WO2023005248A1 - Frequency response measurement system based on harmonic wave, and method - Google Patents

Abstract

A frequency response measurement system based on a harmonic wave. A square wave having a duty cycle of 50% is used as a measurement signal, the oversampling rate of an analog-to-digital converter in the measurement system is set to be a half integer, and frequency responses, on multiple frequency points, of a linear system to be measured are obtained by means of one mathematical operation. Further disclosed is a method for performing frequency response measurement using the frequency response measurement system based on the harmonic wave. The measurement system and method have the advantages of high measurement efficiency and low measurement cost.

Description

A Harmonic-Based Frequency Response Measurement System and Method technical field

The invention belongs to the technical field of linear system frequency response measurement, and in particular relates to a frequency response measurement system and method based on harmonics.

Background technique

Linear systems exist widely. Measuring linear system frequency response is important.

To measure the frequency response of a linear system, the commonly used methods are a bit frequency method, frequency sweep method, etc. Both the point frequency method and the sweep frequency method use a sinusoidal signal as the measurement signal input to the linear system to be tested. Applying a sinusoidal signal for one measurement can only obtain the frequency response at one frequency point. Moreover, both the point-frequency method and the sweep-frequency method require a sine wave generating circuit, and the sine wave generating circuit has disadvantages such as more complex circuits and higher costs than the square wave generating circuit.

Therefore, the point-frequency method and the sweep-frequency method have the problems of relatively low measurement efficiency and relatively high measurement cost. They cannot be used in scenarios with high requirements on measurement efficiency or measurement cost.

Contents of the invention

The purpose of the present invention is to provide a frequency response measurement system and method based on harmonics, so as to solve the technical problems of relatively low measurement efficiency and relatively high measurement cost in the spot frequency method and the frequency sweep method.

In order to solve the above technical problems, a specific technical solution of a harmonic-based frequency response measurement system and method of the present invention is as follows:

A harmonic-based frequency response measurement system comprising:

A frequency controllable square wave generator, the input is the control signal Ctrl0 output by the computing control unit, and the output is a square wave signal x(t);

A linear system to be tested, the input is a square wave x(t) output by a frequency controllable square wave generator, and the output m(t) is connected to a signal conditioning circuit;

A signal conditioning circuit, the input is the output m(t) of the linear system to be tested and the control signal Ctrl2 output by the calculation control unit, and the output y(t) is connected to the analog-to-digital converter;

An analog-to-digital converter, the input is the output y(t) of the signal conditioning circuit and the control signal Ctrl1 output by the calculation control unit, and the output code word y(n) is connected to the calculation processing unit;

A calculation processing unit, the input is the code word y(n) output by the analog-to-digital converter, the output control signals Ctrl0, Ctrl1 and Ctrl2 are respectively connected to the frequency controllable square wave generator, the analog-to-digital converter and the signal conditioning circuit, and output measurement results.

The invention also discloses a frequency response measurement method based on harmonics, which includes several measurement rounds, and each measurement round includes the following four steps:

In the first step, according to the target measurement frequency, the calculation control unit sets the square wave frequency f ₀ and the square wave amplitude and other parameters generated by the square wave generator, and sets the low-pass cut-off frequency f _C of the signal conditioning circuit and the analog-to-digital converter pass Sampling rate OSR, start the square wave generator, where the oversampling rate OSR is a half integer;

In the second step, the calculation processing unit adjusts the gain A _V of the signal conditioning circuit to ensure that the input of the analog-to-digital converter is in a state close to full scale and not saturated;

In the third step, the calculation processing unit performs K-point DFT calculation on the result y(n) output by the analog-to-digital converter, and obtains the frequency spectrum of the signal y(t) at the frequency points f ₀ , 3f ₀ , 5f ₀ , ... Mf ₀ Data Y(f ₀ ), Y(3f ₀ ), Y(5f ₀ ), ... Y(Mf ₀ ), where M is odd and M<OSR;

In the fourth step, the calculation processing unit divides Y(f ₀ ), Y(3f ₀ ), Y(5f ₀ ), ... Y(Mf ₀ ) by the gain A _V (f ₀ ) and A _V of the signal conditioning circuit respectively (3f ₀ ), A _V (5f ₀ ), ... A _V (Mf ₀ ), and then divided by the K-point DFT spectrum data X(f ₀ ), X(3f ₀ ), X( 5f ₀ ),...X(Mf ₀ ), respectively obtain the frequency responses H( _{f 0} ), H(3f _{0 )} , H(3f _{0 )} , H(5f ₀ ), ... H(Mf ₀ ).

Further, in the frequency controllable square wave generator, parameters such as the amplitude, frequency f ₀ and phase of the generated square wave are precisely defined, and the frequency f ₀ of the square wave is adjustable, determined by the control signal Ctrl0 output by the calculation control unit.

