 dB. The standard uncertainty of the contribution due to the mismatch in the receiving part is designated throughout all parts of TR 102 273 [3] as uj37. Its value in this example is 0,11 dB.
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100 028-1
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6.9.2.2.2 Contributions from individual components
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6.9.2.2.2.1 Signal generator Signal generator: absolute output level: In a verification procedure, the signal generator's absolute level uncertainty contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the signal generator absolute output level uncertainty is designated throughout all parts of TR 102 273 [3] as uj38. NOTE 1: In this example case the standard uncertainty of the contribution due to the signal generator absolute output level uncertainty is taken to be 0,00 dB since, once the level has been set in stage one of the procedure, the level is not further adjusted. The uncertainty is therefore assumed to be systematic i.e. it produces the same offset in both stages. Signal generator: output level stability: In any test in which the contribution of the absolute level uncertainty of the signal generator contributes to the combined standard uncertainty of the test i.e. it does not cancel due to the methodology, the contribution from the output level stability is considered to have been included in the signal generator absolute output level, uj38. Conversely, for any level in which the absolute level uncertainty of the signal generator does not contribute to the combined standard uncertainty, the output level stability of the signal generator should be included. The standard uncertainty of the contribution due to the signal generator output level stability is designated throughout all parts of TR 102 273 [3] as uj39. Its value can be derived from manufacturers' data sheet. NOTE 2: In this example case the uncertainty of the contribution due to the signal generator output level stability is obtained from the manufacturers data sheet as ±0,02 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,01155 dB. This is rounded down to 0,01 dB. 6.9.2.2.2.2 Signal generator cable Insertion loss: signal generator cable: The signal generator cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution, due to the insertion loss uncertainty of the signal generator cable, is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator cable is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 138 Cable factor: signal generator cable: Cable factor is defined as the total effect of the signal generator cable's influence on the measuring system including its interaction with the Stripline. It consists of the leakage caused by cable screening inefficiency and introducing an unbalanced current into the Stripline. In a radiated measurement the standard uncertainty of the cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the signal generator cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the transmitting antenna cable is taken as 0,50 dB since the precautions detailed in the methods are assumed to have been observed. 6.9.2.2.2.3 Signal generator attenuator Insertion loss: signal generator attenuator: The signal generator attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution, due to the insertion loss uncertainty of the signal generator attenuator, is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator attenuator is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. 6.9.2.2.2.4 Site factors Ambient effect: Uncertainty is introduced as a result of local ambient signals raising the noise floor at the measurement frequency. The standard uncertainty of the contribution due to the ambient effect is designated throughout all parts of TR 102 273 [3] as uj34. The values of the standard uncertainty should be taken from table 40. Table 40: Uncertainty contribution: Ambient effect Receiving device noise floor (generator OFF) is within: Standard uncertainty of the contribution 3 dB of measurement 1,57 dB 3 dB to 6 dB of measurement 0,80 dB 6 dB to 10 dB of measurement 0,30 dB 10 dB to 20 dB of measurement 0,10 dB 20 dB or more of the measurement 0,00 dB NOTE 1: In this example case the standard uncertainty of the contribution due to the ambient effect is taken as 0,00 dB since the Stripline is assumed to be placed in a shielded room. Stripline: influence of site effects: The influence of site effects comprise those effects resulting from not observing the recommendations given in EN 55020 [7] regarding positioning of the Stripline and layout of the absorber. These can lead to incorrect received levels i.e. values which differ from theoretical calculations. The standard uncertainty of the contribution due to the influence of site effects is designated throughout all parts of TR 102 273 [3] as uj33. NOTE 2: In this example case the standard uncertainty of the contribution due to the influence of site effects is taken to have a standard uncertainty of 3,0 dB (see annex A). In the verification procedure, site effects only contribute to the Stripline radiated attenuation part. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 139 6.9.2.2.2.5 Antenna factor of the monopole Stripline: antenna factor of the monopole: This has been derived from measurements taken within the Stripline. Therefore, the given values incorporate several of the field disturbance factors which the Stripline possesses and which therefore do not have to be allowed for as individual contributions. Amongst these included effects are imaging, characteristic impedance of the line, non-planar nature of the field etc. The standard uncertainty of the contribution due to the antenna factor of the monopole is designated throughout all parts of TR 102 273 [3] as uj30. NOTE: In this example case the standard uncertainty of the contribution due to the antenna factor of the monopole is taken as 1,15 dB. This combined uncertainty source is only present in the Stripline radiated attenuation measurement. 6.9.2.2.2.6 Receiving device attenuator Insertion loss: receiving device attenuator: The receiving device attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the receiving device attenuator is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the receiving device attenuator is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. 6.9.2.2.2.7 Receiving device cable Insertion loss: receiving device cable: The receiving device cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution, due to the insertion loss uncertainty of the receiving device cable, is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the receiving device cable is taken as 0,00 dB since the uncertainty is systematic i.e. it produces the same offset in both stages. Cable factor: receiving device cable: Cable factor is defined as the total effect of the receiving device cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency and introducing an unbalanced current into the monopole. In a radiated measurement the standard uncertainty of the cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the receiving device cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the receiving antenna cable is taken as 0,50 dB since the precautions detailed in the methods have been observed. 6.9.2.2.2.8 Receiving device The first stage of the verification procedure involved setting a reference level on the receiving device for a particular output level from the signal generator. In this the second stage (where the radiated attenuation through the Stripline is measured), a second level is obtained which results in linearity and absolute level uncertainties becoming involved in the calculation of the combined standard uncertainty for the measurement. Receiving device: absolute level: This uncertainty only contributes during the second stage of the procedure if the input attenuation range setting on the receiving device has been changed from its setting in the first stage. The standard uncertainty of the contribution due to the receiving device absolute level uncertainty is designated throughout all parts of TR 102 273 [3] as uj47. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 140 NOTE 1: In this example case the uncertainty of the contribution due to the receiving device absolute level uncertainty (a range change is assumed) is obtained from the manufacturers data as ±0,5 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed. The standard uncertainty of the contribution due to the receiving device absolute level uncertainty is calculated as 0,29 dB. Receiving device: linearity: In any test in which the contribution of the absolute level uncertainty of the receiving device contributes to the combined standard uncertainty of the test i.e. it does not cancel due to the methodology, the contribution from the receiving device linearity is considered to have been included in uj47. Conversely, for any test in which the absolute level uncertainty of the receiving device does not contribute to the combined standard uncertainty the linearity of the receiving device should be included. The standard uncertainty of the contribution due to the receiving device linearity is designated throughout all parts of TR 102 273 [3] as uj48. NOTE 2: In this example case the standard uncertainty of the contribution due to the receiving device linearity is taken as 0,00 dB.
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6.9.2.2.3 Contribution from the random component
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Random uncertainty: The magnitude can be assessed from multiple measurements of the radiated attenuation measurement. The standard uncertainty of the contribution due to the random uncertainty is designated throughout all parts of TR 102 273 [3] as ui01. The radiated attenuation measurement was repeated 10 times. The following results were obtained in dBµV (before correcting for cabling and attenuator network insertion loss): - 65,4; 63,4; 66,0; 65,3; 63,0; 64,9; 65,2; 66,8; 65,5; 63,7. Converting to linear terms: - 1,862 × 10-3; 1,479 × 10-3; 1,995 × 10-3; 1,841 × 10-3; 1,413 × 10-3; 1,758 × 10-3; 1,820 × 10-3; 2,188 × 10-3; 1,884 × 10-3; 1,531 × 10-3; The two sums X and Y are calculated: - X = the sum of the measured values = 17,77 × 10-3; - Y = the sum of the squares of the measured values = 32,10 × 10-6 V2. ( ) = − × − × = − − = − − 1 10 10 10 77 , 17 10 10 , 32 1 2 3 6 2 n n X Y uc random 238,3 ×10-6 (formula 5.6) As the result is obtained as the mean value of 10 measurements and the standard uncertainty of the random uncertainty is: dB 1,17 5, 11 100 10 777 ,1 10 3, 238 3 6 = × × × = − − j random u NOTE: In this example case the standard uncertainty of the contribution due to the random uncertainty is evaluated as 1,17 dB. See also the note in clause 6.4.7. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 141
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6.9.2.2.4 Summary table of contributory components
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A complete list of all the contributions to this part of the verification procedure is given in table 41. Table 41: Contributions from the radiated attenuation measurement uj or i Description of uncertainty contributions dB uj36 mismatch: transmitting part 0,11 uj37 mismatch: receiving part 0,11 uj38 signal generator: absolute output level 0,00 uj39 signal generator: output level stability 0,01 uj41 insertion loss: signal generator cable 0,00 uj19 cable factor: signal generator cable 0,50 uj40 insertion loss: signal generator attenuator 0,00 uj34 ambient effect 0,00 uj33 Stripline: influence of site effects 3,00 uj31 Stripline: antenna factor of the monopole 1,15 uj40 insertion loss: receiving device attenuator 0,00 uj41 insertion loss: receiving device cable 0,00 uj19 cable factor: receiving device cable 0,50 uj47 receiving device: absolute level 0,29 uj48 receiving device: linearity 0,00 ui01 random uncertainty (see note in clause 6.4.7) 1,17 The standard uncertainties from table 41 should be combined by RSS in accordance with TR 102 273 [3], part 1, sub-part 1, clause 5. This gives the combined standard uncertainty (uc Stripline attenuation measurement) for the Stripline attenuation measurement in dB. The value of uc Stripline attenuation measurement is calculated as 3,51 dB.
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6.9.2.2.5 Expanded uncertainty for the verification procedure
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The combined standard uncertainty of the results of the verification procedure is the combination of the components outlined in clauses 6.9.2.1.4 and 6.9.2.2.4. The components to be combined are uc direct attenuation measurement and uc Stripline attenuation measurement. dB 3,51 = 51 ,3 223 ,0 2 2 + = procedure on verificati Stripline c u The expanded uncertainty is ±1,96 x 3,51 = ±6,89 dB at a 95 % confidence level.
