Digital source single-receiver network vector analysis system
By utilizing the periodicity of a real-time signal processor and a digital signal source, combined with a forward/reverse selection switch, a network vector analyzer can accurately measure phase difference and amplitude ratio in a wideband complex signal environment. This solves the problems of inaccurate test frequency and poor stability in existing technologies and is suitable for modern electronics industry.
Patent Information
- Application Number
- CN202210368949.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-04-08
- Publication Date
- 2026-02-03
- Estimated Expiration
- 2042-04-08
AI Technical Summary
Existing network vector analyzers are complex in design for testing the phase difference between transmitted and reflected signals, have insufficiently accurate test frequencies, and poor stability, making them difficult to meet the needs of modern electronics industry.
A digital source single-receiver network vector analysis system is adopted, which utilizes components such as a real-time signal processor, digital-to-analog converter, transmit and receive mixer, local oscillator, directional coupler, test port and selection switch to achieve accurate measurement of amplitude ratio and phase difference through single-receiver mode. The periodicity of digital signal source and forward and reverse selection switch are used to remove phase and amplitude uncertainties, and complex domain ratio calculation is used to optimize signal processing.
It achieves constant measurement of the phase difference between transmitted and reflected signals at each frequency point, simplifies the hardware signal process, improves the authenticity and stability of test results, is suitable for modern communication equipment with wideband complex signals, has more accurate test frequencies, good stability, and is suitable for widespread application.
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Figure CN114924143B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of network vector analysis technology, and in particular to a digital source single-receiver network vector analysis system. Background Technology
[0002] A vector network analyzer (VNA) is a radio frequency / microwave / millimeter-wave test instrument capable of both transmitting and receiving over a wide frequency range. The receiver must be able to accurately measure the relative amplitude and phase changes between the transmitted and received signals, hence the name vector analyzer. The purpose of the test is to characterize the scattering matrix of an unknown circuit "network" (circuit board, cable, connector, converter, filter, amplification and attenuation devices / modules, etc.). For the most commonly used two-port networks, the two most important parameters in the scattering matrix are S... 11 (reflection coefficient) and S 21 (Transmission coefficient). Both of these parameters are complex functions of frequency (containing amplitude and phase information).
[0003] See Figure 1 ,Should Figure 1 Here is a block diagram of an existing network vector analyzer system; Figure 1 In this context, frequency tracking signal source 1 is a single frequency signal generated purely by analog at any given test moment. Many modern communication devices must withstand complex signals modulated over a wideband, therefore, the test signals of high-performance network vector analyzers should also provide complex wideband signals.
[0004] Figure 1 The test signal and correction algorithm module 5 has functions such as circuitry and correction algorithm for accurately testing the amplitude ratio and phase difference between two signals. However, how the test signal and correction algorithm module 5 accurately measures the amplitude ratio and phase difference between two signals, especially the phase difference, is an extremely challenging RF circuit design, especially considering that the directional coupler 2 is not ideal, the positive direction signal will leak into the reverse direction (R), and the reverse direction signal will also enter the positive direction (F).
[0005] Therefore, numerous complex circuit designs and patent applications for phase detection have emerged in order to accurately measure the phase difference between transmitted and reflected signals. Existing network vector analyzers are too complex for accurately measuring the phase difference between transmitted and reflected signals and are unsuitable for the development of modern electronics industry.
[0006] Chinese Patent Application No.: 201310596828.3, Application Date: November 22, 2013, Publication Date: February 19, 2014, Patent Title: A Broadband Vector Network Analyzer. This invention discloses a broadband vector network analyzer, characterized by employing a frequency segmentation method to divide the test frequency range into three frequency bands: low frequency, radio frequency, and microwave. The excitation signal generation, test signal directional separation, and frequency conversion reception methods differ for each frequency band. The instrument generally consists of a network analysis module, a 6-20 GHz front-end module, and a 6 GHz front-end module. The network analysis module includes an excitation signal source submodule, a fixed local oscillator submodule, a local oscillator signal source submodule, and an intermediate frequency processing submodule. The 6 GHz-20 GHz front-end module is connected to the 6 GHz front-end module, sharing the 6-20 GHz front-end module's test port. The two front-end modules are respectively connected to the network analysis module, enabling interaction between the network analysis module and its various submodules. The frequency segmentation processing method adopted in this invention makes the processing of different frequency bands independent of each other, effectively avoiding the difficulties in designing low-frequency and high-frequency measurements under small volume conditions, and realizing a wider frequency measurement range.
