A frequency response test instrument and a complex impedance test instrument

Abstract

A frequency response test instrument and a complex impedance test instrument, both of which include a frequency-adjustable sinusoidal excitation signal source, an excitation signal conditioning circuit, a synchronous analog-to-digital converter (ADC) of at least 2 channels, a single-chip microcomputer, and a host computer, the latter also including a standard resistor. The main common features of the two instruments are: (1) the frequency-adjustable sinusoidal excitation signal source can output a sinusoidal excitation signal as low as 0.01 Hz; (2) both use a method suitable for 2-3 cycles or even shorter sinusoidal signals to accurately estimate the amplitude and initial phase parameters of the two sinusoidal signals. The two instruments have application prospects in frequency response testing of low-frequency circuits and low-frequency complex impedance characteristics testing of biochemical materials.

Description

Technical Field

[0001] The present application relates to a frequency response test instrument and a complex impedance test instrument.

[0002] Frequency response diagram, also called Bode diagram, includes amplitude-frequency response and phase-frequency response, and is a method of characterizing the complete characteristics of a linear system. The horizontal axis of the amplitude-frequency response diagram is frequency, and the vertical axis is the gain of the frequency component passing through the system; the horizontal axis of the phase-frequency response diagram is frequency, and the vertical axis is the phase shift caused by the frequency component passing through the system.

[0003] Complex impedance is a physical quantity that reflects the electrical properties of a passive circuit or a passive two-terminal network. In the complex number solution of AC circuits, simple harmonic quantities such as voltage and current are expressed by their corresponding complex numbers, which are called complex voltage and complex current respectively. Therefore, the ratio of voltage to current is also a complex number, called complex impedance, with the unit of ohm (Ω).

[0004] The algebraic expression of complex impedance is Z=R+jX, where its real part R is called active resistance or simply resistance, and the imaginary part X is called reactance. The complex impedance of a pure resistor is Z=R, the complex impedance of a pure inductor is Z=jωL, and its value XL=ωL is called inductive reactance. The complex impedance of a pure capacitor is Z=1 / jωC=-j1 / ωC, and its value Xc=1 / ωC is called capacitive reactance. The value of a complex impedance varies with frequency, so there is the concept of impedance spectrum, the full name of which is electrical impedance spectrum (EIS), which includes resistance spectrum and reactance spectrum; the horizontal axis of the resistance spectrum is frequency, and the vertical axis is the resistance part of the complex impedance. The horizontal axis of the reactance spectrum is also frequency, and the vertical axis is the reactance part of the complex impedance.

[0005] An instrument for testing the frequency response of a circuit is usually called a network analyzer. If an external accessory is connected to the network analyzer, it can also be used to test complex impedance or impedance spectrum. For example, Keysight's network analyzer E5061B can test both the frequency response of a circuit and complex impedance or impedance spectrum.

[0006] The problem now is that the current mainstream frequency response test instruments or complex impedance test instruments cannot cover the low-frequency band, such as Keysight's E5061B, which can only test frequency response or complex impedance at frequencies ≥5Hz. Background Art

[0007] A typical frequency response test instrument includes: a frequency-adjustable sinusoidal excitation signal source, an excitation signal conditioning circuit, at least 2-channel synchronous analog-to-digital converter (ADC), a single-chip microcomputer, a host computer, etc. A sinusoidal excitation signal output by the signal source is conditioned by the conditioning circuit and then connected to the input end of the circuit under test through a three-way device as the input of the circuit under test and to the ADC as an input of the ADC. At the same time, the sinusoidal wave output by the circuit under test is also connected to the ADC as the input of the ADC. The ADC synchronously acquires a pair of input and output sinusoidal signals of the circuit under test, and then sends them to the single-chip microcomputer and the host computer in turn. The single-chip microcomputer or the host computer performs phase-locked amplification on the pair of input and output sinusoidal signals acquired synchronously, thereby obtaining the gain G and phase shift of the circuit under test at the current frequency. Furthermore, by sweeping the frequency, a complete frequency response diagram can be obtained.

