An Analytical Method for Measuring the System Error of Electromagnetic Pulse Using the Transmission Coefficient Method

Abstract

The present invention relates to an analysis method for a system error in measuring electromagnetic pulses using a transmission coefficient method, and solves the problem that the existing electromagnetic pulse measurement system has limited bandwidth, certain jitter in frequency response within the working frequency band, and different frequency components of different electromagnetic pulse waveforms, so that system errors exist when measuring electromagnetic pulses using the transmission coefficient method. The method comprises the following steps: Step 1: obtaining the frequency response H of the electromagnetic pulse measurement system, constructing a discrete waveform library A, and obtaining the value and occurrence probability of each discrete waveform feature point in the discrete waveform library A; Step 2: calculating the output waveform of each discrete waveform after passing through the electromagnetic pulse measurement system, and obtaining the value of the output waveform feature point; Step 3: obtaining the transmission coefficient k of the electromagnetic pulse measurement system, and calculating the relative error of each discrete waveform after passing through the electromagnetic pulse measurement system; and Step 4: calculating the system error of the measurement result obtained when measuring electromagnetic pulses using the transmission coefficient method.

Description

Technical Field

[0001] The present invention relates to a method for analyzing system errors in electromagnetic pulse measurement, and in particular to a method for analyzing system errors in electromagnetic pulse measurement using a transmission coefficient method. Background Art

[0002] An electromagnetic pulse measurement system, which can be an electromagnetic pulse electric field measurement system or an electromagnetic pulse current measurement system, is a broadband measurement system. One method for estimating the measured signal based on the output of an electromagnetic pulse measurement system involves combining the measurement system's frequency response with a series of filtering, Fourier transform, and post-system identification compensation methods to recover the measured signal. However, this method requires highly targeted back-end processing and places high demands on the user.

[0003] Another method for estimating the measured signal based on the measurement system output is the transmission coefficient method. This method works as follows: when the bandwidth of the electromagnetic pulse measurement system is sufficiently wide relative to the measured signal, the output and input of the electromagnetic pulse measurement system can be assumed to have the same waveform, differing only in amplitude. The transmission coefficient is defined as the ratio of the amplitude of the standard input pulse waveform to the amplitude of the output waveform, obtained through calibration. The specific calculation for estimating using the transmission coefficient method is: multiplying the transmission coefficient by the measurement system's response yields the measured value of the measured signal. This method is simple and easy to use and widely used in engineering. However, typical electromagnetic pulse measurement systems have limited bandwidth and exhibit some jitter in their frequency response within the operating band. Furthermore, the frequency components of different electromagnetic pulses under test vary, resulting in systematic errors in the transmission coefficient method. Currently, there is no quantitative analysis method for this systematic error. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem that the bandwidth of the existing general electromagnetic pulse measurement system is limited, and there is a certain jitter in the frequency response within the working frequency band, and the frequency components of different electromagnetic pulse waveforms are different. Therefore, when using the transmission coefficient method to measure electromagnetic pulses, there is a problem of systematic error. A method for analyzing the systematic error of measuring electromagnetic pulses using the transmission coefficient method is provided.

[0005] The design concept of the present invention is: based on the prior information of the signal to be measured, the relative errors between the measurement results obtained by the transmission coefficient method for all possible signals to be measured and the true value are estimated and calculated. The weight of each relative error is the probability of occurrence of the corresponding signal to be measured. The weighted sum of the infinite norms of all relative errors is the systematic error of the measurement results obtained when measuring electromagnetic pulses using the transmission coefficient method.

[0006] The technical solution adopted in the present invention is:

[0007] A method for analyzing the error of an electromagnetic pulse system measured by a transmission coefficient method is characterized in that it includes the following steps:

[0008] Step 1: Obtain the frequency response H of the electromagnetic pulse measurement system, and construct a discrete waveform library A based on prior information of the waveform to be measured, and obtain the value of each discrete waveform feature point in the discrete waveform library A and the probability of occurrence of each discrete waveform, wherein the discrete waveform library A includes L discrete waveforms;

[0009] Step 2: Based on H in step 1 and the L discrete waveforms in the discrete waveform library A, calculate the output waveform of each discrete waveform after passing through the electromagnetic pulse measurement system, and obtain the value of the output waveform feature point;

[0010] Step 3: Obtain the transmission coefficient k of the electromagnetic pulse measurement system, and based on the transmission coefficient k and the value of the waveform characteristic point output by each discrete waveform after passing through the electromagnetic pulse measurement system in step 2, and the value of the characteristic point of each discrete waveform in step 1, calculate the relative error of each discrete waveform after passing through the electromagnetic pulse measurement system;

[0011] Step 4: Based on the probability of occurrence of each discrete waveform in discrete waveform library A and the relative error of each discrete waveform after passing through the electromagnetic pulse measurement system, calculate the systematic error of the measurement result obtained when measuring the electromagnetic pulse using the transmission coefficient method.

