INTERNATIONAL ELECTROTECHNICAL COMMISSION____________ ELECTROMAGNETIC COMPATIBILITY EMC – Part 4-10: Testing and measurement techniques – Damped oscillatory magnetic field immunity test
Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60050 as well as the following apply
3.1.1 calibration set of operations which establishes, by reference to standards, the relationship which exists, under specified conditions, between an indication and a result of a measurement
Note 1 to entry: This term is based on the "uncertainty" approach
Note 2 to entry: The relationship between the indications and the results of measurement can be expressed, in principle, by a calibration diagram
3.1.2 damped oscillatory wave generator generator delivering a damped oscillation whose frequency can be set to 100 kHz or 1 MHz and whose damping time constant is five periods
3.1.3 immunity ability of a device, equipment or system to perform without degradation in the presence of an electromagnetic disturbance
3.1.4 induction coil conductor loop of defined shape and dimensions, in which a current flows, generating a magnetic field of defined uniformity in a defined volume
3.1.5 induction coil factor ratio between the magnetic field strength generated by an induction coil of given dimensions and the corresponding current value
Note 1 to entry: The field is that measured at the centre of the coil plane, without the EUT
The proximity method involves applying a magnetic field to the Equipment Under Test (EUT) by moving a small induction coil along its side This technique is used to identify areas of the EUT that are particularly sensitive to magnetic fields.
The reference ground is defined as a section of the Earth that is conductive and is typically regarded as having an electrical potential of zero This area is situated beyond the influence of any grounding systems.
3.1.8 system set of interdependent elements constituted to achieve a given objective by performing a specified function
The system is defined as being isolated from its environment and other external systems by an imaginary boundary that disconnects them This boundary signifies that the system can be influenced by the environment and external systems, while also having the capacity to interact with them.
Transient, as both an adjective and a noun, refers to a phenomenon or quantity that fluctuates between two consecutive steady states within a time interval that is brief relative to the time scale of interest.
3.1.10 verification set of operations which is used to check the test equipment system (e.g the test generator and its interconnecting cables) to demonstrate that the test system is functioning
Note 1 to entry: The methods used for verification may be different from those used for calibration
Note 2 to entry: For the purposes of this basic EMC standard this definition is different from the definition given in IEC 60050-311:2001, 311-01-13.
Abbreviations
Damped oscillatory magnetic fields arise from the switching of high-voltage bus-bars by isolators or disconnectors These magnetic fields can significantly impact the reliable operation of various equipment and systems.
The tests aim to showcase the equipment's immunity to damped oscillatory magnetic fields, which are influenced by the equipment's specific location and installation conditions, such as its proximity to disturbance sources.
The wave shape of the test field corresponds to a damped oscillatory wave (see Figure 2) The characteristics are given in 6.2.2
Information on the oscillation frequency is given in Annex C
The preferred range of test levels is given in Table 1
Level Damped oscillatory magnetic field strength
The magnetic field strength is measured in A/m, where 1 A/m equates to a magnetic flux density of 1.26 µT in free space The level "X" can represent any value, whether above, below, or between other levels, and both this level and the test duration must be detailed in the equipment specifications.
The test levels shall be selected according to the installation conditions Classes of installation are given in Annex B
General
The test system comprises the damped oscillatory wave generator and the induction coil for a table-top test setup and, in addition, an RGP for a floor-standing test setup.
Damped oscillatory wave generator
General
The damped oscillatory wave generator shall be able to deliver the required impulse current to the induction coils specified in 6.3
NOTE For this application, a modified version of a damped oscillatory wave generator similar to the generator mentioned in IEC 61000-4-18 is used as a current source
The waveform is specified as a short-circuit current and therefore shall be measured with the induction coil connected
A simplified circuit diagram of the generator is given in Figure 1
U: High voltage source R c: Charging resistor
C: Control duration L: Coil oscillation circuit
C 1, C 2: Capacitors oscillation circuit (switchable from 0,1 MHz to 1 MHz)
Figure 1 – Simplified schematic circuit of the test generator for damped oscillatory magnetic field
Performance characteristics of the generator connected to the
The performance characteristics below are applicable for the generator connected to the standard induction coils outlined in 6.3
Current in the coils (Pk 1 value) see Table 2
Waveform of the damped oscillatory magnetic field see Figure 2
Decay rate D r1 , D r2 Pk 5 shall be > 50 % of the Pk 1 value and Pk 10 shall be < 50 % of the Pk 1 value Repetition rate 1/T rep (see Figure 3) 40/s ± 10 % for 100 kHz and 400/s ± 10 % for
Test duration not less than 2 s
Oscillation frequency is defined as the reciprocal of the period of the first and third zero crossings after the initial peak This period is shown as T in Figure 2
T = 1 às (1 MHz) or 10 às (0,1 MHz)
Figure 2 – Waveform of short-circuit current in the standard coils
Figure 3 – Waveform of short-circuit current showing the repetition time T rep
The formula of the ideal waveform of Figure 2, I DOS (t), is as follows:
− where the parameters for oscillation period T = 1 às are:
T and the parameters for the oscillation period T = 10 às are:
Standard induction coil
The field distribution for the two single-turn standard coils measuring 1 m x 1 m and 1 m x 2.6 m is established and detailed in Annex A, eliminating the need for field verification or calibration Consequently, the current measurement depicted in Figure 4 is adequate for our purposes.