[0007] Although the aforementioned patent documents disclose a broadband vector network analyzer, the test frequency of this broadband vector network analyzer is not accurate enough, the stability is poor, the test method is not simple enough, and its practicality is not strong. Summary of the Invention
[0008] In view of this, the present invention provides a digital source single receiver network vector analysis system with good stability, accurate test frequency, simple structure, easy use, and strong practicality.
[0009] To achieve the objectives of this invention, the following technical solutions can be adopted:
[0010] A digital source single receiver network vector analysis system includes a real-time signal processor, a digital-to-analog converter, a transmit mixer, a local oscillator, a directional coupler, a test transmit port, a test receive port, a coupler and a receive port selection switch, a receive mixer, and an analog-to-digital converter.
[0011] The real-time signal processor transmits the data signal to the transmit mixer via a digital-to-analog converter. The transmit mixer then transmits the data signal to the test transmit port via a directional coupler. The test receive port receives the data signal via a coupler and a receive port selection switch. This coupler and receive port selection switch then transmit the data signal to the real-time signal processor via the receive mixer and an analog-to-digital converter.
[0012] A local oscillator is provided between the transmitting mixer and the receiving mixer, which transmits the digitally controlled frequency source to the transmitting mixer and the receiving mixer respectively; a forward and reverse selection switch is provided between the directional coupler and the coupler and the receiving port selection switch, and the forward and reverse selection switch controls the directional coupler and the coupler and the receiving port selection switch respectively.
[0013] The real-time signal processor includes a signal processor capable of continuously transmitting, receiving, and processing data at high sampling frequencies in real time.
[0014] The real-time signal processor is a signal processor that transmits and receives intermediate frequency (IF) signals; the frequency bandwidth of the IF signal is W, and the frequency bandwidth satisfies the formula:
[0015] F0 is the intermediate frequency, and F s The sampling frequency.
[0016] The test frequency spacing of the signal transmitted by the real-time signal processor is dF; dF satisfies the following formula:
[0017] 1) dF must be divisible by W, let And force K to be even;
[0018] 2) dF must be divisible by F s ,make
[0019] 3) dF must be divisible by F0, let
[0020] The real-time signal processor obtains the multi-frequency digital signal x(n) using the following formula;
[0021]
[0022] Where A(k) represents the weighted amplitude at a certain frequency point, P(k) is the initial phase corresponding to each frequency point, and x(n) is a broadband signal composed of K frequencies with a period of N (number of sampling points).
[0023] The digital-to-analog converter (DAC) is a DAC that generates a fixed periodic multi-frequency signal; the DAC is up-modulated to different radio frequency points through a transmit mixer and a local oscillator; the real-time signal processor controls the local oscillator to generate discrete frequency points F. x The F x It can be obtained through the following formula:
[0024]
[0025] F1 and F2 represent the selected test frequency ranges.
[0026] The beneficial effects of this invention are: 1) This invention achieves accurate measurement of the amplitude ratio and phase difference of two signals in a single-connection manner; this invention fully utilizes the periodicity of the digital signal source, ensuring a constant phase difference between the transmitted and reflected signals at each frequency point in the received data processing. By using a forward / reverse selection switch, dual reception is achieved with single-channel reception; 2) In the calculation steps, this invention uses the complex domain ratio H(f) = H2(f) / H1(f) of the reverse signal to the forward signal. This calculation elegantly eliminates the dependence on the initial phase of the signal and automatically removes the phase and amplitude uncertainties brought about by the entire hardware signal flow system; in a sense, it also solves the temperature drift problem; 3) The signal source of this invention is a wideband signal composed of multiple frequencies, and the test results more realistically reflect the performance status of the tested component in actual applications, demonstrating strong practicality; 4) This invention is simple to use, stable, and accurate in testing, representing a technological upgrade in this field and suitable for widespread application. Attached Figure Description
[0027] Figure 1 This is a block diagram of an existing network vector analyzer system for a digital source single-receiver network vector analysis system according to an embodiment of the present invention;
[0028] Figure 2 This is a system block diagram of a digital source single-receiver network vector analysis system according to an embodiment of the present invention. Detailed Implementation
[0029] The invention will now be described in further detail with reference to the accompanying drawings and real-world examples.