[0008] A typical complex impedance test instrument includes: a frequency-adjustable sinusoidal excitation signal source, an excitation signal conditioning circuit, a synchronous analog-to-digital converter (ADC) of at least 2 channels, a single-chip microcomputer, a host computer, a standard resistor, etc. A sinusoidal excitation signal output by the signal source is conditioned by the conditioning circuit and applied as a voltage to the two ends of the series circuit of the standard resistor r and the measured complex impedance R+jX to form a loop, generating current and voltage on the standard resistor and the measured complex impedance; the voltage signal generated at both ends of the standard resistor and the voltage signal generated at both ends of the measured complex impedance are ideally sinusoidal signals, which are sent to the ADC for detection, and the ADC synchronously collects the two sinusoidal wave signals and sends them to the single-chip microcomputer and the host computer in turn, and the two synchronously collected sinusoidal wave signals are phase-locked and amplified on the single-chip microcomputer or the host computer, so as to calculate the measured complex impedance R+jX at the current frequency; further, by frequency sweeping, a complete complex impedance spectrum can be obtained.

[0009] It can be seen that the core technologies of the above frequency response test instruments and complex impedance test instruments are basically the same, and both of them process the two sinusoidal signals collected synchronously through phase-locked amplification to obtain the results of the frequency response of the circuit under test or the complex impedance value under test. The reason why the current mainstream frequency response and complex impedance instruments cannot cover the low-frequency band is that in practice, the two sinusoidal signals collected synchronously at one frequency always have a certain amount of noise. The phase-locked amplification processing technology of these instruments requires that the length of the collected sinusoidal wave signal is at least 4 cycles to ensure the stability and accuracy of the estimated results; in this case, their analysis waiting time or time delay for low-frequency signals is too long. Taking 0.01Hz as an example, 4 cycles means 400 seconds, that is, it takes at least 6.7 minutes to calculate the frequency response or complex impedance value of a frequency point, so these instruments simply do not cover the low-frequency band. Summary of the invention

[0010] Purpose of the invention.

[0011] A technical solution of a frequency response test instrument and a complex impedance test instrument is proposed, which can stably and accurately estimate the values ​​of frequency response and complex impedance when the excitation signal is less than 4 cycles, and can cover the frequency response and complex impedance tests in the low frequency band down to 0.01 Hz.

[0012] Technical solution.

[0013] A frequency response test instrument comprises a frequency-adjustable sinusoidal excitation signal source, an excitation signal conditioning circuit, a synchronous analog-to-digital converter (ADC) of at least 2 channels, a single-chip microcomputer, and a host computer, characterized in that: (1) the frequency-adjustable sinusoidal excitation signal source can output a sinusoidal excitation signal as low as 0.01 Hz. After being conditioned by the conditioning circuit, the sinusoidal excitation signal is connected to the input end of a circuit under test as the input of the circuit under test and to an ADC as an input of the ADC through a three-way device. At the same time, the sinusoidal signal output by the circuit under test is also connected to the ADC as the input of the ADC; (2) the ADC synchronously collects a pair of input and output sinusoidal signals of the circuit under test and sends them to the single-chip microcomputer and the host computer in turn. The host computer uses a method suitable for 2-3 cycles or even shorter sinusoidal signals to estimate the amplitude and initial phase parameters of the two input and output sinusoidal signals. Let the estimated results be Ai, and Ao, Then the gain G and phase shift of the circuit under test at the current frequency are It can be calculated as G = Ao / Ai, (3) Furthermore, by sweeping the frequency, a complete frequency response diagram can be obtained. Figure 2 shown.

[0014] A complex impedance test instrument comprises a frequency-adjustable sinusoidal excitation signal source, an excitation signal conditioning circuit, a synchronous analog-to-digital converter (ADC) of at least 2 channels, a single-chip microcomputer, a host computer, and a standard resistor, wherein: (1) the frequency-adjustable sinusoidal excitation signal source can output a sinusoidal excitation signal as low as 0.01 Hz, which is conditioned by the conditioning circuit and applied as a voltage to the two ends of a series circuit of a standard resistor r and a complex impedance R+jX to be measured, forming a loop, generating current and voltage on the standard resistor and the complex impedance to be measured; (2) the voltage signal generated at both ends of the standard resistor r and the voltage signal generated at both ends of the complex impedance R+jX to be measured are both sinusoidal signals in an ideal situation, and are sent to the ADC for detection. The ADC synchronously collects the two sinusoidal signals and sends them to the single-chip microcomputer and the host computer in turn. The host computer uses a method suitable for 2-3 cycles or even shorter sinusoidal signals to estimate the amplitude and initial phase parameters of the two sinusoidal signals. Suppose the sinusoidal signal amplitude and initial phase parameter estimation results corresponding to the standard resistor and the complex impedance to be measured are A, B, and C, respectively. r , and A x , Then the measured complex impedance R+jX at the current frequency can be calculated as (3) Furthermore, by sweeping the frequency, a complete complex impedance spectrum can be obtained. Figure 3 shown.