[0012] Furthermore, in step 1, the frequency response H of the electromagnetic pulse measurement system is obtained through the product manual or calibration results.

[0013] Furthermore, in step 2, the output waveform of each discrete waveform after passing through the electromagnetic pulse measurement system is calculated using the following formula:

[0014]

[0015] Among them, x i Indicates the i-th discrete waveform in the discrete waveform library A. and They represent discrete Fourier transform and inverse discrete Fourier transform respectively; u i It represents the output waveform of the i-th discrete waveform in the discrete waveform library A after passing through the electromagnetic pulse measurement system.

[0016] Furthermore, in step 3, the transmission coefficient k is calculated through calibration results or directly obtained from the product manual.

[0017] Furthermore, in step 3, the relative error of each discrete waveform after passing through the electromagnetic pulse measurement system is calculated using the following formula:

[0018]

[0019] Among them, e irepresents the relative error of the i-th discrete waveform in the discrete waveform library A after passing through the electromagnetic pulse measurement system; x i,c Indicates the value of the characteristic point of the i-th discrete waveform in the discrete waveform library A, u i,c Represents the value of the characteristic point of the output waveform corresponding to the i-th discrete waveform in discrete waveform library A.

[0020] Furthermore, in step 4, when the transmission coefficient method is used to measure the electromagnetic pulse, the calculation formula for the systematic error e of the measurement result is:

[0021] By formula Among them, p i Represents the probability of the i-th discrete waveform occurring in the discrete waveform library A.

[0022] Furthermore, if the waveform to be measured is a double exponential waveform, then, in step 1, each discrete waveform characteristic point is a peak value, and the waveform characteristic point output in step 2 is the same as the characteristic point in step 1;

[0023] If the waveform to be measured is a square wave, then, in step 1, each discrete waveform characteristic point is a flat-top amplitude, and the output waveform characteristic point in step 2 is the same as the characteristic point in step 1;

[0024] If the waveform to be measured is a damped oscillatory wave, then, in step 1, each discrete waveform characteristic point is a sub-peak value or a peak value, and the waveform characteristic point output in step 2 is the same as the characteristic point in step 1.

[0025] The beneficial effects of the present invention are:

[0026] 1. In the present invention, based on the estimation of the range of the signal to be measured, a systematic error analysis method of the transmission coefficient method is given, which can quantitatively give the systematic error of the transmission coefficient method in measuring electromagnetic pulses.

[0027] 2. The systematic error calculated by the present invention can be used as a basis for selecting the transmission coefficient method. That is, when the systematic error is sufficiently small compared with other measurement or calibration uncertainty factors, the transmission coefficient method is preferred.

[0028] 3. In the present invention, the system error provided can be used as a basis for selecting an electromagnetic pulse measurement system. For a specified signal to be measured, a measurement system with a smaller system error will have the smallest measurement result error using the transmission coefficient method. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 1. This is a diagram showing the test setup for calibration of the transmission coefficient of an electromagnetic pulse measurement system according to an embodiment of the present invention;

[0030] Figure 2 is the step response of measurement system #1 in the embodiment of the present invention;

[0031] Figure 3 is the step response of the 2# measurement system in the embodiment of the present invention;

[0032] Figure 4 is the probability distribution of all discrete waveform frontiers in the embodiment of the present invention;

[0033] Figure 5 is the probability distribution of the half-width of all discrete waveforms in the embodiment of the present invention;

[0034] Figure 6 is the peak value of the output waveform of all discrete waveforms passing through the 1# measurement system in the embodiment of the present invention;

[0035] Figure 7 is the peak value of the output waveform of all discrete waveforms passing through the 2# measurement system in the embodiment of the present invention;

[0036] Figure 8 is the probability of occurrence of all discrete waveforms in the embodiment of the present invention;