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6.9.3 Example 2: The measurement of a receiver parameter (Sensitivity)
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For the measurement of receiver sensitivity two stages of test are involved. The first stage (determining the Transform Factor of the Stripline) involves measuring the field strength at the point where the receiver will be placed and determining the relationship between the signal generator output power level and the resulting field strength. The second stage (the EUT measurement) involves placing the EUT within the Stripline and adjusting the output level of the signal generator until the required response is obtained on the receiver. The signal generator output power level is then converted to field strength using the Transform Factor. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 142
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6.9.3.1 Uncertainty contributions: Stage 1: EUT measurement
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The first stage of the measurement is to determine the minimum signal generator output level which produces the required response from the EUT. The test equipment set-up is shown in see figure 37. 150 termination Load Central axis of stripline Ferrite beads 10dB attenuator Non-conducting, low dielectric constant support stand EUT with volume centre midway between plates Ω Modulation detection Signal generator Figure 37: Stage 1: EUT measurement Whereas figure 37 shows, schematically, the test equipment set-up for the EUT sensitivity measurement, figure 38, an analysis diagram, provides a detailed picture of the individual uncertainty components (each of which contributes its own uncertainty) for this stage in the measurement. As stated above, the shaded areas represent components common to both stages of the test method.
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6.9.3.1.1 Contributions from the mismatch components
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Mismatch: transmitting part: The uncertainty due to mismatch for the measurement on the EUT concerns only the signal generator, the signal generator cable, the signal generator attenuator and the input to the Stripline. The mismatch uncertainty through this network does, however, contribute equally to both stages of the test for cases in which a field strength measurement is subsequently performed. If, however, the results of the verification procedure are used to calculate the field strength, the contribution of the mismatch uncertainty needs to be calculated, from the approach described in annex G. All the contributions are U-distributed. Signal generator: Output reflection coefficient: |ρG| = 0,20 Cable: Input and output reflection coefficients: |S11| and |S22| = 0,07 Attenuation: 1 dB = |S12| = |S21| = 0,891 Attenuator: Input and output reflection coefficients |S11| = |S22| = 0,05 Attenuation = 10 dB |S12| = |S21| = 0,3162 Stripline: Input reflection coefficient: |ρSL| = 0,333 ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 143 Signal generator Cable factor Cable loss Stripline Signal generator cable 1 Stripline to EUT coupling Signal generator Signal generator attenuator Attenuator 1 10 dB Modulation source Modulation detector Radiated loss EUT Room Site effects + resonances, etc. Mismatch Mismatch Mismatch + + + Figure 38: Schematic of the sensitivity measurement on the EUT Mismatch: transmitting part. All these contributions are U-distributed. Those components that cancel are not calculated. Other contributions are (see annex G): - uj mismatch: generator and cable 1: Constant for both stage 1 and 2. Hence this value does not contribute. - uj mismatch: cable 1 and attenuator 1: Constant for both stage 1 and 2. Hence this value does not contribute. % ,177 1 % 2 100 333 ,0 05 ,0 1 : = × × = Stripline and attenuator mismatch j u ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 144 - uj generator and attenuator 1: Constant for both stage 1 and 2. Hence this value does not contribute. % 0,165 % 2 100 316 ,0 333 ,0 07 ,0 2 1 : = × × × = Stripline and cable mismatch j u % 0,373 % 2 100 316 ,0 891 ,0 333 ,0 2,0 2 2 : = × × × × = Stripline and generator mismatch j u The combined standard uncertainty of the mismatch is then calculated: % 25 1 373 ,0 165 ,0 177 ,1 2 2 2 : , u part ng transmitti mismatch c = + + = Transforming to the logarithmic form (TR 100 028-2 [8], annex E): 1,25 %/11,5 = 0,11 dB. The standard uncertainty of the contribution due to the mismatch in the transmitting part, is designated throughout all parts of TR 102 273 [3] as uj36. Its value in this example is 0,11 dB.
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6.9.3.1.2 Contributions from the individual components
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6.9.3.1.2.1 Signal generator Signal generator: absolute output level: In this test method, the uncertainty due to the setting of the signal generator's absolute output level contributes to both stages. In stage 1, the output level is individually adjusted at each of 8 different positioning angles whilst in stage 2, after an inspection (or calculation) of the 8 different values, the signal generator is set to a specific output level. The standard uncertainty of the contribution due to the signal generator absolute output level uncertainty is designated throughout all parts of TR 102 273 [3] as uj38. Its value can be obtained from the manufacturer's data sheet. NOTE 1: In this example case the uncertainty of the contribution due to the signal generator absolute output level is obtained from the manufacturers data sheet as ±1,0 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,58 dB. Signal generator: output level stability: In any test in which the contribution of the absolute level uncertainty of the signal generator contributes to the combined standard uncertainty of the test i.e. it does not cancel due to the methodology, the contribution from the output level stability is considered to have been included in the signal generator absolute output level, uj38. Conversely, for any level in which the absolute level uncertainty of the signal generator does not contribute to the combined standard uncertainty, the output level stability of the signal generator should be included. The standard uncertainty of the contribution due to the signal generator output level stability is designated throughout all parts of TR 102 273 [3] as uj39. Its value can be derived from manufacturers' data sheet. NOTE 2: In this example case the standard uncertainty of the contribution due to the signal generator output level stability is taken as 0,0 dB as it is covered by the absolute level uncertainty. 6.9.3.1.2.2 Signal generator cable Insertion loss: signal generator cable: The signal generator cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator cable is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator cable is taken as 0,20 dB as the results of the verification procedure have been used to determine the field strength and this value has been taken from the manufacturer's or calibration data. NOTE 2: If a field measurement had been performed using either a monopole of 3-axis probe the value would have been 0,00 dB as the uncertainty is systematic i.e. it produces the same offset in both stages. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 145 Cable factor: signal generator cable: Cable factor is defined as the total effect of the signal generator cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency and introducing an unbalanced current into the Stripline. In a radiated measurement the standard uncertainty of the cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the signal generator cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 3: In this example case the standard uncertainty of the contribution due to the cable factor of the signal generator cable is taken as 0,5 dB since the precautions detailed in the test method have been observed. 6.9.3.1.2.3 Signal generator attenuator Insertion loss: signal generator attenuator: The signal generator attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss of the signal generator attenuator is designated throughout all parts of TR 102 273 [3] as uj40. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator cable is taken as 0,20 dB as the results of the verification procedure have been used to determine the field strength and this value has been taken from the manufacturer's or calibration data. NOTE 2: If a field measurement had been performed using either a monopole of 3-axis probe the value would have been 0,00 dB as the uncertainty is systematic i.e. it produces the same offset in both stages. 6.9.3.1.2.4 Site factors Ambient effect: Uncertainty is introduced as a result of local ambient signals raising the noise floor at the measurement frequency. The standard uncertainty of the contribution due to the ambient effect is designated throughout all parts of TR 102 273 [3] as uj34. The value of the standard uncertainty is the same as for the second stage. NOTE 1: In this example case the standard uncertainty of the contribution due to the ambient effect is taken as 0,00 dB since the Stripline is assumed to have been placed in a shielded room. Stripline: influence of site effects: The influence of site effects comprise those effects, resulting from not observing the recommendations given in EN 55020 [7] regarding positioning of the Stripline and layout of absorber. These can lead to incorrect received levels i.e. values which differ from theoretical calculations. In this example, the recommendations are assumed not to have been fully observed. The standard uncertainty of the contribution due to the influence of site effects is designated throughout all parts of TR 102 273 [3] as uj33. NOTE 2: In this example case the standard uncertainty of the contribution due to the influence of site effects is taken as 3,0 dB since in the verification procedure, site effects only contribute to the Stripline attenuation part and therefore do not cancel. NOTE 3: If a field measurement had been performed using either a monopole of 3-axis probe the value would have been 0,00 dB as the uncertainty is systematic i.e. it produces the same offset in both stages. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 146 6.9.3.1.2.5 EUT Stripline: mutual coupling of the EUT to its images in the plates: The magnitude is dependent on the EUT's size. The EUT is assumed to be positioned midway between the plates. The standard uncertainty of the contribution due to the mutual coupling of the EUT to its images in the plates is designated throughout all parts of TR 102 273 [3] as uj24. Its value can be obtained from table 42. Table 42: Uncertainty contribution of the mutual coupling of the EUT to its images in the plates Size of the EUT relative to the plate separation Standard uncertainty of the contribution size/separation < 33 % 1,15 dB 33 % ≤ size/separation < 50 % 1,73 dB 50 % ≤ size/separation < 70 % 2,89 dB 70 % ≤ size/separation ≤ 87,5 % (max.) 5,77 dB NOTE 1: In this example case the standard uncertainty of the contribution due to the mutual coupling of the EUT to its images in the plates is 1,15 dB since it is assumed the equipment size is < 33 % of the plate separation. Stripline: characteristic impedance: This uncertainty contribution results from the difference between the free-space wave impedance (377 Ω) for which the EUT had been developed and that for the Stripline (150 Ω). The standard uncertainty of the contribution due to the characteristic impedance of the Stripline is designated throughout all parts of TR 102 273 [3] as uj26. NOTE 2: In this example case the standard uncertainty of the contribution due to the characteristic impedance of the Stripline is taken as having a standard uncertainty of 0,58 dB. Stripline: correction factor for the size of the EUT: This uncertainty is the result of changes in the intensity of the electric field between the plates resulting from the presence, and metal content of the EUT. The larger the size of the EUT in the vertical plane of the Stripline, the greater the field intensification effect. Correction factors are supplied within the test method, and the associated standard uncertainty of the contribution of the uncertainty due to the correction factor for the size of the EUT is designated throughout all parts of TR 102 273 [3] as uj32. For EUT mounted centrally in the Stripline, values can be obtained from table 43. Table 43: Uncertainty contribution: Stripline: correction factor for the size of the EUT Height of the EUT (in the E-plane) is: Standard uncertainty of the contribution height < 0,2 m 0,30 dB 0,2 m ≤ height < 0,4 m 0,60 dB 0,4 m ≤ height ≤ 0,7 m 1,20 dB NOTE 3: In this example case the standard uncertainty of the contribution of the uncertainty due to the correction factor for the size of the EUT is taken as 0,60 dB as the EUT is 0,22 m high. EUT: mutual coupling to the power leads: This is the uncertainty associated with the influence (reflections, parasitic effects, etc.) of the power leads on the EUT. The standard uncertainty associated with this effect is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 2,0 dB. The standard uncertainty of the contribution due to the mutual coupling of the EUT to the power leads is designated throughout all parts of TR 102 273 [3] as uj54. NOTE 4: In this example case the standard uncertainty of the contribution due to the mutual coupling of the EUT to the power leads is taken as 0,5 dB since the precautions detailed in the methods have been observed. Stripline: non-planar nature of the field distribution: This uncertainty results from the non-uniform amplitude and phase distribution of the electric field across the EUT. The non-uniformity results from room resonances, constructional problems, moding, reflections, etc. The standard uncertainty of the contribution due to the non-planar nature of the field distribution is designated throughout all parts of TR 102 273 [3] as uj27. NOTE 5: In this example case the standard uncertainty of the contribution due to the non-planar nature of the field distribution is taken as 0,29 dB. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 147 EUT: degradation measurement: This contribution is a RF level uncertainty associated with the uncertainty of measuring 20 dB SINAD, 10-2 bit stream or 80 % message acceptance ratio. The standard uncertainty of the contribution due to the EUT degradation measurement, designated throughout all parts of TR 102 273 [3] as uj52, can be obtained from TR 100 028 (all parts). NOTE 6: In this example case, the standard uncertainty of the contribution is obtained from TR 100 028 (all parts) and its value is 0,68 dB.