[0015] In both the frequency response test instrument and the complex impedance test instrument, the upper computer needs to estimate the amplitude and initial phase parameters of two sinusoidal signals at known frequencies. The characteristic of the above is that the amplitude and initial phase parameters of each sinusoidal signal can be estimated based on the spectrum comparison method, that is, the sinusoidal signal to be analyzed is first subjected to Fourier transform to obtain the spectrum as a reference, and then a series of ideal sinusoidal signals with the same frequency as the sinusoidal signal to be estimated are constructed with the amplitude and initial phase as variables and their spectra are obtained. The amplitude and initial phase parameters are optimized with the maximum correlation or minimum difference between the constructed sinusoidal signal spectrum and the sinusoidal signal spectrum to be estimated as the optimization target, and the optimized amplitude and initial phase parameters are used as the estimation of the amplitude and initial phase parameters of the sinusoidal signal to be analyzed. Experiments show that this frequency domain comparison method is suitable for estimating the amplitude and initial phase parameters of signals with 2-3 cycles or even shorter, and can ensure sufficient accuracy.

[0016] In both the frequency response test instrument and the complex impedance test instrument, the upper computer needs to estimate the amplitude and initial phase parameters of two sinusoidal signals at known frequencies. The characteristic of the above is that the estimation of the amplitude and initial phase parameters of each sinusoidal signal can be performed based on the time domain comparison method, that is, the time domain waveform of the sinusoidal signal to be analyzed is used as a reference, and then a series of ideal sinusoidal signals with the same frequency as the sinusoidal signal to be estimated are constructed with the amplitude and initial phase as variables. The amplitude and initial phase parameters are optimized with the maximum correlation or minimum difference between the constructed ideal sinusoidal signal and the sinusoidal signal to be estimated in the time domain as the optimization target, and the optimized amplitude and initial phase parameters are used as the estimation of the amplitude and initial phase parameters of the sinusoidal signal to be analyzed. Experiments show that this time domain comparison method is suitable for estimating the amplitude and initial phase parameters of signals with 2-3 cycles or even shorter, and can ensure sufficient accuracy.

[0017] Beneficial effects.

[0018] Based on the frequency response test instrument of the present invention constructed in the embodiment, the frequency response of a bandpass filter circuit from 0.01Hz to 250Hz is tested. For each test frequency point, three cycles of sinusoidal signals are collected for analysis. The test results are shown in the attached figure. Figure 4 , Attachment Figure 5 As shown in the figure, after comparison, the test frequency response is consistent with the designed frequency response of this bandpass filter circuit, and the frequency response test as low as 0.01Hz was successfully achieved.

[0019] Based on the complex impedance test instrument of the present invention constructed in the embodiment, the complex impedance of a pair of adhesive-to-adhesive electrode patches in the frequency range of 0.01Hz-80Hz was tested. For each test frequency point, three cycles of sinusoidal signals were collected for analysis. The test results are shown in the attached Figure 6 As shown. There are 5 tests in total, corresponding to the 5 curves data1-data5 in the figure, showing good repeatability. This shows that this complex impedance tester can successfully test complex impedance as low as 0.01Hz.

[0020] Based on the complex impedance test instrument of the present invention constructed in the embodiment, the complex impedance of the short-circuited condition (0 ohm) of the two probes was tested. The test results are shown in the attached Figure 7 As shown in the figure, at several frequency points within the range of 0.01Hz-80Hz, three cycles of sine signals were collected for analysis. The test error was less than 0.1 ohm.

[0021] Based on the complex impedance test instrument of the present invention constructed in the embodiment, a 10k ohm standard resistor was tested. The test results are shown in the attached Figure 8 As shown in the figure. At several frequency points in the range of 0.01Hz-80Hz, three-cycle sinusoidal signals are collected for analysis. Figure 8 It can be seen that the test accuracy of the resistance part can reach ±1 / 10000.