[0037] Figure 9 is the relative error when measuring discrete waveforms by measurement system #1 in the embodiment of the present invention;

[0038] Figure 10 is the relative error when the 2# measurement system measures a discrete waveform in the embodiment of the present invention;

[0039] Figure 11 This is a flow chart of a method for analyzing system errors of a transmission coefficient of an electromagnetic pulse current measurement system in an embodiment of the present invention. DETAILED DESCRIPTION

[0040] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0041] The present invention proposes a method for analyzing the error of electromagnetic pulse system measured by transmission coefficient method, such as Figure 11 As shown, the specific steps include:

[0042] Step 1: Obtain the frequency response H of the electromagnetic pulse measurement system, and construct a discrete waveform library A based on prior information of the waveform to be measured, and obtain the value of each discrete waveform feature point in the discrete waveform library A and the probability of occurrence of each discrete waveform. The discrete waveform library A includes L discrete waveforms. The feature point can be the peak value, flat-top peak value, etc. of the waveform to be measured according to actual needs. In this example, the waveform to be measured is a double exponential waveform. The prior information includes the range of the leading edge tr and the range of the half-width tw of the double exponential waveform. The leading edge range and half-width range of the double exponential waveform are obtained through expert experience or simulation calculation. The peak value of the double exponential waveform is selected as the value of the feature point.

[0043] A. Obtain the frequency response H of the electromagnetic pulse measurement system;

[0044] Taking two electromagnetic pulse measurement systems as an example, it is necessary to ensure that the bandwidth, size, available front edge, measurement range, waveform fidelity, etc. of the selected electromagnetic pulse measurement system meet the test requirements;

[0045] In this example, it is assumed that electromagnetic pulse current measurement system 1 has the same frequency response as a first-order low-pass Butterworth filter and a 3dB bandwidth of 70MHz, and is recorded as measurement system 1#; it is assumed that electromagnetic pulse current measurement system 2 has the same frequency response as a second-order low-pass Chebyshev filter, and the filter has a 3dB bandwidth of 70MHz and a passband jitter of 1dB, and is recorded as measurement system 2#;

[0046] Specifically, the frequency response H of the 1# measurement system and the 2# measurement system can also be obtained through the product manual or calibration results;

[0047] B. The method for constructing a discrete waveform library A based on the prior information of the waveform to be measured and obtaining the value of each discrete waveform feature point in the discrete waveform library A and the probability of each discrete waveform occurring is as follows:

[0048] It is known that the waveform to be measured is a bi-exponential waveform, represented by x(t;θ), where t represents time, and θ = (tr, tw) is a vector composed of two independent parameters that determine the bi-exponential waveform. tr represents the 10% to 90% front edge of the bi-exponential waveform peak, and tw represents the 50% to 50% half-width of the bi-exponential waveform peak. Assume that tr and tw obey the normal distribution tr~N(5,2) and tw~N(80,5), with units in ns; discretize tr and tw, and the obtained intervals are [0.5ns, 9.5ns] and [60ns, 100ns] respectively, with step sizes set to 0.75ns and 1ns. The probability of occurrence of each front edge tr and half-width tw is obtained by integrating the normal distribution, with the integral limit at the boundary being infinite. The integral results are as follows: Figure 4 and Figure 5 As shown, Figure 4 and Figure 5 The vertical coordinate p represents the probability of the front tr and half-width tw occurring in the corresponding intervals. Then, by randomly combining these two intervals, 13×41=533 discrete waveforms can be formed. 533 discrete waveforms constitute the discrete waveform library A, that is, L=533;

[0049] According to each discrete waveform, the peak value of each discrete waveform and the probability of occurrence of each discrete waveform are obtained, and the peak value is the value of the characteristic point;

[0050] Step 2: If Figure 1As shown, according to H, the output waveform of each discrete waveform in the discrete waveform library A after passing through the electromagnetic pulse measurement system is calculated, and the value of the output waveform characteristic point is obtained. In step 2, the output waveform characteristic point is the same as the characteristic point of the discrete waveform in step 1;

[0051] Specific:

[0052] The output waveform of each discrete waveform after passing through the electromagnetic pulse measurement system is calculated using the following formula:

[0053]

[0054] Among them, x i Indicates the i-th discrete waveform in the discrete waveform library A. and They represent discrete Fourier transform and inverse discrete Fourier transform respectively; u i It represents the output waveform of the i-th discrete waveform in the discrete waveform library A after passing through the electromagnetic pulse measurement system;

