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1f7ea7b6418174d53d51b760f9c08c93	100 035	6.3 Test methods	First and foremost, test methods shall, of course, be reproducible. Additionally they should also be realistic with regard to failure effect, be relatively simple and be reasonably rapid to perform. Internationally accepted methods, such as those in IEC 60068 [2], usually meet these requirements. In EN 300 019 series [4] and [5], reference has been given as far as possible to IEC Publications. Significant changes in characteristics or performance due to environmental conditions are often brought about slowly. Thus in order to make a test within a reasonable time these changes need acceleration either by increasing the test severity or by "compressing" the time, etc. Many test methods are implicit accelerated tests, such as humidity and mechanical tests, although generally, and unfortunately, these have an unknown "acceleration factor". However these aspects are important when specifying the test procedure.
1f7ea7b6418174d53d51b760f9c08c93	100 035	6.4 Environmental resistibility test
1f7ea7b6418174d53d51b760f9c08c93	100 035	6.4.1 Purpose and limitations	An environmental resistibility test is generally considered as being a part of a type test. The environmental resistibility test demonstrates characteristic properties of equipment regarding its capability of withstanding certain environmental conditions. These conditions are typically specified as different applications and environmental classes with specified performance requirements. The resistibility requirements shall be a part of the basic equipment specification covering all normal applications. Thus the purpose of an environmental resistibility test is to verify - or render it possible - that equipment will survive and perform as intended when it is used, stored and/or transported. An environmental resistibility test has some inherent limitations. The most important one is that the test only covers the equipment type (e.g. the design) and not the complete population. This is because a resistibility test is generally carried out on only a few specimens hence the test cannot be a "guarantee" for production lots. The test can, however, assure that the equipment, considered as a type, is capable of resisting the expected environment. Some other limitation aspects concern the operational life of the equipment. In general a resistibility test is not able to give evidence either about the reliability or the endurability of the equipment. These aspects are discussed in clause 6.5. Finally the information obtained from a resistibility test is limited, partly because of limited evaluation after exposure and partly because of the fixed test severities (e.g. no step-stress), see figure 5, clause 6.1.
1f7ea7b6418174d53d51b760f9c08c93	100 035	6.4.2 Test sequence	In order to cover the many different influences of several environmental parameters (concerning operational and non-operational conditions), a resistibility test must comprise a number of different tests. Most tests are performed in either one, or a few sequences. This means that each specific test, after a recovery period, is succeeded by the next, specific test in a relevant sequence. Such a test procedure is truly not realistic, but practical. If required two tests can be carried out immediately after each other (a composite test) or two tests can be carried out simultaneously (a combined test). The sequence of tests is important because a conclusive result to the resistibility test may depend on the test sequence. For example, the result of a final insulation test may change significantly depending on whether the test sequence is a dry heat test followed by a damp heat test or vice versa. The general rule is to choose the most severe sequence - if it is reasonably relevant - because the purpose of testing is to demonstrate the potential failure mechanisms. This rule is valid for resistibility testing. Furthermore another rule shall be considered relating to the objective of obtaining early information about failure tendencies or major failures (in order to obtain the most significant information as early as possible). In this case severe - and preferably short and cheap tests - are conducted at the beginning, while the less severe, prolonged and expensive tests are placed later in the sequence. Naturally some of these considerations and rules may be contradictory and not always applicable. If this is so then the test sequence can be based on what is most likely to occur in practice. Any test sequences suggested in the present document aim to utilize the rules mentioned. ETSI ETSI TR 100 035 V2.1.2 (2004-02) 23 If the testing concerns investigation of a prototype during development only one or a few specimens may be available. In this situation the objective of the test sequence is to keep the specimen "alive" as long as possible in order to obtain as much information as possible before damage occurs. Hence the sequence shall start with the least severe test.
1f7ea7b6418174d53d51b760f9c08c93	100 035	6.4.3 Environmental test programme	Complete environmental testing for a specific equipment type typically employs three environmental test specifications: • storage; • transportation; • in use. Each specification comprises several "individual" tests which can be performed in a stated order, i.e. sequence. In order to realize all the testing activities it is necessary to construct a complete environmental test programme. This programme shall be based on the relevant test specifications, and take into account other considerations and detailed information, such as: • equipment functions, properties and technologies; • available resources, time, test facilities, funds, etc.; • engineering experience and judgement; • common sense. The overall objective is to perform the complete programme in an efficient way e.g. by: • utilizing results from previous tests; • deleting needless tests; • avoiding thorough functional testing, if possible. Thus the environmental test programme requires careful and specific consideration. This means that the programme shall be prepared by the test engineer in co-operation with the engineer responsible for the equipment. Figure 9 shows the procedure and the elements for preparing a complete environmental test programme. ETSI ETSI TR 100 035 V2.1.2 (2004-02) 24 TEST SPEC. TEST SPEC. TEST SPEC. TEST SPEC. TEST SPEC. STORAGE TRANSPORT. IN USE IMMUNITY EMISSION CLIM ./ MECH. CLIM. / MECH. CLIM. / MECH. EMC (see note) EMC (see note) TEST METHODS VARIOUS RESOUCES TEST SEQUENCES TEST ENGINEERING ENGINEERING JUDGEMENT EQUIPMENT ENGINEER RESPONSIBLE EQUIPMENT FUNCTIONS & PROPERTIES TEST PROGRAMME NOTE: EMC has been included for completeness although not within the scope of the present document. Figure 9: Outline for the preparation of a complete environmental test programme
1f7ea7b6418174d53d51b760f9c08c93	100 035	6.5 Testing related to operational life
1f7ea7b6418174d53d51b760f9c08c93	100 035	6.5.1 General	So far most of the emphasis has been directed towards the performance of the equipment under extremes of environmental conditions. These cover the environmental classes as well as the tests. A natural consideration is how this emphasis is reflected in the "behaviour" of the equipment during its normal operational life (assuming that all environmental requirements are fulfilled). The conclusion is that such equipment is "debugged" in so far as environmentally induced design failures are concerned, thus avoiding problems from these possible failure effects. Thus the behaviour of the equipment has certainly been improved compared with equipment having poor environmental resistibility. In this special context this might be called improved reliability. However, it must be strongly emphasized that an environmental resistibility test - as part of a type test - must never be confused with a reliability test (see clause 6.5.2). Summarizing, it may be concluded that although an environmental resistibility test is very important, it cannot "stand alone". It is a necessary - but not a sufficient - basis to ensure that the user obtains a reliable performance from the equipment. ETSI ETSI TR 100 035 V2.1.2 (2004-02) 25
1f7ea7b6418174d53d51b760f9c08c93	100 035	6.5.2 Reliability	The environmental conditions have a significant effect on the reliability performance of equipment. A typical example is the component failure rate. This normally increases with increasing temperature, where the average temperature is the determining parameter. A proper reliability test is performed under defined environmental conditions. The following typical test conditions differ from a resistibility test in the following way: • many specimens are under test; • prolonged test time; • reasonably mild environmental conditions; • environmental conditions often varying in a cyclic manner; • simulation of typical use is intended; • field tests often used; • random failures are provoked. Thus there is a visibly significant difference between a resistibility test and a reliability test (see IEC 60605-3 [3]).
1f7ea7b6418174d53d51b760f9c08c93	100 035	6.5.3 Endurability	Similar considerations relating to reliability are also relevant for endurability, i.e. the environmental conditions have a significant effect on the endurability of an equipment (endurability concerns lifetime, ageing, wear etc.). A typical endurance test may be performed under the following conditions: • few specimens under test; • prolonged test time; • often relatively severe environmental conditions due to acceleration; • time dependent failures are provoked; • systematic failures (e.g. design, manufacturing, wear out, failures, etc.) are provoked. Thus some, but not all, of the conditions are significantly different from a resistibility test. Some examples will illustrate these aspects. EXAMPLE 1: High temperature: Exposure to high temperature is a typical example of how the same test method can be utilized in two completely different ways. Only the duration and the test severity are changed. Resistibility test: Short test time with the objective of assessing the functional performance under extreme temperature operation (e.g. 45°C, 16 hours). Endurability test: Long test time with the objective of assessing degradation (e.g. thermal ageing, cracking etc.) at room temperature by means of an accelerated test (e.g. 100°C, 56 days). EXAMPLE 2: Cyclic damp heat: Exposure to damp heat is an example of a single test where the duration of the exposure is usually so significant for the equipment that the test conditions, as well as the objective of the test, are very similar for both a resistibility test and an endurability test. ETSI ETSI TR 100 035 V2.1.2 (2004-02) 26 EXAMPLE 3: Vibration: Generally vibration tests for mobile equipment (e.g. sinusoidal sweep at several g's over several hours) may be considered as a resistibility test as well as a (mild) endurability test. A true endurability test, however, shall consist of a sinusoidal resonance search followed by an exposure with constant acceleration at the resonance frequency. Usually the duration is extended to the order of magnitude of 106 cycles to ensure that any possible fatigue strength failure is proved. In short, the conclusion is that even though the endurability tests have their own specific objectives, some of the resistibility tests may have a tendency to approach the endurability test. However, referring to clause 6.1 and figure 5, it is always important to realize what the objective of the test is, and to which potential failure mechanisms it may apply.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7 Terminology
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.1 Environmental description
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.1.1 Environment, environmental conditions	Environment is the physical and chemical conditions external to the equipment and to which it is subjected at a certain time. The environmental conditions comprise a combination of single environmental parameters and their severities. NOTE: The environmental conditions generally comprise environmental conditions appearing in nature and environmental conditions generated by artificial sources including the equipment itself.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.1.2 Environmental parameters	An environmental parameter represents one or more properties of the physical or chemical environment. EXAMPLE: Some environmental parameters: - air temperature; - humidity; - vibration, sinusoidal or random.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.1.2.1 Detail parameters	In order to define the environmental parameter unambiguously, it may be necessary to state one or more detail parameters. EXAMPLE 1: Some detail parameters for sinusoidal vibration: - displacement or acceleration; - frequency range. Quantitative measures for detail parameters are severities (particularly characteristic severities) and other characteristics. EXAMPLE 2: Environmental parameter: vibration, sinusoidal; Detail parameter: acceleration; Severity: acceleration value; Characteristic: frequency range. ETSI ETSI TR 100 035 V2.1.2 (2004-02) 27
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.1.3 Severity	The severity indicates a quantitative measure for each detail parameter characterizing an environmental parameter - i.e. magnitude, rate and duration. Specified severity values are used to: • characterize environmental classes (by the characteristic severity); • determine test values corresponding to performance requirements.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.1.3.1 Characteristic severity	The characteristic severity for a certain detail parameter in an environmental class states a severity which has a low probability of being exceeded (generally less than 1 %) and which refers to duration, rate of occurrence or location. The characteristic severity applies to requirements on the environment and to resistibility requirements.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.1.4 Environmental class	An environmental class is a representation of the environment at locations having similar properties. The environmental classes are specified and "standardized" to provide an operational frame of reference for: • requirements on the environment; • resistibility requirements; • emission requirements. The environmental class is described in terms of an envelope of the environmental conditions by a number of environmental parameters and the corresponding characteristic severities of the detail parameters or other characteristics. The environmental parameters specified for the class are limited to those which may affect equipment performance.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.1.5 Requirements on the environment	The specified requirements are imposed on the environment at the location where equipment, or parts of equipment are placed. Requirements on the environment may be given by an environmental class.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.1.6 Environmental protection	Environmental protection is a measure for the purpose of either: • protecting the equipment from the surrounding environment (e.g. by lightning arrester, shelter); or • protecting the environment from the influence of the equipment (e.g. by shock absorber).
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.2 Application
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.2.1 In-use	Equipment is in-use when it is directly operational.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.2.1.1 Stationary use	Equipment is mounted firmly on the structure, or on mounting devices, or it is permanently placed at a certain site. It is not intended for portable use, but short periods of handling during erection work, down time, maintenance and repair at the location are included. ETSI ETSI TR 100 035 V2.1.2 (2004-02) 28
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.2.1.2 Portable and non-stationary use	The equipment is frequently moved from place to place. During transfer there is no special packaging for the equipment. The total transfer time may amount to a significant portion of the product's lifetime. The product is not permanently mounted on any structure or placed at a fixed site. The product may be operated while being either in a non-stationary or in a transfer state.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.2.1.3 Mobile use	Equipment is in mobile use when it is primarily intended to be operated in, or on, a vehicle or a ship.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.2.2 Not-in-use	Equipment is not-in-use when it is non-operational. Not-in-use principally covers transport conditions and storage conditions.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.2.2.1 Transport conditions	Transport conditions are the environmental conditions to which equipment will be exposed during transportation, including loading, unloading and temporary storage. The equipment is not-in-use under these conditions.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.2.2.2 Storage conditions	Storage conditions are the environmental conditions to which equipment will be exposed during warehousing.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.2.2.3 Storage	The equipment is placed at a certain site for long periods but is not intended for use during these periods.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.2.2.4 Weatherprotected location	A location at which the equipment is protected from weather influences: • totally weather-protected location: direct weather influences are totally excluded; • partially weather-protected location: direct weather influences are not completely excluded.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.2.2.5 Non weatherprotected location	A location at which the equipment is not protected from direct weather influences.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3 Performance requirements	The performance requirements shall be specified under defined environmental conditions.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3.1 Normal performance	All specified performance requirements shall be fulfilled.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3.2 Reduced performance	All specified, primary function requirements shall be fulfilled, possibly with wider margins. ETSI ETSI TR 100 035 V2.1.2 (2004-02) 29
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3.2.1 Primary functions	The primary functions of equipment are those properties essential for the use of the equipment. EXAMPLE: Some primary functions of a telephone set: - transmitting and receiving voice; - transmitting dialling (or tones); - receiving ringing.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3.2.2 Secondary functions	The secondary functions of equipment are properties which facilitate/improve the use of the equipment. EXAMPLE: Some secondary functions of a telephone set: - storing last called number; - displaying "dialled" number.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3.2.3 Intermittent function	Intermittent function is a functional failure and often of a short duration and may occur occasionally under severe environmental conditions. Automatic recovery to normal performance is required when the environmental conditions (the exposure) return within the limits of the class, unless otherwise specified.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3.2.4 Cessation of function	Cessation of function is a functional failure that may occur under very severe environmental conditions. Any damage or permanent malfunction shall be confined to those parts of the equipment which were exposed to the environment.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3.3 Resistibility requirements
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3.3.1 Environmental resistibility	Environmental resistibility is the capability of an equipment to endure or resist a relevant environment for a short or long period of time. This means that the equipment shall be able to fulfil certain performance requirements when - or after - being exposed to one or more specific environmental influences. The extent of the influence is determined by the severities and the duration of the test.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3.3.2 Performance requirements	Performance requirements should be interpreted in a very broad sense. It may for example be a requirement for a surface just to "look nice". Another requirement may be that the equipment should fulfil all specified technical functions. A third requirement may be that the equipment should be capable of surviving.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3.4 Failure consequences	Failure consequences denote all significant consequences of environmentally caused failures, such as loss of service, equipment, revenue and reputation, and costs for repair and changes. Failure consequences are graded as minor failure consequences, moderate failure consequences and severe failure consequences considering that various types of equipment - although placed at locations covered by the same environmental class - are not required to be tested at the same severity. ETSI ETSI TR 100 035 V2.1.2 (2004-02) 30
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3.4.1 Minor failure consequences	Equipment has minor failure consequences when: • its functions or facilities are dispensable for a limited period of time without significant inconvenience; • repair (or replacement) can be made simply and cheaply; and • alternative equipment is available.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3.4.2 Moderate failure consequences	Equipment has moderate failure consequences when: • a failure causes limited inconvenience; and • the failure may be repaired without compromising the contractual responsibilities. This category is standard unless special circumstances are indicated.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3.4.3 Severe failure consequences	Equipment has severe failure consequences when: • a failure compromises the function of vital, centralized systems or services of a security-related nature; and • large costs are involved in restoration.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.3.5 Emission requirements	Emission requirements are the required limitations of the emission (e.g. dissipated heat) from equipment in a designated environmental class. The objective of the emission requirements is to make the interference to the environment "negligible", such that the environmental conditions remain covered by the original environmental class (i.e. retained within the specified characteristic severity).
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.4 Testing
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.4.1 Environmental testing	Environmental testing is usually a well-defined and reproducible laboratory test exposure of equipment to one or more environmental parameters having specified severities and in a specified sequence. In relevant cases environmental testing may also be carried out under defined field conditions. Environmental testing normally consists of: • pre-conditioning; • initial examination and measurements; • exposure (conditioning) according to the test method/procedure and including measurements; • recovery; • final examination and measurements (IEC 60068-1 [2]). Environmental testing is intended to demonstrate, with some measure of assurance, by reproducing the effects of the environment that an equipment (or component) will survive and perform under specified environments. ETSI ETSI TR 100 035 V2.1.2 (2004-02) 31
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.4.2 Environmental test programme	A complete environmental test programme for a specific kind of equipment consists of the relevant environmental test specifications (normally) supplemented by a stated test sequence and other detailed information (e.g. engineering judgements) considering that the environmental test programme can be performed in an efficient way. Generally the environmental test programme is prepared by the test engineer in co-operation with the engineer responsible for the equipment.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.4.3 Environmental test specification	The environmental test specification states, with reference to the test methods, the relevant parameters with their test severities in relation to the performance requirements and failure consequences.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.4.4 Standard atmospheric conditions for testing	Standard atmospheric conditions for testing are the environmental conditions which have to be fulfilled during measurements and tests. The standard atmospheric conditions for testing are defined by IEC 60068-1 [2], with the following values: • Temperature: 15°C to 35°C. • Relative humidity: 25 % to 75 %. • Air pressure: 86 kPa to 106 kPa.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.4.5 Type test	A type test is a representative test of the characteristics, including performance, of the equipment type (i.e. the design) of equipment. The type test may lead to a type qualification approval.
1f7ea7b6418174d53d51b760f9c08c93	100 035	7.5 Environmental specification	An environmental specification states: • the requirements on the environment, given by an environmental class; • the environmental test specification corresponding to the environmental class when the nature and application of the equipment are taken into consideration. ETSI ETSI TR 100 035 V2.1.2 (2004-02) 32 Annex A: Alphabetic index Clause Page Application ..............................................................................................................7.2 27 Atmospheric, standard atmospheric conditions for testing.......................................7.4.4 31 Cessation of function ...............................................................................................7.3.2.4 29 Class, environmental class ......................................................................................7.1.4 27 Conditions, environmental conditions .....................................................................7.1.1 26 Conditions, standard atmospheric conditions for testing..........................................7.4.4 31 Conditions, storage conditions ................................................................................7.2.2.2 28 Conditions, transport conditions ..............................................................................7.2.2.1 28 Consequences, failure consequences .......................................................................7.3.4 29 Consequences, severe failure consequences ............................................................7.3.4.3 30 Consequences, moderate failure consequences .......................................................7.3.4.2 30 Consequences, minor failure consequences ............................................................7.3.4.1 30 Description, environmental description ...................................................................7.1 26 Detail parameters .....................................................................................................7.1.2.1 26 Emission requirements ............................................................................................7.3.5 30 Environmental class ................................................................................................7.1.4 27 Environmental description ......................................................................................7.1 26 Environmental parameters .......................................................................................7.1.2 26 Environmental protection ........................................................................................7.1.6 27 Environmental specification ....................................................................................7.5 31 Environmental test program ....................................................................................7.4.2 31 Environmental test specifications ............................................................................7.4.3 31 Environmental testing .............................................................................................7.4.1 30 Environment, environmental conditions .................................................................7.1.1 26 Environment, requirements on the environment .....................................................7.1.5 27 Environmental resistibility ......................................................................................7.3.3.1 29 Failure consequences ...............................................................................................7.3.4 29 Failure consequences, severe failure consequences ................................................7.3.4.3 30 Failure consequences, moderate failure consequences ............................................7.3.4.2 30 Failure consequences, minor failure consequences .................................................7.3.4.1 30 Function, cessation of function ...............................................................................7.3.2.4 29 Function, intermittent function ................................................................................7.3.2.3 29 Function, primary functions ....................................................................................7.3.2.1 29 Function, secondary functions .................................................................................7.3.2.2 29 In-use .......................................................................................................................7.2.1 27 Intermittent function ................................................................................................7.3.2.3 29 Location, weather protected ....................................................................................7.2.2.4 28 Location, non-weather protected .............................................................................7.2.2.5 28 Minor failure consequences .....................................................................................7.3.4.1 30 Mobile use ...............................................................................................................7.2.1.3 28 Moderate failure consequences ...............................................................................7.3.4.2 30 Non stationary use, Portable and non-stationary use ...............................................7.2.1.2 28 Non-weather protected location ..............................................................................7.2.2.5 28 Normal failure consequences ..................................................................................7.3.4.2 30 Normal performance ...............................................................................................7.3.1 28 Not-in-use ................................................................................................................7.2.2 28 Parameter, detail parameter .....................................................................................7.1.2.1 26 Parameter, environmental parameter .......................................................................7.1.2 26 Performance requirements .......................................................................................7.3 28 Performance, normal performance ..........................................................................7.3.1 28 Performance, reduced performance .........................................................................7.3.2 28 Performance requirements .......................................................................................7.3.3.2 29 Portable and non stationary use ...............................................................................7.2.1.2 28 Primary functions ....................................................................................................7.3.2.1 29 ETSI ETSI TR 100 035 V2.1.2 (2004-02) 33 Protection, environmental protection ......................................................................7.1.6 27 Reduced performance ..............................................................................................7.3.2 28 Requirements on the environment ...........................................................................7.1.5 27 Requirements, emission requirements .....................................................................7.3.5 30 Requirements, performance requirements ...............................................................7.3.3.2 29 Requirements, resistibility requirements .................................................................7.3.3 29 Resistibility requirements ........................................................................................7.3.3 29 Secondary functions ................................................................................................7.3.2.2 29 Severe failure consequences ....................................................................................7.3.4.3 30 Severity, characteristic severity ...............................................................................7.1.3.1 27 Severity ...................................................................................................................7.1.3 27 Specification, environmental specification ..............................................................7.5 31 Specification, environmental test specification .......................................................7.4.3 31 Standard atmospheric conditions for testing ...........................................................7.4.4 31 Stationary use ..........................................................................................................7.2.1.1 27 Storage .....................................................................................................................7.2.2.3 28 Storage conditions ...................................................................................................7.2.2.2 28 Test programme, environmental ..............................................................................7.4.2 31 Testing .....................................................................................................................7.4 30 Testing, environmental testing ................................................................................7.4.1 30 Testing, standard atmospheric conditions for testing ..............................................7.4.4 31 Test, environmental test specification .....................................................................7.4.3 31 Transport conditions ................................................................................................7.2.2.1 28 Type test ..................................................................................................................7.4.5 31 Use, in-use ...............................................................................................................7.2.1 27 Use, mobile use .......................................................................................................7.2.1.3 28 Use, not-in-use ........................................................................................................7.2.2 28 Use, portable and non-stationary use .......................................................................7.2.1.2 28 Use, stationary use ...................................................................................................7.2.1.1 27 Weather protected location ......................................................................................7.2.2.4 28 ETSI ETSI TR 100 035 V2.1.2 (2004-02) 34 History Document history Edition 1 July 1992 Publication as ETR 035 V2.1.1 May 2003 Publication V2.1.2 February 2004 Publication
9183669bb4288f694ed0630f17da78b6	100 028-2	1 Scope	The present document provides a method to be applied to all the applicable deliverables, and supports TR 100 027 [1]. It covers the following aspects relating to measurements: a) methods for the calculation of the total uncertainty for each of the measured parameters; b) recommended maximum acceptable uncertainties for each of the measured parameters; c) a method of applying the uncertainties in the interpretation of the results. The present document provides the methods of evaluating and calculating the measurement uncertainties and the required corrections on measurement conditions and results (these corrections are necessary in order to remove the errors caused by certain deviations of the test system due to its known characteristics (such as the RF signal path attenuation and mismatch loss, etc.)).