[0022] Based on the complex impedance test instrument of the present invention constructed in the embodiment, a 10k ohm standard resistor was tested. The test results are shown in the attached Fig. 9 As shown in the figure. At several frequency points in the range of 0.01Hz-80Hz, one cycle of sinusoidal signal is collected for analysis. Fig. 9 It can be seen that the test accuracy of the resistance part can reach ±4 / 10000, which is lower than the case of collecting 3 cycles of sinusoidal signal analysis.

[0023] The above tests show that the technical solution of this application is feasible. Compared with the current mainstream solution, this application can stably and accurately estimate the frequency response and complex impedance values ​​when the excitation signal is less than 4 cycles, and can fully cover the circuit frequency response and complex impedance test in the low frequency band as low as 0.01Hz. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 , a schematic diagram of common features of a frequency response test instrument and a complex impedance test instrument of the present application.

[0025] Figure 2 , a schematic diagram of a frequency response test instrument solution of the present application.

[0026] Figure 3 , a schematic diagram of a complex impedance testing instrument scheme of the present application.

[0027] Figure 4 , the result of testing the frequency response of a circuit using the instrument of the present application. In the figure, Gain is gain, Phase is phase shift, the horizontal axis is frequency (f) axis, the unit is Hz, and the frequency sweep range is 0.01Hz-250Hz. At each frequency point, 3 cycles of sinusoidal signals are collected for analysis.

[0028] Figure 5 , Figure 4 A partial magnification of the frequency response test results (0.01Hz-10Hz). In the figure, Gain is gain, Phase is phase shift, and the horizontal axis is the frequency (f) axis, in Hz.

[0029] Figure 6 , a schematic diagram of the complex impedance results of a pair of glue-to-glue bonded electrodes at 0.01Hz-80Hz tested using the instrument of this application. Three cycles of sinusoidal signals are collected at each frequency point for analysis. The vertical axis R is the real part of the complex impedance, in ohms (ohm), the vertical axis X is the imaginary part of the complex impedance, in ohms (ohm), and the horizontal axis is the frequency axis, in Hz. A total of 5 tests, corresponding to data1-data5 respectively.

[0030] Figure 7 , a schematic diagram of the complex impedance (0 ohm) results of the short-circuited condition of two probes tested using the instrument of the present application. Three cycles of sinusoidal signals are collected for analysis at several frequency points in the range of 0.01Hz-80Hz. The vertical axis R is the real part of the complex impedance, in ohms, the vertical axis X is the imaginary part of the complex impedance, in ohms, and the horizontal axis is the frequency axis, in Hz.

[0031] Figure 8 , a schematic diagram of the results of testing a 10k ohm standard resistor using the instrument of the present application. Three cycles of sinusoidal signals are collected for analysis at several frequency points in the range of 0.01Hz-80Hz. The vertical axis R is the real part of the complex impedance, in ohms, the vertical axis X is the imaginary part of the complex impedance, in ohms, and the horizontal axis is the frequency axis, in Hz.

[0032] Fig. 9 , a schematic diagram of the results of testing a 10k ohm standard resistor using the instrument of the present application. At several frequency points in the range of 0.01Hz-80Hz, a 1-cycle sinusoidal signal is collected for analysis. The vertical axis R is the real part of the complex impedance, in ohms, the vertical axis X is the imaginary part of the complex impedance, in ohms, and the horizontal axis is the frequency axis, in Hz. DETAILED DESCRIPTION