[0055] The output waveform peak values of the 1# measurement system and the 2# measurement system are as follows: Figure 6 and Figure 7 As shown, Figure 6 and Figure 7 U in c Indicates peak value;

[0056] Step 3: Obtain the transmission coefficient k of the electromagnetic pulse measurement system, and based on the transmission coefficient k and the value of the waveform characteristic point output by each discrete waveform after passing through the electromagnetic pulse measurement system in step 2, and the value of the characteristic point of each discrete waveform in step 1, calculate the relative error of each discrete waveform after passing through the electromagnetic pulse measurement system;

[0057] 3.1 Obtain the transmission coefficient k of the electromagnetic pulse measurement system;

[0058] Specifically: There are two ways to obtain the transmission coefficient k of measurement system 1# and measurement system 2#. One is to obtain it through the corresponding product manual; the other is to calculate the transmission coefficient k of measurement system 1# and measurement system 2# through calibration results. Among them, it is necessary to use a standard pulse source waveform to calibrate measurement system 1# and measurement system 2#, and the standard pulse source waveform must be verified, traceable, and meet the calibration requirements. The calculation formula of the transmission coefficient k is as follows:

[0059]

[0060] Among them, S std It represents the characteristic point value of the standard pulse source waveform output S, U outIt indicates the characteristic point value of the standard pulse source waveform after passing through the electromagnetic pulse measurement system. The characteristic point value is generally the peak value or amplitude of the standard pulse source waveform. S and U take the same characteristic point.

[0061] Assume that an ideal square wave is used to calibrate the transmission coefficient of the measurement system. The calibration settings are as follows: Figure 1 The step responses of measurement system 1# and measurement system 2# are shown as follows: Figure 2 and Figure 3 As shown, Figure 2 and Figure 3 In the example, the horizontal axis represents the sampling time and the vertical axis represents the amplitude. std =1, for square wave U out Take the peak value. It can be seen from the figure that the square wave U out In steady state, the peak value U of the 1# measurement system out1 =1,2# peak value of measurement system U out2 =0.8913, through the formula The calculated transmission coefficient of measurement system #1 is k1 = 1 V / A, and the transmission coefficient of measurement system #2 is k2 = 1.122 V / A.

[0062] In actual measurement, due to manual operation and other reasons, the calculated transmission coefficient k may have errors. Therefore, the standard pulse source waveform can be used to calibrate the 1# measurement system and the 2# measurement system multiple times, calculate multiple transmission coefficients k respectively, and calculate the average value; or perform curve fitting on the multiple transmission coefficients k, and the slope of the corresponding curve is the transmission coefficient k of the 1# measurement system and the 2# measurement system;

[0063] If the transmission coefficient k is calculated by simulation, there is no dispersion in the results of multiple measurements, because multiple groups of results within the measurement range are equal, so there is no need to perform multiple measurements;

[0064] 3.2 Based on the transmission coefficient k and the value of the waveform characteristic point output by each discrete waveform after passing through the electromagnetic pulse measurement system in step 2, and the value of each discrete waveform characteristic point in step 1, calculate the relative error of each discrete waveform after passing through the electromagnetic pulse measurement system;

[0065] In the discrete waveform library A, the relative error calculation formula of the i-th discrete waveform after passing through the pulse measurement system is as follows:

[0066]

[0067] Among them, e i Indicates the relative error of the i-th discrete waveform in the discrete waveform library A after passing through the pulse measurement system; x i,cIndicates the value of the characteristic point (i.e., peak value) of the i-th discrete waveform in the discrete waveform library A, u i,c Represents the value of the characteristic point (i.e., peak value) of the output waveform corresponding to the i-th discrete waveform in the discrete waveform library A, such as Figure 6 and Figure 7 As shown, they are the output waveform peak values of the 1# measurement system and the 2# measurement system respectively.