[0030] Real-time Example 1
[0031] See Figure 1 Existing network vector analyzers typically include a frequency tracking signal source 1, a directional coupler 2, a test port 3, dual receivers 4, and a test signal and correction algorithm module 5. At any given test moment, the frequency tracking signal source 1 is a single frequency signal generated purely analogically. Many modern communication devices must withstand complex signals modulated with wideband bandwidth; therefore, high-performance network vector analyzers should also provide wideband complex signals for their test signals.
[0032] The test signal and correction algorithm module 5 has functions such as circuitry and correction algorithm for accurately testing the amplitude ratio and phase difference between two signals. However, how the test signal and correction algorithm module 5 accurately measures the amplitude ratio and phase difference between two signals, especially the phase difference, is an extremely challenging RF circuit design, especially considering that the directional coupler 2 is not ideal, the positive direction signal will leak into the reverse direction (R), and the reverse direction signal will also enter the positive direction (F).
[0033] Therefore, existing vector analyzers have low test frequency accuracy and poor stability, making it difficult to meet the needs of high-precision testing.
[0034] See Figure 2 The digital source single receiver network vector analysis system includes a real-time signal processor (DSP) 100, a digital-to-analog converter (DAC) 101, a transmit mixer 102, a local oscillator 110, a directional coupler 103, a test transmit port 104, a test receive port 108, a coupler and receive port selection switch 107, a receive mixer 106, and an analog-to-digital converter (ADC) 105.
[0035] The real-time signal processor (DSP) 100 transmits the data signal to the transmit mixer 102 via the digital-to-analog converter (DAC) 101. The transmit mixer 102 then transmits the data signal to the test transmit port 104 via the directional coupler 103. The test receive port 108 receives the data signal via a coupler and a receive port selection switch 107. This coupler and receive port selection switch 107 then transmits the data signal to the real-time signal processor (DSP) 100 via the receive mixer 106 and the analog-to-digital converter 105.
[0036] A local oscillator 110 is provided between the transmitting mixer 102 and the receiving mixer 106. The local oscillator 110 transmits the digitally controlled frequency source to the transmitting mixer 102 and the receiving mixer 106 respectively. A forward and reverse selection switch 109 is provided between the directional coupler 103 and the coupler and receiving port selection switch 107. The forward and reverse selection switch 109 controls the directional coupler 103 and the coupler and receiving port selection switch 107 respectively.
[0037] In this embodiment, preferably, the local oscillator 110 is a digitally controlled frequency source local oscillator 110.
[0038] In this embodiment, the real-time signal processor (DSP) 100 generates the required digital signal source for transmission, converts it into a corresponding intermediate frequency (spectrum) analog signal through the digital-to-analog converter (DAC) 101, and transmits it to the transmit mixer 102 to up-modulate the transmission signal to the desired test frequency range. The transmit mixer 102 transmits the transmission signal to the test transmit port 104 through the directional coupler 103, thus entering the circuit network under test.
[0039] The test receiving port 108 transmits the received analog frequency (spectrum) signal to the receiving mixer 106 via the coupler and the receiving port selection switch 107, down-diverts it back to an intermediate frequency (spectrum) analog signal, and then converts it into a receiving digital signal source via the analog-to-digital converter 105, and transmits it to the real-time signal processor.
[0040] In this embodiment, the real-time signal processor (DSP) 100 employs a real-time continuous digital signal source. This digital signal source can generate both single-frequency signals and wideband complex signals.
[0041] In this real-time example, the real-time signal processor (DSP) 100 employs single-receiver real-time continuous digital broadband signal processing during signal reception. Since there is known, precise, and controllable phase difference information between the received signal and the digital source signal, a single-channel reception is sufficient to accurately, stably, and simply detect the phase difference and amplitude ratio between the transmitted and received signals.
[0042] In this embodiment, preferably, the real-time signal processor (DSP) 100 can control the local oscillator 110 and the forward / reverse selection switch 109 respectively through the control line 111.