9183669bb4288f694ed0630f17da78b6	100 028-2	2 References	For the purposes of this Technical Report (TR), the following references apply: [1] ETSI TR 100 027: "Electromagnetic compatibility and Radio spectrum Matters (ERM); Methods of measurement for private mobile radio equipment". [2] ETSI TR 102 273 (all parts): "Electromagnetic compatibility and Radio spectrum Matters (ERM); Improvement of radiated methods of measurement (using test sites) and evaluation of the corresponding measurement uncertainties". [3] ITU-T Recommendation O.41: "Psophometer for use on telephone-type circuits". [4] EN 55020: "Electromagnetic Immunity of Broadcast Receivers and Associated Equipment". [5] ETSI ETR 028: "Radio Equipment and Systems (RES); Uncertainties in the measurement of mobile radio equipment characteristics". [6] ETSI TR 100 028-1: "Electromagnetic compatibility and Radio spectrum Matters (ERM); Uncertainties in the measurement of mobile radio equipment characteristics; Part 1".
9183669bb4288f694ed0630f17da78b6	100 028-2	3 Definitions, symbols and abbreviations
9183669bb4288f694ed0630f17da78b6	100 028-2	3.1 Definitions	For the purposes of the present document, the following terms and definitions apply: accuracy: this term is defined, in relation to the measured value, in clause 4.1.1 of TR 100 028-2; it has also been used in the rest of the document in relation to instruments AF load: is normally a resistor of sufficient power rating to accept the maximum audio output power from the EUT NOTE: The value of the resistor should be that stated by the manufacturer and should be the impedance of the audio transducer at 1 000 Hz. In some cases it may be necessary to place an isolating transformer between the output terminals of the receiver under test and the load. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 12 AF termination: any connection other than the audio frequency load which may be required for the purpose of testing the receiver (i.e. in a case where it is required that the bit stream be measured, the connection may be made, via a suitable interface, to the discriminator of the receiver under test) NOTE: The termination device should be agreed between the manufacturer and the testing authority and details should be included in the test report. If special equipment is required then it should be provided by the manufacturer. antenna: part of a transmitting or receiving system that is designed to radiate or to receive electromagnetic waves antenna factor: quantity relating the strength of the field in which the antenna is immersed to the output voltage across the load connected to the antenna NOTE: When properly applied to the meter reading of the measuring instrument, yields the electric field strength in V/m or the magnetic field strength in A/m. antenna gain: ratio of the maximum radiation intensity from an (assumed lossless) antenna to the radiation intensity that would be obtained if the same power were radiated isotropically by a similarly lossless antenna bit error ratio: ratio of the number of bits in error to the total number of bits combining network: multipole network allowing the addition of two or more test signals produced by different sources (e.g. for connection to a receiver input) NOTE: Sources of test signals should be connected in such a way that the impedance presented to the receiver should be 50 Ω. The effects of any intermodulation products and noise produced in the signal generators should be negligible. correction factor: numerical factor by which the uncorrected result of a measurement is multiplied to compensate for an assumed systematic error confidence level: probability of the accumulated error of a measurement being within the stated range of uncertainty of measurement directivity: ratio of the maximum radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions (i.e. directivity = antenna gain + losses) duplex filter: device fitted internally or externally to a transmitter/receiver combination to allow simultaneous transmission and reception with a single antenna connection error of measurement (absolute): result of a measurement minus the true value of the measurand error (relative): ratio of an error to the true value estimated standard deviation: From a sample of n results of a measurement the estimated standard deviation is given by the formula: 1 1 2 − − = ∑ = n ) x (x n i i σ xi being the ith result of measurement (i = 1,2,3, ...,n) and x the arithmetic mean of the n results considered. A practical form of this formula is: 1 2 − − = n n X Y σ Where X is the sum of the measured values and Y is the sum of the squares of the measured values. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 13 The term standard deviation has also been used in the present document to characterize a particular probability density. Under such conditions, the term standard deviation may relate to situations where there is only one result for a measurement. expansion factor: multiplicative factor used to change the confidence level associated with a particular value of a measurement uncertainty NOTE: The mathematical definition of the expansion factor can be found in clause D.5.6.2.2. extreme test conditions: defined in terms of temperature and supply voltage NOTE: Tests should be made with the extremes of temperature and voltage applied simultaneously The upper and lower temperature limits are specified in the relevant deliverable. The test report should state the actual temperatures measured. error (of a measuring instrument): indication of a measuring instrument minus the (conventional) true value free field: field (wave or potential) which has a constant ratio between the electric and magnetic field intensities free space: region free of obstructions and characterized by the constitutive parameters of a vacuum impedance: measure of the complex resistive and reactive attributes of a component in an alternating current circuit impedance (wave): complex factor relating the transverse component of the electric field to the transverse component of the magnetic field at every point in any specified plane, for a given mode influence quantity: quantity which is not the subject of the measurement but which influences the value of the quantity to be measured or the indications of the measuring instrument intermittent operation: manufacturer should state the maximum time that the equipment is intended to transmit and the necessary standby period before repeating a transmit period isotropic radiator: hypothetical, lossless antenna having equal radiation intensity in all directions limited frequency range: is a specified smaller frequency range within the full frequency range over which the measurement is made NOTE: The details of the calculation of the limited frequency range should be given in the relevant deliverable. maximum permissible frequency deviation: maximum value of frequency deviation stated for the relevant channel separation in the relevant deliverable measuring system: complete set of measuring instruments and other equipment assembled to carry out a specified measurement task measurement repeatability: closeness of the agreement between the results of successive measurements of the same measurand carried out subject to all the following conditions: - the same method of measurement; - the same observer; - the same measuring instrument; - the same location; - the same conditions of use; - repetition over a short period of time. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 14 measurement reproducibility: closeness of agreement between the results of measurements of the same measurand, where the individual measurements are carried out changing conditions such as: - method of measurement; - observer; - measuring instrument; - location; - conditions of use; - time. measurand: quantity subjected to measurement noise gradient of EUT: function characterizing the relationship between the RF input signal level and the performance of the EUT, e.g. the SINAD of the AF output signal nominal frequency: one of the channel frequencies on which the equipment is designed to operate nominal mains voltage: declared voltage or any of the declared voltages for which the equipment was designed normal test conditions: defined in terms of temperature, humidity and supply voltage stated in the relevant deliverable normal deviation: frequency deviation for analogue signals which is equal to 12 % of the channel separation psophometric weighting network: should be as described in ITU-T Recommendation O.41 polarization: figure traced as a function of time by the extremity of the electric vector at a fixed point in space, for an electromagnetic wave quantity (measurable): attribute of a phenomenon or a body which may be distinguished qualitatively and determined quantitatively rated audio output power: maximum output power under normal test conditions, and at standard test modulations, as declared by the manufacturer rated radio frequency output power: maximum carrier power under normal test conditions, as declared by the manufacturer shielded enclosure: structure that protects its interior from the effects of an exterior electric or magnetic field, or conversely, protects the surrounding environment from the effect of an interior electric or magnetic field SINAD sensitivity: minimum standard modulated carrier-signal input required to produce a specified SINAD ratio at the receiver output stochastic (random) variable: variable whose value is not exactly known, but is characterized by a distribution or probability function, or a mean value and a standard deviation (e.g. a measurand and the related measurement uncertainty) test load: 50 Ω substantially non-reactive, non-radiating power attenuator which is capable of safely dissipating the power from the transmitter test modulation: test modulating signal is a baseband signal which modulates a carrier and is dependent upon the type of EUT and also the measurement to be performed trigger device: circuit or mechanism to trigger the oscilloscope timebase at the required instant It may control the transmit function or inversely receive an appropriate command from the transmitter. uncertainty: parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to that measurement uncertainty (random): component of the uncertainty of measurement which, in the course of a number of measurements of the same measurand, varies in an unpredictable way (and has not being considered otherwise) ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 15 uncertainty (systematic): component of the uncertainty of measurement which, in the course of a number of measurements of the same measurand remains constant or varies in a predictable way uncertainty (Type A): uncertainties evaluated using the statistical analysis of a series of observations uncertainty (Type B): uncertainties evaluated using other means than the statistical analysis of a series of observations uncertainty (limits of uncertainty of a measuring instrument): extreme values of uncertainty permitted by specifications, regulations etc. for a given measuring instrument NOTE: This term is also known as "tolerance". uncertainty (standard): expression characterizing the uncertainty for that component, for each individual uncertainty component NOTE: It is the standard deviation of the corresponding distribution. uncertainty (combined standard): uncertainty characterizing the complete measurement or part thereof, it is calculated by combining appropriately the standard uncertainties for each of the individual contributions identified in the measurement considered or in the part of it which has been considered NOTE: In the case of additive components (linearly combined components where all the corresponding coefficients are equal to one) and when all these contributions are independent of each other (stochastic), this combination is calculated by using the Root of the Sum of the Squares (the RSS method). A more complete methodology for the calculation of the combined standard uncertainty is given in annex D; see, in particular, clause D.3.12. uncertainty (expanded): expanded uncertainty is the uncertainty value corresponding to a specific confidence level different from that inherent to the calculations made in order to find the combined standard uncertainty NOTE: The combined standard uncertainty is multiplied by a constant to obtain the expanded uncertainty limits (see TR 100 028-1 [6], clause 5.3 and also clause D.5 (and more specifically clause D.5.6.2). upper specified AF limit: maximum audio frequency of the audio pass-band and is dependent on the channel separation wanted signal level: level of +6 dB/µV emf referred to the receiver input under normal test conditions, for conducted measurements NOTE 1: Under extreme test conditions the value is +12 dB/µV emf. NOTE 2: For analogue measurements the wanted signal level has been chosen to be equal to the limit value of the measured usable sensitivity. For bit stream and message measurements the wanted signal has been chosen to be +3 dB above the limit value of measured usable sensitivity.
9183669bb4288f694ed0630f17da78b6	100 028-2	3.2 Symbols	For the purposes of the present document, the following symbols apply: β 2π/λ (radians/m) γ incidence angle with ground plane (°) λ wavelength (m) φH phase angle of reflection coefficient (°) η 120π Ω - the intrinsic impedance of free space (Ω) µ permeability (H/m) AFR antenna factor of the receive antenna (dB/m) AFT antenna factor of the transmit antenna (dB/m) AFTOT mutual coupling correction factor (dB) Ccross cross correlation coefficient D(θ,φ) directivity of the source d distance between dipoles (m) δ skin depth (m) d1 an antenna or EUT aperture size (m) ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 16 d2 an antenna or EUT aperture size (m) ddir path length of the direct signal (m) drefl path length of the reflected signal (m) E electric field intensity (V/m) EDHmax calculated maximum electric field strength in the receiving antenna height scan from a half wavelength dipole with 1 pW of radiated power (for horizontal polarization) (µV/m) EDVmax calculated maximum electric field strength in the receiving antenna height scan from a half wavelength dipole with 1 pW of radiated power (for vertical polarization) (µV/m) eff antenna efficiency factor φ angle (°) ∆f bandwidth (Hz) f frequency (Hz) G(θ,φ) gain of the source (which is the source directivity multiplied by the antenna efficiency factor) H magnetic field intensity (A/m) I0 the (assumed constant) current (A) Im the maximum current amplitude k 2π/λ k a factor from Student's t distribution k Boltzmann's constant (1,38 x 10-23 J/°K) K relative dielectric constant l the length of the infinitesimal dipole (m) L the overall length of the dipole (m) l the point on the dipole being considered (m) λ wavelength (m) Pe (n) probability of error n Pp (n) probability of position n Pr antenna noise power (W) Prec power received (W) Pt power transmitted (W) θ angle (°) ρ reflection coefficient r the distance to the field point (m) ρg reflection coefficient of the generator part of a connection ρl reflection coefficient of the load part of the connection Rs equivalent surface resistance (Ω) σ conductivity (S/m) σ standard deviation SNRb* signal to noise ratio at a specific BER SNRb signal to noise ratio per bit TA antenna temperature (°K) U the expanded uncertainty corresponding to a confidence level of x %: U = k × uc uc the combined standard uncertainty ui general type A standard uncertainty ui01 random uncertainty uj general type B uncertainty uj01 reflectivity of absorbing material: EUT to the test antenna uj02 reflectivity of absorbing material: substitution or measuring antenna to the test antenna uj03 reflectivity of absorbing material: transmitting antenna to the receiving antenna uj04 mutual coupling: EUT to its images in the absorbing material uj05 mutual coupling: de-tuning effect of the absorbing material on the EUT uj06 mutual coupling: substitution, measuring or test antenna to its image in the absorbing material uj07 mutual coupling: transmitting or receiving antenna to its image in the absorbing material uj08 mutual coupling: amplitude effect of the test antenna on the EUT ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 17 uj09 mutual coupling: de-tuning effect of the test antenna on the EUT uj10 mutual coupling: transmitting antenna to the receiving antenna uj11 mutual coupling: substitution or measuring antenna to the test antenna uj12 mutual coupling: interpolation of mutual coupling and mismatch loss correction factors uj13 mutual coupling: EUT to its image in the ground plane uj14 mutual coupling: substitution, measuring or test antenna to its image in the ground plane uj15 mutual coupling: transmitting or receiving antenna to its image in the ground plane uj16 range length uj17 correction: off boresight angle in the elevation plane uj18 correction: measurement distance uj19 cable factor uj20 position of the phase centre: within the EUT volume uj21 positioning of the phase centre: within the EUT over the axis of rotation of the turntable uj22 position of the phase centre: measuring, substitution, receiving, transmitting or test antenna uj23 position of the phase centre: LPDA uj24 stripline: mutual coupling of the EUT to its images in the plates uj25 stripline: mutual coupling of the 3-axis probe to its image in the plates uj26 stripline: characteristic impedance uj27 stripline: non-planar nature of the field distribution uj28 stripline: field strength measurement as determined by the 3-axis probe uj29 stripline: Transform Factor uj30 stripline: interpolation of values for the Transform Factor uj31 stripline: antenna factor of the monopole uj32 stripline: correction factor for the size of the EUT uj33 stripline: influence of site effects uj34 ambient effect uj35 mismatch: direct attenuation measurement uj36 mismatch: transmitting part uj37 mismatch: receiving part uj38 signal generator: absolute output level uj39 signal generator: output level stability uj40 insertion loss: attenuator uj41 insertion loss: cable uj42 insertion loss: adapter uj43 insertion loss: antenna balun uj44 antenna: antenna factor of the transmitting, receiving or measuring antenna uj45 antenna: gain of the test or substitution antenna uj46 antenna: tuning uj47 receiving device: absolute level uj48 receiving device: linearity uj49 receiving device: power measuring receiver uj50 EUT: influence of the ambient temperature on the ERP of the carrier uj51 EUT: influence of the ambient temperature on the spurious emission level uj52 EUT: degradation measurement uj53 EUT: influence of setting the power supply on the ERP of the carrier uj54 EUT: influence of setting the power supply on the spurious emission level uj55 EUT: mutual coupling to the power leads uj56 frequency counter: absolute reading uj57 frequency counter: estimating the average reading uj58 Salty man/Salty-lite: human simulation ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 18 uj59 Salty man/Salty-lite: field enhancement and de-tuning of the EUT uj60 Test Fixture: effect on the EUT uj61 Test Fixture: climatic facility effect on the EUT Vdirect received voltage for cables connected via an adapter (dBµV/m) Vsite received voltage for cables connected to the antennas (dBµV/m) W0 radiated power density (W/m2) Other symbols which are used only in annexes D or E of the present document are defined in the corresponding annexes.