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6.9.3.1.3 Contribution from the random component
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Random uncertainty: The magnitude can be assessed from multiple measurements of the receiver sensitivity measurement. The standard uncertainty of the contribution due to the random uncertainty is designated throughout all parts of TR 102 273 [3] as ui01. The receiver sensitivity measurement was repeated 10 times. The following results were obtained in dBµV (before correcting for cabling and attenuator network insertion loss): - 65,4; 63,4; 66,0; 65,3; 63,0; 64,9; 65,2; 66,8; 65,5; 63,7. Converting to linear terms: - 1,862 × 10-3; 1,479 × 10-3; 1,995 × 10-3; 1,841 × 10-3; 1,413 × 10-3; 1,758 × 10-3; 1,820 × 10-3; 2,188 × 10-3; 1,884 × 10-3; 1,531 × 10-3. The two sums X and Y are calculated: - X = the sum of the measured values = 17,77 × 10-3; - Y = the sum of the squares of the measured values = 32,10 × 10-6 V2. ( ) = − × − × = − − = − − 1 10 10 10 77 , 17 10 10 , 32 1 2 3 6 2 n n X Y uc random 238,3 ×10-6 (formula 5.6) As the result is obtained as the mean value of 10 measurements and the standard uncertainty of the random uncertainty is: dB ,17 1 5, 11 100 10 777 ,1 10 3, 238 3 6 = × × × = − − j random u NOTE: In this example case the standard uncertainty of the contribution due to the random uncertainty is 1,17 dB. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 148
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6.9.3.1.4 Summary table of contributory components
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A complete list of all the contributions to this part of the test method is given in table 44. Table 44: Contributions from the measurement on the EUT uj or i Description of uncertainty contributions dB uj36 mismatch: transmitting part: a) Using results of the verification procedure; b) Using a monopole for field measurement; c) Using a 3-axis probe for field measurement. 0,11 0,00 0,00 uj38 signal generator: absolute output level 0,58 uj39 signal generator: output level stability 0,00 uj41 insertion loss: signal generator cable: a) Using results of the verification procedure; b) Using a monopole for field measurement; c) Using 3-axis probe for field measurement. 0,20 0,00 0,00 uj19 cable factor: signal generator cable 0,50 uj40 insertion loss: signal generator attenuator: a) Using results of the verification procedure; b) Using a monopole for field measurement; c) Using a 3-axis probe for field measurement. 0,20 0,00 0,00 uj34 ambient effect 0,00 uj33 Stripline: influence of site effects: a) Using results of the verification procedure; b) Using a monopole for field measurement; c) Using a 3-axis probe for field measurement. 3,00 0,00 0,00 uj24 Stripline: mutual coupling of the EUT to its images in the plates 1,15 uj26 Stripline: characteristic impedance 0,58 uj32 Stripline: correction factor for the size of the EUT 0,60 uj55 EUT: mutual coupling to the power leads 0,50 uj27 Stripline: non-planar nature of the field distribution 0,29 uj52 EUT: degradation measurement 0,68 ui01 random uncertainty 1,17 The standard uncertainties from table 44 should be combined by RSS in accordance with TR 102 273 [3], part 1, sub-part 1, clause 5. This gives the combined standard uncertainty for the direct attenuation measurement in dB as follows: - using results of the verification procedure = uc measurement of the EUT = 3,72 dB; - using a monopole for field measurement = uc measurement of the EUT = 2,18 dB; - using a 3-axis probe for field measurement = uc measurement of the EUT = 2,18 dB. 6.9.3.2 Uncertainty contributions: Stage 2: Field measurement using the results of the verification procedure Stripline: interpolation of values for the Transform Factor: In this case, the frequency of test does not coincide with a frequency at which the verification procedure was carried out. Therefore, a contribution is included to account for the interpolation between Transform Factor values. The standard uncertainty of the contribution due to the interpolation of values for the Transform Factor of the Stripline is designated throughout all parts of TR 102 273 [3] as uj30. NOTE: In this example case the standard uncertainty of the contribution due to the interpolation of values for the Transform Factor is taken as 0,29 dB. The appropriate standard uncertainties from table 44 should be combined with uj30 by RSS in accordance with TR 102 273 [3], part 1, sub-part 1, clause 5. This gives the combined standard uncertainty (uc EUT measurement) for the EUT measurement in dB. The value of uc EUT measurement is calculated as 3,56 dB. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 149
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6.9.3.2.1 Expanded uncertainty for the receiver sensitivity measurement
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The combined standard uncertainty of the results of the receiver sensitivity measurement is the combination of uc Stripline attenuation measurement and uc EUT measurement. dB 5,11 = 72 ,3 51 ,3 2 2 + = t measuremen y sensitivit receiver c u The expanded uncertainty is ±1,96 x 5,11= ±10,0 dB at a 95 % confidence level.
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6.9.3.3 Uncertainty contributions: Stage 2: Field measurement using a monopole
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The second stage involves replacing the EUT with a field measuring device (either a monopole antenna or a 3-axis probe) and, setting a particular output level from the signal generator (minimum or average), measuring the corresponding field strength, see figure 39. NOTE: In this case monopole field measurement involves mounting the monopole through a hole in the lower plate of the Stripline (so that the feed point to the monopole is flush with the surface of the lower plate) and measuring the field strength. 150 termination Load Central axis of Stripline Signal generator Ferrite beads 10dB attenuators ΩΩΩΩ Monopole Receiving device Figure 39: Stage 2: Field measurement using a monopole
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6.9.3.3.1 Contributions from the mismatch components
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Mismatch in the transmitting and receiving parts: Whereas figure 39 shows schematically the equipment set-up for field measurement using a monopole, figure 40 provides a detailed picture of the individual uncertainty contributions. Mismatch: transmitting part: The mismatch uncertainty between the signal generator, signal generator cable, signal generator attenuator and the Stripline input can be calculated from the approach described in annex G. The mismatch uncertainty through this network does, however, contribute equally to both stages of the test for cases in which a field strength measurement is subsequently performed since there are no changes from stage 1 to this part of the test set-up. The standard uncertainty of the contribution due to the mismatch in the transmitting part is designated throughout all parts of TR 102 273 [3] as uj36. NOTE: In this example case the standard uncertainty of the contribution due to mismatch in the transmitting part is taken as 0,00 dB, since the uncertainty is systematic i.e. it produces the same offset in both stages. Mismatch: receiving part: The mismatch uncertainty in the receiving part i.e. between the monopole, receiving device attenuator, receiving device cable and the receiving device is calculated from the approach described in annex G. This mismatch uncertainty contributes only during the field measurement part of the test and therefore contributes to the combined standard uncertainty. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 150 Signal generator Cable loss Cable factor Cable factor Cable loss Receiving device Stripline Receiving Signal generator device Receiving device cable 2 Radiated Loss Attenuator 1 10 dB Signal generator cable 1 Attenuator 2 10 dB Stripline to monopole coupling Monopole + Mismatch Mismatch + + Mismatch + + Site effects Room resonances, etc. Mismatch Mismatch Mismatch + + + Figure 40: Schematic of the field measurement using a monopole Monopole: Input reflection coefficient: |ρM| = 0,333 Attenuator: Input and output reflection coefficients |S11| = |S22| = 0,05 Attenuation = 10 dB |S12| = |S21| = 0,3162 Cable: Input and output reflection coefficients: |S11| and |S22| = 0,07 Attenuation: 1 dB = |S12| = |S21| = 0,891 Receiving device: Output reflection coefficient: |ρRD| = 0,20 All these contributions are U-distributed. Other contributions are (see annex G): % ,177 1 % 2 100 05 ,0 333 ,0 : = × × = attenuator and antenna mismatch j u - uj attenuator 2 and cable 2: Constant for both stage 1 and 2. Hence this value does not contribute. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 151 - uj cable 2 and receiving device: Constant for both stage 1 and 2. Hence this value does not contribute. % 0,165 % 2 100 316 ,0 07 ,0 333 ,0 2 2 : = × × × = cable and antenna mismatch j u - uj attenuator 2 and receiving device: Constant for both stage 1 and 2. Hence this value does not contribute. % 0,373 % 2 100 891 ,0 316 ,0 2,0 333 ,0 2 2 : = × × × × = device receiving and antenna mismatch j u The combined standard uncertainty of the mismatch is then calculated: % 25 1 373 ,0 165 ,0 177 ,1 2 2 2 : , u part receiving mismatch j = + + = Transforming to the logarithmic form (TR 100 028-2 [8], annex E): 1,25 %/11,5 = 0,11 dB. The standard uncertainty of the contribution, due to the mismatch in the receiving part, is designated throughout all parts of TR 102 273 [3] as uj37. Its value in this example is 0,11 dB.