[0043] In this embodiment, preferably, the real-time signal processor (DSP) 100 includes a signal processor capable of real-time continuous data transmission, reception, and processing at intermediate frequency (spectrum), as well as control functions for all parts of the entire system.
[0044] Furthermore, preferably, the real-time signal processor (DSP) 100 is a chip with the model number TMS320C6657.
[0045] In this real-time example, the digital-to-analog converter (DAC) 101 is a high sampling frequency digital-to-analog converter (DAC), preferably, the digital-to-analog converter (DAC) 101 is a chip with the model number MAX5885.
[0046] In this real-time example, in actual implementation, the transmitting mixer 102 can be composed of several mixers of different frequency bands according to the frequency range requirements.
[0047] In this real-time example, the directional coupler 103 is a broadband directional coupler, where F (Forward) represents the forward coupling outlet and R (Reverse) represents the reverse coupling outlet.
[0048] In this real-time example, the test transmission port 104 is the signal transmission port; when measuring the reflection coefficient (S 11 When measuring the transmission coefficient (S), only test transmission port 104 needs to be connected; 21 When testing the transmit port 104 and the receive port 108, it is necessary to test both simultaneously.
[0049] In this real-time example, the forward / reverse selection switch (F / R) 109 is a digitally controlled wideband two-to-one switch. Under the control of the real-time signal processor (DSP) 100, the forward / reverse selection switch (F / R) 109 either transmits the signal from the forward output (F port) of the directional coupler 103 to the directional coupler 103, or transmits the signal from the reverse output (R port) to the coupler and receiver port selection switch 107.
[0050] In this real-time example, the coupler and receiver port selection switch 107 is another wideband digitally controlled two-to-one switch. Its task, under the control of the real-time signal processor (DSP) 100, is to either transmit the coupler output signal from the forward / reverse selection switch (F / R) 109 to the receiver mixer 106, or select the signal transmitted through the test receiver port 108. (Measurement of reflection coefficient (S...)) 11 When the coupler and receiver port selection switch 107 are connected to the forward / reverse selection switch (F / R) 109, the transmission coefficient (S) is tested. 21 When the coupler and receiver port selection switch 107 selects to connect to test receiver port 108.
[0051] The test receiving port 108 tests the reflection coefficient (S). 11 This port is not used when testing the transmission coefficient (S). 21 When using this method, you need to use the test receive port 108.
[0052] The receiving mixer 106 is a series of mixers identical to the transmitting mixer 102. The transmitting mixer 102 performs up-conversion, while the receiving mixer 106 performs down-conversion.
[0053] The analog-to-digital converter (ADC) 105 is a high-speed sampling ADC (analog-to-digital converter), preferably, the ADC 105 is a chip of the LTC2163 series.
[0054] The local oscillator 110 is a digitally controlled frequency source that generates discrete frequency signals uniformly distributed within the test frequency range under the control of a real-time signal processor (DSP) 100.
[0055] In this embodiment, preferably, the real-time signal processor (DSP) 100 is a signal processor that transmits and receives intermediate frequency (IF) signals; the frequency bandwidth of the IF signal is W, and the frequency bandwidth satisfies the formula:
[0056] F0 is the intermediate frequency, and F s The sampling frequency.
[0057] In this embodiment, based on user requirements (such as the number of test points within a certain test range or the maximum test distance in DTF testing), the spacing between two adjacent frequency points is designed and denoted as dF; the dF must simultaneously satisfy the following formula:
[0058] 1) dF must be divisible by W, let And force K to be even;
[0059] 2) dF must be divisible by F s ,make
[0060] 3) dF must be divisible by F0, let
[0061] In this embodiment, preferably, the real-time signal processor (DSP) 100 obtains the multi-frequency digital signal x(n) using the following formula;
[0062]
[0063] In the above expression, A(k) represents the weighted amplitude at a certain frequency point. In practice, A(k) = 1, and P(k) is the initial phase corresponding to each frequency point.
[0064] The objective of selecting P(k) is to minimize the peak-to-average power ratio (PAPR) of the final signal x(n). The digital signal x(n) is a wideband signal (bandwidth W, sampling frequency F) consisting of K frequencies with a period of N (number of sampling points). s The signal was repeatedly sent to the digital-to-analog converter (DAC) 101 to complete the task of transmitting the intermediate frequency signal.