Figure 4 – Example of a current measurement of standard induction coils
The induction coil must be constructed from copper, aluminum, or any other conductive non-magnetic material, designed with a cross-section and mechanical arrangement that ensures stable positioning during testing.
The characteristics of induction coils with respect to the magnetic field distribution are given in Annex A.
Calibration of the test system
The essential characteristics of the test system shall be calibrated by a current measurement (see Figure 4)
To ensure accurate verification of the output current, the generator must be connected to the standard induction coil as outlined in section 6.3 This connection should be made using twisted conductors or a coaxial cable, with a maximum length of 3 meters and an appropriate cross-section.
Calibrations conducted at test level 5 with the 1 m × 2.6 m standard induction coil are not governed by the specifications in Table 3 Instead, these calibrations must exclusively utilize the 1 m × 1 m standard induction coil.
The following specifications given in Table 2 and Table 3 shall be verified
Table 2 – Peak current specifications of the test system
System using 1 m × 1 m standard induction coil System using 1 m × 2,6 m standard induction coil
111 special/0,9 not applicable not applicable 15,2 45,5 see note 2 special/0,66
NOTE 1 The values 0,9 and 0,66 are the calculated coil factors of standard induction coils
NOTE 2 The calculated value is 152; however, there is currently no commercial generator available
Table 3 – Waveform specifications of the test system
Oscillation period T = 10 às ± 1 às T = 1 às ± 0,1 às
Repetition time of the pulses T rep = 25 ms ± 2,5 ms T rep = 2,5 ms ± 0,25 ms
Decay rate of one pulse D r 1 = I ( PK 5 ) (÷I PK 1 ) > 50 %
The calibrations shall be performed at all levels which are used by laboratories
The calibrations shall be carried out with a current probe and oscilloscope or other equivalent measurement instrumentation with a 10 MHz minimum bandwidth
Test equipment
The following equipment is part of the test setup:
– auxiliary equipment (AE) when required;
– cables (of specified type and length);
– RGP in case of testing floor standing equipment.
Verification of the test instrumentation
The purpose of verification is to ensure that the test setup is operating correctly The test setup includes:
– the damped oscillatory wave generator;
– the interconnection cables of the test equipment
To verify that the system is functioning correctly, the following signal should be checked: – impulse present at the standard induction coil terminals
It is sufficient to verify that the impulse is present at any level by using suitable measuring equipment (e.g current probe, oscilloscope)
NOTE Test laboratories can define an internal control reference value assigned to this verification procedure.
Test setup for table-top EUT
Table-top EUTs must be positioned on a non-conductive table For testing EUTs measuring up to 0.6 m × 0.6 m × 0.5 m (L × W × H), a standard 1 m × 1 m induction coil is applicable Alternatively, a 1 m × 2.6 m standard induction coil can be utilized for EUTs with dimensions up to 0.6 m × 0.6 m × 2 m (L × W × H).
The induction coil shall be positioned in three orthogonal orientations
When an EUT does not fit into the induction coil of 1 m x2,6 m, the proximity method (see 7.4) shall be applied
During testing, it is essential to minimize the impact of cables on results by routing them away from the induction coil This careful cabling arrangement should be considered when determining the maximum size of the Equipment Under Test (EUT).
An RGP is unnecessary below the EUT, as illustrated in Figure 5 It is essential to maintain a distance of at least 0.5 meters between the induction coil and any conductive surfaces, such as the walls and floor of a shielded enclosure.
Figure 5 – Example of test setup for table-top equipment
Test setup for floor standing EUT
The standard induction coil used for testing floor-standing equipment, such as racks, features a rectangular design measuring 1 m × 2.6 m, with one short side potentially serving as the reference ground plane (RGP) for larger equipment Additionally, a smaller 1 m × 1 m induction coil is suitable for testing floor-standing equipment with maximum dimensions of 0.6 m × 0.6 m.