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100 028-1
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6.9.3.3.2 Contributions from the individual components
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6.9.3.3.2.1 Signal generator Signal generator: absolute output level: In this test method, the uncertainty due to the setting of the signal generator's absolute output level contributes to both stages. In stage 1, the output level is individually adjusted at each of 8 different positioning angles whilst in stage 2, after an inspection (or calculation) of the 8 different values, the signal generator is set to a specific output level. The standard uncertainty of the contribution due to the signal generator absolute output level is designated throughout all parts of TR 102 273 [3] as uj38. Its value can be obtained from the manufacturer's data sheet. NOTE 1: In this example case the uncertainty of the contribution due to the signal generator absolute output level uncertainty from the manufacturer's data sheet is ±1,0 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,58 dB. Signal generator: output level stability: In any test in which the contribution of the absolute level uncertainty of the signal generator contributes to the combined standard uncertainty of the test i.e. it does not cancel due to the methodology, the contribution from the output level stability is considered to have been included in the signal generator absolute output level, uj38. Conversely, for any level in which the absolute level uncertainty of the signal generator does not contribute to the combined standard uncertainty, the output level stability of the signal generator should be included. The standard uncertainty of the contribution due to the signal generator output level stability is designated throughout all parts of TR 102 273 [3] as uj39. Its value can be derived from manufacturers' data sheet. NOTE 2: In this example case the standard uncertainty of the contribution due to the signal generator output level stability is taken as 0,00 dB as it is covered by the absolute level uncertainty. 6.9.3.3.2.2 Signal generator cable Insertion loss: signal generator cable: The signal generator cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator cable is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator cable is taken as 0,00 dB since the uncertainty is systematic i.e. it is assumed constant and common to both stages of the measurement. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 152 Cable factor: signal generator cable: Cable factor is defined as the total effect of the signal generator cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency and introducing an unbalanced current into the Stripline. In a radiated measurement the standard uncertainty of the uncertainty due to cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the signal generator cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the signal generator cable is taken as 0,00 dB since the precautions detailed in the methods have been observed and the field strength is to be measured. 6.9.3.3.2.3 Signal generator attenuator Insertion loss: signal generator attenuator: The signal generator attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator attenuator is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator attenuator is 0,00 dB since the precautions detailed in the methods have been observed and the field strength is to be measured. 6.9.3.3.2.4 Site factors Ambient effect: Ambient effect is the uncertainty caused by local ambient signals raising the noise floor at the measurement frequency. The standard uncertainty of the contribution due to the ambient effect is designated throughout all parts of TR 102 273 [3] as uj34. The value of the standard uncertainty should be taken from table 45. Table 45: Uncertainty contribution: Ambient effect Receiving device noise floor (EUT OFF) is within: Standard uncertainty of the contribution 3 dB of measurement 1,57 dB 3 dB to 6 dB of measurement 0,80 dB 6 dB to 10 dB of measurement 0,30 dB 10 dB to 20 dB of measurement 0,10 dB 20 dB or more of the measurement 0,00 dB NOTE 1: In this example case the standard uncertainty of the contribution due to the ambient effect is taken as 0,00 dB since the Stripline is assumed to have been placed in a shielded room. Stripline: influence of site effects: The influence of site effects comprise those effects, resulting from not observing the recommendations given in EN 55020 [7] regarding positioning of the Stripline and layout of the absorber. These can lead to incorrect received levels i.e. values which differ from theoretical calculations. The standard uncertainty of the contribution due to the influence of site effects is designated throughout all parts of TR 102 273 [3] as uj33. NOTE 2: In this example case the standard uncertainty of the contribution due to the influence of site effects is taken to be 0,00 dB since in this test method, site effects contribute equally to both stages as the recommendations are assumed to have been fully observed. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 153 6.9.3.3.2.5 Antenna factor of the monopole Stripline: antenna factor of the monopole: This has been derived from measurements taken within the Stripline. Therefore, the given values incorporate several of the field disturbance factors which the Stripline possesses and which therefore do not have to be allowed for as individual contributions. Amongst these included effects are imaging, characteristic impedance of the line, non-planar nature of the field etc. The standard uncertainty of the contribution due to the antenna factor of the monopole is designated throughout all parts of TR 102 273 [3] as uj30. NOTE: In this example case the standard uncertainty of the contribution due to the antenna factor of the monopole is taken as 1,15 dB. This combined uncertainty source is only present in the actual measurement. 6.9.3.3.2.6 Monopole attenuator Insertion loss: Monopole attenuator: The monopole attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. The standard uncertainty of the contribution due to the insertion loss uncertainty of the monopole attenuator is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the monopole attenuator is taken as 0,1 dB since the uncertainty contributes only to stage 2 of this test method. 6.9.3.3.2.7 Receiving device cable Insertion loss: receiving device cable: The receiving device cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the receiving device cable is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the receiving device cable is taken as 0,15 dB since the uncertainty is only present in the second stage of this test method. Cable factor: receiving device cable: Cable factor is defined as the total effect of the receiving device cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency and introducing an unbalanced current into the monopole. In a radiated measurement the standard uncertainty of the cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the receiving device cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the receiving antenna cable is taken as 0,50 dB since the precautions detailed in the methods are assumed to have been observed. 6.9.3.3.2.8 Receiving device Receiving device: absolute level: This uncertainty only contributes during the second stage of the procedure if the input attenuation range setting on the receiving device has been changed from its setting in the first stage. The standard uncertainty of the contribution due to the receiving device absolute level uncertainty is designated throughout all parts of TR 102 273 [3] as uj47. NOTE 1: In this example case the standard uncertainty of the contribution due to the receiving device absolute level uncertainty (a range change is assumed) is obtained from the manufacturers data as ±0,5 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,29 dB. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 154 Receiving device: linearity: In any test in which the contribution of the absolute level uncertainty of the receiving device contributes to the combined standard uncertainty of the test i.e. it does not cancel due to the methodology, the contribution from the receiving device linearity is considered to have been included in uj47. Conversely, for any test in which the absolute level uncertainty of the receiving device does not contribute to the combined standard uncertainty the linearity of the receiving device should be included. The standard uncertainty of the contribution due to the receiving device linearity is designated throughout all parts of TR 102 273 [3] as uj48. NOTE 2: In this example case the standard uncertainty of the contribution due to the receiving device linearity is taken as 0,00 dB.
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6.9.3.3.3 Contribution from the random component
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Random uncertainty: The magnitude can be assessed from multiple measurements of the field strength measurement. The standard uncertainty of the contribution due to the random uncertainty is designated throughout all parts of TR 102 273 [3] as ui01. The field strength measurement was repeated 10 times. The following results were obtained in dBµV (before correcting for cabling and attenuator network insertion loss): - 65,4; 63,4; 66,0; 65,3; 63,0; 64,9; 65,2; 66,8; 65,5; 63,7. Converting to linear terms: - 1,862 × 10-3; 1,479 × 10-3; 1,995 × 10-3; 1,841 × 10-3; 1,413 × 10-3; 1,758 × 10-3; 1,820 × 10-3; 2,188 × 10-3; 1,884 × 10-3; 1,531 × 10-3; The two sums X and Y are calculated: - X = the sum of the measured values = 17,77 × 10-3; - Y = the sum of the squares of the measured values = 32,10 × 10-6 V2. ( ) = − × − × = − − = − − 1 10 10 10 77 , 17 10 10 , 32 1 2 3 6 2 n n X Y uc random 238,3 ×10-6 (formula 5.6) As the result is obtained as the mean value of 10 measurements and the standard uncertainty of the random uncertainty is: dB ,17 1 5, 11 100 10 777 ,1 10 3, 238 3 6 = × × × = − − j random u NOTE: In this example case the standard uncertainty of the contribution due to the random uncertainty is 1,17 dB. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 155
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6.9.3.3.4 Summary table of contributions
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A complete list of all the contributions to this part of the test method is given in table 46. Table 46: Contributions from the monopole field measurement uj or i Description of uncertainty contributions dB uj36 mismatch: transmitting part 0,00 uj37 mismatch: receiving part 0,11 uj38 signal generator: absolute output level 0,58 uj39 signal generator: output level stability 0,00 uj41 insertion loss: signal generator cable 0,00 uj19 cable factor: signal generator cable 0,50 uj40 insertion loss: signal generator attenuator 0,00 uj34 ambient effect 0,00 uj33 Stripline: influence of site effects 0,00 uj31 Stripline: antenna factor of the monopole 1,15 uj40 insertion loss: monopole attenuator 0,10 uj41 insertion loss: receiving device cable 0,15 uj19 cable factor: receiving device cable 0,50 uj47 receiving device: absolute level 0,29 uj48 receiving device: linearity 0,00 ui01 random uncertainty 1,17 The standard uncertainties from table 46 should be combined by RSS in accordance with TR 102 273 [3], part 1, sub-part 1, clause 5. This gives the combined standard uncertainty (uc field measurement using a monopole) for the field measurement using a monopole in dB. The value of uc field measurement using a monopole is calculated as 1,91 dB.
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6.9.3.3.5 Expanded uncertainty for the receiver sensitivity measurement
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The combined standard uncertainty of the results of the receiver sensitivity measurement is the combination of the components outlined in clauses 6.9.3.1.4 and 6.9.2.4.4. The components to be combined are uc measurement of the EUT and uc field measurement using a monopole. dB 2,90 = 91 ,1 18 ,2 2 2 + = c u The expanded uncertainty is ±1,96 x 2,90 = ±5,68 dB at a 95 % confidence level.