9183669bb4288f694ed0630f17da78b6	100 028-2	3.3 Abbreviations	For the purposes of the present document, the following abbreviations apply: AF Audio Frequency BER Bit Error Ratio BIPM International Bureau of Weights and Measures (Bureau International des Poids et Mesures) c calculated on the basis of given and measured data d derived from a measuring equipment specification emf Electromotive force EUT Equipment Under Test m measured p power level value v voltage level value r indicates rectangular distribution RF Radio Frequency RSS Root-Sum-of-the-Squares u indicates U-distribution VSWR Voltage Standing Wave Ratio
9183669bb4288f694ed0630f17da78b6	100 028-2	4 Receiver measurement examples	The following clauses show example measurement uncertainty calculations for a range of test configurations involving a variety of uncertainty contributions. Components essential for the measurement uncertainty calculations are shown in the accompanying drawings. Influence quantities (such as supply voltage and ambient temperature) are not shown in the drawings although they are present in the examples. Symbols and abbreviations used in the examples are explained in clauses 3.2 and 3.3 of TR 100 028-1 [6]. The test configuration, uncertainty contributions and the calculations are only examples and may not include all the possibilities. It is important that, where applicable, the errors are identified as either systematic or random for the purpose of making the calculations. Each example is calculated for a confidence level of 95 %. Many of the calculations on the following pages have been reproduced in spreadsheet form to provide the reader with a structured and time-saving approach to calculating measurement uncertainty. The spreadsheets also allow the reader to make modifications to the calculations to meet individual needs where the effects of each contribution can be assessed more effectively. Where the related spreadsheet has been made available by ETSI, an appropriate reference has been included in the text. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 19
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1 Conducted
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.1 Maximum usable sensitivity
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.1.1 Maximum usable sensitivity for analogue speech	a) Methodology cable Psophometric weighting network and SINAD meter AF load Receiver under test Signal generator Figure 1: Maximum usable sensitivity measurement configuration (Analogue Speech) A signal generator is connected to the antenna connector of a receiver under test via a cable (see figure 1). The low frequency output of the receiver is suitably terminated and fed to a psophometric filter connected to a SINAD meter. The signal generator is modulated with normal modulation. The level is adjusted until the SINAD meter reading is 20 dB. Maximum usable sensitivity is recorded as the signal generator level after correction for cable loss. b) Measurement uncertainty Mismatch uncertainty: - signal generator reflection coefficient is 0,2 (d); - receiver reflection coefficient (table F.1) is 0,2; - cable reflection coefficients are 0,1 (m). In the calculation of mismatch uncertainty the cable attenuation is assumed to be 0,0 dB (x1 linear). (v) % 414 1 2 100 1 0 2 0 u cable and generator : mismatch j , % , , = × × = (v) % 414 1 2 100 2 0 1 0 u receiver and cable : mismatch j , % , , = × × = (v) % 828 2 2 100 1 2 0 2 0 u 2 receiver and generator : mismatch j , % , , = × × × = The combined standard uncertainty for mismatch is: (v) % 464 3 828 ,2 414 ,1 414 ,1 u 2 2 2 : mismatch c , = + + = RF level uncertainty: Signal generator level uncertainty is ±1 dB (d)(r): dB 0,577 3 0 1 = = , u evel enerator l j signal g Uncertainty of the cable attenuation is ±0,104 dB (c)(σ). The combined standard uncertainty for the level is: dB , , , , 659 0 104 ,0 577 0 5 11 464 3 u 2 2 2 : level c = + +       = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 20 SINAD and deviation uncertainty: SINAD meter uncertainty is ±1 dB (d)(r): dB 0,577 3 0 1 = = , u ter j SINAD me Deviation uncertainty is ±5,3 % (d)(r) % 3,06 3 3 5 = = , u n j deviatio NOTE: Deviation and SINAD uncertainties can be combined directly (with the same units) as the relationship is linear. The combined standard uncertainty for SINAD is: dB , , , , 635 0 5 11 06 3 577 0 u 2 2 : deviation & SINAD c =       + = SINAD uncertainty is converted to an RF level uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 1,0 % RF level/% SINAD; - standard deviation of 0,2 % RF level/% SINAD. Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - mean value of 1,0 dB RF level/dB SINAD; - standard deviation of 0,2 dB RF level /dB SINAD. Therefore: ( ) ( ) ( ) ( ) dB 0,648 = 2 0 0 1 635 0 2 2 2 & /dB dB , /dB dB , dB , u SINAD el RF i/p lev SINAD el RF i/p lev Deviation d SINAD c converte + × = Uncertainty due to temperature: Ambient temperature uncertainty is ±3°C. Ambient temperature uncertainty is converted to a level uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 2,5 % V/°C; - standard deviation of 1,2 % V/°C. Therefore: ( ) ( ) ( ) (v) % 8 4 2 1 5 2 3 3 u 2 2 2 ambient converted j , = C % / , C % / , C       + ×         = o o o ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 21 Random uncertainty: Random uncertainty is 0,2 dB (m)(σ). The combined standard uncertainty for maximum usable sensitivity is: 2 random i 2 ambient converted j 2 deviation & SINAD converted c 2 level c y sensitivit maximum c u u u u u + + + = dB , = , , , , , 034 1 2 0 5 11 8 4 648 0 659 0 u 2 2 2 2 y sensitivit maximum c +       + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,034 dB = 2,03 dB (see clause D.5.6.2). c) Spreadsheet implementation of measurement uncertainty This calculation has been implemented in a corresponding spreadsheet (see file "Maximum usable sensitivity.xls") and is available in tr_10002802v010401p0.zip.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.1.2 Maximum usable sensitivity for a bit stream	a) Methodology cable Receiver under test Termination AF Bit error measuring test set Bit stream generator Signal generator Figure 2: Maximum usable sensitivity measurement configuration (Bit Stream) A signal generator is connected to the antenna connector of a receiver via a cable (see figure 2). The signal generator is set to the nominal frequency of the receiver and modulated by appropriate test modulation. The amplitude of the signal from the generator is adjusted until a bit error ratio of 10-2 is obtained from a sample size of 2 500 bits. The maximum usable sensitivity for a bit stream is recorded as the signal generator level after correction for the cable loss. b) Measurement uncertainty Mismatch uncertainty: - signal generator reflection coefficient is 0,2 (d); - receiver reflection coefficient (see table F.1) is 0,2; - cable reflection coefficients are 0,1 (m). In the calculation of mismatch uncertainty the cable attenuation is assumed to be 0,0 dB (x1 linear). (v) % 414 1 2 100 1 0 2 0 u cable and generator : mismatch j , % , , = × × = (v) % 414 1 2 100 2 0 1 0 u receiver and cable : mismatch j , % , , = × × = (v) % 828 2 2 100 1 2 0 2 0 u 2 receiver and generator : mismatch j , % , , = × × × = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 22 The combined standard uncertainty for mismatch is: (v) % 464 3 828 2 414 1 414 1 u 2 2 2 mismatch c , , , , = + + = RF level uncertainty: Signal generator level uncertainty ±1 dB (d)(r): dB 0,577 3 0 1 = = , u evel enerator l j signal g Uncertainty of the cable attenuation is ±0,104 dB (c)(σ). The combined standard uncertainty for the level is: dB , , , , , 659 0 014 0 577 0 5 11 464 3 u 2 2 2 level c = + +       = Uncertainty due to temperature: Ambient temperature uncertainty is ±3°C. Ambient temperature uncertainty is converted to a level uncertainty by means of formula 5.2 (see TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 2,5 % V/°C; - standard deviation of 1,2 % V/°C. Therefore: ( ) ( ) ( ) (v) % 4,8 = 2 1 5 2 3 3 u 2 2 2 ambient converted j       + ×         = C % / , C % / , C o o o Random uncertainty: Random uncertainty is 0,2 dB (σ)(m). BER uncertainty: Case 1: Error associated with digital non-coherent direct modulation In this case the RF signal is directly modulated. It has been assumed that the SNRb is proportional to the RF input level. σBER must be transformed to an RF input level uncertainty by means of the SNRb(BER) function. The BER uncertainty is calculated using formula 6.10: 3 10 2 2500 99 0 01 0 - j BER = , , = u × × The theoretical signal to noise ratio for a BER of 10-2 is calculated using formula 6.19: SNRb = -2 × ln (2 × 0,01) = 7,824. At a BER of 10-2 the slope of the BER function is 0,5 × BER = 0,5 × 10-2 (formula 6.21). The resulting level uncertainty (formula 6.16) is: (p) 11 5 100 824 7 10 5 0 10 2 u 2 3 BER converted j % , % = , , = - - × × × This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 23 Case 2a: Error associated with digital non-coherent sub-carrier modulation above the knee point For above the knee point case 1 applies because the C/N to S/N ratio is still 1:1. Case 2b: Error associated with digital non-coherent sub-carrier modulation below the knee point RF level uncertainty due to the sub-carrier modulation is determined by applying the dependency values from table F.1 (for the equivalent analogue measurements) to the results of case 1 (5,11 % power) using formula 5.2 (of TR 100 028-1 [6]). Dependency values found in table F.1 (noise gradient, below the knee point) are: - mean value of 0,375 % RF level/% SINAD; - standard deviation of 0,075 % RF level/% SINAD. Therefore: ( ) ( ) ( ) ( ) (p) % 954 1 075 0 375 0 11 5 u 2 2 2 BER converted j , = / % % , / % % , % , = SINAD el RF i/p lev SINAD el RF i/p lev + × This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 3: Error associated with digital coherent direct modulation The BER uncertainty is calculated using formula 6.10: 3 10 2 2500 99 0 01 0 - j BER = , , u × × = The theoretical signal to noise ratio for a BER of 10-2 is read from figure 18 where SNRb(0,01) = 2,7. At this signal-to-noise ratio, the slope of the BER function is 012 0 7 2 2 1 = 7 2 , = e , π , - × × × (formula 6.14) The BER uncertainty is then transformed to level uncertainty using formula 6.16: 6,97%(p) = 100% x x2,8 10 10,25x 10 2x = 3 - -3 level σ This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 4a: Error associated with digital coherent sub-carrier modulation operating above the knee point For above the knee point case 3 applies. Case 4b: Error associated with digital coherent sub-carrier modulation below the knee point RF level uncertainty due to the sub-carrier modulation is determined by applying the dependency values from table F.1 (for the equivalent analogue measurements) to the results of case 3 (6,17 % power) using formula 5.2 (of TR 100 028-1 [6]). Dependency values found in table F.1 (noise gradient, below the knee point) are: - mean value of 0,375 % RF level/% SINAD; - standard deviation of 0,075 % RF level/% SINAD. Therefore: ( ) ( ) ( ) ( ) (p) % 36 2 % % 075 0 % % 375 0 17 6 u 2 2 2 BER converted j , = / , / , % , SINAD el RF i/p lev SINAD el RF i/p lev + × = This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. The combined standard uncertainty for maximum usable sensitivity (for a bit stream) is: 2 BER converted j 2 random j 2 ambient converted j 2 level c y sensitivit maximum c u u u u u + + + = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 24 Combined standard uncertainty: Total uncertainty: Case 1 and case 2a dB 0,84 = 0 23 11 5 2 0 5 11 8 4 659 0 2 2 2 2       + +       + = , , , , , , u sitivity aximun sen c m Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,84 dB = ±1,65 dB (see clause D.5.6.2). Total uncertainty: Case 2b dB , = , , , , , , 81 0 0 23 954 1 2 0 5 11 8 4 659 0 u 2 2 2 2 y sensitivit aximun m c       + +       + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,81 dB = ±1,59 dB (see clause D.5.6.2). Total uncertainty: Case 3 and case 4a dB , = , , , , , , 85 0 0 23 17 6 2 0 5 11 8 4 659 0 u 2 2 2 2 y sensitivit aximun m c       + +       + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,85 dB = ±1,67 dB (see clause D.5.6.2). Total uncertainty: Case 4b dB , = , , , , , , 81 0 0 23 36 2 2 0 5 11 8 4 659 0 u 2 2 2 2 y sensitivit aximun m c       + +       + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,81 dB = ±1,59 dB (see clause D.5.6.2).
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.1.3 Maximum usable sensitivity for messages	a) Methodology A signal generator is connected to the antenna connector of a receiver under test via a cable (see figure 3). The signal generator is at the nominal frequency of the receiver and is modulated by appropriate modulation. The test signal is applied repeatedly until the specified success calling rate is achieved. The maximum usable sensitivity is recorded as the average level from the signal generator (from 10 samples) after correction for the loss of the cable. cable Receiver under test Termination AF Response measuring test set Signal generator Message generator Figure 3: Measured usable sensitivity measurement configuration (Messages) ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 25 b) Measurement uncertainty Mismatch uncertainty: - signal generator reflection coefficient is 0,2 (d); - receiver reflection coefficient (see table F.1) is 0,2; - cable reflection coefficients are 0,1 (m). In the calculation of mismatch uncertainty the cable attenuation is assumed to be 0,0 dB. (v) % 414 1 2 100 1 0 2 0 u cable and generator : mismatch j , % , , = × × = (v) % 414 1 2 100 2 0 1 0 u receiver and cable : mismatch j , % , , = × × = (v) % 828 2 2 100 1 2 0 2 0 u 2 receiver and generator : mismatch j , % , , = × × × = The combined standard uncertainty for mismatch is: (v) % 464 3 828 2 414 1 414 1 u 2 2 2 : mismatch c , , , , = + + = RF level uncertainty: Signal generator level uncertainty is ±1 dB (d)(r): dB 0,577 3 0 1 = = , u evel enerator l j signal g Uncertainty of the cable attenuation is 0,104 dB (c)(σ). The combined standard uncertainty for the level is: dB , , , , , 659 0 104 0 577 0 5 11 464 3 u 2 2 2 level c = + +       = Uncertainty due to methodology: The standard uncertainty for the measurement methodology (as the result is the average value of 10 samples) of 0,28 dB is taken from clause 6.7.4 of TR 100 028-1 [6] and is used in this example (m)(σ). Uncertainty due to temperature: Ambient temperature uncertainty is ±3°C. Ambient temperature uncertainty is converted to a level uncertainty by means of formula 5.2 (see TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 2,5 %V/°C; - standard deviation of 1,2 %V/°C. Therefore: ( ) ( ) ( ) (v) % 8 4 2 1 5 2 3 3 u 2 2 2 ambient converted j , = C % / , C % / , C       + ×         = o o o ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 26 Random uncertainty: Random uncertainty 0,2 dB (m)(σ). The combined standard uncertainty for maximum usable sensitivity (for messages) is: 2 random j 2 ambient converted j 2 y methodolog j 2 level c y sensitivit maximum c u u u u u + + + = dB , = , , , , , 853 0 2 0 5 11 8 4 28 0 659 0 u 2 2 2 2 y sensitivit ximum ma c +       + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,853 dB = ±1,67 dB (see clause D.5.6.2).
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.2 Co-channel rejection
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.2.1 Co-channel rejection for analogue speech	a) Methodology A receiver under test is connected to two signal generators through a combining network. A 6 dB attenuator is inserted between generator A and the combiner to reduce mismatch uncertainty when the test configuration is used for other tests involving out of band signals. The audio frequency output from the receiver is connected, suitably terminated, to a SINAD meter through a psophometric filter (see figure 4). Co-channel rejection is recorded (for a given SINAD reading) as the difference between the signal levels from generator A and generator B after correction for the attenuator. Receiver under test AF load or accoustic coupler Signal generator A Signal generator B 6 dB att. Resistive combiner 6 dB Psophometric weighting network and SINAD meter Figure 4: Co-channel rejection measurement configuration for analogue speech b) Measurement uncertainty Generator A level uncertainty (wanted signal) is ±1 dB (d)(r): dB 0,577 3 1 = = ignal j wanted s u Generator B level uncertainty (unwanted signal) is ±1 dB (d)(r): dB 0,577 3 1 = = signal j unwanted u 6 dB attenuator uncertainty is 0,2 dB (c)(σ). Combiner nominal insertion loss is 6 dB (x 0,5 linear - required for mismatch calculations). ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 27 Combiner tracking is ±0,1 dB: dB 0,058 3 1,0 = = tracking j combiner u Mismatch uncertainty - generator reflection coefficients (A and B) are 0,2 (d); - combiner reflection coefficients are 0,1 (d); - receiver under test reflection coefficient (see table F.1) is 0,2; - attenuator reflection coefficients are 0,1 (d). As each port of the combiner combines two other ports, the mismatch uncertainty in any one path will also be affected by the third port. Mismatch between generator A and EUT: (v) % 414 ,1 % 2 100 1,0 2,0 u att and A generator : mismatch j = × × = (v) % 707 0 % 2 100 1,0 1,0 u combiner and att : mismatch j , = × × = (v) % 414 ,1 % 2 100 2,0 1,0 u EUT and biner com : mismatch j = × × = (v) % 354 ,0 % 2 100 5,0 1,0 2,0 u 2 combiner and A generator : mismatch j = × × × = (v) % 354 ,0 % 2 100 5,0 2,0 1,0 u 2 EUT and att : mismatch j = × × × = (v) % 177 ,0 % 2 100 5,0 5,0 2,0 2,0 u 2 2 EUT and A generator j = × × × × = Uncertainty contribution due to the third combiner port: (v) % 177 ,0 % 2 100 5,0 5,0 2,0 2,0 u 2 2 B generator and A generator : mismatch j = × × × × = (v) % 354 ,0 % 2 100 5,0 2,0 1,0 u 2 B generator and attenuator : mismatch j = × × × = (v) % 707 ,0 % 2 100 5,0 2,0 2,0 u 2 EUT and B generator : mismatch j = × × × = Uncertainty due to the reflection coefficient at the third port: (v) % 071 ,7 % 2 5,0 100 5,0 5,0 2,0 u B generator : mismatch j = × × × × = Total mismatch uncertainty from generator A to EUT: 0,65dB 5, 11 071 ,7 707 ,0 354 ,0 177 ,0 177 ,0 354 ,0 354 ,0 414 ,1 707 ,0 414 ,1 2 2 2 2 2 2 2 2 2 2 = + + + + + + + + + = EUT to A gen c u ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 28 Mismatch between generator B and EUT: (v) % 414 ,1 % 2 100 1,0 2,0 u combiner and B generator mismatch: j = × × = (v) % 414 ,1 % 2 100 2,0 1,0 u EUT and combiner : mismatch j = × × = (v) % 707 ,0 % 2 100 5,0 2,0 2,0 u 2 EUT and B generator : mismatch j = × × × = Uncertainty contribution due to the third combiner port: (v) % 354 ,0 % 2 100 5,0 1,0 2,0 u 2 attenuator and B generator : mismatch j = × × × = (v) % 354 ,0 % 2 100 5,0 1,0 2,0 u 2 att and EUT : mismatch j = × × × = (v) % 177 ,0 % 2 100 5,0 5,0 2,0 2,0 u 2 2 A generator and B generator : mismatch j = × × × × = (v) % 177 ,0 % 2 100 5,0 5,0 2,0 2,0 u 2 2 A generator and EUT : mismatch j = × × × × = Uncertainty due to the reflection coefficient at the third port: (v) % 536 ,3 % 2 5,0 100 5,0 5,0 1,0 u att : mismatch j = × × × × = (v) % 768 ,1 % 2 5,0 100 5,0 5,0 5,0 2,0 u 2 A generator : mismatch j = × × × × × = Total mismatch uncertainty from generator B to EUT: dB , , , , , , , , , , , 39 0 5 11 768 1 536 3 177 0 177 0 354 0 354 0 707 0 414 1 414 1 u 2 2 2 2 2 2 2 2 2 EUT to B gen : mismatch c = + + + + + + + + = The combined standard uncertainty for mismatch is: 2 EUT to B gen c 2 EUT to A gen c mismatch c u u u + = dB 0,76 39 ,0 65 ,0 2 2 = + = c mismatch u Total level difference uncertainty: 2 2 2 2 2 mismatch c tracking combiner j atten j signal unwanted j signal wanted j fference c level di u u u u u u + + + + = 1,13dB = 76 0 058 ,0 2,0 577 0 577 0 2 2 2 2 2 , , , u fference c level di + + + + = Total level uncertainty of wanted signal: 2 2 2 EUT to A gen c attenuator j signal wanted j signal c wanted u u u u + + = dB 0,892 = 65 0 2 0 577 0 2 2 2 , , , = u ignal c wanted s + + ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 29 The wanted level uncertainty is converted to an RF level difference uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 0,5 % RF level/% RF level; - standard deviation of 0,2 % RF level/% RF level. Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - mean value of 0,5 dB RF level/dB RF level; - standard deviation of 0,2 dB RF level/dB RF level. Therefore: ( ) ( ) ( ) ( ) dB 0,480 = /dB dB 2 0 /dB dB 5 0 dB 892 0 u 2 level RF level RF 2 level RF level RF 2 wanted converted c , , , = + × SINAD uncertainty: SINAD meter uncertainty ±1 dB (d): dB 0,577 3 1 = ter j SINAD me u Deviation uncertainty (wanted signal) is ±5,3 % (d)(r): % 3,06 3 3,5 = = ignal n wanted s j deviatio u Deviation uncertainty (unwanted signal) is ±5,3 % (d)(r). Deviation is assumed to be 3 kHz so deviation uncertainty in Hz = (5,3 %/100) x 3,0 kHz = ±159 Hz. Deviation uncertainty of the unwanted signal is converted to a SINAD uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 0,05 % SINAD/Hz; - standard deviation of 0,02 % SINAD/Hz. Therefore: ( ) ( ) ( ) ( ) % 4,94 = 02 0 05 0 3 159 2 2 2 % / Hz , % / Hz , Hz = u to SINAD converted n j deviatio + ×         The combined standard uncertainty for the SINAD is: dB 0,767 = 5 11 94 4 5 11 06 3 577 0 2 2 2 , , , , , = uc SINAD       +       + SINAD uncertainty is converted to an RF level uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 0,7 % RF level/% SINAD; - standard deviation of 0,2 % RF level/% SINAD. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 30 Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - mean value of 0,7 dB RF level/dB SINAD; - standard deviation of 0,2 dB RF level /dB SINAD. Therefore: ( ) ( ) ( ) ( ) dB 0,558 = 2 0 7,0 767 0 u 2 2 2 Deviation & SINAD converted c /dB dB , /dB dB dB , SINAD el RF i/p lev SINAD el RF i/p lev + × = Random uncertainty: Random uncertainty is 0,2 dB (σ)(m). The combined standard uncertainty for co-channel rejection (analogue speech) is: 2 random j 2 deviation & SINAD converted c 2 wanted converted c 2 difference level c rejection channel co c u u u u u + + + = − dB , = , , , , 36 1 2 0 558 0 480 0 13 1 u 2 2 2 2 rejection channel co c + + + = − Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,36 dB = ±2,67 dB (see clause D.5.6.2). c) Spreadsheet implementation of measurement uncertainty This calculation has been implemented in a corresponding spreadsheet (see file "Co-channel rejection.xls") and is available in tr_10002802v010401p0.zip.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.2.2 Co-channel rejection for bit stream	a) Methodology A receiver under test is connected to two signal generators through a combining network (see figure 5). A 6 dB attenuator is inserted between generator A and the combiner to reduce mismatch uncertainty when the test configuration is used for other tests involving out of band signals. Signal generator A is set to a suitable level at the nominal frequency of the receiver and modulated by appropriate modulation. Signal generator B, also modulated by appropriate modulation, is adjusted until a bit error ratio of 10-2 is obtained from a sample size of 2 500 bits. Co-channel rejection is recorded as the difference between the signal levels from generator A and generator B after correction for the attenuator. Bit error test set measuring Termination Receiver under test Bit stream generator Signal generator A Signal generator B 6 dB att. Resistive combiner 6 dB Figure 5: Co-channel rejection measurement configuration for bit stream ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 31 b) Measurement uncertainty Generator A level uncertainty (wanted signal) ±1 dB (d)(r): 0,577dB 3 1 = = ignal j wanted s u Generator B level uncertainty (unwanted signal) ±1 dB (d)(r): dB , 577 0 3 1 u signal unwanted j = = 6 dB attenuator uncertainty is 0,2 dB (c)(σ). Combiner nominal insertion loss is 6 dB (x 0,5 linear - required for mismatch calculations). Combiner tracking ±0,1 dB: dB 0,058 3 1,0 = = tracking j combiner u Mismatch uncertainty - generator reflection coefficients (for A and B) are 0,2 (d); - combiner reflection coefficients are 0,1 (d); - receiver under test reflection coefficient (see table F.1) is 0,2; - attenuator reflection coefficients are 0,1 (d). Mismatch for a bit stream is calculated in the same way as for analogue speech (clause 4.1.2.1) where: Total mismatch uncertainty from generator A to EUT: dB , , , , , , , , , , , , 65 0 5 11 071 7 707 0 354 0 177 0 177 0 354 0 354 0 414 1 707 0 414 1 u 2 2 2 2 2 2 2 2 2 2 EUT to A gen c = + + + + + + + + + = Total mismatch uncertainty from generator B to EUT: dB , , , , , , , , , , , 39 0 5 11 768 1 536 3 177 0 354 0 177 0 354 0 707 0 414 1 414 1 u 2 2 2 2 2 2 2 2 2 EUT to B gen c = + + + + + + + + = The combined standard uncertainty for mismatch is: 2 2 EUT to B gen c EUT to A gen c c mismatch u u u + = dB 0,76 39 ,0 65 ,0 2 2 = + = c mismatch u Total level difference uncertainty: 2 2 2 2 2 mismatch c tracking combiner j atten j signal unwanted j signal wanted j fference c level di u u u u u u + + + + = 1,13dB = 76 0 058 ,0 2,0 577 0 577 0 2 2 2 2 2 , , , u fference c level di + + + + = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 32 Total level uncertainty of wanted signal: 2 2 2 EUT to A gen c attenuator j signal wanted j signal c wanted u u u u + + = dB 0,892 = 65 0 2 0 577 0 2 2 2 , , , = u ignal c wanted s + + The wanted level uncertainty is then converted to an RF level difference uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 0,5 % RF level/% RF level; - standard deviation of 0,2 % RF level/% RF level. Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - mean value of 0,5 dB RF level/dB RF level; - standard deviation of 0,2 dB RF level /dB RF level. Therefore: ( ) ( ) ( ) ( ) dB 0,480 = /dB dB 2 0 /dB dB 5 0 dB 892 0 u 2 level RF level RF 2 level RF level RF 2 wanted converted c , , , = + × Random uncertainty: Random uncertainty (valid for all measurements) is 0,2 dB (m)(σ). BER uncertainty: Case 1: Error associated with digital non-coherent direct modulation In this case the RF signal is directly modulated. It has been assumed that the SNRb is proportional to the RF input level. σ BER must be transformed to an RF input level uncertainty by means of the SNRb(BER) function. The BER uncertainty is calculated using formula 6.10: 3 10 2 2500 99 0 01 0 - j BER = , , = u × × The theoretical signal to noise ratio for a BER of 10-2 is calculated using formula 6.19: SNRb = -2 × ln (2 × 0,01) = 7,824. At a BER of 10-2 the slope of the BER function is 0,5 × BER = 0,5 × 10-2 (formula 6.21). The resulting level uncertainty (formula 6.16) is: %(p) 11 5 100 824 7 10 5 0 10 2 u 2 3 BER converted j , % = , , = - - × × × This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 2a: Error associated with digital non-coherent sub-carrier modulation above the knee point For above the knee point case 1 applies because the C/N to S/N ratio is still 1:1. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 33 Case 2b: Error associated with digital non-coherent sub-carrier modulation below the knee point RF level uncertainty due to the sub-carrier modulation is determined by applying the dependency values from table F.1 (for the equivalent analogue measurements) to the results of case 1 (5,11 % power) using formula 5.2 (see TR 100 028-1 [6]). Dependency values found in table F.1 (noise gradient, below the knee point) are: - mean value of 0,7 % RF level/% SINAD; - standard deviation is 0,2 % RF level/% SINAD. Therefore: ( ) ( ) ( ) ( ) (p) % 720 3 2 0 7 0 11 5 u 2 2 2 BER converted j , = / % % , / % % , % , = SINAD el RF i/p lev SINAD el RF i/p lev + × This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 3: Error associated with digital coherent direct modulation The BER uncertainty is calculated using formula 6.10: 3 10 2 2500 99 0 01 0 - j BER = , , u × × = The theoretical signal to noise ratio for a BER of 10-2 is read from figure 18 where SNRb(0,01) = 2,7. At this signal to noise ratio, the slope of the BER function is 012 0 7 2 2 1 7 2 , = e , π = , - × × × (formula 6.14). The BER uncertainty is then transformed to level uncertainty using formula 6.16: 6,97%(p) = 100% x x2,8 10 10,25x 10 2x = 3 - -3 level σ This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 4a: Error associated with digital coherent sub-carrier modulation operating above the knee point For above the knee point case 3 applies. Case 4b: Error associated with digital coherent sub-carrier modulation below the knee point RF level uncertainty due to the sub-carrier modulation is determined by applying the dependency values from table F.1 (for the equivalent analogue measurements) to the results of case 3 (6,17 % power) using formula 5.2 (of TR 100 028-1 [6]). Dependency values found in table F.1 (noise gradient, below the knee point) are: - mean value of 0,7 % RF level/% SINAD; - standard deviation of 0,2 % RF level/% SINAD. Therefore: ( ) ( ) ( ) ( ) (p) % 49 4 2 0 7 0 17 6 u 2 2 2 BER converted j , = / % % , / % % , % , SINAD el RF i/p lev SINAD el RF i/p lev + × = This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. The combined standard uncertainty for co-channel rejection (for a bit stream) is: 2 BER converted j 2 random j 2 wanted converted c 2 difference level c rejection channel co c u u u u u + + + = − ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 34 Total uncertainty: Case 1 and 2a dB 1,26 = 0 23 11 5 2 0 480 0 13 1 2 2 2 2 , , , , , u rejection channel c co       + + + = − Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,26 dB = ±2,47 dB (see clause D.5.6.2). Total uncertainty: Case 2b dB 25 1 0 23 720 3 2 0 480 0 13 1 u 2 2 2 2 rejection channel co c , = , , , , ,       + + + = − Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,25 dB = ±2,45 dB (see clause D.5.6.2). Total uncertainty: Case 3 and 4a dB 27 1 0 23 17 6 2 0 480 0 13 1 u 2 2 2 2 rejection channel co c , = , , , , ,       + + + = − Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,27 dB = ±2,49 dB (see clause D.5.6.2). Total uncertainty: Case 4b dB u rejection channel co c 26 ,1 = 0, 23 49 ,4 2,0 480 ,0 13 ,1 2 2 2 2       + + + = − Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,26 dB = ±2,47 dB (see clause D.5.6.2).