[0065] In this embodiment, the digital-to-analog converter (DAC) 101 is a DAC that generates a fixed periodic multi-frequency signal; the DAC 101 is up-modulated to different radio frequency points through the transmit mixer 102 and the local oscillator 110; the real-time signal processor 100 controls the local oscillator 110 to generate discrete frequency points F. x The F x It can be obtained through the following formula:
[0066]
[0067] F1 and F2 represent the selected test frequency ranges.
[0068] During digital signal processing in this invention:
[0069] At each radio frequency F x On the receiving end, the real-time signal processor (DSP) 100 must perform the following signal processing (assuming S...). 11 Measurement):
[0070] 1) When receiving ADC signals, the DSP must adopt block processing. Each data block must consist of consecutive sampled data points. The length of the data block must be an integer multiple of N. Let L = B * N, where B is an integer.
[0071] 2) The interval between any two data blocks must also be an integer multiple of N, which digitally guarantees that the phase difference between the transmitted and received signals is constant.
[0072] 3) Set the forward / reverse selection switch 109 to F (coupler and receiver port selection switch 107 always selects the forward / reverse selection switch 109), and add the data blocks of length L = B * N into "small blocks": This forms a data block y(n) of length N.
[0073] 4) The y(n) signal is applied at the following frequencies: Perform a discrete Fourier transform to obtain K complex numbers H1(j), j = 0, 1, 2, ..., K-1.
[0074] 5) Set the forward / reverse selection switch 109 to port R, and then perform the same calculation steps as in steps 3 and 4 above to obtain H2(j).
[0075] 6) Adjust the local oscillator 110 to the next frequency (F). x +W), then repeat steps 3), 4), 5) above, and add the data to the corresponding H1(j), H2(j) (that is, continuously expand the length of these two complex vector columns) until the local oscillator has swept all frequency points, we will get two complex vector columns H1(f), H2(f), f=0,1,2,…,(m2-m1+1)*K.
[0076] 7) Combine the two complex vector sequences above into a single complex vector sequence H(f) = H2(f) / H1(f). We will now prove that we can measure S using H(f). 11 (f) parameter.
[0077] This invention measures the reflection coefficient (S) 11 The calculation derivation is as follows:
[0078] Assuming that the outgoing signal on the directional coupler 103 is X(f) and the returning signal is Y(f), then the present invention has the following set of equations describing the characteristics of the coupler and the two measured vectors H1(f) and H2(f):
[0079] H1(f)=D 11 *X(f)+D 12 *Y(f)
[0080] H2(f)=D 21 *X(f)+D 22 *Y(f)
[0081] The above D 11 D 12 D 21 D 22 These are scattering matrix parameters that describe the characteristics of the coupler; these values will be determined by standard device correction.
[0082] Simplifying the above system of equations, we can obtain:
[0083]
[0084] Where R(f) = Y(f) / X(f) is the S we need. 11 (f) Parameters
[0085] The correction process of this invention is as follows:
[0086] Three standard impedance components, 50Ω, are connected to the test transmitter port 104. The components are open-circuited (impedance = ∞) and short-circuited (impedance = 0). For each component, the present invention performs data processing over a complete frequency range to obtain the corresponding complex vector sequence H(f). Based on the expression for H(f) above, the following relationship can be obtained:
[0087] 1. Standard 50Ω impedance, Because R = 0;
[0088] 2. Clear the way, Because R = 1;
[0089] 3. Short circuit, Because R = -1;
[0090] H above l H o H s These are complex vector columns obtained across the entire frequency band after correction. They will be permanently stored until new corrected data replaces them. This corrected data is used to calculate the unknown S. 11 The prerequisites for the parameters.
[0091] Reflectance coefficient (S) 11 Final calculation formula
[0092] In this embodiment, based on the above algebraic relationships, we can obtain:
[0093] C=(H o -H s ) / (2*H l -Ho -H s ), A = H l *C,B=H o *(C+1)-A
[0094] Corresponding to an unknown network under test, this invention collects its corresponding complex vector column H. x (f), then the required S 11 (f) is:
[0095]
[0096] Note that A, C, and B are all complex sequences dependent on frequency f. All the operations above are complex number operations.