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6.9.3.4 Uncertainty contributions: Stage 2: Field measurement using 3-axis probe
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In this case, field measurement involves the use of a 3-axis probe and measuring the vertical component of the electric field. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 156
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6.9.3.4.1 Contributions from the mismatch components
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Whereas figure 41 shows schematically the equipment set-up for field measurement using a 3-axis probe, figure 42 provides a detailed picture of the individual uncertainty contributions. 150 termination Load Central axes of Signal generator Ferrite beads 10dB attenuator ΩΩΩΩ Stripline 3 axis probe Digital readout Figure 41: Stage 2: Field measurement using a 3-axis probe Mismatch: transmitting part: The mismatch uncertainty between the signal generator, signal generator cable, signal generator attenuator and the Stripline input can be calculated from the approach described in annex G. The mismatch uncertainty through this network does, however, contribute equally to both stages of the test for cases in which a field strength measurement is subsequently performed since there are no changes from stage 1 to this part of the test set-up. The standard uncertainty of the contribution due to the mismatch in the transmitting part is designated throughout all parts of TR 102 273 [3] as uj36. NOTE 1: In this example case the standard uncertainty of the contribution due to mismatch in the transmitting part is taken as 0,00 dB, since the uncertainty is systematic i.e. it produces the same offset in both stages. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 157 Cable factor Cable loss Stripline Digital readout Signal generator Signal generator cable 1 Signal generator Attenuator 1 10 dB Radiated Loss to 3 axis probe Stripline coupling resonances, etc. Site effects Indicating device 3 axis probe + Room Mismatch Mismatch Mismatch + + + Figure 42: Schematic of the field measurement using a 3-axis probe
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6.9.3.4.2 Contributions from the individual components
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6.9.3.4.2.1 Signal generator Signal generator: absolute output level: In this test method, the uncertainty due to the setting of the signal generator's absolute output level contributes to both stages. In stage 1, the output level is individually adjusted at each of 8 different positioning angles whilst in stage 2, after an inspection (or calculation) of the 8 different values, the signal generator is set to a specific output level. The standard uncertainty of the contribution due to the signal generator absolute output level uncertainty is designated throughout all parts of TR 102 273 [3] as uj38. Its value can be obtained from the manufacturer's data. NOTE 1: In this example case the uncertainty of the contribution due to the signal generator absolute output level is obtained from the manufacturers data sheet as ±1,0 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,58 dB. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 158 Signal generator: output level stability: In any test in which the contribution of the absolute level uncertainty of the signal generator contributes to the combined standard uncertainty of the test i.e. it does not cancel due to the methodology, the contribution from the output level stability is considered to have been included in the signal generator absolute output level, uj38. Conversely, for any level in which the absolute level uncertainty of the signal generator does not contribute to the combined standard uncertainty, the output level stability of the signal generator should be included. The standard uncertainty of the contribution due to the signal generator output level stability is designated throughout all parts of TR 102 273 [3] as uj39. Its value can be derived from manufacturers' data sheet. NOTE 2: In this example case the standard uncertainty of the contribution due to the signal generator output level stability is taken as 0,00 dB as it is covered by the absolute level uncertainty. 6.9.3.4.2.2 Signal generator cable Insertion loss: signal generator cable: The signal generator cable has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the cable is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator cable is designated throughout all parts of TR 102 273 [3] as uj41. NOTE 1: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator cable is taken as 0,00 dB as a field strength measurement is performed using the 3-axis probe. Cable factor: signal generator cable: Cable factor is defined as the total effect of the signal generator cable's influence on the measuring system including its interaction with the site. It consists of the leakage caused by cable screening inefficiency and introducing an unbalanced current into the Stripline. In a radiated measurement the standard uncertainty of the uncertainty due to cable factor, associated with each cable, is 0,5 dB provided that the precautions detailed in the methods have been observed. i.e. routing and dressing of cables with ferrites. If no prevention has been attempted the standard uncertainty is 4,0 dB (justification for these values is given in TR 102 273 [3], part 1, sub-part 2, annex E). The standard uncertainty of the contribution due to the cable factor of the signal generator cable is designated throughout all parts of TR 102 273 [3] as uj19. NOTE 2: In this example case the standard uncertainty of the contribution due to the cable factor of the signal generator cable is taken as 0,00 dB since the precautions detailed in the methods have been observed and the field strength is to be measured. 6.9.3.4.2.3 Signal generator attenuator Insertion loss: signal generator attenuator: The signal generator attenuator has an insertion loss as well as an uncertainty associated with the measurement of its magnitude. The value of insertion loss and its uncertainty remain valid provided the attenuator is not used outside the manufacturer's specification. At any given frequency the insertion loss acts as a systematic offset and contributes equally to both stages of the measurement. The standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator attenuator is designated throughout all parts of TR 102 273 [3] as uj40. NOTE: In this example case the standard uncertainty of the contribution due to the insertion loss uncertainty of the signal generator attenuator is 0,00 dB since the precautions detailed in the methods have been observed and the field strength is to be measured. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 159 6.9.3.4.2.4 Site factors Ambient effect: Uncertainty is introduced as a result of local ambient signals raising the noise floor at the measurement frequency. The standard uncertainty of the contribution due to the ambient effect is designated throughout all parts of TR 102 273 [3] as uj34. The values of the standard uncertainties should be taken from table 47. Table 47: Uncertainty contribution: Ambient effect Receiving device noise floor (generator OFF) is within: Standard uncertainty of the contribution 3 dB of measurement 1,57 dB 3 dB to 6 dB of measurement 0,80 dB 6 dB to 10 dB of measurement 0,30 dB 10 dB to 20 dB of measurement 0,10 dB 20 dB or more of the measurement 0,00 dB NOTE 1: In this example case the standard uncertainty of the contribution due to the ambient effect is taken as 0,00 dB since the Stripline is assumed to have been placed in a shielded room. Stripline: influence of site effects: The influence of site effects comprise those effects, resulting from not observing the recommendations given in EN 55020 [7] regarding positioning of the Stripline and layout of absorber. These can lead to incorrect received levels i.e. values which differ from theoretical calculations. The standard uncertainty of the contribution due to the influence of site effects is designated throughout all parts of TR 102 273 [3] as uj33. NOTE 2: In this example case the standard uncertainty of the contribution due to the influence of site effects is taken to be 0,00 dB since in this test method, site effects contribute equally to both stages as the recommendations are assumed to have been fully observed. Stripline: characteristic impedance: This uncertainty contribution results from the difference between the free-space wave impedance (377 Ω) for which the 3-axis probe had been developed and that for the Stripline (150 Ω). The standard uncertainty of the contribution due to the characteristic impedance of the Stripline is designated throughout all parts of TR 102 273 [3] as uj26. NOTE 3: In this example case the standard uncertainty of the contribution due to the characteristic impedance of the Stripline is taken as having a standard uncertainty of 0,58 dB. Stripline: mutual coupling of the 3-axis probe to its image in the plates: This contribution is to take account of the fact that the probe has images in both plates of the Stripline. The standard uncertainty of the contribution due to the mutual coupling of the 3-axis probe to its image in the plates is designated throughout all parts of TR 102 273 [3] as uj25. NOTE 4: In this example case the uncertainty of the contribution due to the mutual coupling of the 3-axis probe to its image in the plates is taken as ±0,5 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,29 dB. 6.9.3.4.2.5 3-axis probe field measurement Stripline: field strength measurement as determined by the 3-axis probe: The standard uncertainty of the contribution, due to the field strength measurement uncertainty as determined by the 3-axis probe, is designated throughout all parts of TR 102 273 [3] as uj28. Its value can be derived from the manufacturers data sheet. NOTE: In this example case the uncertainty of the contribution due to the field strength measurement as determined by the 3-axis probe is obtained from the manufacturer's data sheet as ±1 dB. As nothing is said about the distribution of this uncertainty, a rectangular distribution (see TR 102 273 [3], part 1, sub-part 1, clause 5.1.2) in logs is assumed, and the standard uncertainty is calculated as 0,58 dB. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 160
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6.9.3.4.3 Contribution from the random component
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Random uncertainty: The magnitude can be assessed from multiple measurements of the receiver sensitivity. The standard uncertainty of the contribution due to the random uncertainty is designated throughout all parts of TR 102 273 [3] as ui01. The field strength measurement was repeated 10 times. The following results were obtained in dBµV (before correcting for cabling and attenuator network insertion loss): - 65,4; 63,4; 66,0; 65,3; 63,0; 64,9; 65,2; 66,8; 65,5; 63,7. Converting to linear terms: - 1,862 × 10-3; 1,479 × 10-3; 1,995 × 10-3; 1,841 × 10-3; 1,413 × 10-3; 1,758 × 10-3; 1,820 × 10-3; 2,188 × 10-3; 1,884 × 10-3; 1,531 × 10-3; The two sums X and Y are calculated: - X = the sum of the measured values = 17,77 × 10-3; - Y = the sum of the squares of the measured values = 32,10 × 10-6 V2. ( ) = − × − × = − − = − − 1 10 10 10 77 , 17 10 10 , 32 1 2 3 6 2 n n X Y uc random 238,3 ×10-6 (formula 5.6) As the result is obtained as the mean value of 10 measurements and the standard uncertainty of the random uncertainty is: dB 1,17 5, 11 100 10 777 ,1 10 3, 238 3 6 = × × × = − − j random u NOTE: In this example case the standard uncertainty of the contribution due to the random uncertainty is evaluated as 1,17 dB. See also the note relating to the random uncertainty in clause 6.4.7.
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6.9.3.4.4 Summary table of contributory components
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A complete list of all the contributions to this part of the test method is given in table 48. Table 48: Contributions from the 3-axis probe field measurement uj or i Description of uncertainty contributions dB uj36 mismatch: transmitting part 0,00 uj38 signal generator: absolute output level 0,58 uj39 signal generator: output level stability 0,00 uj41 insertion loss: signal generator cable 0,00 uj19 cable factor: signal generator cable 0,50 uj40 insertion loss: signal generator attenuator 0,00 uj34 ambient effect 0,00 uj33 Stripline: influence of site effects 0,00 uj26 Stripline: characteristic impedance 0,58 uj25 Stripline: mutual coupling of the 3-axis probe to its image in the plates 0,29 uj28 Stripline: field strength measurement as determined by the 3-axis probe 0,58 ui01 random uncertainty (see note in clause 6.4.7) 1,17 ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 161 The standard uncertainties from table 48 should be combined by RSS in accordance with TR 102 273 [3], part 1, sub-part 1, clause 5. This gives the combined standard uncertainty (uc 3-axis probe) for the receiver sensitivity measurement in dB. The value of uc 3-axis probe is calculated as 1,65 dB.
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6.9.3.4.5 Expanded uncertainty for the receiver sensitivity measurement
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The combined standard uncertainty of the results of the receiver sensitivity measurement is the combination of the components outlined in clauses 6.9.3.1.4 and 6.9.3.4.4. The components to be combined are uc EUT measurement and uc 3-axis probe. dB 2,73 = 65 ,1 18 ,2 2 2 + = c u The expanded uncertainty is ±1,96 x 2,73 = ±5,36 dB at a 95 % confidence level.
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6.10 Uncertainty of fully automated test systems.