[0033] The present application discloses an embodiment of a frequency response test instrument. ADI9833 is used as a frequency-adjustable sinusoidal excitation signal source, an excitation signal conditioning circuit is built based on the programmable gain amplifier PGA281, an ADS1294 four-channel synchronous analog-to-digital converter (ADC) is selected, STM32 is selected as the single-chip microcomputer, and an ordinary PC is selected as the host computer. ADI9833 is equipped with a 1MHz active oscillator, so the minimum frequency of the excitation signal can be as low as 10^6 / 2^28=0.0037Hz. After the excitation signal is conditioned by the conditioning circuit, it is connected to the input end of the circuit under test as the input of the circuit under test through a three-way device, and is connected to the ADC as one of the inputs of the ADC. At the same time, the sinusoidal signal output by the circuit under test is also connected to the ADC as the input of the ADC. The ADC synchronously collects a pair of input and output sinusoidal signals of the circuit under test and sends them to the single-chip microcomputer and the host computer. See Figure 2 As shown. The circuit board of the other parts including the single-chip microcomputer except the host computer forms a module. The communication between the single-chip microcomputer and the host computer adopts the USB to serial port chip CH343G for communication. The host computer programming implements the amplitude and initial phase parameter estimation method suitable for 2-3 cycles or even shorter sinusoidal signals. Specifically, the proposed estimation method based on time domain comparison is adopted. By solving the optimization problem, the amplitude and phase parameters of the two sinusoidal signals of the input and output of the measured circuit are estimated, and they are set as Ai, and Ao, Then further estimate the gain G and phase shift of the circuit under test at the current frequency G = Ao / Ai, Furthermore, by sweeping the frequency, a complete frequency response diagram can be obtained.

[0034] The present application discloses an embodiment of a complex impedance test instrument. ADI9833 is used as a frequency-adjustable sinusoidal excitation signal source, an excitation signal conditioning circuit is built based on a programmable gain amplifier PGA281, an ADS1294 four-channel synchronous analog-to-digital converter (ADC) is selected, an STM32 is selected as a single-chip microcomputer, an ordinary PC is selected as a host computer, and a 10k ohm standard resistor r is selected. ADI9833 is equipped with a 1MHz active crystal oscillator, so the minimum frequency of the excitation signal can be as low as 10^6 / 2^28=0.0037Hz. After the sinusoidal excitation signal is conditioned by the conditioning circuit, it is added as a voltage to both ends of the series circuit of the standard resistor r and the measured complex impedance R+jX to form a loop, generating current and voltage on the standard resistor and the measured complex impedance. The voltage signal generated at both ends of the standard resistor and the voltage signal generated at both ends of the measured complex impedance are ideally sinusoidal signals, which are sent to the ADC for detection. The ADC synchronously collects these two sinusoidal signals and sends them to the single-chip microcomputer and the host computer in turn. Figure 3As shown. The circuit board of the other parts including the single-chip microcomputer except the host computer is made into a module. The communication between the single-chip microcomputer and the host computer is implemented by using the USB to serial port chip CH343G. The host computer programming implements the amplitude and initial phase parameter estimation method suitable for 2-3 cycles or even shorter sinusoidal signals. Specifically, the proposed estimation method based on time domain comparison is used to estimate the amplitude and initial phase parameters of the two sinusoidal signals. Assume that the estimated amplitude and initial phase parameters of the sinusoidal signal of the voltage across the standard resistance and the measured complex impedance are A and B respectively. r , and Ax, Then the measured complex impedance R+jX at the current frequency can be calculated as Furthermore, by sweeping the frequency, a complete complex impedance spectrum can be obtained.