[0068] Use measurement system 1# and measurement system 2# to calculate the relative error of each discrete waveform. Figure 9 and Figure 10 As shown in the figure, e1# represents the relative error of each discrete waveform peak value calculated by using the 1# measurement system, and e2# represents the relative error of each discrete waveform peak value calculated by using the 2# measurement system;

[0069] Step 4: Based on the probability of occurrence of each discrete waveform in discrete waveform library A and the relative error of each discrete waveform after passing through the electromagnetic pulse measurement system, calculate the systematic error of the measurement result obtained when measuring the electromagnetic pulse using the transmission coefficient method;

[0070] The calculation formula of the systematic error e of the measurement result is as follows:

[0071]

[0072] Among them, p i Indicates the probability of the occurrence of the i-th discrete waveform in the discrete waveform library A. In this example, the probability corresponding to different combinations of tr and tw is as follows: Figure 8 As shown;

[0073] The system errors of the 1# measurement system and the 2# measurement system calculated using the above formula are 3.36% and 9.36% respectively.

[0074] This indicates that for a given signal to be measured, measurement system 1# and measurement system 2#, both of which have a 70 MHz bandwidth, have better performance.

Claims

1. A method for analyzing the error of electromagnetic pulse system measured by transmission coefficient method, characterized in that: The following steps are involved: Step 1: Obtain the frequency response H of the electromagnetic pulse measurement system, and construct a discrete waveform library A based on prior information of the waveform to be measured, and obtain the value of each discrete waveform feature point in the discrete waveform library A and the probability of occurrence of each discrete waveform, wherein the discrete waveform library A includes L discrete waveforms; Step 2: Based on H in step 1 and the L discrete waveforms in the discrete waveform library A, calculate the output waveform of each discrete waveform after passing through the electromagnetic pulse measurement system, and obtain the value of the output waveform feature point; Step 3: Obtain the transmission coefficient k of the electromagnetic pulse measurement system, and based on the transmission coefficient k and the value of the waveform characteristic point output by each discrete waveform after passing through the electromagnetic pulse measurement system in step 2, and the value of the characteristic point of each discrete waveform in step 1, calculate the relative error of each discrete waveform after passing through the electromagnetic pulse measurement system; Step 4: Based on the probability of occurrence of each discrete waveform in discrete waveform library A and the relative error of each discrete waveform after passing through the electromagnetic pulse measurement system, calculate the systematic error of the measurement result obtained when measuring the electromagnetic pulse using the transmission coefficient method; In step 2, the output waveform of each discrete waveform after passing through the electromagnetic pulse measurement system is calculated using the following formula: Among them, x i Indicates the i-th discrete waveform in the discrete waveform library A. and They represent discrete Fourier transform and inverse discrete Fourier transform respectively; u i It represents the output waveform of the i-th discrete waveform in the discrete waveform library A after passing through the electromagnetic pulse measurement system; In step 3, the relative error of each discrete waveform after passing through the electromagnetic pulse measurement system is calculated using the following formula: Among them, e i represents the relative error of the i-th discrete waveform in the discrete waveform library A after passing through the electromagnetic pulse measurement system; x i,c Indicates the value of the characteristic point of the i-th discrete waveform in the discrete waveform library A, u i,c Represents the value of the characteristic point of the output waveform corresponding to the i-th discrete waveform in the discrete waveform library A; In step 4, when the transmission coefficient method is used to measure the electromagnetic pulse, the calculation formula for the systematic error e of the measurement result is: By formula Among them, p i Represents the probability of the i-th discrete waveform occurring in the discrete waveform library A.

2. The method for analyzing the error of electromagnetic pulse system measured by the transmission coefficient method according to claim 1, characterized in that: In step 1, the frequency response H of the electromagnetic pulse measurement system is obtained through the product manual or calibration results.

3. The method for analyzing the error of electromagnetic pulse system measured by the transmission coefficient method according to claim 2, characterized in that: In step 3, the transmission coefficient k is calculated using the calibration results or obtained directly from the product manual.

4. The method for analyzing the error of an electromagnetic pulse system measured by the transmission coefficient method according to any one of claims 1 to 3, characterized in that: If the waveform to be measured is a double exponential waveform, then, in step 1, each discrete waveform characteristic point is a peak value, and the waveform characteristic point output in step 2 is the same as the characteristic point in step 1; If the waveform to be measured is a square wave, then, in step 1, each discrete waveform characteristic point is a flat-top amplitude, and the output waveform characteristic point in step 2 is the same as the characteristic point in step 1; If the waveform to be measured is a damped oscillatory wave, then, in step 1, each discrete waveform characteristic point is a sub-peak value or a peak value, and the waveform characteristic point output in step 2 is the same as the characteristic point in step 1.

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