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So far the uncertainty calculations for manual measurements have been examined. But in many radio technologies testing is performed using fully automated test systems. In technologies such as GSM, DECT and Bluetooth, certification and type approval is based on measurements using such test systems. This gives an improvement in reproducibility and test time compared to manual measurements, but the measurement uncertainty for such test systems has yet to be documented. One major reason is that the procedures and calculations outlined for the more simple test methods do not cover fully automated test systems due to the complexity, even though the basic principles still apply. The measurements are basically carried out in the same way as the manual measurements. A conducted power measurement is still performed by connecting the EUT to a power measuring instrument through a combining network consisting of cables, attenuators and maybe filters. Then a power measurement is carried out, and a correction factor is applied to the reading of the instrument to get the final test result. Similarly a receiver measurement is done by connecting one or more RF signal generators to an EUT through a combining network and adjusting the output levels from the generators each time using correction factors. The major difference between the manual measurement and the fully automated test system measurement is how this correction factor is derived. For fully automated systems this is normally done by executing Path Compensation procedures. The purpose of path compensation procedures is (as mentioned) to generate correction factors, and in a well designed test system these correction factors eliminate all errors leaving "only" some irreducible stability and mismatch errors. In most fully automated test systems the path compensation procedures are a combination of measurements performed at the same time as the actual measurement as well as periodic measurements on sub parts of the test system, but to have a full picture of the uncertainties involved the path compensation and the actual measurement should be seen as one procedure. With a well designed overall path compensation procedure it is easy to see that if all instruments and components were stable and linear and had an impedance of exactly 50 Ohms then the only uncertainty contribution would be the absolute uncertainty of the power meter. But as with the manual measurements the instruments are not totally stable, and there are mismatch uncertainties due to non-ideal coaxial components. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 162
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6.10.1 Test system properties
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A fully automated test system normally consists of a set of test instruments (usually exactly the same as the ones used in the manual measurements), but in addition it contains a switch unit. The purpose of the switch unit is to create the correct set-ups using attenuators, power combiners, filters, amplifiers, and cables. The set-ups inside the switch unit is then realized using RF switches controlled by a system controller – normally a PC with appropriate test software. A switch unit often consists of more than 100 components. A fully automated test system can perform all the common radio tests: Transmitter tests including output power, timing, modulation, output spectrum, and spurious emissions, and receiver tests including 1, 2, and 3 signal measurements as the test system contains 3 RF signal generators. The BER measurement or the signal-to-noise measurement is not shown. It is assumed to be either a part of signal generator 1 or some external equipment connected to the base band output of the EUT. It is not important for the analysis of the test system because once the level uncertainties are calculated, the rest (BER , signal-to-noise, modulation, or timing) are the same as with the manual measurements. Signal generator 1 generates the wanted signal Signal generator 2 generates the low frequency unwanted signal Signal generator 3 generates the high frequency unwanted signal (Both signal generator 2 and 3 can also produce in-band signals for 3 signal measurements.) The signal analyser is capable of measuring both power, frequency, and modulation, but for the purpose of this analysis only power is considered. Tests are normally carried out as follows: The EUT is connected to a specific EUT connector on the test system. Then the test operator selects and activates some tests, and some test results are produced by the test system. Depending on the degree of automation the operator may be prompted to control the EUT from time to time – for instance to set up a connection with the EUT or to switch the EUT to a different channel. It is normally not visible to the operator how the tests are carried out by the test system, but this is often described in the test system documentation. As a part of a test the path compensation related to that test can be run prior to the actual testing. This depends on the flexibility and complexity of the switch unit and the test software.
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6.10.2 General aspects of the measurement uncertainty
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As indicated previously, the main difference between manual testing and a fully automated test system is how the correction factors are generated. From a measurement uncertainty point of view this is very important because this is X one of the major contributions to the overall RF level uncertainty of the actual measurement. The other contributions are: - Instruments stability; - Instruments linearity; - Mismatch between the EUT and the test system; - RF switch repeatability. Often it is the power meter that is the essential instrument in the path compensation, and the one which provides the traceability to external standards. The uncertainty of the correction factor is very dependant on how the correction factor is measured. The contributions to the uncertainty are: - Absolute power meter uncertainty; - Instruments stability; - Instruments linearity; - Mismatch between the instruments and the individual components of the switch unit; - Errors due to interpolation between correction factors at different frequencies. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 163 As will be shown, the mismatch uncertainty is the most complex component of the overall measurement uncertainty. It can for complex fully automated systems be the combination of several thousands of individual mismatch contributions. The amount of contributions can, however, be reduced by disregarding very small contributions. The contributions tend to be greater than with the manual measurements because more cables and switches are necessary to provide the needed flexibility. For the purpose of the measurement uncertainty analysis, two fully automated test systems will be considered: a "simple" test system, and a "complex" test system.
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6.10.3 The "simple" test system
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The test system is shown in figure 43: Figure 43: The "simple" test system
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6.10.3.1 Transmitter measurement
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For the "simple" test system the path compensation procedures and the actual measurement for transmitter measurements using the correction factors, are as follows: The path compensation is performed as follows: - Switch 1 is set so the generators are connected to the Sig. gen. out connector. - Switch 2 is set so the signal analyser is connected to the EUT connector. Measurement 1: 1) A power meter is connected to the RF out connector through a cable and a 10 dB attenuator. 2) The RF generators are in turn adjusted to a suitable level which gives a reading in the operational range of the power meter. When one generator is active the others are turned down, so they do not contribute to the measurement, but their output impedance is still 50 ohms. A series of measurements covering the frequency range of interest is carried out and for each frequency the reading is stored by the test system. Signal analyser Generator 1 Generator 2 Generator 3 Power combiner Filters and attenuators Switch 2 Switch 1 Sig. gen. out EUT EUT conn. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 164 Measurement 2: 1) The power meter is removed and the open end of the 10 dB attenuator is connected to the EUT connector. For all the frequencies and generator level settings in step 4 the power level is measured by the signal analyser. This is preferably done with the same analyser setting as the one used in the actual EUT measurement. The readings are stored by the test system. For each frequency the correction factor is calculated as the difference (in dB) between the signal analyser reading XX and the power meter XX. Measurement 3: ( The actual measurement): 1) The EUT is connected to the EUT connector. 2) The power level of the signal generated by the EUT is measured, and the signal analyser reading is stored by the test system. 3) The final result is then calculated as the reading from step 2 (in dBm) minus the correction factor calculated in the path compensation procedure at the appropriate frequency. (If a correction factor at the measuring frequency does not exist it is found by interpolation between the two correction factors at the nearest frequencies on each side.) 6.10.3.1.1 Error analysis The combined path compensation procedure and the actual test consists of 3 individual measurements as shown in figure 44: two measurements in the path compensation part and one in the actual measurement. In each of the 3 measurements a signal source is connected to a measuring instrument through a network consisting of several components and a level is measured. In the following the total procedure is analysed. The following assumptions apply for the analysis: - The generator has a static error of Egen dB in measurement 1 (compared to the setting of the generator level); - Between measurement 1 and measurement 2 there is a generator drift error dEgen dB; - The attenuation between the generator and the sig. gen. out connector is Att1 dB; - Between measurement 1 and measurement 2 there is an attenuation change in the network between the generator and the sig. gen. out. connector of dAtt1 dB; - The attenuation of the external cable and attenuator is Att2 dB; - Between measurement 1 and measurement 2 there is an attenuation change in the external cable and attenuator of dAtt2 dB; - There is a static error of Epow dB in power measurements using the power meter; - The attenuation between the EUT connector and the signal analyser i Att3 dB; - Between measurement 2 and measurement 3 there is an attenuation change in the network between the EUT connector and the signal analyser of dAtt3 dB; - There is a static error of Esa dB in the power measurement in measurement 2 using the signal analyser; - Between measurement 2 and measurement 3 there is a signal analyser drift error dEsa dB; - The EUT has an output power of Pout dBm; - The generator level is set to Pgen dBm in measurement 1 and 2; - If the value read from the signal analyser in measurement 3 differs from the value in measurement 2 there is a signal analyser linearity (or log fidelity) error dElog. In measurement 1 the reading on the power meter is: P1 = Pgen + Egen – Att1 – Att2 + Epow dBm ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 165 In measurement 2 the reading on the signal analyser is: P2 = Pgen + Egen + dEgen – Att1 – dAtt1 – Att2 – dAtt2 – Att3 + Esa dBm The correction factor is: Ccorr = P2 – P1 = (Pgen + Egen + dEgen – Att1 – dAtt1 – Att2 – dAtt2 – Att3 + Esa) – (Pgen + Egen – Att1 – Att2 + Epow) = dEgen – dAtt1 – dAtt2 – Att3 + Esa – Epow dB In measurement 3 the reading from the signal analyser is: P3 = Pout – (Att3 + dAtt3) + Esa + dEsa + dElog dBm The measured result after having applied the correction factor to the reading from measurement 3 is: Pmeas = P3 – Ccorr = Pout – (Att3 + d Att3) + Esa + dEsa + dElog – (dEgen – dAtt1 – dAtt2 – Att3 + Esa – Epow) = Pout + dAtt3 + dEsa +dElog – dEgen + dAtt1 + dAtt2 + Epow dBm As can be seen from the calculated result all static errors in the combined measurement except the power meter error have cancelled. Apart from that only the drift and linearity errors remain. The remaining errors are: - the absolute uncertainty of the power meter - the linearity (or log fidelity) of the signal analyser due to the fact that the level measured by the signal analyser in actual measurement may be different from the level measured in the path compensation - signal analyser drift between the different measurements - signal generator drift between the different measurements - repeatability of the switches in the switch unit - change of the insertion losses between the different measurements Since the path compensation is performed at discrete frequencies there is an additional error - error due to interpolation between correction factors at different frequencies Finally, in addition to the uncertainties mentioned there is a mismatch uncertainty in each measurement. The mismatch uncertainty is analysed in clause 6.10.3.1.2
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6.10.3.1.2 Mismatch uncertainty
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For each measurement there is a mismatch uncertainty which is the combination of all the mismatch uncertainties between all of the parts in the path between the signal source and the measuring instrument. Fortunately many of the mismatch uncertainties are cancelled due to the total procedure. Firstly the two measurements involved in the path compensation procedure are considered. The correction factor is the difference between the two values measured; this means that the total error is the difference between the errors in the two measurements, so all errors which are identical cancel. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 166 Signal analyser Generator Attenuators, cables, and filters Combiner and cables Switch unit Switch 2 Switch 1 Sig. gen. out EUT conn. 10 dB att Power meter Measurement 1:Path compensation: power meter reading Signal analyser Generator Attenuators, cables, and filters Combiner and cables Switch unit Switch 2 Switch 1 Sig. gen. out EUT conn. 10 dB att Measurement 2:Path compensation: signal analyser reading Signal analyser Generator Attenuators, cables, and filters Combiner and cables Switch unit Switch 2 Switch 1 Sig. gen. out EUT conn. EUT Measurement 3: The actual measurement Figure 44: The three set-ups in the transmitter measurement From figure 44 it can be seen that all the mismatch uncertainties from the path between the 10 dB attenuator and the RF signal generators cancel because they are present in both measurements 1 and 2. In measurement 1 all the mismatch uncertainties associated with the power meter remain. The rest are cancelled. In measurement 2 all mismatch uncertainties from the path between the 10 dB attenuator and the signal analyser remain, as they only appear here. For the same reason all the mismatch uncertainties where one of the parts is to the right of the EUT connector, and the other part is to the left of the EUT connector remain. Then when measurement 3 (the actual measurement) is taken into account it can be seen that parts of the mismatch uncertainties from measurement 2 cancel, since they are also present in measurement 3: all the uncertainties from the path between the EUT connector and the signal analyser. What is left in measurement 3 are all the mismatch uncertainties where the EUT is one of the parts. The rest cancel with measurement 2. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 167 The total mismatch uncertainty in the total measurement including the path compensation is then the combination of the following part uncertainties: 1) all mismatch uncertainties where the power sensor is one of the parts (measurement 1); 2) all mismatch uncertainties where the two parts are on each side of the EUT conn. (measurement 2); 3) all mismatch uncertainties where the EUT is one of the parts (measurement 3). Based on this the calculation of the total mismatch uncertainty can be done in two ways. If all VSWRs and insertion losses (or gains) of the individual components in the test system are known all the contributions can be calculated and combined. But a more simple approach is to measure (or estimate by other methods) the reflection coefficient Rg of the free end of the 10 dB attenuator, measure (or take from the specification sheet) the reflection coefficient Rp of the power meter, measure the reflection coefficient Ri of the EUT connector, and measure (or estimate) the reflection coefficient Reut of the EUT. If these 4 reflection coefficients are known, the total uncertainty is the combination of - Ri*Rp/√2 (from measurement 1); - Rg*Ri//√2 (from measurement 2); - Reut*Ri//√2 (from measurement 3). This is exactly the same result as if the measurement had been done manually with a generator, a power meter, and a signal analyser if the switch unit paths are considered as parts of the individual instruments. But the method of analysing the "simple" test system is important, because the same method is used in the "complex" test system, and here the result are not similar to any simple manual measurement.