Claims

1. A frequency response test instrument, comprising a frequency-adjustable sinusoidal excitation signal source, an excitation signal conditioning circuit, at least 2-channel synchronous analog-to-digital converter ADC, a single-chip microcomputer, and a host computer, characterized in that: (1) The frequency-adjustable sinusoidal excitation signal source can output a sinusoidal excitation signal as low as 0.01 Hz. After being conditioned by the conditioning circuit, it is connected to the input end of the circuit under test through a three-way device as the input of the circuit under test, and to the ADC as an input of the ADC on the other hand. At the same time, the sinusoidal signal output by the circuit under test is also connected to the ADC as the input of the ADC; (2) The ADC synchronously collects a pair of input and output sinusoidal signals of the circuit under test, and sends them to the microcontroller and the host computer in turn. The host computer uses a method suitable for 2-3 cycles or even shorter than 1 cycle of sinusoidal signals to estimate the amplitude and initial phase parameters of the two input and output sinusoidal signals. The estimation of the amplitude and initial phase parameters of each sinusoidal signal can be carried out based on the spectrum comparison method, that is, the sinusoidal signal to be analyzed is first subjected to Fourier transform to obtain the spectrum as a reference, and then a series of sinusoidal signals with the same frequency as the sinusoidal signal to be estimated are constructed with the amplitude and initial phase as variables. The ideal sinusoidal signal is constructed and their spectra are obtained. The correlation between the constructed sinusoidal signal spectrum and the sinusoidal signal spectrum to be estimated is maximized or the difference is minimized as the optimization goal. The amplitude and initial phase parameters are optimized, and the optimized amplitude and initial phase parameters are used as the estimation of the amplitude and initial phase parameters of the sinusoidal signal to be analyzed. Alternatively, the estimation of the amplitude and initial phase parameters of each sinusoidal signal can be based on the time domain comparison method, that is, the time domain waveform of the sinusoidal signal to be analyzed is used as the benchmark, and then a series of ideal sinusoidal signals with the same frequency as the sinusoidal signal to be estimated are constructed with the amplitude and initial phase as variables. The correlation between the constructed ideal sinusoidal signal and the sinusoidal signal to be estimated in the time domain is maximized or the difference is minimized as the optimization goal. The amplitude and initial phase parameters are optimized, and the optimized amplitude and initial phase parameters are used as the estimation of the amplitude and initial phase parameters of the sinusoidal signal to be analyzed. Let the estimation results be Ai, and Ao, Then the gain G and phase shift of the circuit under test at the current frequency are It can be calculated as G = Ao / Ai, (3) Furthermore, by sweeping the frequency, a complete frequency response diagram can be obtained.

2. A complex impedance test instrument, comprising a frequency-adjustable sinusoidal excitation signal source, an excitation signal conditioning circuit, at least 2-channel synchronous analog-to-digital converter ADC, a single-chip microcomputer, a host computer, and a standard resistor, characterized in that: (1) The frequency-adjustable sinusoidal excitation signal source can output a sinusoidal excitation signal as low as 0.01 Hz. After being conditioned by the conditioning circuit, it is added as a voltage to the two ends of the series circuit of the standard resistor r and the measured complex impedance R+jX to form a loop, generating current and voltage on the standard resistor and the measured complex impedance; (2) The voltage signal generated at both ends of the standard resistor r and the voltage signal generated at both ends of the measured complex impedance R+jX are ideally sinusoidal signals, which are sent to the ADC for detection. The ADC synchronously collects these two sinusoidal signals and sends them to the microcontroller and the host computer in turn. The host computer uses a method suitable for 2-3 cycles or even shorter than 1 cycle of sinusoidal signals to estimate the amplitude and initial phase parameters of the two sinusoidal signals. The estimation of the amplitude and initial phase parameters of each sinusoidal signal can be based on the spectrum comparison method, that is, the sinusoidal signal to be analyzed is first subjected to Fourier transform to obtain the spectrum as a reference, and then a series of sinusoidal signals with the same frequency as the sinusoidal signal to be estimated are constructed with the amplitude and initial phase as variables. The ideal sinusoidal signal is obtained and their spectra are obtained. The correlation degree between the constructed sinusoidal signal spectrum and the sinusoidal signal spectrum to be estimated is maximized or the difference degree is minimized as the optimization goal. The two parameters of amplitude and initial phase are optimized, and the optimized amplitude and initial phase parameters are used as the estimation of the amplitude and initial phase parameters of the sinusoidal signal to be analyzed. Alternatively, the estimation of the amplitude and initial phase parameters of each sinusoidal signal can be based on the time domain comparison method, that is, the time domain waveform of the sinusoidal signal to be analyzed is used as the benchmark, and then a series of ideal sinusoidal signals with the same frequency as the sinusoidal signal to be estimated are constructed with the amplitude and initial phase as variables. The correlation degree between the constructed ideal sinusoidal signal and the sinusoidal signal to be estimated in the time domain is maximized or the difference degree is minimized as the optimization goal. The two parameters of amplitude and initial phase are optimized, and the optimized amplitude and initial phase parameters are used as the estimation of the amplitude and initial phase parameters of the sinusoidal signal to be analyzed. Suppose the sinusoidal signal amplitude and initial phase parameter estimation results corresponding to the standard resistance and the measured complex impedance are A respectively. r , and A x , Then the measured complex impedance R+jX at the current frequency can be calculated as (3) Furthermore, by frequency sweeping, a complete complex impedance spectrum can be obtained.

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