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.2.3 Co-channel rejection for messages	a) Methodology A receiver under test is connected to two signal generators through a combining network (see figure 6). A 6 dB attenuator is inserted between generator A and the combiner to reduce mismatch uncertainty when the test configuration is used for other tests involving out of band signals. Signal generator A is set to a suitable level at the nominal frequency of the receiver and modulated by appropriate modulation. The signal from generator B, also modulated by appropriate modulation, is then varied in level until the specified success calling rate is achieved. Co-channel rejection is recorded as the difference between the average level of generator A (from 10 samples) and generator B, after correction for the 6 dB attenuator. Response test set measuring Termination Receiver under test Message generator Signal generator A Signal generator B resistive 6 dB att. 6 dB combiner Figure 6: Co-channel rejection measurement configuration for messages ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 35 b) Measurement uncertainty Generator A level uncertainty (wanted signal) ±1 dB (d)(r): 0,577dB 3 1 = = ignal j wanted s u Generator B level uncertainty (unwanted signal) ±1 dB (d)(r): dB , 577 0 3 1 u signal unwanted j = = 6 dB attenuator uncertainty is 0,2 dB (m)(σ). Combiner nominal insertion loss is 6 dB (x 0,5 linear - required for mismatch calculations). Combiner tracking ±0,1 dB: dB 0,058 3 1,0 = = tracking j combiner u Mismatch uncertainty - generator reflection coefficients (for A and B) are 0,2 (d); - combiner reflection coefficients are 0,1 (d); - receiver under test reflection coefficient (see table F.1) is 0,2; - attenuator reflection coefficients are 0,1 (d). Mismatch for messages is calculated in the same way as for analogue speech (clause 4.1.2.1) where: Total mismatch uncertainty from generator A to EUT: 0,65dB 5, 11 071 ,7 707 ,0 354 ,0 177 ,0 177 ,0 354 ,0 354 ,0 414 ,1 707 ,0 414 ,1 2 2 2 2 2 2 2 2 2 2 = + + + + + + + + + = EUT to A gen c u Total mismatch uncertainty from generator B to EUT: 0,39dB 5, 11 768 ,1 536 ,3 177 ,0 354 ,0 177 ,0 354 ,0 707 ,0 414 ,1 414 ,1 2 2 2 2 2 2 2 2 2 = + + + + + + + + = EUT to B gen c u The combined standard uncertainty for mismatch is: 2 2 EUT to B gen c EUT to A gen c c mismatch u u u + = dB 0,76 39 ,0 65 ,0 2 2 = + = c mismatch u Total level difference uncertainty: 2 mismatch c 2 tracking combiner j 2 atten j 2 signal unwanted j 2 signal wanted j difference level c u u u u u u + + + + = 1,13dB = 76 0 058 ,0 2,0 577 0 577 0 2 2 2 2 2 , , , u fference c level di + + + + = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 36 Total level uncertainty of wanted signal: 2 2 2 EUT to A gen c attenuator j signal wanted j signal c wanted u u u u + + = dB 0,892 = 65 0 2 0 577 0 2 2 2 , , , = u ignal c wanted s + + The wanted level uncertainty is then converted to an RF level difference uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 0,5 % RF level/% RF level; - standard deviation of 0,2 % RF level/% RF level. Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - mean value of 0,5 dB RF level/dB RF level; - standard deviation of 0,2 dB RF level/dB RF level. Therefore: ( ) ( ) ( ) ( ) dB 0,480 = /dB dB 2 0 /dB dB 5 0 dB 892 0 u 2 level RF level RF 2 level RF level RF 2 wanted converted c , , , = + × Uncertainty of methodology: The standard uncertainty of the measurement methodology (as the result is the average value of 10 samples) of 0,28 dB is taken from clause 6.7.4 of TR 100 028-1 [6] and is used in this example (m)(σ). Random uncertainty: Random uncertainty 0,2 dB (c)(σ). The combined standard uncertainty for co-channel rejection is: 2 y methodolog j random j 2 wanted converted c 2 difference level c rejection channel co c u u u u u + + + = − dB 1,28 = 28 ,0 2,0 480 ,0 13 ,1 2 2 2 2 + + + = − rejection channel c co u Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,28 dB = ±2,51 dB (see clause D.5.6.2).
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.3 Adjacent channel selectivity
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.3.1 Adjacent channel selectivity for analogue speech	The only difference between this test and the co-channel rejection test in clause 4.1.2.1 is that the interfering signal resides in the adjacent channel. All other factors are the same and, assuming the single side-band phase noise of the interfering signal generator does not adversely effect adjacent channel performance the calculation of measurement uncertainty is the same as for clause 4.1.2.1.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.3.2 Adjacent channel selectivity for bit streams	The only difference between this test and the co-channel rejection test in clause 4.1.2.2 is that the interfering signal resides in the adjacent channel. All other factors are the same, and assuming the single side-band phase noise of the interfering signal generator does not adversely effect adjacent channel performance the calculation of measurement uncertainty is the same as for clause 4.1.2.2. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 37
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.3.3 Adjacent channel selectivity for messages	The only difference between this test and the co-channel rejection test in clause 4.1.2.3 is that the interfering signal resides in the adjacent channel. All other factors are the same, and assuming the single side-band phase noise of the interfering signal generator does not adversely effect adjacent channel performance the calculation of measurement uncertainty is the same as for clause 4.1.2.3.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.4 Spurious response immunity
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.4.1 Spurious response immunity measurements for analogue speech	A receiver under test is connected to two signal generators through a combining network (see figure 7). A 6 dB attenuator is inserted between generator A and the combiner to reduce out of band mismatch uncertainty. The audio frequency output from the receiver is connected, suitably terminated to a SINAD meter through a psophometric filter. Spurious response immunity is recorded (for a given SINAD reading) as the difference between the signal levels from generator A and generator B, after correction for the attenuator. Receiver under test AF load or accoustic coupler Signal generator A Signal generator B 6 dB att. Resistive combiner 6 dB Psophometric weighting network and SINAD meter Figure 7: Spurious response immunity measurement configuration for analogue speech
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.4.1.1 In band measurements	a) Measurement uncertainty Generator A level uncertainty (wanted signal) is ±1 dB (d)(r): dB 0,577 3 1 = = ignal j wanted s u Generator B level uncertainty (unwanted signal) is ±1 dB (d)(r): dB 0,577 3 1 = = signal j unwanted u 6 dB attenuator uncertainty is 0,2 dB (c)(σ). Attenuator loss is 6dB (x 0,5 linear - required for mismatch calculations). Combiner nominal insertion loss is 6 dB (required for mismatch calculations). Combiner tracking is ±0,1 dB: dB 0,058 3 1,0 = = tracking j combiner u ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 38 Mismatch uncertainty (in band) - generator reflection coefficients (A and B) are 0,2 (d); - combiner reflection coefficients are 0,1 (d); - receiver under test reflection coefficient (see table F.1) is 0,2; - attenuator reflection coefficients are 0,1 (d). As each port of the combiner combines two other ports, the mismatch uncertainty in any one path will also be affected by the third port. Mismatch between generator A and EUT: (v) % 414 ,1 % 2 100 1,0 2,0 u att and A generator : mismatch j = × × = (v) % 707 ,0 % 2 100 1,0 1,0 u combiner and att : mismatch j = × × = (v) % 414 ,1 % 2 100 2,0 1,0 u EUT and biner com : mismatch j = × × = (v) % 354 ,0 % 2 100 5,0 1,0 2,0 u 2 combiner and A generator : mismatch j = × × × = (v) % 354 ,0 % 2 100 5,0 2,0 1,0 u 2 EUT and att : mismatch j = × × × = (v) % 177 ,0 % 2 100 5,0 5,0 2,0 2,0 u 2 2 EUT and A generator : mismatch j = × × × × = Uncertainty contribution due to the third combiner port: (v) % 177 ,0 % 2 100 5,0 5,0 2,0 2,0 u 2 2 B generator and A generator : mismatch j = × × × × = (v) % 354 ,0 % 2 100 5,0 2,0 1,0 u 2 B generator and attenuator : mismatch j = × × × = (v) % 707 ,0 % 2 100 5,0 2,0 2,0 u 2 EUT and B generator : mismatch j = × × × = Uncertainty due to the reflection coefficient at the third port: (v) % 071 ,7 % 2 5,0 100 5,0 5,0 2,0 u B generator : mismatch j = × × × × = Total mismatch uncertainty from generator A to EUT: dB , , , , , , , , , , , , 65 0 5 11 071 7 707 0 354 0 177 0 177 0 354 0 354 0 414 1 707 0 414 1 u 2 2 2 2 2 2 2 2 2 2 EUT A to gen c = + + + + + + + + + = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 39 Mismatch between generator B and EUT: (v) % 414 ,1 % 2 100 1,0 2,0 u combiner and B generator : mismatch j = × × = (v) % 414 ,1 % 2 100 2,0 1,0 u EUT and combiner : mismatch j = × × = (v) % 707 ,0 % 2 100 5,0 2,0 2,0 u 2 EUT and B generator : mismatch j = × × × = Uncertainty contribution due to the third combiner port: (v) % 354 ,0 % 2 100 5,0 1,0 2,0 u 2 attenuator and B generator : mismatch j = × × × = (v) % 354 ,0 % 2 100 5,0 1,0 2,0 u 2 att and EUT : mismatch j = × × × = (v) % 177 ,0 % 2 100 5,0 5,0 2,0 2,0 u 2 2 A generator and B generator : mismatch j = × × × × = (v) % 177 ,0 % 2 100 5,0 5,0 2,0 2,0 u 2 2 A generator and EUT : mismatch j = × × × × = Uncertainty due to the reflection coefficient at the third port: (v) % 536 ,3 % 2 5,0 100 5,0 5,0 1,0 u att : mismatch j = × × × × = (v) % 768 ,1 % 2 5,0 100 5,0 5,0 5,0 2,0 u 2 A generator : mismatch j = × × × × × = Total mismatch uncertainty from generator B to EUT: dB , , , , , , , , , , , 39 0 5 11 768 1 536 3 177 0 177 0 354 0 354 0 707 0 414 1 414 1 u 2 2 2 2 2 2 2 2 2 EUT to B gen c = + + + + + + + + = The combined standard uncertainty for mismatch (in band) is: 2 EUT to B gen c 2 EUT A to gen c mismatch c u u u + = dB 0,76 39 ,0 65 ,0 2 2 = + = c mismatch u Total level difference uncertainty: 2 2 2 2 2 mismatch c tracking combiner j atten j signal unwanted j signal wanted j fference c level di u u u u u u + + + + = 1,13dB = 76 0 058 ,0 2,0 577 0 577 0 2 2 2 2 2 , , , u fference c level di + + + + = Total level uncertainty of wanted signal: 2 2 2 EUT to A gen c attenuator j signal wanted j signal c wanted u u u u + + = dB 0,892 = 65 0 2 0 577 0 2 2 2 , , , = u ignal c wanted s + + ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 40 The wanted level uncertainty is then converted to an RF level difference uncertainty by means of formula 5.2 (see TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 0,5 % RF level/% RF level; - standard deviation of 0,2 % RF level/% RF level. Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - mean value of 0,5 dB RF level/dB RF level; - standard deviation of 0,2 dB RF level/dB RF level. Therefore: ( ) ( ) ( ) ( ) dB 0,480 = /dB dB 2 0 /dB dB 5 0 dB 892 0 u 2 level RF level RF 2 level RF level RF 2 wanted converted c , , , = + × SINAD uncertainty: SINAD meter uncertainty is ±1 dB (d)(r): dB 0,577 3 1 = = ter j SINAD me u Deviation uncertainty (wanted signal) is ±5,3 % (d)(r): % 3,06 3 3,5 = = ignal n wanted s j deviatio u Deviation uncertainty (unwanted signal) is ±5,3 % (d)(r). Deviation is assumed to be 3 kHz so deviation uncertainty in Hz = (5,3 %/100) x 3,0 kHz = ±159 Hz. The deviation uncertainty of the unwanted signal is converted to a SINAD uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F1. Dependency values found in table F.1 are: - mean value of 0,05 % SINAD/Hz; - standard deviation of 0,02 % SINAD/Hz. Therefore: ( ) ( ) ( ) ( ) % 4,94 = 02 0 05 0 3 159 2 2 2 % / Hz , % / Hz , Hz = u to SINAD converted n j deviatio + ×         The combined standard uncertainty for the SINAD is: dB 0,767 = 5 11 94 4 5 11 06 3 577 0 2 2 2 , , , , , = uc SINAD       +       + SINAD uncertainty is converted to an RF level uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 0,7 % RF level/% SINAD; - standard deviation of 0,2 % RF level/% SINAD. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 41 Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - a mean value of 0,7 dB RF level/dB SINAD; - a standard deviation of 0,2 dB RF level/dB SINAD. Therefore: ( ) ( ) ( ) ( ) dB , = , , dB , = 558 0 dB / dB 2 0 dB / dB 7 0 767 0 u 2 SINAD level i/p RF 2 SINAD level i/p RF 2 SINAD converted c + × Random uncertainty: Random uncertainty (valid for all measurements) 0,2 dB (m)(σ). The combined standard uncertainty for in-band spurious response immunity (analogue speech) is: 2 random j 2 SINAD converted c 2 wanted converted c 2 difference level c immunity response spurious c u u u u u + + + = dB , = , , , , 36 1 2 0 558 0 480 0 13 1 u 2 2 2 2 immunity response spurious c + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,36 dB = ±2,67 dB (see clause D.5.6.2). b) Spreadsheet implementation of measurement uncertainty This calculation has been implemented in a corresponding spreadsheet (see file "Spurious response in band.xls") and is available in tr_10002802v010301p0.zip.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.4.1.2 Out of band measurements	a) Measurement uncertainty Generator A level uncertainty (wanted signal) is ±1 dB (d)(r): dB 0,577 3 1 = = ignal j wanted s u As generator B (unwanted signal) will go beyond 1 GHz, the level uncertainty is ±1,5 dB (d)(r): dB 0,866 3 5,1 = = signal j unwanted u 6 dB attenuator uncertainty is 0,2 dB (m)(σ). Attenuator loss is 6 dB (x 0,5 linear - required for mismatch calculations). Combiner nominal insertion loss is 6 dB (x 0,5 linear - required for mismatch calculations). Combiner tracking is ±0,6 dB: dB 0,346 3 6,0 = = tracking j combiner u In this example (out-of-band) tracking uncertainty is much higher due to the fact that the two signals are at different frequencies. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 42 Mismatch uncertainty (in band) - generator A reflection coefficient is 0,2 (d); - generator B reflection coefficient is 0,2 (d); - combiner reflection coefficients are 0,1 (d); - receiver under test reflection coefficient (see table F.1) is 0,2; - attenuator reflection coefficients are 0,1 (d). Mismatch uncertainty (out of band) - generator A reflection coefficient is 0,35 (d); - generator B reflection coefficient is 0,35 (d); - combiner reflection coefficients are 0,2 (d); - receiver under test reflection coefficient (see table F.1) is 0,8; - attenuator reflection coefficients are 0,2 (d). As each port of the combiner combines two other ports, the mismatch uncertainty in any one path will also be affected by the third port. Mismatch between generator A and EUT: (v) 414 ,1 % 2 100 1,0 2,0 u att and A generator : mismatch j % = × × = (v) % 707 ,0 % 2 100 1,0 1,0 u combiner and att : mismatch j = × × = (v) % 414 ,1 % 2 100 2,0 1,0 u EUT and biner com : mismatch j = × × = (v) % 354 ,0 % 2 100 5,0 1,0 2,0 u 2 combiner and A generator : mismatch j = × × × = (v) % 354 ,0 % 2 100 5,0 2,0 1,0 u 2 EUT and att : mismatch j = × × × = (v) % 177 ,0 % 2 100 5,0 5,0 2,0 2,0 u 2 2 EUT and A generator : mismatch j = × × × × = Uncertainty contribution due to the third combiner port: (v) % 354 ,0 % 2 100 5,0 2,0 1,0 u 2 B generator and attenuator : mismatch j = × × × = (v) % 707 ,0 % 2 100 5,0 2,0 2,0 u 2 EUT and B generator : mismatch j = × × × = (v) % 177 ,0 % 2 100 5,0 5,0 2,0 2,0 u 2 2 B generator and A generator : mismatch j = × × × × = Uncertainty due to the reflection coefficient at the third port: (v) % 071 ,7 % 2 5,0 100 5,0 5,0 2,0 u B generator : mismatch j = × × × × = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 43 Total mismatch uncertainty from generator A to EUT: dB , , , , , , , , , , , , 65 0 5 11 071 7 707 0 354 0 177 0 177 0 354 0 354 0 414 1 707 0 414 1 u 2 2 2 2 2 2 2 2 2 2 EUT A to gen c = + + + + + + + + + = Mismatch between generator B and EUT: (v) % 950 ,4 % 2 100 2,0 35 ,0 u combiner and B generator : mismatch j = × × = (v) % 314 , 11 % 2 100 8,0 2,0 u EUT and combiner : mismatch j = × × = (v) % 950 ,4 % 2 100 5,0 8,0 35 ,0 u 2 EUT and B generator : mismatch j = × × × = Uncertainty contribution due to the third combiner port: (v) % 237 ,1 % 2 100 5,0 2,0 35 ,0 u 2 attenuator and B generator : mismatch j = × × × = (v) % 828 ,2 % 2 100 5,0 2,0 8,0 u 2 att and EUT : mismatch j = × × × = (v) % 541 ,0 % 2 100 5,0 5,0 35 ,0 35 ,0 u 2 2 A generator and B generator : mismatch j = × × × × = (v) % 237 ,1 % 2 100 5,0 5,0 35 ,0 8,0 u 2 2 A generator and EUT : mismatch j = × × × × = Uncertainty due to the reflection coefficient at the third port: (v) % 071 ,7 % 2 5,0 100 5,0 5,0 2,0 u att : mismatch j = × × × × = (v) % 094 ,3 % 2 5,0 100 5,0 5,0 5,0 35 ,0 u 2 A generator : mismatch j = × × × × × = Total mismatch uncertainty from generator B to EUT: dB , , , , , , , , , , , 37 1 5 11 094 3 071 7 237 1 828 2 541 0 237 1 950 4 314 11 950 4 u 2 2 2 2 2 2 2 2 2 EUT to B gen c = + + + + + + + + = The combined standard uncertainty for mismatch (in band) is: 2 2 EUT to B gen c EUT to A gen c c mismatch u u u + = dB 1,516 37 ,1 65 ,0 2 2 = + = c mismatch u Total level difference uncertainty: 2 2 2 2 2 mismatch c tracking combiner j atten j signal unwanted j signal wanted j fference c level di u u u u u u + + + + = 1,88dB = 516 1 346 ,0 2,0 866 0 577 0 2 2 2 2 2 , , , u fference c level di + + + + = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 44 Total level uncertainty of wanted signal: 2 EUT to A gen mismatch: c 2 attenuator j 2 signal wanted j signal wanted c u u u u + + = dB 0,892 = 65 0 2 0 577 0 2 2 2 , , , = u ignal c wanted s + + The wanted level uncertainty is then converted to an RF level difference uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 0,5 % RF level/% RF level; - standard deviation of 0,2 % RF level/% RF level. Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - a mean value of 0,5 dB RF level/dB RF level; - a standard deviation of 0,2 dB RF level /dB RF level. Therefore: ( ) ( ) ( ) ( ) dB 0,480 = /dB dB 2 0 /dB dB 5 0 dB 892 0 u 2 level RF level RF 2 level RF level RF 2 wanted converted c , , , = + × SINAD uncertainty: SINAD meter uncertainty is ±1 dB (d): dB 0,577 3 1 = = ter j SINAD me u Deviation uncertainty (wanted signal) is ±5,3 % (r)(d): % 3,06 3 3,5 = = ignal n wanted s j deviatio u Deviation uncertainty (unwanted signal) is ±5,3 % (r)(d). Deviation is assumed to be 3 kHz so deviation uncertainty in Hz = (5,3 %/100) x 3,0 kHz = ±159 Hz. The deviation uncertainty of the unwanted signal is converted to a SINAD uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 0,05 % SINAD/Hz; - standard deviation of 0,02 % SINAD/Hz. Therefore: ( ) ( ) ( ) ( ) % 4,94 = 02 0 05 0 3 159 2 2 2 % / Hz , % / Hz , Hz = u to SINAD converted n j deviatio + ×         The combined standard uncertainty for the SINAD is: dB 0,767 = 5 11 94 4 5 11 06 3 577 0 2 2 2 , , , , , = uc SINAD       +       + ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 45 SINAD uncertainty is converted to an RF level uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 0,7 % RF level/% SINAD; - standard deviation of 0,2 % RF level/% SINAD. Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - mean value of 0,7 dB RF level/dB SINAD; - standard deviation of 0,2 dB RF level/dB SINAD. Therefore: ( ) ( ) ( ) ( ) dB , = / dB dB , / dB dB , dB , = SINAD el RF i/p lev SINAD el RF i/p lev 558 0 2 0 7 0 767 0 u 2 2 2 SINAD converted c + × Random uncertainty: Random uncertainty (valid for all measurements) 0,2 dB (c)(σ). The combined standard uncertainty for out of band spurious response immunity (analogue speech) is: 2 random j 2 SINAD converted c 2 wanted converted c 2 difference level c immunity reponse spurious c u u u u u + + + = dB , = , , , , s 03 2 2 0 558 0 480 0 88 1 u 2 2 2 2 immunity response purious c + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 2,03 dB = ±3,98 dB (see clause D.5.6.2). NOTE: The uncertainty could be further reduced by inserting a 6 dB attenuator between generator B and the combiner. b) Spreadsheet implementation of measurement uncertainty This calculation has been implemented in a corresponding spreadsheet (see file "Spurious response out of band.xls") and is available in tr_10002802v010401p0.zip.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.4.2 Spurious response immunity measurements for bit stream	A receiver under test is connected to two signal generators through a combining network (see figure 8). A 6 dB attenuator is inserted between generator A and the combiner to reduce out of band mismatch uncertainty. Signal generator A is set to a suitable level at the nominal frequency of the receiver and modulated by appropriate modulation. Signal generator B, also modulated by appropriate modulation, is adjusted until a bit error ratio of 10-2 is obtained from a sample size of 2 500 bits. Spurious response immunity is recorded as the difference between the signal levels from generator A and generator B after correction for the attenuator. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 46 Bit error test set measuring Termination Receiver under test Bit stream generator Signal generator A Signal generator B combiner resistive 6 dB att. 6 dB Figure 8: Spurious response immunity measurement configuration for bit stream