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6.10.3.2 Receiver measurements
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For the "simple" test system the path compensation procedures for receiver measurements and the actual measurement using the correction factors, are as follows: The path compensation (measurement 1) is done as follows: 1) Switch 1 and switch 2 is set so the generators are connected to the EUT connector. 2) Then the power meter is connected to the EUT connector. 3) The RF generators are in turn adjusted to a suitable level which gives a reading in the operational range of the power meter. When one generator is active the others are turned down, so they do not contribute to the measurement, but their output impedance is still 50 ohms. A series of measurements covering the frequency range of interest is done and for each frequency the reading are stored by the test system. 4) For each frequency point the correction factor is calculated as the difference (in dB) between the power meter reading and the generator setting. The actual measurement (measurement 2) is done as follows: 1) The EUT is connected to the EUT connector. 2) The generator is set to the wanted signal level (in dBm) minus the correction factor at the appropriate frequency. (If a correction factor at the measuring frequency does not exist it is found by interpolation between the two correction factors at the nearest frequencies on each side.) 3) Then the appropriate receiver measurement is done (BER or signal-to-noise ratio). ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 168 6.10.3.2.1 Error analysis The combined path compensation procedure and the actual test consists of 2 individual measurements as shown in figure 45: two measurements in the path compensation part and one in the actual measurement. In each of the 2 measurements a signal source is connected to a measuring instrument through a network consisting of several components and a level is measured. In the following the total procedure is analysed. The following assumptions apply for the analysis: - The generator has an static error of Egen dB in measurement 1(compared to the setting of the generator level). - The generator has a linearity/log fidelity error of Elog dB between the levels in measurement 1 and measurement 2. - Between measurement 1 and measurement 2 there is a generator drift error dEgen dB. - The attenuation between the generator and the EUT connector is Att1 dB in measurement 1. - Between measurement 1 and measurement 2 there is an attenuation change in the network between the generator and the EUT connector of dAtt1 dB. - There is a static error of Epow dB in the power meter measurement in measurement 1. - The generator level is set to Pgen1 dBm in measurement 1. - The wanted level at the EUT connector is Pwanted dBm in the actual measurement. In measurement 1 the reading on the power meter is: P1 = Pgen1 + Egen – Att1 + Epow dBm The correction factor is calculated to be Ccorr = Pgen1 – P1 = Pgen1 - (Pgen1 + Egen – Att1 + Epow) = -Egen + Att1 – Epow In measurement 2 the generator level is set to Pgen2 = Pwanted + Ccorr = Pwanted -Egen + Att1 – Epow dBm The level at the EUT connector in the actual measurement is Peut = Pgen2 + Egen + dEgen + Elog – Att1 – dAtt1 = Pwanted -Egen + Att1 – Epow + Egen + dEgen + Elog – Att1 – dAtt1 = Pwanted – Epow + dEgen + Elog – dAtt1 As can be seen from the calculated result, again all static errors in the combined measurement except the power meter error have cancelled. Apart from that only the drift and linearity errors remain. The remaining errors are: - the absolute uncertainty of the power meter - the linearity (or log fidelity) of the signal generator due to the fact that the level setting of the generator in actual measurement may be different from the level setting in the path compensation - change of the insertion loss between the path compensation and the actual measurement including repeatability of the switches in the switch unit Since the path compensation is performed at discrete frequencies there is an additional error: - error due to interpolation between correction factors at different frequencies ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 169 Finally, in addition to the uncertainties mentioned there is a mismatch uncertainty in each measurement. The mismatch uncertainty is analysed in clause 6.10.3.2.2
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6.10.3.2.2 Mismatch uncertainty
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Signal analyser Generator Attenuators, cables, and filters Combiner and cables Switch unit Switch 2 Switch 1 Sig. gen. out EUT conn. Path compensation: power meter reading Power meter Signal analyser Generator Attenuators, cables, and filters Combiner and cables Switch unit Switch 2 Switch 1 Sig. gen. out EUT conn. The actual measurement EUT Figure 45: The two set-ups in a receiver measurement As can be seen from figure 45, performing a similar analysis as with the transmitter measurement, the remaining mismatch uncertainty from the first measurement is the combination of all the mismatch uncertainties associated with the power meter, and from the actual measurement all the mismatch uncertainties associated with the EUT. Again, based on this the calculation of the total mismatch uncertainty can be done in two ways. If all VSWRs and insertion losses (or gains) of the individual components in the test system are known all the contributions can be calculated and combined. But a more simple approach is to measure (or estimate by other methods) the reflection coefficient Ro of the EUT connector, measure (or take from the specification sheet) the reflection coefficient Rp of the power meter, and measure (or estimate) the reflection coefficient Reut of the EUT. If these 3 reflection coefficients are known, the total uncertainty is the combination of - Ro x Rp/√2 (from the path compensation) - Reut x Rp//√2 (from the actual measurement) ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 170 Again exactly the same result as if the measurement had been done manually with a generator and power meter if the switch unit paths are considered as parts of the individual instruments. For the "simple" test system it was not necessary to go through this lengthy analysis to get the uncertainty, because the analogy to the simple measurements can be directly seen. But the method is important to understand and to use, because it is needed for the analysis of more complex test systems where the similarity to simple measuring set-ups does not exist.
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6.10.4 The "complex" test system
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As the "simple" test system, the "complex" system consists of a set of measuring instruments and a switch unit. And as with the "simple" test system the RF level traceability is provided by very accurate power meters rather than the other RF instruments. The main difference between the "simple" and the "complex" test system is that the path compensation procedures and RF level setting procedures are more complex and involve reference and switch points inside the switch unit, which cannot be accessed from the outside. The benefit is that most of the path compensation procedures can be done directly in connection with the actual measurements without need of test operator intervention. This reduces the potential stability errors which can be present in measurements with "simple" test systems due to the time between path compensation and measurements. The error sources are generally the same for the two types of test systems, and the methods used to perform the analysis are the same, but the mismatch uncertainty is very complex, and can be difficult to estimate. Signal analyser Gen 1 Gen 2 Gen 3 Power splitter 6 dB comb. 2 Att. 1 10 dB 6 dB comb. 1 Power sensor A S11 S12 S10 Dir. coupler 2 S22 S21 Att. 3 20 dB S24 S23 S18 S17 EUT conn. Sig.gen.out conn. Dir. coupler 1 Ext. signalling device Att. 2 10 dB S1 S2 S3 S8 S4 S5 S6 S7 S9 Att. 4 20 dB S20 S19 1 2 3 4 5 6 1 2 3 4 5 6 S26 S25 1 2 3 4 5 6 1 2 3 4 5 6 S27 S28 50 Ohm 50 Ohm 50 Ohm 50 Ohm S16 Figure 46: A complex test system Figure 46 shows a "complex" type of test system which is capable of doing all normal RF measurements. More complicated test systems exist, but the following analysis will be similar for all of them. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 171 The path compensation for this test system consists of two procedures: an external path compensation procedure which requires the test operator to connect cables and power meter to some external connectors and an internal path compensation procedure. This external path compensation characterizes a small part of the switch unit consisting of only cables, attenuators, and switches – in other words passive components which can be assumed to be stable over a relatively long time period. For transmitter measurements this part of the switch unit is the part from switch S5 to the EUT connector. For receiver measurements it is the part between switch S4 and the EUT connector. The rest of the switch unit and the instruments are covered by internal path compensation procedures which do not require test operators intervention, and they are run prior to the actual measurements as an integral part of each test. As with the "simple" test system the traceability is provided by an external power meter, which is the only instrument where the absolute uncertainty is important. Any systematic errors in the other instruments are compensated for. The error sources are basically the same as with the "simple" test system: - Absolute power meter uncertainty. - Instruments stability. - Instruments linearity. - Mismatch between the instruments and the individual components of the switch unit. - Errors due to interpolation between correction factors at different frequencies. The difference compared to a "simple” test system is that the mismatch uncertainty is more complex because there are more procedures involved in the testing and path compensations and because some of the reflection coefficients of interest are inside the switch unit. To measure them, the switch unit would have to be disassembled.