The RGP shall have a minimum thickness of 0,65 mm and a minimum size of 1 m × 1 m The EUT shall be insulated from the RGP
Figure 6 – Example of test setup for floor standing equipment showing the horizontal orthogonal plane
For floor-standing equipment, such as cabinets, where the top of the Equipment Under Test (EUT) exceeds 0.75 m from the Reference Ground Plane (RGP), multiple testing positions are required Additionally, the induction coil depicted in Figure 6 must not be positioned below 0.5 m An example of testing using a vertical orthogonal plane is illustrated in Figure 7.
Figure 7 – Example of test setup for floor standing equipment showing the vertical orthogonal plane
The test volume of the rectangular coil is 0,6 m × 0,6 m × 2 m (L × W × H)
When an EUT does not fit into the rectangular coil of 1 m × 2,6 m, the proximity method (see Figure 8 and 7.5 for more detailed information) shall be applied
To ensure accurate test results, it is essential to minimize the impact of cables near the induction coil Proper routing of the cables can significantly affect the outcomes, so their dimensions should be carefully considered Additionally, the minimized cable size must be factored into determining the maximum allowable size of the Equipment Under Test (EUT).
Figure 8 – Example of test setup using the proximity method
Test setup for damped oscillatory field applied in-situ
In-situ testing is often the sole viable method for assessing large machinery and similar equipment, particularly when a reference ground plane (RGP) is unavailable In such cases, the proximity method becomes the only practical testing approach For effective in-situ testing, a standard induction coil measuring 1 m × 1 m should be utilized, ensuring it is isolated from the equipment under test (EUT) Additionally, it is crucial to maintain a distance of (10 ± 1) cm between the standard induction coil and the EUT.
NOTE The distance has been defined to ensure the same field strength as in the center of the standard induction coil
General
– the verification of the test instrumentation according to 7.2;
– the establishment of the laboratory reference conditions;
– the confirmation of the correct operation of the EUT;
– the execution of the test;
– the evaluation of the test results (see Clause 9).
Laboratory reference conditions
Climatic conditions
Laboratory climatic conditions must adhere to the limits set by the manufacturers for both the Equipment Under Test (EUT) and the test equipment, unless specified otherwise in generic, product-family, or product standards.
Tests shall not be performed if the relative humidity is so high as to cause condensation on the EUT or the test equipment.
Electromagnetic conditions
The electromagnetic conditions of the laboratory shall be such as to guarantee the correct operation of the EUT so as not to influence the test results
Execution of the test
Verification shall be performed It is preferable to perform the verification prior to the test (see 7.2)
The test shall be performed according to a test plan which shall specify the test setup, including:
• test duration (not less than 2 s);
• representative operating conditions of the EUT;
• locations of the standard induction coil relative to the EUT (test points);
• selection and justification of test points (recommended are areas of EUT susceptible to damped oscillatory magnetic fields)
Testing and calibration shall be performed based on the waveform specified in Figure 2 and Figure 3
NOTE Product committees can apply longer test durations, if appropriate for their products
The test duration shall be applied only one time for each orientation
Test results will be categorized based on the equipment's loss of function or performance degradation compared to the manufacturer's defined standards or agreements with the purchaser The classification includes: a) normal performance within specified limits; b) temporary loss of function that resolves automatically after the disturbance; c) temporary loss requiring operator intervention for recovery; and d) irrecoverable loss of function due to hardware or software damage or data loss.
The manufacturer’s specification may define effects on the EUT which may be considered insignificant, and therefore acceptable
This classification serves as a valuable guide for committees developing performance criteria for generic, product, and product-family standards It also provides a framework for establishing performance criteria agreements between manufacturers and purchasers, particularly in cases where appropriate standards are lacking.
Equipment shall not become dangerous or unsafe as a result of the application of the tests
The test report shall contain all the information necessary to reproduce the test In particular, the following shall be recorded:
– the items specified in the test plan required by 8.3;
– identification of the EUT and any associated equipment, for example, brand name, product type, serial number;
– identification of the test equipment, for example, brand name, product type, serial number; – any special environmental conditions in which the test was performed, for example, shielded enclosure;
– any specific conditions necessary to enable the test to be performed;
– the performance level defined by the manufacturer, requestor or purchaser;
The performance criteria outlined in the relevant generic, product, or product-family standards must be considered, along with any observed effects on the Equipment Under Test (EUT) during or after the application of test disturbances, including the duration of these effects.