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.4.2.1 In band measurements	Generator A level uncertainty (wanted signal) is ±1 dB (d)(r): dB 0,577 3 1 = = ignal j wanted s u Generator B level uncertainty (unwanted signal) is ±1 dB (d)(r): dB 0,577 3 1 = = signal j unwanted u 6 dB attenuator uncertainty is 0,2 dB (c)(σ). Attenuator loss is 6 dB (x 0,5 linear - required for mismatch calculations). Combiner nominal insertion loss is 6 dB (x 0,5 linear - required for mismatch calculations). Combiner tracking is ±0,1 dB: dB 0,058 3 1,0 = = tracking j combiner u Mismatch uncertainty (in band) - generator reflection coefficients (A and B) are 0,2 (d); - combiner reflection coefficients are 0,1 (d); - receiver under test reflection coefficient (see table F.1) is 0,2; - attenuator reflection coefficients are 0,1 (d). As each port of the combiner combines two other ports, the mismatch uncertainty in any one path will also be affected by the third port. Mismatch for a bit stream (in-band) is calculated in the same way as for analogue speech (see clause 4.1.4.1.1) where: Total mismatch uncertainty from generator A to EUT: dB , , , , , , , , , , , , 65 0 5 11 071 7 707 0 354 0 177 0 177 0 354 0 354 0 414 1 707 0 414 1 u 2 2 2 2 2 2 2 2 2 2 EUT A to gen c = + + + + + + + + + = Total mismatch uncertainty from generator B to EUT: dB , , , , , , , , , , , 39 0 5 11 768 1 536 3 177 0 354 0 177 0 354 0 707 0 414 1 414 1 u 2 2 2 2 2 2 2 2 2 EUT to B gen c = + + + + + + + + = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 47 The combined standard uncertainty for mismatch (in band) is: 2 EUT to B gen c 2 EUT A to gen c mismatch c u u u + = dB 0,76 39 ,0 65 ,0 2 2 = + = c mismatch u Total level difference uncertainty: 2 2 2 2 2 mismatch c tracking combiner j atten j signal unwanted j signal wanted j fference c level di u u u u u u + + + + = 1,13dB = 76 0 058 ,0 2,0 577 0 577 0 2 2 2 2 2 , , , u fference c level di + + + + = Total level uncertainty of wanted signal: 2 2 2 EUT to A gen c attenuator j signal wanted j signal c wanted u u u u + + = dB 0,892 = 65 0 2 0 577 0 2 2 2 , , , = u ignal c wanted s + + The wanted level uncertainty is then converted to an RF level difference uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 0,5 % RF level/% RF level; - standard deviation of 0,2 % RF level/% RF level. Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - a mean value of 0,5 dB RF level/dB RF level; - a standard deviation of 0,2 dB RF level /dB RF level. Therefore: ( ) ( ) ( ) ( ) dB 0,480 = /dB dB 2 0 /dB dB 5 0 dB 892 0 u 2 level RF level RF 2 level RF level RF 2 wanted converted c , , , = + × Random uncertainty: Random uncertainty (valid for all measurements) 0,2 dB (m)(σ). BER uncertainty: Case 1: Error associated with digital non-coherent direct modulation In this case the RF signal is directly modulated. It has been assumed that the SNRb is proportional to the RF input level. σBER must be transformed to an RF input level uncertainty by means of the SNRb(BER) function. The BER uncertainty is calculated using formula 6.10 (clause 6.6 of TR 100 028-1 [6]): 3 10 2 2500 99 0 01 0 - j BER = , , = u × × The theoretical signal to noise ratio for a BER of 10-2 is calculated using formula 6.19: SNRb = -2 × ln (2 × 0,01) = 7,824. At a BER of 10-2 the slope of the BER function is 0,5 × BER = 0,5 × 10-2 (formula 6.21). ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 48 The resulting level uncertainty (formula 6.16) is: (p) 11 5 100 824 7 10 5 0 10 2 u 2 3 BER converted j % , % = , , = - - × × × This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 2a: Error associated with digital non-coherent sub-carrier modulation above the knee point For above the knee point case 1 applies because the C/N to S/N ratio is still 1:1. Case 2b: Error associated with digital non-coherent sub-carrier modulation below the knee point RF level uncertainty due to the sub-carrier modulation is determined by applying the dependency values from table F.1 (for the equivalent analogue measurements) to the results of case 1 (5,11 % power) using formula 5.2 (of TR 100 028-1 [6]). Dependency values found in table F.1 (noise gradient, below the knee point) are: - mean value of 0,7 % RF level/% SINAD; - standard deviation of 0,2 % RF level/% SINAD. Therefore: ( ) ( ) ( ) ( ) (p) % 3,720 = 2 0 7 0 11 5 u 2 2 2 BER converted j SINAD el RF i/p lev SINAD el RF i/p lev / % % , / % % , % , = + × This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 3: Error associated with digital coherent direct modulation The BER uncertainty is calculated using formula 6.10 (clause 6.6 of TR 100 028-1 [6]): 3 10 2 2500 99 0 01 0 - j BER = , , u × × = The theoretical signal to noise ratio for a BER of 10-2 is read from figure 8 where SNRb(0,01) = 2,7. At this signal to noise ratio, the slope of the BER function is 012 0 7 2 2 1 7 2 , = e , π = , - × × × (formula 6.14). The BER uncertainty is then transformed to level uncertainty using formula 6.16: %(p) 17 6 = % 100 7 2 012 0 10 2 u 3 BER coinverted j , , , = - × × This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 4a: Error associated with digital coherent sub-carrier modulation operating above the knee point For above the knee point case 3 applies. Case 4b: Error associated with digital coherent sub-carrier modulation below the knee point RF level uncertainty due to the sub-carrier modulation is determined by applying the dependency values from table F.1 (for the equivalent analogue measurements) to the results of case 3 (6,17 % power) using formula 5.2 (of TR 100 028-1 [6]). Dependency values found in table F.1 (noise gradient, below the knee point) are: - mean value of 0,7 % RF level/% SINAD; - standard deviation of 0,2 % RF level/% SINAD. Therefore: ( ) ( ) ( ) ( ) (p) % 49 4 2 0 7 0 17 6 u 2 2 2 BER converted j , = / % % , / % % , % , SINAD el RF i/p lev SINAD el RF i/p lev + × = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 49 This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty: The combined standard uncertainty for spurious response immunity (for a bit stream) is: 2 BER converted j 2 random j 2 wanted converted j 2 difference level c immunity response spurious c u u u u u + + + = Total uncertainty: Case 1 and case 2a dB 1,26 = 0 23 11 5 2 0 48 0 13 1 2 2 2 2 , , , , , u immunity response c spurious       + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,26 dB = ±2,47 dB (see clause D.5.6.2). Total uncertainty: Case 2b dB 1,25 = 0 23 72 ,3 2 0 48 0 13 1 2 2 2 2 , , , , u immunity response c spurious       + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,25 dB = ±2,45 dB (see clause D.5.6.2). Total uncertainty: Case 3 and case 4a dB , = , , , , , 27 1 0 23 17 6 2 0 48 0 13 1 u 2 2 2 2 immunity response spurious c       + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,27 dB = ±2,4 dB (see clause D.5.6.2). Total uncertainty: Case 4b dB , = , , , , , 26 1 0 23 49 4 2 0 48 0 13 1 u 2 2 2 2 immunity response spurious c       + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,26 dB = ±2,47 dB (see clause D.5.6.2).
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.4.2.2 Out of band measurements	Generator A level uncertainty (wanted signal) is ±1 dB (d)(r): dB 0,577 3 1 = = ignal j wanted s u As generator B (unwanted signal) will go beyond 1 GHz, the level uncertainty is ±1,5 dB (d)(r): dB 0,866 3 5,1 = = signal j unwanted u 6 dB attenuator uncertainty is 0,2 dB (σ)(m). Attenuator loss is 6 dB (x 0,5 linear - required for mismatch calculations). Combiner nominal insertion loss is 6 dB (x 0,5 linear - required for mismatch calculations). Combiner tracking is ±0,6 dB: dB 0,346 3 6,0 = = tracking j combiner u ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 50 In this example (out-of-band) tracking uncertainty is much higher due to the fact that the two signals are at different frequencies. Mismatch uncertainty (in band) - generator A reflection coefficient is 0,2 (d); - generator B reflection coefficient is 0,2 (d); - combiner reflection coefficients are 0,1 (d); - receiver under test reflection coefficient (see table F.1) is 0,2; - attenuator reflection coefficients are 0,1 (d). Mismatch uncertainty (out of band) - generator A reflection coefficient is 0,35 (d); - generator B reflection coefficient is 0,35 (d); - combiner reflection coefficients are 0,2 (d); - receiver under test reflection coefficient (see table F.1) is 0,8; - attenuator reflection coefficients are 0,2 (d). As each port of the combiner combines two other ports, the mismatch uncertainty in any one path will also be affected by the third port. Mismatch for a bit stream (out-of-band) is calculated in the same way as for analogue speech (see clause 4.1.4.1.2) where: Total mismatch uncertainty from generator A to EUT: 0,65dB 5, 11 071 ,7 707 ,0 354 ,0 177 ,0 177 ,0 354 ,0 354 ,0 414 ,1 707 ,0 414 ,1 2 2 2 2 2 2 2 2 2 2 = + + + + + + + + + = EUT to A gen c u Total mismatch uncertainty from generator B to EUT: 1,37dB 5, 11 094 ,3 071 ,7 237 ,1 828 ,2 541 ,0 237 ,1 950 ,4 314 , 11 950 ,4 2 2 2 2 2 2 2 2 2 = + + + + + + + + = EUT to B gen c u The combined standard uncertainty for mismatch (in band) is: 2 EUT to B gen c 2 EUT A to gen c mismatch c u u u + = dB 1,516 37 ,1 65 ,0 2 2 = + = c mismatch u Total level difference uncertainty: 2 2 2 2 2 mismatch c tracking combiner j atten j signal unwanted j signal wanted j fference c level di u u u u u u + + + + = 1,88dB = 516 1 346 ,0 2,0 866 0 577 0 2 2 2 2 2 , , , u fference c level di + + + + = Total level uncertainty of wanted signal: 2 2 2 EUT to A gen c attenuator j signal wanted j signal c wanted u u u u + + = dB 0,892 = 65 0 2 0 577 0 2 2 2 , , , = u ignal c wanted s + + ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 51 The wanted level uncertainty is converted to an RF level difference uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F1. Dependency values found in table F.1 are: - mean value of 0,5 % RF level/% RF level; - standard deviation of 0,2 % RF level/% RF level. Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - mean value of 0,5 dB RF level/dB RF level; - standard deviation of 0,2 dB RF level/dB RF level. Therefore: ( ) ( ) ( ) ( ) dB 0,480 = /dB dB 2 0 /dB dB 5 0 dB 892 0 u 2 level RF level RF 2 level RF level RF 2 wanted converted c , , , = + × Random uncertainty: Random uncertainty (valid for all measurements) 0,2 dB (m)(σ). BER uncertainty: Case 1: Error associated with digital non-coherent direct modulation In this case the RF signal is directly modulated. It has been assumed that the SNRb is proportional to the RF input level. σBER must be transformed to an RF input level uncertainty by means of the SNRb(BER) function. The BER uncertainty is calculated using formula 6.10 (clause 6.6 of TR 100 028-1 [6]): 3 10 2 2500 99 0 01 0 - j BER = , , = u × × The theoretical signal to noise ratio for a BER of 10-2 is calculated using formula 6.19: SNRb = -2 × ln (2 × 0,01) = 7,824. At a BER of 10-2 the slope of the BER function is 0,5 × BER = 0,5 × 10-2 (formula 6.21). The resulting level uncertainty (formula 6.16) is: %(p) 5,11 = % 100 824 7 10 5 0 10 2 2 3 , , = u - - BER ed j coinvert × × × This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 2a: Error associated with digital non-coherent sub-carrier modulation above the knee point For above the knee point case 1 applies because the C/N to S/N ratio is still 1:1. Case 2b: Error associated with digital non-coherent sub-carrier modulation below the knee point RF level uncertainty due to the sub-carrier modulation is determined by applying the dependency values from table F.1 (for the equivalent analogue measurements) to the results of case 1 (5,11 % power) using formula 5.2 (of TR 100 028-1 [6]). Dependency values found in table F.1 (noise gradient, below the knee point) are: - mean value is 0,7 % RF level/% SINAD; - standard deviation is 0,2 % RF level/% SINAD. Therefore: ( ) ( ) ( ) ( ) (p) % 720 3 2 0 7 0 11 5 u 2 2 2 BER converted j , = / % % , / % % , % , = SINAD el RF i/p lev SINAD el RF i/p lev + × ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 52 This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 3: Error associated with digital coherent direct modulation The BER uncertainty is calculated using formula 6.10: 3 10 2 2500 99 0 01 0 - j BER = , , u × × = The theoretical signal to noise ratio for a BER of 10-2 is read from figure 8 where SNRb(0,01) = 2,7. At this signal to noise ratio, the slope of the BER function is 012 0 7 2 2 1 7 2 , = e , π = , - × × × . The BER uncertainty is then transformed to level uncertainty using formula 6.16: %(p) 17 6 = % 100 7 2 012 0 10 2 u 3 BER converted j , , , = - × × This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 4a: Error associated with digital coherent sub-carrier modulation operating above the knee point For above the knee point case 3 applies. Case 4b: Error associated with digital coherent sub-carrier modulation below the knee point RF level uncertainty due to the sub-carrier modulation is determined by applying the dependency values from table F.1 (for the equivalent analogue measurements) to the results of case 3 (6,17 % power) using formula 5.2 (of TR 100 028-1 [6]). Dependency values found in table F.1 (noise gradient, below the knee point) are: - mean value is 0,7 % RF level/% SINAD; - standard deviation is 0,2 % RF level/% SINAD. Therefore: ( ) ( ) ( ) ( ) (p) % 4,49 = % % 2 0 % % 7 0 17 6 u 2 2 2 BER converted j SINAD el RF i/p lev SINAD el RF i/p lev / , / , % , + × = This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty: The combined standard uncertainty for spurious response immunity (for a bit stream) is: 2 BER converted j 2 random j 2 wanted converted j 2 difference level c immunity response spurious c u u u u u + + + = Total uncertainty: Case 1 and case 2a dB 1,96 = 0 23 11 5 2 0 480 0 88 1 2 2 2 2 , , , , , u immunity response c spurious       + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,96 dB = ±3,84 dB (see clause D.5.6.2). Total uncertainty: Case 2b dB 1,96 = 0 23 72 ,3 2 0 480 0 88 1 2 2 2 2 , , , , u immunity response c spurious       + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,96 dB = ±3,84 dB (see clause D.5.6.2). ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 53 Total uncertainty: Case 3 and case 4a dB , = , , , , , 97 1 0 23 17 6 2 0 480 0 88 1 u 2 2 2 2 immunity response spurious c       + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,97 dB = ±3,86 dB (see clause D.5.6.2). Total uncertainty: Case 4b dB , = , , , , 96 1 0 23 49 ,4 2 0 480 0 88 1 u 2 2 2 2 immunity response spurious c       + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,96 dB = ±3,84 dB (see clause D.5.6.2). NOTE: The uncertainty could be further reduced by inserting a 6 dB attenuator between generator B and the combiner.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.4.3 Spurious response immunity measurements for messages	A receiver under test is connected to two signal generators through a combining network (see figure 9). A 6 dB attenuator is inserted between generator A and the combiner to reduce out of band mismatch uncertainty. Signal generator A is set to a suitable level at the nominal frequency of the receiver and modulated by appropriate modulation. The signal from generator B, also modulated by appropriate modulation, is then varied in level until the specified success calling rate is achieved. Co-channel rejection is recorded as the difference between the average level of generator A (from 10 samples) and generator B, after correction for the 6 dB attenuator. Response test set measuring Termination Receiver under test Message generator Signal generator A Signal generator B resistive 6 dB att. 6 dB combiner Figure 9: Spurious response immunity measurement configuration for messages
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.4.3.1 In band measurements	Generator A level uncertainty (wanted signal) is ±1 dB (d)(r): dB 0,577 3 1 = = ignal j wanted s u Generator B level uncertainty (unwanted signal) is ±1 dB (d)(r): dB 0,577 3 1 = = signal j unwanted u 6 dB attenuator uncertainty is 0,2 dB (m)(σ). Attenuator loss is 6 dB (x 0,5 linear - required for mismatch calculations). Combiner nominal insertion loss is 6 dB (x 0,5 linear - required for mismatch calculations). ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 54 Combiner tracking is ±0,1 dB: dB 0,058 3 1,0 = = tracking j combiner u Mismatch uncertainty (in band) - generator reflection coefficients (A and B) are 0,2 (d); - combiner reflection coefficients are 0,1 (d); - receiver under test reflection coefficient (table F.1) is 0,2; - attenuator reflection coefficients are 0,1 (d). As each port of the combiner combines two other ports, the mismatch uncertainty in any one path will also be affected by the third port. Mismatch for messages (in-band) is calculated in the same way as for analogue speech (see clause 4.1.4.1.1) where: Total mismatch uncertainty from generator A to EUT: 0,65dB 5, 11 071 ,7 707 ,0 354 ,0 177 ,0 177 ,0 354 ,0 354 ,0 414 ,1 707 ,0 414 ,1 2 2 2 2 2 2 2 2 2 2 = + + + + + + + + + = EUT to A gen c u Total mismatch uncertainty from generator B to EUT: 0,39dB 5, 11 768 ,1 536 ,3 177 ,0 354 ,0 177 ,0 354 ,0 707 ,0 414 ,1 414 ,1 2 2 2 2 2 2 2 2 2 = + + + + + + + + = EUT to B gen c u The combined standard uncertainty for mismatch (in band) is: 2 EUT to B gen c 2 EUT A to gen c mismatch c u u u + = dB 0,76 39 ,0 65 ,0 2 2 = + = c mismatch u Total level difference uncertainty: 2 mismatch c 2 tracking combiner j 2 atten j 2 signal unwanted j 2 signal wanted j difference level c u u u u u u + + + + = 1,13dB = 76 0 058 ,0 2,0 577 0 577 0 2 2 2 2 2 , , , u fference c level di + + + + = Total level uncertainty of wanted signal: 2 2 2 EUT to A gen c attenuator j signal wanted j signal c wanted u u u u + + = dB 0,892 = 65 0 2 0 577 0 2 2 2 , , , = u ignal c wanted s + + The wanted level uncertainty is then converted to an RF level difference uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 0,5 % RF level/% RF level; - standard deviation of 0,2 % RF level/% RF level. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 55 Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - mean value of 0,5 dB RF level/dB RF level; - standard deviation of 0,2 dB RF level/dB RF level. Therefore: ( ) ( ) ( ) ( ) dB 0,480 = /dB dB 2 0 /dB dB 5 0 dB 892 0 u 2 level RF level RF 2 level RF level RF 2 wanted converted c , , , = + × Uncertainty of methodology: The standard uncertainty of the measurement methodology (as the result is the average value of 10 samples) of 0,28 dB is taken from clause 6.7.4 of TR 100 028-1 [6] and is used in this example (m)(σ). Random uncertainty: Random uncertainty (valid for all measurements) is 0,2 dB (m)(σ). The combined standard uncertainty for in-band spurious response immunity (messages) is: 2 y methodolog j 2 random c 2 wanted converted c 2 difference level c immunity response spurious c u u u u u + + + = dB 1,28 = 28 ,0 2,0 480 ,0 13 ,1 u 2 2 2 2 immunity response spurious c + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,28 dB = ±2,5 dB (see clause D.5.6.2).