[0097] Other data formulas in this invention are:
[0098] 1. Return attenuation: RTL(f) = -20 * log 10 (|S 11 (f)|)
[0099] 2. Standing Wave Ratio (VSWR): VSWR(f) = (|1+|S 11 ||) / (1-|S 11 |)
[0100] 3. Smith Chart: A chart that plots complex numbers S... 11 (f) Displayed in the Smith Chart polar coordinate system
[0101] 4. DTF (Distance to Fault), or time-domain reflectometer result: r(t) = |S 11 Inverse Fourier transform of (f)|.
[0102] In this embodiment, the transmission coefficient (S) 21 The testing steps are as follows:
[0103] The coupler and receiver port selection switch 107 are constantly connected to the test receiver port 108. Then, with the same transmit signal design, data reception and data block processing, and frequency adjustment, but without adjusting the forward / reverse selection switch 109, the test transmit port 104 and test receiver port 108 are first connected using a calibration cable, and the complex vector sequence H is measured. c (f) Then connect to the unknown network under test and obtain H x (f), then, the measured S 21 (f) means:
[0104] S 21 (f)=H x (f) / H c (f).
[0105] This invention achieves precise measurement of the amplitude ratio and phase difference of two signals using a single receiver, fully utilizing the periodicity of the digital signal source. In receiving data processing, it ensures a constant phase difference between the transmitted and reflected signals at each frequency point. Through the forward / reverse selection switch 109, this invention achieves dual-reception with a single-channel receiver. This invention is highly practical, stable, and provides more accurate frequency testing.
[0106] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention.
Claims
1. A vector analysis system for a digital source single-receiver network, characterized in that: Includes a real-time signal processor, a digital-to-analog converter, a transmit mixer, a local oscillator, a directional coupler, a test transmit port, a test receive port, a coupler and receive port selection switch, a receive mixer, and an analog-to-digital converter; The real-time signal processor transmits the data signal to the transmit mixer via a digital-to-analog converter. The transmit mixer then transmits the data signal to the test transmit port via a directional coupler. The test receive port receives the data signal via a coupler and a receive port selection switch. This coupler and receive port selection switch then transmit the data signal to the real-time signal processor via the receive mixer and an analog-to-digital converter. A local oscillator is provided between the transmitting mixer and the receiving mixer, which transmits the digitally controlled frequency source to the transmitting mixer and the receiving mixer respectively; a forward and reverse selection switch is provided between the directional coupler and the coupler and the receiving port selection switch, and the forward and reverse selection switch controls the directional coupler and the coupler and the receiving port selection switch respectively.
2. The digital source single-receiver network vector analysis system according to claim 1, characterized in that: The real-time signal processor includes a signal processor capable of continuously transmitting, receiving, and processing data at high sampling frequencies in real time.
3. The digital source single-receiver network vector analysis system according to claim 2, characterized in that: The real-time signal processor is a signal processor that transmits and receives intermediate frequency (IF) signals; the frequency bandwidth of the IF signal is W, and the frequency bandwidth satisfies the formula: ; The above is F 0 Intermediate frequency, the F S The sampling frequency.
4. The digital source single-receiver network vector analysis system according to claim 1 or 2, characterized in that: The test frequency spacing of the signal transmitted by the real-time signal processor is: dF The dF Satisfy the following formula: 1). dF W must be divisible by W, let and forced K It is an even number; 2). dF Must be divisible Fs ,make ; 3). dF Must be divisible F 0 ,make .
5. The digital source single-receiver network vector analysis system according to claim 4, characterized in that: The real-time signal processor obtains the multi-frequency digital signal using the following formula. x(n) ; ; in, A(k) The weighted amplitude represents a specific frequency point. P(k) It is the initial phase corresponding to each frequency point; x(n) The number of sampling points in one period is N of K A broadband signal composed of frequencies.
6. The digital source single-receiver network vector analysis system according to claim 5, characterized in that: The digital-to-analog converter is a digital-to-analog converter that generates a fixed periodic multi-frequency signal; The digital-to-analog converter is up-modulated to different radio frequency points via a transmitter mixer and a local oscillator; the real-time signal processor controls the local oscillator to generate discrete frequency points. Fx The Fx It can be obtained through the following formula: in, F 1 ,F 2 To select the test frequency range.
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