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6.10.4.1 Receiver measurements
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For the purpose of analysing receiver measurements the "complex" test system can be simplified as shown in figure 47: EUT Sub network A Sub network B Generator Power meter A EUT conn S4 Sub network C Switch unit Figure 47: Model for analysis of receiver measurements In figure 47: Sub network A consists of everything between a generator and switch S4. Sub network B consists of everything between switch S4 and the EUT connector. Sub network C consists of everything between switch S4 and power meter A. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 172 Each sub network contain cables, switches, attenuators, filters, and other components. The external path compensation is performed as follows. This is not done in connection with every measurement, but may be done with for instance 3 month intervals. Measurement 1: 1) A power meter (power meter B) is connected to the EUT connector. Switch S4 is set so the generator is connected to power meter B. 2) The RF generator is set to a level which gives a reading in the operational range of the power meter. When one generator is active the others are turned down, so they do not contribute to the measurement, but their output impedance is still 50 ohms. A series of measurements covering the frequency range of interest is done and for each frequency the reading are stored by the test system. Measurement 2: 1) Then switch S4 is set so the generator is connected to power meter A. 2) For all the frequencies and generator level settings in measurement 1 step 2 the power level is measured by power meter A. The readings are stored by the test system 3) For each frequency the correction factor is calculated as the difference (in dB) between the reading from power meter B and power meter A. These are the external correction factors (path compensation data) stored by the test system. The internal path compensation is performed as follows. This is done immediately prior to every measurement as an integral part of the test case. Measurement 3: 1) Switch S4 is set so the generator is connected to power meter A. 2) Then the RF generator is set to a level which gives a reading in the operational range of the power meter. When one generator is active the others are turned down, so they do not contribute to the measurement, but their output impedance is still 50 ohms. A series of power meter readings and generator level settings covering the frequency range of interest is done and for each frequency the reading and setting are stored by the test system. 3) For each frequency the correction factor is calculated as the difference (in dB) between the power meter reading and the generator level setting. These are the internal correction factors (path compensation data) stored by the test system. The actual test is performed as follows. (For 2 or 3 signal measurements the following level setting procedure is done for each signal generator). Measurement 4: 1) The EUT is connected to the EUT connector. 2) Switch S4 is set so the generator is connected to the EUT connector. 3) The generator is set to the wanted signal level (in dBm) minus the external and the internal correction factor at the appropriate frequency. (If a correction factor at the measuring frequency does not exist it is found by interpolation between the two correction factors at the nearest frequencies on each side.) 4) Then the appropriate receiver measurement is done (BER or signal-to-noise ratio). ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 173
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6.10.4.1.1 Error analysis
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The combined path compensation procedure and the actual test consists of 4 individual measurements as shown in figure 48 to figure 50: two measurements in the external the path compensation part, one in the internal path compensation and one in the actual measurement. In each of the 4 measurements a signal source is connected to a measuring instrument through a network consisting of several components and a level is measured. In the following the total procedure is analysed. The following assumptions apply for the analysis: - The generator has an static error of Egen1 dB in the measurement 1 (compared to the setting of the generator level). - Between measurement 1 and measurement 2 there is a generator drift error dEgen1 dB. - The generator has an static error of Egen2 dB in the measurement 3(compared to the setting of the generator level). - Between measurement 3 and measurement 4 there is a generator drift and linearity error dEgen2 dB (The generator level may not be the same in the path compensation and the measurement – therefore the linearity/log fidelity error). - The attenuation between the generator and the switch S4 is AttD dB in measurement 1. - Between measurement 1 and measurement 2 there is an attenuation change in AttD of dAttD dB. - The attenuation between the input of switch S4 and the EUT connector is AttB dB in measurement 1. - Between measurement 1 and measurement 4 there is an attenuation change in AttB of dAttB dB. - The attenuation between the input of switch S4 and power meter A is AttC dB in measurement 2. - Between measurement 2 and measurement 3 there is an attenuation change in AttC of dAttC dB. - The attenuation between the generator and the switch S4 is AttA dB in measurement 3. - Between measurement 3 and measurement 4 there is an attenuation change in AttA of dAttA dB. - There is a static error of EpowA dB in the power meter A measurement in measurement 2. - Between measurement 2 and measurement 3 there is a change in EpowA of dEpowA. - The generator level is set to Pgen1 dBm in measurement 1 and 2. - The generator level is set to Pgen2 dBm in measurement 3. - The generator level is set to Pgen3 dBm in measurement 4. - The wanted level at the EUT connector is Pwanted dBm in the actual measurement. In measurement 1 the reading from power meter B is: P1 = Pgen1 + Egen1 – AttD – AttB + EpowB In measurement 2 the reading from power meter A is: P2 = Pgen1 + Egen1 + dEgen1 – AttD – dAttD – AttC + EpowA The external correction factor Ccorr1 = P1 – P2 = (Pgen1 + Egen1 – AttD – AttB + EpowB) - (Pgen1 + Egen1 + dEgen1 – AttD – dAttD – AttC + EpowA) = - dEgen1 + dAttD + AttC – EpowA – AttB + EpowB ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 174 In measurement 3 the reading from power meter A is: P3 = Pgen2 + Egen2-AttA-AttC-dAttC + EpowA + dEpowA The internal correction factor Ccorr2 = P3 – Pgen2 = Pgen2 + Egen2-AttA-AttC-dAttC + EpowA + dEpowA – Pgen2 = Egen2-AttA-AttC-dAttC + EpowA + dEpowA In measurement 4 (the actual measurement) the generator level is set to Pgen3 = Pwanted – Ccorr1 – Ccorr2 The level at the EUT connector is: P4 = Pgen3 + Egen2 + dEgen2 – AttA – dAttA – AttC – dAttC = Pwanted – Ccorr1 – Ccorr2 + Egen2 + dEgen2 – AttA – dAttA – AttB – dAttB = Pwanted – (-dEgen1 + dAttD + AttC-EpowA-AttB + EpowB) – (Egen2-AttA-AttC -dAttC + EpowA + dEpowA) + Egen2 + dEgen2 – AttA – dAttA – AttB – dAttB = Pwanted + dEgen1 – dAttD - EpowB + dAttC - dEpowA + dEgen2 – dAttA – dAttB Again, as can be seen from the calculated result, again static errors in the combined measurement except the power meter B error have cancelled. Apart from that only the drift and linearity errors remain. The remaining errors are: - the absolute uncertainty of the power meter; - the linearity (or log fidelity) of the signal generator due to the fact that the level setting of the generator in actual measurement may be different from the level setting in the path compensation; - change of the insertion loss between the path compensation and the actual measurement including repeatability of the switches in the switch unit. Since the path compensation is performed at discrete frequencies there is an additional error - error due to interpolation between correction factors at different frequencies. Finally, in addition to the uncertainties mentioned there is a mismatch uncertainty in each measurement. The mismatch uncertainty is analysed in clause 6.10.4.1.2. ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 175
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6.10.4.1.2 Mismatch uncertainties
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For the analysis of the overall mismatch uncertainty, firstly the external path compensation is analysed. The settings are shown on figure 48. (The reason for introducing sub network D is that it is not necessarily the same sub network used in the actual measurement): Power meter B Sub network D Sub network B Generator Power meter A EUT conn. S4 Sub network C Switch unit Power meter B Sub network D Sub network B Generator Power meter A EUT conn. S4 Sub network C Switch unit Measurement 1 Measurement 2 Figure 48: The external path compensation In the power meter B reading (measurement 1) the following mismatch uncertainties contribute to the reading: Between Generator and sub network D Between sub network D and switch S4 Between switch S4 and sub network B Between sub network B and power meter B Between Generator and switch S4 (through sub network D) Between sub network D and sub network B Between switch S4 and power meter B Between Generator and sub network B (through sub network D) Between sub network D and power meter B Between Generator and power meter B (through sub network D) ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 176 In the power meter A reading (measurement 2) the following mismatch uncertainties contribute to the reading: Between Generator and sub network D Between sub network D and switch S4 Between switch S4 and sub network C Between sub network C and power meter A Between Generator and switch S4 (through sub network D) Between sub network D and sub network C Between switch S4 and power meter A Between Generator and sub network C (through sub network D) Between sub network D and power meter A Between Generator and power meter A (through sub network D) As can be seen some of the mismatch uncertainties are part of both measurements (between Generator and switch S4), so they cancel. The following mismatch uncertainties remain: Between switch S4 and sub network B Between sub network B and power meter B Between sub network D and sub network B Between switch S4 and power meter B Between Generator and sub network B (through sub network D) Between sub network D and power meter B Between Generator and power meter B (through sub network D) Between switch S4 and sub network C Between sub network C and power meter A Between sub network D and sub network C Between switch S4 and power meter A Between Generator and sub network C (through sub network D) Between sub network D and power meter A Between Generator and power meter A (through sub network D) ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 177 Some of these uncertainties will cancel later in the process. Then the internal path compensation (with settings as shown in figure 49) is analysed: EUT Sub network A Sub network B Generator Power meter A EUT conn. S4 Sub network C Switch unit Measurement 3 Figure 49: The internal path compensation In the internal path compensation (measurement 3) the following mismatch uncertainties contribute to the reading: Between Generator and sub network A Between sub network A and switch S4 Between switch S4 and sub network C Between sub network C and power meter A Between Generator and switch S4 (through sub network A) Between sub network A and sub network C Between switch S4 and power meter A Between Generator and sub network C (through sub network A) Between sub network A and power meter A Between Generator and power meter A (through sub network A) As can be seen, again, some of the mismatch uncertainties are part of both the internal and the external path compensation (between switch S4 and power meter A), so they cancel. The following mismatch uncertainties remain from the total path compensation: Between switch S4 and sub network B Between sub network B and power meter B Between sub network D and sub network B Between switch S4 and power meter B Between Generator and sub network B (through sub network D) Between sub network D and power meter B Between Generator and power meter B (through sub network D) Between sub network D and sub network C ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 178 Between switch S4 and power meter A Between Generator and sub network C (through sub network D) Between sub network D and power meter A Between Generator and power meter A (through sub network D) Between Generator and sub network A Between sub network A and switch S4 Between Generator and switch S4 (through sub network A) Between sub network A and sub network C Between switch S4 and power meter A Between Generator and sub network C (through sub network A) Between sub network A and power meter A Between Generator and power meter A (through sub network A) Again, some of these uncertainties will cancel later in the process. Then the actual measurement (with settings as shown in figure 50) is analysed: EUT Sub network A Sub network B Generator Power meter A EUT conn. S4 Sub network C Switch unit Measurement 4 Figure 50: The actual measurement In the actual measurement (measurement 4) the following mismatch uncertainties contribute: Between Generator and sub network A Between sub network A and switch S4 Between switch S4 and sub network B Between sub network B and the EUT Between Generator and switch S4 (through sub network A) Between sub network A and sub network B Between switch S4 and the EUT Between Generator and sub network B (through sub network A) Between sub network A and the EUT Between Generator and the EUT (through sub network A) ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 179 As can be seen, again, some of the mismatch uncertainties are part of both path compensation and the actual measurement (between switch S4 and sub network B), so they cancel. The following mismatch uncertainties remain in the total measurement: Between sub network B and power meter B Between sub network D and sub network B Between switch S4 and power meter B Between Generator and sub network B (through sub network D) Between sub network D and power meter B Between Generator and power meter B (through sub network D) Between sub network D and sub network C Between switch S4 and power meter A Between Generator and sub network C (through sub network D) Between sub network D and power meter A Between Generator and power meter A (through sub network D) Between sub network A and sub network C Between switch S4 and power meter A Between Generator and sub network C (through sub network A) Between sub network A and power meter A Between Generator and power meter A (through sub network A) Between sub network B and the EUT Between sub network A and sub network B Between switch S4 and the EUT Between Generator and sub network B (through sub network A) Between sub network A and the EUT Between Generator and the EUT (through sub network A) ETSI ETSI TR 100 028-1 V1.4.1 (2001-12) 180
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