– the rationale for the pass/fail decision (based on the performance criterion specified in the generic, product or product-family standard, or agreed between the manufacturer and the purchaser);
– any specific conditions of use, for example cable length or type, shielding or grounding, or EUT operating conditions, which are required to achieve compliance;
– the induction coils selected for the tests;
– the position and orientation of the induction coil relative to EUT
Information on the field distribution of standard induction coils
General
Annex A outlines the maximum dimensions of an EUT and its placement within standard induction coils A magnetic field is deemed sufficiently uniform when its strength varies by no more than ±3 dB from the field strength at the center of the induction coil.
For the field computations the finite cross-section of the loop conductors are neglected (thin wire approximation).
Determination of the coil factor
General
The induction coil factor must be calculated to determine the current needed in the induction coil for achieving the desired magnetic field strength at its center.
Coil factor calculation
The coil factor, denoted as \( k_{CF} \), can be determined using the geometrical dimensions of the induction coil For a single-turn, rectangular induction coil with sides \( a + b \) and \( c \), the calculation of the coil factor is based on these dimensions.
The magnetic field at point P, denoted as H(P), is determined by the induction coil current I, as expressed in equation (A.1) This equation is applicable when the largest dimension of the coil conductor's cross-section is significantly smaller than the shortest side of the induction coil For a square induction coil with side length c, if point P is located at the center, then both dimensions a and b equal c/2 In the case of a rectangular coil, a and b are equal when P is at the center Additionally, if the reference ground plane (RGP) is positioned at the bottom side of the coil, equation (A.1) remains valid by considering the image of the physical coil When P is at the center of the physical coil, the correction factor (k CF) for the coil, which includes both the physical coil and its image, is also represented by equation (A.1) with respect to dimension b.
Figure A.1 – Rectangular induction coil with sides a + b and c
The +3 dB and –3 dB isolines for magnetic field strength are illustrated in Figure A.2 for the x-y plane and in Figure A.3 for the x-z plane The maximum dimensions of the Equipment Under Test (EUT) are 0.6 m in width, 0.6 m in length, and 0.5 m in height.
NOTE The –3 dB isoline is not shown because it is outside the loop
Figure A.2 – +3 dB isoline for the magnetic field strength (magnitude) in the x - y plane for the 1 m × 1 m induction coil
Maximum EUT size (width × length = 0,6 m × 0,6 m) x-y plane x-z plane
Figure A.3 – +3 dB and –3 dB isolines for the magnetic field strength (magnitude) in the x - z plane for the 1 m × 1 m induction coil
A.4 1 m × 2,6 m standard induction coil with reference ground plane
The +3 dB and -3 dB isolines representing the magnetic field strength are illustrated in Figure A.4 for the x-z plane and in Figure A.5 for the x-y plane The maximum dimensions of the Equipment Under Test (EUT) are 0.6 m in width, 0.6 m in length, and 2 m in height.
For the calculation of the ± 3 dB isolines the size of the reference ground plane is considered as infinite
NOTE The –3 dB isoline is not shown because it is outside the loop
Figure A.4 – +3 dB isoline for the magnetic field strength (magnitude) in the x - z plane for the 1 m × 2,6 m induction coil with reference ground plane
Maximum EUT size (width × height = 0,6 m × 2,0m) x-z plane
Maximum EUT size (width × height = 0,6 m × 0,5 m) x-z plane
Figure A.5 – +3 dB and –3 dB isolines for the magnetic field strength (magnitude) in the x - y plane for the 1 m × 2,6 m induction coil with reference ground plane
A.5 1 m × 2,6 m standard induction coil without reference ground plane
The +3 dB and –3 dB isolines for magnetic field strength are illustrated in Figure A.6 for the x-y plane and in Figure A.7 for the x-z plane The maximum dimensions of the Equipment Under Test (EUT) are 0.6 m in width, 0.6 m in length, and 2 m in height.
NOTE The –3 dB isoline is not shown because it is outside the loop
Figure A.6 – +3 dB isoline for the magnetic field strength (magnitude) in the x - y plane for the 1 m × 2,6 m induction coil without reference ground plane
Maximum EUT size (width × length = 0,6 m × 0,6 m)
Figure A.7 – +3 dB and –3 dB isolines for the magnetic field strength (magnitude) in the x - z plane for the 1 m × 2,6 m induction coil without reference ground plane
Maximum EUT size (width × height = 0,6 m × 0,6 m)
Selection of the test levels
Test levels shall be selected in accordance with the electromagnetic environment in which the equipment concerned is intended to be used taking into account most realistic installation conditions
Recommendations for test levels are given in Clause 5 The actual selection of test levels should take into account
– the potential proximity of damped oscillatory magnetic field disturbances sources to the equipment concerned;
– the installation conditions typically to be expected for an installation in the electromagnetic environment under consideration;
– the need and amount of compatibility margins, i.e the margin between the maximum disturbance level and considered immunity level
The selection of appropriate test levels for equipment is influenced by the electromagnetic environment in which it will operate A guide for determining test levels for damped oscillatory magnetic fields testing can be based on typical installation practices that reflect the relevant electromagnetic environment.