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.4.3.2 Out of band measurements	Generator A level uncertainty (wanted signal) is ±1 dB (d)(r): dB 0,577 3 1 = = ignal j wanted s u As generator B (unwanted signal) will go beyond 1 GHz, the level uncertainty is ±1,5 dB (d)(r): dB 0,866 3 5,1 = = signal j unwanted u 6 dB attenuator uncertainty is 0,2 dB (c)(σ). Attenuator loss is 6 dB (x 0,5 linear - required for mismatch calculations). Combiner nominal insertion loss is 6 dB (x 0,5 linear - required for mismatch calculations). Combiner tracking is ±0,6 dB: dB 0,346 3 6,0 = = tracking j combiner u In this example (out-of-band) tracking uncertainty is much higher due to the fact that the two signals are at different frequencies. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 56 Mismatch uncertainty (in band) - generator A reflection coefficient is 0,2 (d); - generator B reflection coefficient is 0,2 (d); - combiner reflection coefficients are 0,1 (d); - receiver under test reflection coefficient (see table F.1) is 0,2; - attenuator reflection coefficients are 0,1 (d). Mismatch uncertainty (out of band) - generator A reflection coefficient is 0,35 (d); - generator B reflection coefficient is 0,35 (d); - combiner reflection coefficients are 0,2 (d); - receiver under test reflection coefficient (see table F.1) is 0,8; - attenuator reflection coefficients are 0,2 (d). As each port of the combiner combines two other ports, the mismatch uncertainty in any one path will also be affected by the third port. Mismatch for a bit stream (out-of-band) is calculated in the same way as for analogue speech (see clause 4.1.4.1.2) where: Total mismatch uncertainty from generator A to EUT: 0,65dB 5, 11 071 ,7 707 ,0 354 ,0 177 ,0 177 ,0 354 ,0 354 ,0 414 ,1 707 ,0 414 ,1 2 2 2 2 2 2 2 2 2 2 = + + + + + + + + + = EUT to A gen c u Total mismatch uncertainty from generator B to EUT: 1,37dB 5, 11 094 ,3 071 ,7 237 ,1 828 ,2 541 ,0 237 ,1 950 ,4 314 , 11 950 ,4 2 2 2 2 2 2 2 2 2 = + + + + + + + + = EUT to B gen c u The combined standard uncertainty for mismatch (in band) is: 2 EUT to B gen c 2 EUT A to gen c mismatch c u u u + = dB 1,516 37 ,1 65 ,0 2 2 = + = c mismatch u Total level difference uncertainty: 2 2 2 2 2 mismatch c tracking combiner j atten j signal unwanted j signal wanted j fference c level di u u u u u u + + + + = 1,88dB = 516 1 346 ,0 2,0 866 0 577 0 2 2 2 2 2 , , , u fference c level di + + + + = Total level uncertainty of wanted signal: 2 2 2 EUT to A gen c attenuator j signal wanted j signal c wanted u u u u + + = dB 0,892 = 65 0 2 0 577 0 2 2 2 , , , = u ignal c wanted s + + ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 57 The wanted level uncertainty is then converted to an RF level difference uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 0,5 % RF level/% RF level; - standard deviation of 0,2 % RF level/% RF level. Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - mean value of 0,5 dB RF level/dB RF level; - standard deviation of 0,2 dB RF level/dB RF level. Therefore: ( ) ( ) ( ) ( ) dB 0,480 = /dB dB 2 0 /dB dB 5 0 dB 892 0 u 2 level RF level RF 2 level RF level RF 2 wanted converted c , , , = + × Uncertainty of methodology: The standard uncertainty of the measurement methodology (as the result is the average value of 10 samples) of 0,28 dB is taken from clause 6.7.4 of TR 100 028-1 [6] and is used in this example (m)(σ). Random uncertainty: Random uncertainty (valid for all measurements) 0,2 dB (m)(σ). The combined standard uncertainty for out of band measurements is: 2 y methodolog j 2 random c 2 wanted converted c 2 difference level c immunity response spurious c u u u u u + + + = dB 1,97 = 28 ,0 2,0 480 ,0 88 ,1 2 2 2 2 u immunity response c spurious + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,97 dB = ±3,86 dB (see clause D.5.6.2). NOTE: The uncertainty could be further reduced by inserting a 6 dB attenuator between generator B and the combiner.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.5 Intermodulation immunity
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.5.1 Intermodulation immunity (analogue speech)	a) Methodology Three signal generators are connected via three cables to a combining network, in this case a hybrid coupler, whose output is connected directly to a 10 dB attenuator (with a low VSWR) in order to have a good isolation between the three generators. The output of the attenuator is connected to the antenna connection of the receiver under test through a cable, as illustrated in figure 10. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 58 Unwanted signal generator A f0 ± d cable generator B Unwanted signal f0 ± 2*d cable generator C Wanted signal f0 cable Psophometric weighting network and SINAD meter EUT AF load or acoustic coupler 10 dB att. cable Figure 10: Intermodulation immunity measurement configuration (analogue speech) Generator A (f0 ± d) and generator B (f0 ± 2 × d) are used to produce two unwanted signals with sufficient level to cause 3rd order intermodulation in the wanted channel of the receiver due to non linearities. Generator C is used to produce a wanted signal f0. NOTE 1: f0 is the receive channel frequency and d is a selected frequency (normally 2 or 4 channel separations) from f0. The audio frequency output from the receiver is connected to a suitable termination and a SINAD meter via a psophometric filter. The unwanted signals are adjusted in level (equally) until a given reduction in SINAD reading is achieved. Intermodulation immunity is recorded as the ratio of the signal level from the wanted signal generator to the (equal) signal levels of the unwanted signal generators. b) Measurement uncertainty: Generator level uncertainty is ±1 dB (d)(r): dB , 577 0 3 1 u A/B/C gen j = = (applicable to all generators) In this example calculation, insertion loss for the cables, coupler and attenuator have been individually measured and the standard uncertainty calculated from the various components of uncertainty attributed during their measurement. Cable attenuation (for each cable) is 0,1 dB and uncertainty: uj cable loss = ±0,1 dB (m)(σ) Coupler attenuation is 3,0 dB and uncertainty: uj coupler att = ±0,15 dB (m)(σ) Attenuator attenuation is 10 dB (x 0,316 linear - required for mismatch calculations) and uncertainty: uj att = 0,1 dB (m)(σ) NOTE 2: In this example case, the three signal generators are identical and are connected to the receiver under test in an identical way. As a consequence, the RF level uncertainties at the input of the receiver under test from each generator are assumed to be the same i.e. uc signal A = uc signal B = uc signal C. Therefore, only the level of the signal from generator A will be calculated in detail. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 59 c) Mismatch uncertainty contributions - signal generator reflection coefficients are 0,20 (d); - coupler reflection coefficients are 0,07 (d); - cable reflection coefficients are 0,10 (d); - attenuator reflection coefficients are 0,07 (d); - receiver under test reflection coefficients are 0,20 (d). Mismatch uncertainty generator A to the EUT. NOTE 3: The hybrid coupler provides isolation between the generators of greater than 30 dB (d) making any interaction negligible and associated mismatch calculations unnecessary. Cable insertion loss has been assumed to be 0 dB (multiplication by 1 in linear terms) in the following calculations. Coupler loss of 3 dB (multiplication by 0,708 in linear terms) is taken into consideration in the following calculations. The cable connecting generator A to the coupler is referred to as the input cable, and the cable connecting the coupler to the receiver under test is referred to as the output cable. Mismatch uncertainty between signal generator A and the receiver under test is calculated from the following: (v) % 414 ,1 % 2 100 1,0 2,0 u cable input and generator : mismatch j = × × = (v) % 495 ,0 % 2 100 07 ,0 1,0 u coupler and cable input : mismatch j = × × = (v) % 346 ,0 % 2 100 07 ,0 07 ,0 u att and coupler : mismatch j = × × = (v) % 495 ,0 % 2 100 1,0 07 ,0 u cable output and att : mismatch j = × × = (v) % 414 ,1 % 2 100 2,0 1,0 u EUT and cable output : mismatch j = × × = (v) % 99 ,0 % 2 100 1 07 ,0 2,0 u 2 coupler and A generator : mismatch j = × × × = (v) % 248 ,0 % 2 100 708 ,0 07 ,0 1,0 u 2 att and cable input : mismatch j = × × × = (v) % 049 ,0 % 2 100 316 ,0 1,0 07 ,0 u 2 cable output and coupler : mismatch j = × × × = (v) % 99 ,0 % 2 100 1 2,0 07 ,0 u 2 EUT and att : mismatch j = × × × = (v) % 496 ,0 % 2 100 708 ,0 1 07 ,0 2,0 u 2 2 att and A generator : mismatch j = × × × × = (v) % 035 ,0 % 2 100 316 ,0 708 ,0 1,0 1,0 u 2 2 cable output and cable input : mismatch j = × × × × = (v) % 099 ,0 % 2 100 0,1 316 ,0 2,0 07 ,0 u 2 2 EUT and coupler : mismatch j = × × × × = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 60 (v) % 071 ,0 % 2 100 316 ,0 708 ,0 0,1 1,0 2,0 u 2 2 2 cable output and A generator : mismatch j = × × × × × = (v) % 071 ,0 % 2 100 0,1 316 ,0 708 ,0 2,0 1,0 u 2 2 2 EUT and cable input : mismatch j = × × × × × = (v) % 142 ,0 % 2 100 1 316 ,0 708 ,0 0,1 2,0 2,0 u 2 2 2 2 EUT and A generator : mismatch j = × × × × × × = As the isolation between input ports is > 30 dB any mismatch uncertainty components from the other input ports are negligible. The RSS of all the mismatch uncertainty components detailed above = 2,63 %. The total mismatch uncertainty from any generator to the receiver under test = 2,63/11,5 = 0,23 dB. The total level uncertainty of the signal from generator A at the receiver input is: 2 attenuator j 2 mismatch j 2 coupler i 2 (output) loss cable j 2 (input) loss cable j 2 A Gen j A signal c u u u u u u u + + + + + = dB , , + , + , + , + , = 66 ,0 1 0 23 0 15 0 10 0 10 0 577 0 u 2 2 2 2 2 2 A signal c = + As previously stated uc signal A = uc signal B = uc signal C therefore: uc signal. B = 0,66 dB and uc signal C = 0,66 dB. Intermodulation product level uncertainties: Uncertainty due to unwanted signal level (Generator A): In clause 6.5.5.2.1 it is shown that the dependency function for the unwanted signal (from signal generator A) at frequency f0 ± d is 2/3 (see clauses D.3.4.5.2 and D.5). The uncertainty of the measured result due to the level of signal A (uj level due to A) is therefore 0,66 × 2/3 = 0,44 dB. Uncertainty due to unwanted signal level (Generator B): In clause 6.5.5.2.1 it is also shown that the dependency function for the unwanted signal (from signal generator B) at frequency f0 ± 2 × d is 1/3 (see clauses D.3.4.5.2 and D.5). The uncertainty of the measured result due to the level of signal B (uj level due to B) is therefore 0,66 × 1/3 = 0,22 dB. Uncertainty due to wanted signal level (Generator C): In clause 6.5.5.2.2 it is shown that the dependency function of the wanted signal (from signal generator C) is 1/3 (see clauses D.3.4.5.2 and D.5). The uncertainty of the measured result due to the level of signal C is therefore: 0,66 × 1/3 dB = 0,22 dB. Random uncertainty: The standard deviation of random uncertainty is taken as 0,2 dB (m)(σ). SINAD measurement uncertainty: SINAD meter uncertainty is ±1 dB (d)(r): dB 0,577 3 1 = = ter j SINAD me u Deviation uncertainty (wanted signal) is ±5 % (d)(r): 2,89% 3 5 = = signal wanted n j Deviatio u ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 61 The combined standard uncertainty for SINAD is: 0,63dB 5, 11 89 ,2 577 ,0 2 2 =       + = deviation and SINAD c u Two cases will now be considered for this example, above and below the knee point. For the case above the knee point: SINAD uncertainty is converted to a signal to noise ratio uncertainty at the receiver input by means of formula 5.2 (see TR 100 028-1 [6]). Dependency values found in table F.1 are: - mean value of 1,0 % RF level/% SINAD; - standard deviation of 0,2 % RF level/% SINAD. Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - mean value of 1,0 dB RF level/dB SINAD; - standard deviation of 0,2 dB RF level /dB SINAD. Therefore: ( ) ( ) ( ) ( ) dB 0,64 = 2 0 0 1 63 0 2 2 2 /dB dB , /dB dB , dB , u SINAD el RF i/p lev SINAD el RF i/p lev c SNR + × = Changes in the signal to noise ratio uncertainty at the receiver input must now be related to changes in the equal level of the unwanted signals. In clause 6.5.5.3 it is shown that the dependency function for signal-to-noise ratio uncertainty is 1/3 (a change in signal to noise ratio will result in 1/3 as much of a change in the level of the two equal unwanted signals). The uncertainty of the measured result due to the SINAD uncertainty is therefore: uj level due to SINAD = 0,64 × 1/3 dB = 0,21 dB For the case below the knee point: SINAD uncertainty is converted to a signal to noise ratio uncertainty at the receiver input by means of formula 5.2 (see TR 100 028-1 [6]). Dependency values are found in table F.1 are: - mean value of 0,375 % RF level/% SINAD; - standard deviation of 0,075 % RF level/% SINAD. Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - mean value of 0,375 dB RF level/dB SINAD; - standard deviation of 0,075 dB RF level /dB SINAD. Therefore: ( ) ( ) ( ) ( ) dB 0,24 = 075 0 375 ,0 63 0 2 2 2 /dB dB , /dB dB dB , u SINAD el RF i/p lev SINAD el RF i/p lev c SNR + × = Changes in the signal to noise ratio uncertainty at the receiver input must now be related to changes in the equal level of the unwanted signals. In clause 6.5.5.3 it is shown that the dependency function for signal-to-noise ratio uncertainty is 1/3 (a change in signal to noise ratio will result in 1/3 as much of a change in the level of the two equal unwanted signals). The uncertainty of the measured result due to the SINAD uncertainty is therefore: uj level due to SINAD = 0,24 × 1/3 dB = 0,08 dB ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 62 Combined standard uncertainty: The combined standard uncertainty for intermodulation immunity is: 2 SINAD to due level j 2 random i 2 C to due level c 2 B to due level c 2 A to due level c immunity ation intermodul c u u u u u u + + + + = Combined uncertainty above the knee point: dB , = , , , , , 61 0 21 0 2 0 22 0 22 0 44 0 u 2 2 2 2 2 immunity ation intermodul c + + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,61 dB = ±1,20 dB (see clause D.5.6.2). Combined uncertainty below the knee point: dB , = , , , , , 58 0 08 0 2 0 22 0 22 0 44 0 u 2 2 2 2 2 immunityy ation intermodul c + + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,58 dB = ±1,14 dB (see clause D.5.6.2). c) Spreadsheet implementation of measurement uncertainty The 'above the knee' calculation has been implemented in a corresponding spreadsheet (see file "Intermodulation immunity.xls") and is available in tr_10002802v010301p0.zip.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.5.2 Intermodulation immunity (bit stream)	a) Methodology Three signal generators are connected via three cables to a combining network, in this case a hybrid coupler, whose output is connected directly to a 10 dB attenuator (with a low VSWR) in order to have a good isolation between the three generators. The output of the attenuator is connected to the antenna connection of the receiver under test through a cable, as illustrated in figure 11. Unwanted signal generator A f0 ± d generator B Unwanted signal f0 ± 2*d generator C Wanted signal f0 Bit stream generator Bit error measuring test set Termination EUT cable cable cable 10 dB att . cable Figure 11: Intermodulation response measurement configuration (bit stream) Generator A (f0 ± d) and generator B (f0 ± 2 × d) are used to produce two unwanted signals with sufficient level to cause 3rd order intermodulation in the wanted channel of the receiver due to non linearities. Generator C is used to produce a wanted signal f0. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 63 NOTE 1: f0 is the receive channel frequency and d is a selected frequency (normally 2 or 4 channel separations) from f0. The data output from the receiver is connected to a bit error tester. The unwanted signals are adjusted in level (equally) until a BER of 10-2 is achieved from a sample size of 10 000 bits. Intermodulation immunity is recorded as the ratio of the signal level of the wanted signal generator to the (equal) signal levels of the unwanted signal generators. b) Measurement uncertainty Generator level uncertainty is ±1 dB (d)(r): dB , 577 0 3 1 u A/B/C gen j = = (applicable to all generators) In this example calculation, insertion loss for the cables, coupler and attenuator have been individually measured and the standard uncertainty calculated from the various components of uncertainty attributed during their measurement. Cable loss (for each cable) is 0,1 dB and uncertainty: uj cable loss = ±0,1 dB (m)(σ) Coupler attenuation is 3,0 dB and uncertainty: uj coupler att = ±0,15 dB (m)(σ) Attenuator attenuation is 10 dB (x 0,316 linear - required for mismatch calculations) and uncertainty: uj att = 0,1 dB (m)(σ) NOTE 2: In this example case, the three signal generators are identical and are connected to the receiver under test in an identical way. As a consequence, the RF level uncertainties at the input of the receiver under test from each generator are assumed to be the same i.e. uc signal A = uc signal B = uc signal C. Therefore, only the level uncertainty of signal generator A will be calculated in detail. Mismatch contributions: - signal generator reflection coefficients are 0,20 (d); - coupler reflection coefficients are 0,07 (d); - cable reflection coefficients are 0,10 (d); - attenuator reflection coefficients are 0,07 (d); - receiver under test reflection coefficients are 0,20 (d). Mismatch uncertainty generator A to the EUT. NOTE 3: The hybrid coupler provides isolation between the generators of greater than 30 dB making any interaction negligible and associated mismatch calculations unnecessary. Cable insertion loss has been assumed to be 0 dB (multiplication by 1 in linear terms) in the following calculations. Coupler loss of 3 dB (multiplication by 0,708 in linear terms) is however taken into consideration in the following calculations. The cable connecting generator A to the coupler is referred to as the input cable, and the cable connecting the coupler to the receiver under test is referred to as the output cable. Mismatch uncertainty between signal generator A and the receiver under test is calculated from the following: (v) % 414 ,1 % 2 100 1,0 2,0 u cable input and generator : mismatch j = × × = (v) % 495 ,0 % 2 100 07 ,0 1,0 u coupler and cable input : mismatch j = × × = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 64 (v) % 346 ,0 % 2 100 07 ,0 07 ,0 u att and coupler : mismatch j = × × = (v) % 495 ,0 % 2 100 1,0 07 ,0 u cable output and att : mismatch j = × × = (v) % 414 ,1 % 2 100 2,0 1,0 u EUT and cable output : mismatch j = × × = (v) % 99 ,0 % 2 100 1 07 ,0 2,0 u 2 coupler and generator : mismatch j = × × × = (v) % 248 ,0 % 2 100 708 ,0 07 ,0 1,0 u 2 att and cable input : mismatch j = × × × = (v) % 049 ,0 % 2 100 316 ,0 1,0 07 ,0 u 2 cable output and coupler : mismatch j = × × × = (v) % 99 ,0 % 2 100 1 2,0 07 ,0 u 2 EUT and att : mismatch j = × × × = (v) % 496 ,0 % 2 100 708 ,0 1 07 ,0 2,0 u 2 2 att and generator : mismatch j = × × × × = (v) % 035 ,0 % 2 100 316 ,0 708 ,0 1,0 1,0 u 2 2 cable output and cable input : mismatch j = × × × × = (v) % 099 ,0 % 2 100 0,1 316 ,0 2,0 07 ,0 u 2 2 EUT and coupler : mismatch j = × × × × = (v) % 071 ,0 % 2 100 316 ,0 708 ,0 0,1 1,0 2,0 u 2 2 2 cable output and generator : mismatch j = × × × × × = (v) % 071 ,0 % 2 100 0,1 316 ,0 708 ,0 2,0 1,0 u 2 2 2 EUT and cable input : mismatch j = × × × × × = (v) % 142 ,0 % 2 100 1 316 ,0 708 ,0 0,1 2,0 2,0 u 2 2 2 2 EUT and generator : mismatch j = × × × × × × = As the isolation between input ports is > 30 dB any mismatch uncertainty components from the other input ports are negligible. The RSS of all the mismatch uncertainty components detailed above = 2,63 %. The total mismatch uncertainty from any generator to the receiver under test uj mismatch = 2,63/11,5 = 0,23 dB. The total level uncertainty of signal generator A at the receiver input is: 2 attenuator j 2 mismatch j 2 coupler i 2 (output) loss cable j 2 (input) loss cable j 2 A Gen j A signal c u u u u u u u + + + + + = dB , , , + , + , + , + , 66 0 1 0 23 0 15 0 10 0 10 0 577 0 = u 2 2 2 2 2 2 A signal c = + As previously stated uc signal A = uc signal B = uc signal C therefore: uc signal. B = 0,66 dB and uc signal C = 0,66 dB. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 65 Intermodulation product level uncertainties: Uncertainty due to unwanted signal level (Generator A): In clause 6.5.5.2.1 it is shown that the dependency function for the unwanted signal (from signal generator A) at frequency f0 ± d is 2/3 (see clauses D.3.4.5.2 and D.5). The uncertainty of the measured result due to the level of signal A (uj level due to A) is therefore 0,66 × 2/3 = 0,44 dB. Uncertainty due to unwanted signal level (Generator B): In clause 6.5.5.2.1 it is also shown that the dependency function for the unwanted signal (from signal generator B) at frequency f0 ± 2 × d is 1/3 (see clauses D.3.4.5.2 and D.5). The uncertainty of the measured result due to the level of signal B (uj level due to B) is therefore 0,66 × 1/3 = 0,22 dB. Uncertainty due to wanted signal level (Generator C): In clause 6.5.5.2.2 it is shown that the dependency function of the wanted signal (from signal generator C) is 1/3 (see clauses D.3.4.5.2 and D.5). The uncertainty of the measured result due to the level of signal C (uj level due to C) is therefore: 0,66 × 1/3 dB = 0,22 dB. Random uncertainty: The standard deviation of the random uncertainty is taken as 0,2 dB (m)(σ). BER uncertainty: Case 1: Uncertainty associated with digital non-coherent direct modulation BER uncertainty is calculated using formula 6.10: 3 10 995 ,0 10000 ) 01 ,0 1( 01 ,0 − × = − × = BER j u The theoretical signal to noise ratio per bit for a BER of 10-2 is calculated using formula 6.19: SNRb = -2 × ln (2 × 0,01) = 7,824. At a BER of 10-2, the slope of the BER function is 0,5 × BER = 0,005 (formula 6.21). BER uncertainty is then converted to signal-to-noise ratio uncertainty using formula 6.16: ) ( % 54 ,2 % 100 824 ,7 005 ,0 10 995 ,0 3 p SNR slope u u b BER j SNR j = × × × = × = − This is converted to dB: 0,11dB = 23 54 ,2 = u j SNR Changes in the signal to noise ratio uncertainty at the receiver input must now be related to changes in the equal level of the unwanted signals. In clause 6.5.5.3 it is shown that the dependency function for signal-to-noise ratio uncertainty is 1/3 (a change in signal to noise ratio will result in 1/3 as much of a change in the level of the two equal unwanted signals). The uncertainty of the unwanted signals due to the BER uncertainty is therefore: uj level due to BER = 0,11 × 1/3 dB = 0,04 dB This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 66 Case 2a: Uncertainty associated with digital non-coherent sub-carrier modulation above the knee point In this case the calculations in case 1 apply and relate to the signal-to-noise ratio of the sub carrier. However as the signal-to-noise ratio dependency function is 1 dB/dB above the knee point, the calculations and the result from case 1 apply directly (0,04 dB). This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 2b: Uncertainty associated with digital non-coherent sub-carrier modulation below the knee point (see clause 6.6.4.6) As in the previous case, the calculations in case 1 apply and relate to the signal-to-noise ratio of the sub carrier. However for measurements below the knee point, a dependency function must be applied to convert the sub-carrier signal-to-noise ratio uncertainty (2,54 % determined in case 1) to signal-to-noise ratio in the receiving channel. The conversion is performed by means of formula 5.2 (of TR 100 028-1 [6]). Dependency values (noise gradient) found in table F.1 are: - mean value of 0,375 %/% SINAD; - standard deviation of 0,075 %/% SINAD. Therefore: ( ) ( ) ( ) ( ) (p) % 1,08 = % % 2 0 % / % 375 0 54 ,2 2 2 2 SINAD SINAD SNR converted j / , , % = u + × 0,05dB = 23 08 ,1 = u j BER Changes in the signal to noise ratio uncertainty at the receiver input must now be related to changes in the equal level of the unwanted signals. In clause 6.5.5.3 it is shown that the dependency function for signal-to-noise ratio uncertainty is 1/3 (a change in signal to noise ratio will result in 1/3 as much of a change in the level of the two equal unwanted signals). The uncertainty of the two unwanted signals due to the BER uncertainty is therefore: uj level due to BER = 0,05 × 1/3 dB = 0,02 dB This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 3: Uncertainty associated with digital coherent direct modulation (see clause 6.6.4.2) BER uncertainty is calculated using formula 6.10: 3 10 995 ,0 10000 ) 01 ,0 1( 01 ,0 − × = − × = BER j u The theoretical signal to noise ratio per bit for a BER of 10-2 is found from figure 8 and is 2,7. The slope of the BER function is 012 ,0 7,2 2 1 2 1 7,2 = × × × = × × × − − e e SNR SNR π π (formula 6.14). BER uncertainty is then converted to signal-to-noise ratio uncertainty using formula 6.16: ) ( % 07 ,3 % 100 7,2 012 ,0 10 995 ,0 3 p SNR slope u u b BER j SNR j = × × × = × = − This is converted to dB: dB , = , = 13 0 23 07 3 u SNR j ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 67 Changes in the signal to noise ratio uncertainty at the receiver input must now be related to changes in the equal level of the unwanted signals. In clause 6.5.5.3 it is shown that the dependency function for signal-to-noise ratio uncertainty is 1/3 (a change in signal to noise ratio will result in 1/3 as much of a change in the level of the two equal unwanted signals). The uncertainty of the unwanted signals due to the BER uncertainty is therefore: uj level due to BER = 0,13 × 1/3 dB = 0,04 dB This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 4a: Uncertainty associated with digital coherent sub-carrier modulation above the knee point In this case the calculations in case 3 apply and relate to the signal-to-noise ratio of the sub carrier. However as the signal-to-noise ratio dependency function is 1 dB/dB above the knee point, the calculations and the result from case 3 apply directly (0,04 dB). This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. Case 4b: Uncertainty associated with digital coherent sub-carrier modulation below the knee point As in the previous case, the calculations in case 3 apply and relate to the signal-to-noise ratio of the sub-carrier. However for measurements below the knee point, a dependency function must be applied to convert the sub-carrier signal-to-noise ratio uncertainty (3,44 % determined in case 3) to signal-to-noise ratio in the receiving channel. The conversion is performed by means of formula 5.2 (of TR 100 028-1 [6]). Dependency values (noise gradient) found in table F.1 are: - mean value of 0,375 %/% SINAD; - standard deviation is 0,075 %/% SINAD. Therefore: ( ) ( ) ( ) ( ) (p) % 30 1 2 0 375 0 07 3 u 2 2 2 SNR converted j , = % / % , %/% , % , = SINAD SINAD + × dB 06 0 23 30 1 u BER j , = , = Changes in the signal to noise ratio uncertainty at the receiver input must now be related to changes in the equal level of the unwanted signals. In clause 6.5.5.3 it is shown that the dependency function for signal-to-noise ratio uncertainty is 1/3 (a change in signal to noise ratio will result in 1/3 as much of a change in the level of the two equal unwanted signals). The uncertainty of the two unwanted signals due to the BER uncertainty is therefore: uj level due to BER = 0,06 × 1/3 dB = 0,02 dB This RF level uncertainty is then combined with the rest of the part uncertainties to give the total RF level uncertainty. The combined standard uncertainty for intermodulation response rejection (for a bit stream) is: 2 BER to due level j 2 random i 2 C to due level c 2 B to due level c 2 A to due level c immunity ation intermodul c u u u u u u + + + + = Total uncertainty: Case 1 and case 2a dB , = , , , , , 58 0 04 0 2 0 22 0 22 0 44 0 u 2 2 2 2 2 immunity ation intermodul c + + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,58 dB = ±1,14 dB (see clause D.5.6.2). Total uncertainty: Case 2b dB , = , , , , , 58 0 02 0 2 0 22 0 22 0 44 0 u 2 2 2 2 2 immunity ation intermodul c + + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,58 dB = ±1,14 dB (see clause D.5.6.2). ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 68 Total uncertainty: Case 3 and case 4a dB , = , , , , , 58 0 04 0 2 0 22 0 22 0 44 0 u 2 2 2 2 2 immunity ation intermodul c + + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,58 dB = ±1,14 dB (see clause D.5.6.2). Total uncertainty: Case 4b dB , = , , , , , 58 0 02 0 2 0 22 0 22 0 44 0 u 2 2 2 2 2 immunity ation intermodul c + + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,58 dB = ±1,14 dB (see clause D.5.6.2).
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.5.3 Intermodulation immunity (messages)	a) Methodology Three signal generators are connected via three cables to a combining network, in this case a hybrid coupler, whose output is connected directly to a 10 dB attenuator (with a low VSWR) in order to have a good isolation between the three generators. The output of the attenuator is connected to the antenna connection of the receiver under test through a cable, as illustrated in figure 12. Unwanted signal generator A f0 ± d generator B Unwanted signal f0 ± 2*d generator C Wanted signal f0 Termination Response measuring test set Message generator EUT cable cable cable 10 dB att . cable Figure 12: Intermodulation immunity measurement configuration (messages) Generator A (f0 ± d) and generator B (f0 ± 2 × d) are used to produce two unwanted signals with sufficient level to cause 3rd order intermodulation in the wanted channel of the receiver due to non linearities. Generator C is used to produce a wanted signal f0. NOTE 1: f0 is the receive channel frequency and d is a selected frequency (normally 2 or 4 channel separations) from f0. The data output from the receiver is connected to a response measuring test set and the test message applied repeatedly with various levels of (equal) unwanted signal until the specified message acceptance ratio is achieved. Intermodulation immunity is recorded as the average ratio of the signal level from the wanted signal generator to the (equal) signal levels of the unwanted signal generators over 10 measurements. In this example the message consists of 50 bits. One bit error can be corrected. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 69 b) Uncertainty calculations Generator level uncertainty is ±1 dB (d)(r): dB 0,58 3 1 u A/B/C gen j = = (applicable to all generators) In this example calculation, insertion loss for the cables, coupler and attenuator have been individually measured and the standard uncertainty calculated from the various components of uncertainty attributed during their measurement. Cable loss (for each cable) is 0,1 dB and uncertainty: uj cable loss = ±0,1 dB (m)(σ) Coupler attenuation is 3,0 dB and uncertainty: uj coupler att = ±0,15 dB (m)(σ) Attenuator attenuation is 10 dB (x 0,316 linear - required for mismatch calculations) and uncertainty: uj att = 0,1 dB (m)(σ) NOTE 2: In this example case, the three signal generators are identical and are connected to the receiver under test in an identical way. As a consequence the RF level uncertainties at the input of the receiver under test from each generator are assumed to be the same i.e. uc signal A = uc signal B = uc signal C. Therefore, only the level uncertainty of signal generator A will be calculated in detail. Mismatch contributions: - signal generator reflection coefficients are 0,20 (d); - coupler reflection coefficients are 0,07 (d); - cable reflection coefficients are 0,10 (d); - attenuator reflection coefficients are 0,07 (d); - receiver under test reflection coefficients are 0,20 (d). Mismatch uncertainty generator A to the EUT. NOTE 3: The hybrid coupler provides isolation between the generators of greater than 30 dB making any interaction negligible and associated mismatch calculations unnecessary. Cable insertion loss has been assumed to be 0 dB (multiplication by 1 in linear terms) in the following calculations. Coupler loss of 3 dB (multiplication by 0,708 in linear terms) is however taken into consideration in the following calculations. The cable connecting generator A to the coupler is referred to as the input cable, and the cable connecting the coupler to the receiver under test is referred to as the output cable. Mismatch uncertainty between signal generator A and the receiver under test is calculated from the following: (v) % 414 ,1 % 2 100 1,0 2,0 u cable input and generator : mismatch j = × × = (v) % 495 ,0 % 2 100 07 ,0 1,0 u coupler and cable input : mismatch j = × × = (v) % 347 ,0 % 2 100 07 ,0 07 ,0 u att and coupler : mismatch j = × × = (v) % 495 ,0 % 2 100 1,0 07 ,0 u cable output and att : mismatch j = × × = (v) % 414 ,1 % 2 100 2,0 1,0 u EUT and cable output : mismatch j = × × = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 70 (v) % 99 ,0 % 2 100 1 07 ,0 2,0 u 2 coupler and generator : mismatch j = × × × = (v) % 247 ,0 % 2 100 708 ,0 07 ,0 1,0 u 2 att and cable input : mismatch j = × × × = (v) % 049 ,0 % 2 100 316 ,0 1,0 07 ,0 u 2 cable output and coupler : mismatch j = × × × = (v) % 99 ,0 % 2 100 1 2,0 07 ,0 u 2 EUT and att : mismatch j = × × × = (v) % 496 ,0 % 2 100 708 ,0 1 07 ,0 2,0 u 2 2 att and generator : mismatch j = × × × × = (v) % 035 ,0 % 2 100 316 ,0 708 ,0 1,0 1,0 u 2 2 cable output and cable input : mismatch j = × × × × = (v) % 099 ,0 % 2 100 0,1 316 ,0 2,0 07 ,0 u 2 2 EUT and coupler : mismatch j = × × × × = (v) % 071 ,0 % 2 100 316 ,0 708 ,0 0,1 1,0 2,0 u 2 2 2 cable output and generator : mismatch j = × × × × × = (v) % 071 ,0 % 2 100 0,1 316 ,0 708 ,0 2,0 1,0 u 2 2 2 EUT and cable input : mismatch j = × × × × × = (v) % 142 ,0 % 2 100 1 316 ,0 708 ,0 0,1 2,0 2,0 u 2 2 2 2 EUT and generator : mismatch j = × × × × × × = As the isolation between input ports is > 30 dB, any mismatch uncertainty components from the other input ports are negligible. The RSS of all the mismatch uncertainty components detailed above = 2,63 %. The total mismatch uncertainty from any generator to the receiver under test uj mismatch = 2,63/11,5 = 0,23 dB. The total level uncertainty of the signal from generator A at the receiver input is: 2 attenuator j 2 mismatch j 2 coupler i 2 (output) loss cable j 2 (input) loss cable j 2 A g j A signal c u u u u u u u + + + + + = en dB , , + , + , + , + , 66 ,0 1 0 23 0 15 0 10 0 10 0 58 0 = u 2 2 2 2 2 2 A signal c = + As previously stated uc signal A = uc signal B = uc signal C therefore: uc signal. B = 0,66 dB and uc signal C = 0,66 dB. Intermodulation product level uncertainties: Uncertainty due to unwanted signal level (Generator A): In clause 6.5.5.2.1 it is shown that the dependency function for the unwanted signal (from signal generator A) at frequency f0 ± d is 2/3. The uncertainty of the measured result due to the level of signal A (uj level due to A) is therefore 0,66 × 2/3 = 0,44 dB. Uncertainty due to unwanted signal level (Generator B): In clause 6.5.5.2.1 it is also shown that the dependency function for the unwanted signal (from signal generator B) at frequency f0 ± 2 × d is 1/3. The uncertainty of the measured result due to the level of signal B (uj level due to B) is therefore 0,66 × 1/3 = 0,22 dB. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 71 Uncertainty due to wanted signal level (Generator C): In clause 6.5.5.2.2 it is shown that the dependency function of the wanted signal (from signal generator C) is 1/3. The uncertainty of the measured result due to the level of signal C (uj level due to C) is therefore: 0,66 × 1/3 dB = 0,22 dB. Random uncertainty: The standard deviation of random uncertainty is taken as 0,2 dB (m)(σ). Message acceptance measurement uncertainty: Case 1: Uncertainty associated with digital non-coherent direct modulation In the following calculation the signal-to-noise ratio of the receiver is assumed to change 3 dB per dB level change of the two unwanted signals due to the third order function. The calculations are carried out using signal-to-noise ratio values, but the uncertainties involved are applicable to the measured values (the actual ratios between the wanted signal level and the unwanted signal levels). The straddle (up-down) method level recordings are "generator settings" between 1 dB and 4 dB corresponding to receiver signal-to-noise levels between 1 dB and 12 dB. The corresponding message acceptance at these signal-to-noise ratios are: (The calculation method is shown in clause 6.6.4.5 of TR 100 028-1 [6], and the corresponding receiver signal-to-noise ratios are used.) Message acceptance at reading = 1 dB. The receiver signal-to-noise ratio is 3 dB corresponding to 1,995. The BER corresponding to this value is: 1844 ,0 5,0 995 ,1 5,0 = × = × − e BER and the message acceptance 00046 ,0 ) ) 1844 ,0 1( 1844 ,0 50 ( ) 1844 ,0 1( )1( ) 0 ( )1( 49 50 = − × × + − = + = p p Ma Message acceptance at reading = 2 dB. The receiver signal-to-noise ratio is 6 dB corresponding to 3,98. The BER corresponding to this value is: 0683 ,0 5,0 98 ,3 5,0 = × = × − e BER and the message acceptance 1356 ,0 ) ) 0683 ,0 1( 0683 ,0 50 ( ) 0683 ,0 1( )1( ) 0 ( ) 2 ( 49 50 = − × × + − = + = p p Ma Message acceptance at reading = 3 dB. The receiver signal-to-noise ratio is 9 dB corresponding to 7,94. The BER corresponding to this value is: 0094 ,0 5,0 94 ,7 5,0 = × = × − e BER and the message acceptance 9192 ,0 ) ) 0094 ,0 1( 0094 ,0 50 ( ) 0094 ,0 1( )1( ) 0 ( ) 3 ( 49 50 = − × × + − = + = p p Ma Message acceptance at reading = 4 dB. The receiver signal-to-noise ratio is 12 dB corresponding to 15,85. The BER corresponding to this value is: 00018 ,0 5,0 85 , 15 5,0 = × = × − e BER and the message acceptance 9999 ,0 ) ) 00018 ,0 1( 00018 ,0 50 ( ) 00018 ,0 1( )1( ) 0 ( ) 4 ( 49 50 = − × × + − = + = p p Ma Based on these 4 values, the probabilities of each reading can be calculated. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 72 The method is given in clause 6.7 of TR 100 028-1 [6]: 1 dB: Probability of going up = 1 - 0,000463 = 1,00 Probability of going down = 0,000463 = 9,7 × 10-11 2 dB: Probability of going up = 1 - 0,13563 = 0,998 Probability of going down = 0,13563 = 0,0025 3 dB: Probability of going up = 1 - 0,91923 = 0,2233 Probability of going down = 0,91923 = 0,7767 4 dB: Probability of going up = 1 - 0,99993 = 0,0003 Probability of going down = 0,99993 = 0,9997 Based on these 4 sets of probabilities, the probability of each reading can be calculated: (as the probability of going down to 1 dB from 2 dB is 0,0025, the 1 dB reading is disregarded in the following, leaving 3 equations) - p(2 dB) = p(3 dB) × 0,7767; - p(3 dB) = p(2 dB) × 1,0 + p(4 dB) × 1,0; - p(4 dB) = p(3 dB) × 0,2233; - In addition p(2 dB) + p(3 dB) + p(4 dB) = 1,0. The results are: - p(2 dB) = 0,388; - p(3 dB) = 0,500; - p(4 dB) = 0,112. From these values the standard deviation of the uncertainty caused by the straddle method is calculated: - X = 2 × 0,388 + 3 × 0,500 + 4 × 0,112 = 2,72 dB; - Y = 22 × 0,388 + 32 × 0,500 + 42 × 0,112 = 7,84 dB. dB 0,211 10 72 ,2 84 ,7 10 2 2 = − = − = X Y u straddle j Case 2a: Uncertainty associated with digital non-coherent sub-carrier based modulation above the knee point As the signal-to-noise ratio dependency function is 1 dB/dB above the knee point the calculations and the result from Case 1 applies. Case 2b: Uncertainty associated with digital non-coherent sub-carrier based modulation below the knee point Below the knee point the receiver signal-to-noise ratio will change 3 dB per dB unwanted signal level change. In addition the signal-to-noise ratio of the sub-carrier will change approximately 3 dB per dB receiver signal-to-noise ratio. This causes the signal-to-noise ratio of the sub-carrier to change approximately 9 dB per dB unwanted signal level change. The straddle method will therefore be switching between two level settings of the unwanted signal levels: one where the message acceptance is approximately 1,0 and one where the message acceptance is approximately 0,0. The result will be the average of these two settings, but the correct value can be anywhere between the two settings. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 73 Therefore the measurement uncertainty limits are ±0,5 dB with a rectangular distribution giving the standard deviation: dB 0,29 3 5,0 = = straddle j u Case 3: Uncertainty associated with digital coherent direct modulation In the following calculation the signal-to-noise ratio of the receiver is assumed to change 3 dB per dB level change of the two unwanted signals due to the third order function. The calculations are carried out using signal-to-noise ratio values, but the uncertainties involved are applicable to the measured values (the actual ratios between the wanted signal level and the unwanted signal levels). The straddle (up-down) method level recordings are "generator settings" between 0 dB and 3 dB corresponding to receiver signal-to-noise levels between 0 dB and 9 dB. The corresponding message acceptance at these signal-to-noise ratios are (the calculation method is shown in clause 6.6.4.2 of TR 100 028-1 [6], and the corresponding receiver signal-to-noise ratios are used). Message acceptance at reading = 0 dB. The receiver signal-to-noise ratio is 0 dB corresponding to 1,0. The BER corresponding to this value is read from figure 21 to be 0,08 and the message acceptance: 08 ,0 ) ) 08 ,0 1( 08 ,0 50 ( ) 08 ,0 1( )1( ) 0 ( ) 0 ( 49 50 = − × × + − = + = p p Ma Message acceptance at reading = 1 dB. The receiver signal-to-noise ratio is 3 dB corresponding to 2,00. The BER corresponding to this value is read from figure 21 to be 0,024 and the message acceptance: 662 ,0 ) ) 024 ,0 1( 024 ,0 50 ( ) 024 ,0 1( )1( ) 0 ( )1( 49 50 = − × × + − = + = p p Ma Message acceptance at reading = 2 dB. The receiver signal-to-noise ratio is 6 dB corresponding to 3,98. The BER corresponding to this value is read from figure 21 to be 0,0024 and the message acceptance. 994 ,0 ) ) 0024 ,0 1( 0024 ,0 50 ( ) 0024 ,0 1( )1( ) 0 ( ) 2 ( 49 50 = − × × + − = + = p p Ma Message acceptance at reading = 3 dB. The receiver signal-to-noise ratio is 9 dB corresponding to 7,94. The BER corresponding to this value is read from figure 21 to be 0,00003 and the message acceptance. 0,1 ) ) 00003 ,0 1( 00003 ,0 50 ( ) 00003 ,0 1( )1( ) 0 ( ) 3 ( 49 50 = − × × + − = + = p p Ma Based on these 4 values, the probabilities of each reading can be calculated. The method is given in clause 6.7 of TR 100 028-1 [6]: 0 dB: Probability of going up = 1 - 0,083 = 0,9995; Probability of going down = 0,083 = 0,0005; 1 dB: Probability of going up = 1 - 0,6623 = 0,710; Probability of going down = 0,6623 = 0,290; 2 dB: Probability of going up = 1 - 0,9943 = 0,018; Probability of going down = 0,9943 = 0,982; ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 74 3 dB: Probability of going up = 1 - 0,999993 = 0,00003; Probability of going down = 0,999993 = 0,99997. Based on these 4 sets of probabilities, the probability of each reading can be calculated: (as the probability of going up to 3 dB from 2 dB is 0,018, the 3 dB reading is disregarded in the following, leaving 3 equations): - p(0 dB) = p(1 dB) × 0,290; - p(1 dB) = p(0 dB) × 1,0 + p(2 dB) × 1,0; - p(2 dB) = p(1 dB) × 0,710; - In addition p(2 dB) + p(3 dB) + p(4 dB) = 1,0. The results are: - p(0 dB) = 0,145; - p(1 dB) = 0,500; - p(2 dB) = 0,355. From these values the standard deviation of the uncertainty caused by the straddle method is calculated: - X = 0 × 0,145 + 1 × 0,500 + 2 × 0,355 = 1,21 dB; - Y = 02 × 0,145 + 12 × 0,500 + 22 × 0,355 = 1,92 dB. dB 0,213 10 21 ,1 92 ,1 10 2 2 = − = − = X Y u straddle j Case 4a: Uncertainty associated with digital non-coherent sub-carrier based modulation above the knee point As the signal-to-noise ratio dependency function is 1 dB/dB above the knee point the calculations and the result from Case 1 applies. Case 4b: Uncertainty associated with digital non-coherent sub-carrier based modulation below the knee point Below the knee point the receiver signal-to-noise ratio will change 3 dB per dB unwanted signal level change. In addition the signal-to-noise ratio of the sub-carrier will change approximately. 3 dB per dB receiver signal-to-noise ratio. This causes the signal-to-noise ratio of the sub-carrier to change approximately 9 dB per dB unwanted signal level change. The straddle method will therefore be a switching between two level settings of the unwanted signal levels: one where the message acceptance is approximately. 1,0 and one where the message acceptance is approximately 0,0. The result will be the average of these two settings, but the correct value can be anywhere between the two settings. Therefore the measurement uncertainty limits are ± 0,5 dB with a rectangular distribution giving the standard deviation dB 0,29 3 5,0 = = straddle j u The combined standard uncertainty for intermodulation response rejection (for message acceptance) is: 2 straddle j 2 random i 2 C to due level c 2 B to due level c 2 A to due level c immunity ation intermodul c u u u u u u + + + + = Total uncertainty: Case 1 and case 2a dB , = , , , , , 61 0 211 0 2 0 22 0 22 0 44 0 u 2 2 2 2 2 immunity ation intermodul c + + + + = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 75 Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,61 dB = ±1,2 dB (see clause D.5.6.2). Total uncertainty: Case 2b dB , = , , , , , 64 0 29 0 2 0 22 0 22 0 44 0 u 2 2 2 2 2 immunity ation intermodul c + + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,64 dB = ±1,25 dB (see clause D.5.6.2). Total uncertainty: Case 3 and case 4a dB , = , , , , , 61 0 213 0 2 0 22 0 22 0 44 0 u 2 2 2 2 2 immunity ation intermodul c + + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,61 dB = ±1,2 dB (see clause D.5.6.2). Total uncertainty: Case 4b dB 0,64 = 29 ,0 2 0 22 0 22 0 44 0 u 2 2 2 2 2 immunity ation intermodul c , , , , + + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,64 dB = ±1,25 dB (see clause D.5.6.2).
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.6 Blocking immunity or desensitization
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.6.1 Blocking immunity or desensitization for analogue speech	The only difference between this test and the spurious response immunity test in clause 4.1.4.1 is that the interfering signal has a narrower frequency sweep. All other factors are the same and, assuming the single side-band phase noise of the interfering signal generator does not adversely effect performance, the calculation of measurement uncertainty is the same as for clause 4.1.4.1.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.6.2 Blocking immunity or desensitization for bit streams	The only difference between this test and the spurious response immunity test in clause 4.1.4.2 is that the interfering signal has a narrower frequency sweep. All other factors are the same and, assuming the single side-band phase noise of the interfering signal generator does not adversely effect performance, the calculation of measurement uncertainty is the same as for clause 4.1.4.2.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.6.3 Blocking immunity or desensitization for messages	The only difference between this test and the spurious response immunity test in clause 4.1.4.3 is that the interfering signal has a narrower frequency sweep. All other factors are the same and, assuming the single side-band phase noise of the interfering signal generator does not adversely effect performance, the calculation of measurement uncertainty is the same as for clause 4.1.4.3. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 76
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.7 Conducted spurious emissions	a) Direct reading method A spectrum analyser is calibrated from its internal reference source using a cable with negligible loss at the calibration reference frequency. The receiver under test is then connected to the spectrum analyser (see figure 13a) and an absolute reading for each spurious signal obtained on the analyser. The levels are corrected for cable loss (which becomes significant at the higher spurious frequencies) and recorded as the results for a direct reading. For this example, measurement uncertainty must include components of uncertainty for the spectrum analyser, cable loss and various mismatches between the receiver, cables and spectrum analyser. cable alternative cable position when calibrating Spectrum analyser Receiver under test cal ref o/p Figure 13a: Conducted spurious emission measurement configuration (direct method) b) Measurement uncertainty for the direct method Mismatch uncertainty: Mismatch uncertainty when calibrating the spectrum analyser: - spectrum analyser calibration reference output reflection coefficient is 0,2 (d); - spectrum analyser input reflection coefficient is 0,1 (d); - calibration cable reflection coefficient is 0,2 (d). For calculation of mismatch, attenuation of the calibration cable is assumed to be 0,00 dB (x 1 linear): (v) % 828 ,2 2 100 2 0 2 0 u cable and output reference n calibratio : mismatch j % , , = × × = (v) % 414 ,1 2 100 2 0 1 0 u cable and input analyser spectrum : mismatch j % , , = × × = (v) % 414 ,1 2 100 0,1 2 0 1 0 u 2 output cal analyzer spectrum and input analyser spectrum : mismatch j % , , = × × × = The combined standard uncertainty for mismatch during calibration is: (v) % 464 ,3 414 ,1 828 ,2 414 1 u 2 2 2 n calibratio : mismatch j , = + + = Mismatch uncertainty when measuring the receiver spurious: - receiver reflection coefficient is 0,7 (see table F.1); - measurement cable reflection coefficient is 0,2 (d); - spectrum analyser input reflection coefficient is 0,1 (d). ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 77 For the calculation of mismatch, measurement cable attenuation is assumed to be 0,00 dB (x1 linear - providing worst case mismatch). (v) % 899 9 2 100 2 0 7 0 u cable and receiver : mismatch j , % , , = × × = (v) % 414 1 2 100 1 0 2 0 u analyser spectrum and cable : mismatch j , % , , = × × = (v) % 950 ,4 2 100 0,1 1 0 7 0 u 2 analyser spectrum and receiver : mismatch j % , , = × × × = The combined standard uncertainty for mismatch with the receiver connected is: (v) % 158 , 11 950 ,4 414 1 899 ,9 u 2 2 2 connected receiver : mismatch j , = + + = The combined standard uncertainty for mismatch is: (v) % 683 , 11 464 ,3 158 , 11 u 2 2 : mismatch j = + = Uncertainty when making the measurement on the spectrum analyser: dB , , 173 0 3 3 0 u reference n calibratio j = = dB , , 443 1 3 5 2 u response frequency j = = dB , , 289 0 3 5 0 u switching bandwidth j = = dB , , 866 0 3 5 1 u fidelity log j = = dB ,115 0 3 2,0 u switching attenuator input j = = Standard uncertainty of measurement cable is 0,2 dB (m)(σ). NOTE 1: The uncertainty of the cable loss during calibration of the spectrum analyser is assumed to be negligible. Random uncertainty: Random uncertainty is ±0,2 dB (m)(σ). Uncertainty due to supply voltage: Supply voltage uncertainty is ±100 mV (r). Supply voltage uncertainty must be converted to an RF level uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 10 % (p)/V; - standard deviation of 3 % (p)/V. Therefore: ( ) ( ) ( ) ( ) ) ( + ×         ) ( % 603 0 = V / % 0,3 V / % 0 10 3 V 1,0 u 2 2 2 voltage supply converted j σ p , , = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 78 The combined standard uncertainty is: (dB) = , , , , , , , , , , 018 ,2 0 23 603 0 2 0 2 0 115 0 866 0 289 0 443 1 173 0 5 11 683 , 11 u 2 2 2 2 2 2 2 2 2 emission spurious conducted c       + + + + + + + +       = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 2,018 dB = ±3,96 dB (see clause D.5.6.2). c) Spreadsheet implementation of measurement uncertainty This calculation has been implemented in a corresponding spreadsheet (see file "Rx conducted spurious emissions (direct).xls") and is available in tr_10002802v010301p0.zip. d) Substitution method In order to reduce measurement uncertainty, the receiver may be substituted by a signal generator and the level from the generator increased until the same reading (as obtained with the receiver) is obtained again on the analyser. The level on the signal generator is then recorded as the result using substitution. In this case, the large uncertainty of the spectrum analyser is replaced with the much lower uncertainty of the signal generator, and the cable uncertainty can also be ignored since it is common to both measurements. cable alternative cable position when substituting Spectrum analyser Signal generator Receiver under test Figure 13b: Conducted spurious emission measurement configuration (substitution method) e) Measurement uncertainty for the substitution method Mismatch uncertainty - receiver reflection coefficient is 0,7 (table F.1); - measurement cable reflection coefficient is 0,2 (m); - spectrum analyser input reflection coefficient is 0,1 (d); - signal generator reflection coefficient is 0,35 (d). For the calculation of mismatch, cable attenuation is assumed to be 0,00 dB (x 1 linear - providing a worst case mismatch). (v) % 899 ,9 2 100 2 0 7 0 u cable and receiver : mismatch j % , , = × × = (v) % 414 1 2 100 1 0 2 0 u analyser spectrum and cable : mismatch j , % , , = × × = (v) % 950 ,4 2 100 0,1 1 0 7 0 u 2 analyser spectrum and receiver : mismatch j % , , = × × × = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 79 (v) % 950 4 2 100 2 0 35 0 u cable and generator : mismatch j , % , , = × × = (v) % 475 ,2 2 100 0,1 1 0 35 0 u 2 analyser spectrum and generator : mismatch j % , , = × × × = The combined standard uncertainty for mismatch is: (v) % 455 , 12 475 ,2 950 ,4 950 ,4 414 1 899 ,9 u 2 2 2 2 2 mismatch c , = + + + + = Uncertainty when making the measurement: Signal generator (substitution signal) uncertainty ±1,5 dB (d): dB , , u enerator j Signal g 866 0 3 5 1 = = Random uncertainty: Random uncertainty is 0,2 dB (m)(σ). Uncertainty due to supply voltage: Supply voltage uncertainty is ±100 mV (r). Supply voltage uncertainty must be converted to an RF level uncertainty by means of formula 5.2 (see TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value of 10 % (p)/V; - standard deviation of 3 % (p)/V. Therefore: ( ) ( ) ( ) ( ) ) ( + ×         ) ( % 0,603 = V / % 0,3 V / % 10,0 3 V 1,0 u 2 2 2 voltage supply converted j σ p = The combined standard uncertainty is: dB = , , , = 401 ,1 0 23 603 0 2,0 866 ,0 5 11 455 , 12 u 2 2 2 2 emission spurious conducted c       + + +       Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 1,401 dB = ±2,75 dB (see clause D.5.6.2). NOTE 2: The substitution example has a far lower measurement uncertainty than the direct example.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.8 Amplitude characteristic for analogue speech	a) Methodology The receiver under test is connected to a signal generator via a cable. The output from the receiver is connected to an AF voltmeter and load. The signal generator is adjusted to produce an appropriate level (usually near the threshold of limiting) and a reading on the AF voltmeter obtained. The signal generator is then adjusted to produce a considerably higher level and a second reading on the AF voltmeter obtained. The amplitude characteristic is recorded as the ratio (in dBs) between the two readings. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 80 Modulating AF oscillator Signal generator Receiver under test AF load AF Voltmeter cable Figure 14: Amplitude characteristic measurement configuration Uncertainty contributions affecting RF input level must be included for the first measurement (combined and converted to AF level uncertainty by an appropriate dependency function) because at low RF levels below limiting, a small change in receiver RF input level may result in a relatively large change in AF output. In the second measurement (well above limiting) the resulting change at in AF output will usually be relatively small and the uncertainty of the RF input signal therefore considered negligible. b) Measurement uncertainty Mismatch uncertainty: - signal generator reflection coefficient is 0,2 (d); - receiver reflection coefficient (see table F.1) is 0,2; - cable reflection coefficients are 0,1 (d). In the calculation of mismatch uncertainty the cable attenuation is assumed to be 0,0 dB (x 1 linear). (v) % 414 1 2 100 1 0 2 0 u cable and generator : mismatch j , % , , = × × = (v) % 414 1 2 100 2 0 1 0 u receiver and cable : mismatch j , % , , = × × = (v) % 828 2 2 100 1 2 0 2 0 u 2 receiver and generator : mismatch j , % , , = × × × = The combined standard uncertainty is: (v) % 464 3 828 ,2 414 ,1 414 ,1 u 2 2 2 : mismatch c , = + + = AF level uncertainty: Signal generator level uncertainty 1 dB (d)(r): dB , , 577 0 3 0 1 u level generator signal j = ± = Uncertainty of the cable attenuation is 0,1 dB (m)(σ). The combined standard uncertainty for the level is: dB 659 ,0 1,0 577 ,0 5, 11 464 ,3 u 2 2 2 : level c = + +       = ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 81 RF level uncertainty is converted to AF level uncertainty by means of formula 5.2 (of TR 100 028-1 [6]) and table F.1. Dependency values found in table F.1 are: - mean value is 0,05 %/%; - standard deviation is 0,02 %/% level. Dependency values must be converted from percentage to dBs using table 1 in clause 5.2 of TR 100 028-1 [6]. Since like units are involved (i.e. % per %), the dependency values can be considered as: - mean value of 0,05 dB/dB; - standard deviation of 0,02 dB/dB level. Therefore: ( ) ( ) ( ) dB , = dB / dB , dB / dB , dB , 035 0 02 0 05 0 659 0 u 2 2 2 level AF j + × = In the first measurement there may be some variation in the AF voltmeter reading due to noise. Noise variation at low RF level is 0,2 dB (m)(σ). In the second measurement the AF level is well above the system noise floor and the variation therefore negligible. AF volt meter uncertainty is ±0,2 dB (d) (r) (Must be allowed for twice): dB 0,115 3 0,2 u meter volt j = = The combined standard uncertainty for amplitude characteristic is: dB , , , , , 260 0 115 0 115 0 2 0 035 0 u 2 2 2 2 stic characteri amplitude c = + + + = Using an expansion factor (coverage factor) of k = 1,96, the expanded measurement uncertainty is ±1,96 × 0,260 dB = ±0,51 dB (see TR 100 028-1 [6], clause D.5.6.2). c) Spreadsheet implementation of measurement uncertainty This calculation has been implemented in a corresponding spreadsheet (see file "Amplitude characteristic.xls") and is available in tr_10002802v010301p0.zip.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.9 Audio frequency response for analogue speech	Example not provided.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.10 Harmonic distortion for analogue speech	Example not provided.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.11 Hum and noise for analogue speech	Example not provided.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.12 Multi-path sensitivity	Example not provided.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.13 Bit error ratio	Example not provided. ETSI ETSI TR 100 028-2 V1.4.1 (2001-12) 82
9183669bb4288f694ed0630f17da78b6	100 028-2	4.1.14 Opening delay for data	Example not provided.
9183669bb4288f694ed0630f17da78b6	100 028-2	4.2 Radiated
9183669bb4288f694ed0630f17da78b6	100 028-2	4.2.1 Sensitivity tests (30 MHz to 1 000 MHz)	A fully worked example illustrating the methodology to be used can be found in TR 102 273 [2], part 1, clause 11.

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