Class 1: Electromagnetic environment with particular mitigation measures employed in order to allow electromagnetic phenomena to occur to a certain extent only (e.g phenomenon does not occur, phenomenon occurs with a relatively low amplitude only, etc.)
Controlled electromagnetic environment: where sensitive devices are planned to be used (e.g electron microscopes, cathode ray tubes, etc.)
The test is not applicable to equipment intended to be used in this class of environment
Class 2: Electromagnetic environment representative for residential areas
The test is irrelevant for equipment designed for this environmental class, as these locations are not affected by switching phenomena found in medium- and high-voltage substations.
Class 3: Electromagnetic environment representative for office/commercial areas
This class of environments is typically found near medium-voltage and high-voltage switchgear or conductors that carry related transients For example, a computer room located close to a sub-station exemplifies such a setting.
Class 4: Electromagnetic environment representative for industrial areas
This class of environment is defined by the presence of medium- or high-voltage substations and conductors that carry transient fault currents Key features include control rooms of substations and areas with high-current equipment and installations, which exemplify these locations.
Class 5: Harsh electromagnetic environment which can be characterized by the following attributes: conductors, bus-bars or M.V.or H.V Iines carrying tens of kA
Switchyard areas of heavy industrial plants, M.V/H.V sub-stations and power stations might be representatives for locations with such an electromagnetic environment
Electromagnetic separation of interference sources from equipment circuits, cables, and lines may necessitate varying test levels based on the quality of installations A case-by-case assessment is often required to determine the appropriate levels.
Equipment lines such as cabling, bus bars, and overhead lines in high electromagnetic environments may extend into areas designated for lower test levels Therefore, it is essential to re-evaluate these locations to determine the appropriate test levels required.
The selection of test levels for electromagnetic environments serves as a general guideline However, specific equipment features or unique circumstances may necessitate a different test level than what is typically associated with a given electromagnetic environment It is essential for the involved parties, such as product committees, to conduct a thorough assessment to determine the most suitable test level.
Damped oscillatory magnetic field frequency
The phenomenon is typical of the switching of isolators in H.V sub-stations, and particularly in H.V bus-bars
The operation of high voltage (H.V.) isolators generates sharp front-wave transients with durations around tens of nanoseconds These transients are mitigated by the overall capacitance of the H.V equipment structures as they travel through the system.
The evolution of the voltage front-wave involves reflections caused by the mismatch in characteristic impedance of high voltage (H.V.) circuits Consequently, the transient voltage and current in H.V bus-bars exhibit a fundamental oscillation frequency, which is influenced by the circuit length and propagation time.
General
The compliance of the realized disturbance quantity with the specified standard is typically verified through a series of measurements, such as using an oscilloscope with a current probe to measure the peak of a damped oscillatory current impulse Each measurement carries a degree of measurement uncertainty (MU), stemming from both the limitations of the measuring instruments and the inherent variability of the measurand The assessment of MU is conducted in accordance with the principles and methods outlined in IEC TR 61000-1-6.
To evaluate measurement uncertainty (MU), it is essential to identify the sources of uncertainty associated with both the measuring instruments and the measurand Additionally, one must establish the functional relationship, or measurement model, between the influencing input quantities and the resulting output quantity It is also necessary to estimate the standard uncertainty of the input quantities and to determine an interval that confidently contains the true value of the measurand.
Further details are given in IEC TR 61000-1-6
The estimates and uncertainties related to a specific disturbance quantity do not reflect the level of alignment between the simulated electromagnetic phenomena, as outlined in the fundamental standard, and the actual electromagnetic phenomena observed in the real world outside the laboratory.
The impact of disturbance parameters on the Equipment Under Test (EUT) is often unpredictable, and due to the typically nonlinear behavior of the EUT, it is impossible to define a single estimate and uncertainty for the disturbance quantity Consequently, each parameter of the disturbance quantity must be paired with its respective estimate and uncertainty, resulting in multiple uncertainty budgets.
Legend
I P Peak of the damped oscillatory current impulse injected into the coil
H P Peak of the magnetic field impulse k CF Coil factor of the induction coil: H P = k CF × I P
NOTE The meaning and the relations among the symbols u(x i ), c i , u i (y), u c (y), U(y) and y are explained in IEC TR
D.3 Uncertainty contributors to the peak current and to the damped oscillatory magnetic field measurement uncertainty
The following list shows the contributors used to assess both the measuring instrumentation and test setup influences:
• bandwidth of the measuring system
• shape of the impulse response of the measuring system
• oscilloscope horizontal axis measurement error
• oscilloscope vertical axis measurement error
• measurement system, measurand and setup repeatability (type A)
• calibration of oscilloscope and measuring system
• coil factor of the induction coil
Uncertainty of peak current and damped oscillatory magnetic field calibration
General
In magnetic field testing, the disturbance quantities include the damped oscillatory current from the test generator and the damped oscillatory magnetic field applied to the Equipment Under Test (EUT) An uncertainty budget for each measured parameter of these disturbance quantities is essential, specifically for the impulse current (I P) and the impulse magnetic field (H P) The magnetic field produced by the induction coil is directly proportional to the current at its terminals, with the coil factor (k CF) serving as the constant of proportionality Consequently, the impulse magnetic field mirrors the waveshape of the impulse current, leading to the relationship H P = k CF × I P.
The disturbance is characterized by additional parameters such as oscillation frequency and damping While evaluating the measurement uncertainty of these parameters is necessary, it is less complex than assessing the impulse peak Consequently, this discussion emphasizes the measurement uncertainty associated with the peak of the impulse.
The method for assessing the impulse measurement uncertainty (MU) is outlined in sections D.4.4 and D.4.5 An example of the uncertainty budget for peak current impulse is presented in Table D.1, which details the most significant input quantities, the numerical values and types of probability density functions for each contributor to the MU, and the results of the necessary calculations for determining the uncertainty budget.
Peak current
The measurand is the peak of the damped oscillatory current impulse calculated by using the functional relationship
V PR is the impulse voltage peak reading
R T is the transfer resistance of the current probe δR is the correction for non-repeatability δV is the d.c vertical accuracy of the scope
B is the –3 dB bandwidth of the measuring system β is the coefficient whose value is (63,8 ± 7,1) kHz at the oscillation frequency f 0 0,1 MHz and (638 ± 71) kHz at the oscillation frequency f 0 = 1 MHz
The damped oscillatory current impulse oscillation frequency f 0 = 1 MHz is assumed for the following example of uncertainty budget
Table D.1 – Example of uncertainty budget for the peak of the damped oscillatory current impulse ( I p )
Symbol Estimate Unit Error bound Unit PDF a Divisor u ( x i ) c i Unit u i ( y ) Unit
(k=1) 1,00 0,030 115,5 A 3,46 A δV 0 1 0,02 1 rectangular 1,73 0,011 6 115,5 A 1,33 A ò 638 kHz 71 kHz rectangular 1,73 40,99 0,001 48 A/kHz 0,061 A
Expressed in % of 115 A 8,6 % a Probability density function
The voltage peak reading at the output of a current probe or across a current shunt is referred to as V PR The error bound is calculated based on the assumption that the oscilloscope has an 8-bit vertical resolution and utilizes interpolation capabilities, specifically a triangular probability density function In cases where interpolation is either unavailable or inactive, a rectangular probability density function is employed instead.
The transfer impedance (or sensitivity) of the current shunt or probe, denoted as \( R_T \), is estimated to be 0.001 Ω with a 5% error bound, following a rectangular probability density function Additionally, \( \delta R \) measures the non-repeatability associated with the measurement setup, layout, and instrumentation.
This is a type A evaluation based on the formula of the experimental standard deviation s(q k ) of a sample of n repeated measurements q j and given by
The arithmetic mean of the \( q_j \) values is denoted as \( q \), with \( \delta R \) expressed in relative terms, assuming an estimate of 0% and a 3% error bound (1 standard deviation) Additionally, \( \delta V \) quantifies the amplitude measurement inaccuracy of the scope at direct current (d.c.), also expressed in relative terms, with a 2% error bound based on a rectangular probability density function and an estimate of 0% The coefficient \( \beta \) is influenced by the shape of both the measuring system's impulse response and the standard impulse waveform near the peak The interval \( (638 \pm 71) \) kHz represents a broad class of systems, each characterized by a unique impulse response shape.
The bandwidth \( B \) of the measuring system can be determined through direct measurement or calculated from the individual bandwidths \( B_i \) of each component, including the current probe or shunt, cable, and oscilloscope, using a specific equation.
An estimate of 10 MHz and a 1 MHz error bound of a rectangular probability density function are assumed for B
The peak of the magnetic field impulse, denoted as \( H_P \), is determined by the equation \( H_P = k_{CF} \times I_P \), where \( k_{CF} \) is the coil factor obtained through a calibration procedure at power frequency For instance, if the measured \( k_{CF} \) is 0.90, such as in a square induction loop with a side length of 1 m, and the expanded uncertainty is 5%, the best estimate for \( H_P \) is 104 A/m, with an expanded uncertainty of 9.9% (refer to Table D.1).
Further MU contributions to amplitude and time measurements
The following contributions may also have an impact on the MU budget:
The d.c offset of an oscilloscope affects the uncertainty in voltage peak measurements when the peak is determined from the nominal d.c zero line However, this uncertainty can be disregarded if the oscilloscope's readout software measures the peak from the pulse baseline.
Time base error and jitter: The oscilloscope specifications may be taken as error bounds of rectangular probability density functions Usually these contributions are negligible
Vertical resolution is influenced by the vertical amplitude resolution \(\Delta A\) and the slope of the trace \(\frac{dA}{dt}\) The associated uncertainty is given by \(\frac{\Delta A/2}{dA/dt}\) When trace interpolation is applied, a triangular probability density function is utilized; otherwise, a rectangular probability density function is employed This contribution becomes significant when \(|\frac{dA}{dt}| < \frac{\Delta A}{T_i}\), where \(T_i\) represents the oscilloscope's sampling interval.
Rise time of the step response and bandwidth of the frequency
Let T MS be the rise time of the step response of the measuring system as defined by equation (D.4)
T π s (D.4) where h 0 ( ) t is the impulse response of the measuring system having a normalized area, i.e
0 ∞ ∫ dt t h , and T s is the delay time given by
Equation (D.4) is easier to handle, from the mathematical point of view, than the usual one based on the 10 % and 90 % threshold levels Nonetheless, in the technical applications, the
10 % to 90 % rise time definition is usually adopted Given the –3 dB bandwidth of the system the two definitions lead to comparable rise times Indeed, if we define
The values of α derived from two definitions of rise-time are similar, as shown in MS α (D.6) Table D.2 presents α values corresponding to various impulse response shapes, indicating that a unique α cannot be determined This is because α is influenced by the chosen definition of rise time, whether based on thresholds or equation (D.4), as well as the shape of the measuring system's impulse response A reasonable estimate for α can be calculated as the arithmetic mean of the minimum values.
The values of α range from a minimum of \$321 \times 10^{-3}\$ to a maximum of \$399 \times 10^{-3}\$, with a central value of \$360 \times 10^{-3}\$ In the absence of specific information about the measuring system beyond its bandwidth, any value of α within this range is considered equally likely Thus, α is treated as a random variable with a rectangular probability density function defined by these bounds The standard uncertainty of α reflects the system's insensitivity to both the chosen mathematical model for rise-time and the shape of the system's impulse response.
Table D.2 – α factor (see equation (D.6)) of different unidirectional impulse responses corresponding to the same bandwidth of the system B
Values of α are multiplied by 10 3 Gaussian I order II order
(crit damp.) Rectangular Triangular α , using equation (D.4) 332 399 363 321 326 α , 10 % to 90 % 339 350 344 354 353
Impulse peak distortion due to the limited bandwidth of the measuring
The distorted impulse waveform V out ( ) t at the output of the measuring system is given by the convolution integral
The input impulse waveform, denoted as \( V(t) \), interacts with the measuring system's impulse response \( h(t) \), resulting in \( A \cdot h(t) = h_0(t) \), where \( A \) represents the d.c attenuation To analyze the input waveform, it can be approximated using its Taylor series expansion around the peak time \( t_p \), when the input achieves its maximum value \( V_p \).
The first order term is absent from equation D.8 due to \( V'(\cdot) t_p = 0 \) Additionally, \( V''(\cdot) t_p < 0 \) indicates a downward concavity (maximum), while \( V'''(\cdot) t_p > 0 \) suggests that the rise time is shorter than the fall time for the standard waveforms considered By substituting equation D.8 into equation D.7 and simplifying, we find that this holds true when the measuring system's bandwidth is significantly larger than that of the input signal, rendering higher-order power series terms negligible.
V V β (D.9) where V pd is the output impulse peak, A is the d.c attenuation of the measuring system and
The parameter \$\beta\$ is influenced by the second derivative of the standard input waveform and the parameter \$\alpha\$ as defined in section D.4.4 For uncertainty calculations, a straightforward mathematical expression for the standard damped oscillatory waveform is provided.
= (D.11) where f 0 = ω 0 /(2π) is the oscillation frequency and ζ is the damping The value of β can be analytically derived from equations (D.10) and (D.11) as f 0 b>>α π (D.12)
The value of β, as obtained from equation (D.12), is reported in Table D.3
Table D.3 – β factor (equation (D.12)) of the damped oscillatory waveform kHz f 0 = 0,1 MHz f 0 = 1 MHz β 63,8 ± 7,1 638 ± 71
NOTE 1 Equation (D.12) is an approximation because the exponential decay about the instant t=t p is neglected
NOTE 2 The values of β obtained by using equation (D.12) and reported in Table D.3 do not appreciably differ from the ones obtained through computation from the mathematical waveform defined in this standard
NOTE 3 Damping ζ can be obtained by measuring the ratio ρ > 1 between the amplitude of one maximum (or minimum) of the oscillation and the next one It is given by equation (D.11) π ρ ζ ln
For a compliant waveform, ζ is in the range 0,02 to 0,04.
Application of uncertainties in the damped oscillatory wave generator
To ensure that the oscillatory transients of the current and magnetic field meet specifications, calibration results must fall within the defined limits of the standard, as tolerances are not diminished by measurement uncertainty (MU).
Further guidance is given in IEC TR 61000-1-6:2012, Clause 6
General
Annex E presents additional insights into the H-field distributions both inside and outside the coils, utilizing 3D numerical simulations for dynamic results in the time domain and 2D numerical plots for frequency domain analysis This serves as an extension of the static results depicted in the 2D plots of Annex A.
Simulations
The simulations of Figures E.1 to E.10 are performed as follows:
• The coils are excited by an ideal current source (see the symbol "port") having the mathematical waveform as defined in the text of this standard and normalized at 1 A
• Two extreme shape conductors of the coil are considered: rectangular of size 10 cm × 1 cm (reported in Annex E) and round wire of 1 mm radius (results not reported for brevity)
• Default mesh cells are used to speed up the computation for the plots of Figures E.2 and E.3; for the other figures optimized mesh cells are used for better accuracy
The H-field amplitude, denoted as \( H_x^i \), represents the component of the H-field that is aligned with the x-axis Here, the subscript \( i \) indicates the position of the H-field probe, ranging from the center of the loop to the farthest point.
• The 2D H-field plots are calculated at 1 MHz frequency and 0 dB refers to 1 A/m.
Comments
From the simulations, the following considerations arise:
• The computed H-field waveform has the same shape as that of the coil current source
• Very little difference can be noted when comparing computed H-field waveforms with two extreme conductor shapes for the same coil size
The induction coil factors for square and rectangular coils are 0.90 m\(^{-1}\) and 0.65 m\(^{-1}\), respectively, indicating that these values are largely independent of the coil conductor's shape.
• It is confirmed also by transient simulations that the variation of the H-field is less than +3 dB for the areas shown in Annex A
• It is shown and quantified that the H-field increases rapidly when the probe used for H- field computation approaches the conductors of the coil
The H-field value outside the loop is significantly lower, ranging from 20 dB to 40 dB (or 1/10 to 1/100), compared to the field at the center of the loop This difference is crucial to consider when conducting the proximity test method.
NOTE The amplitude of the Hx-field inside the loop is negative due to the chosen probe directions
Figure E.1 – Current with period of 1 às and H-field in the center of the 1 m × 1 m standard induction coil
Figure E.2 – Hx –field along the side of 1 m × 1 m standard induction coil in A/m
Figure E.3 – Hx –field in direction x perpendicular to the plane of the 1 m × 1 m standard induction coil
Figure E.4 – Hx –field along the side in dB for 1 m × 1 m standard induction coil
Figure E.5 – Hx –field along the diagonal in dB for the 1 m × 1 m standard induction coil
Figure E.6 – Hx –field plot on y - z plane for the 1 m × 1 m standard induction coil
Figure E.7 – Hx -field plot on x - y plane for the 1 m × 1 m standard induction coil
Figure E.8 – Hx –field along the vertical middle line in dB for the 1 m × 2,6 m standard induction coil
∆H (dB) = 20 log (|H d |) – 20 log (|H d=0m |) ±3 dB area
Figure E.9 – Hx –field 2D–plot on y - z plane for the 1 m × 2,6 m standard induction coil
Figure E.10 – Hx –field 2D–plot on x - y plane at z = 0,5 m for the 1 m × 2,6 m standard induction coil
IEC TR 61000-1-6:2012, Electromagnetic compatibility (EMC) – Part 1-6: General – Guide to the assessment of measurement uncertainty
IEC 61000-4-18, Electromagnetic compatibility (EMC) – Part 4-18: Testing and measurement techniques – Damped oscillatory wave immunity test
IEC Guide 107, Electromagnetic compatibility – Guide to the drafting of electromagnetic compatibility publications