Further, the signal conditioning circuit performs linear amplification and low-pass filtering on the input signal m(t), its gain A _V is adjustable, and the cut-off frequency f _C of the low-pass filtering is adjustable, and the control output by the calculation control unit Signal Ctrl2 decides.

Further, the sampling frequency f _s of the analog-to-digital converter is determined by the control signal Ctrl1 output by the calculation control unit, and the square wave frequency f ₀ satisfies f _s =K×f ₀ , where K is an odd number.

Further, the calculation processing unit can perform mathematical operations, can output control signals, can read external digital code word input, and it outputs control signal Ctrl0 to access the frequency controllable square wave generator to control parameters such as square wave frequency; The output control signal Ctrl1 is connected to the analog-to-digital converter to control the sampling frequency of the analog-to-digital converter; the output control signal Ctrl2 is connected to the signal conditioning circuit to control the gain A _V and the low-pass cut-off frequency f _C of the signal conditioning circuit; and output the measurement results.

Further, said M<K/2.

A harmonic-based frequency response measurement system and method of the present invention have the following advantages: the frequency response at multiple frequency points of the linear system to be tested can be obtained through one measurement; the use of a square wave generator instead of a sine wave generation circuit simplifies The circuit is improved and the cost is reduced.

Description of drawings

FIG. 1 is a schematic diagram of the basic framework of a frequency response measurement system based on harmonics of the present invention.

Fig. 2 is a schematic diagram of main steps of a frequency response measurement method based on harmonics in the present invention.

Fig. 3 is a schematic diagram of the basic framework of a specific embodiment of the present invention.

Detailed ways

In order to better understand the purpose, structure and function of the present invention, a harmonic-based frequency response measurement system and method of the present invention will be further described in detail below in conjunction with the accompanying drawings.

As shown in Figure 1, a harmonic-based frequency response measurement system includes:

A frequency controllable square wave generator, the input is the control signal Ctrl0 output by the computing control unit, and the output is a square wave signal x(t);

A linear system to be tested, the input is a square wave x(t) output by a frequency controllable square wave generator, and the output m(t) is connected to a signal conditioning circuit;

A signal conditioning circuit, the input is the output m(t) of the linear system to be tested and the control signal Ctrl2 output by the calculation control unit, and the output y(t) is connected to the analog-to-digital converter;

An analog-to-digital converter, the input is the output y(t) of the signal conditioning circuit and the control signal Ctrl1 output by the calculation control unit, and the output code word y(n) is connected to the calculation processing unit;

A calculation processing unit, the input is the code word y(n) output by the analog-to-digital converter, the output control signals Ctrl0, Ctrl1 and Ctrl2 are respectively connected to the frequency controllable square wave generator, the analog-to-digital converter and the signal conditioning circuit, and output measurement results.

As shown in Figure 2, a kind of frequency response measurement method based on harmonics of the present invention can comprise several measurement rounds, and each measurement round mainly comprises following four steps:

In the first step, according to the target measurement frequency, the calculation control unit sets the square wave frequency f ₀ and the square wave amplitude and other parameters generated by the square wave generator, and sets the low-pass cut-off frequency f _C of the signal conditioning circuit and the analog-to-digital converter pass Sampling rate OSR, start the square wave generator, where the oversampling rate OSR is a half integer;

In the second step, the calculation processing unit adjusts the gain A _V of the signal conditioning circuit to ensure that the input of the analog-to-digital converter is in a state close to full scale and not saturated;

In the third step, the calculation processing unit performs K-point DFT calculation on the result y(n) output by the analog-to-digital converter, and obtains the frequency spectrum of the signal y(t) at the frequency points f ₀ , 3f ₀ , 5f ₀ , ... Mf ₀ Data Y(f ₀ ), Y(3f ₀ ), Y(5f ₀ ), ... Y(Mf ₀ ), where M is odd and M<OSR;

In the fourth step, the calculation processing unit divides Y(f ₀ ), Y(3f ₀ ), Y(5f ₀ ), ... Y(Mf ₀ ) by the gain A _V (f ₀ ) and A _V of the signal conditioning circuit respectively (3f ₀ ), A _V (5f ₀ ), ... A _V (Mf ₀ ), and then divided by the K-point DFT spectrum data X(f ₀ ), X(3f ₀ ), X( 5f ₀ ),...X(Mf ₀ ), respectively obtain the frequency responses H( _{f 0} ), H(3f _{0 )} , H(3f _{0 )} , H(5f ₀ ), ... H(Mf ₀ ).

Preferably, in the frequency controllable square wave generator, parameters such as the generated square wave amplitude, frequency f ₀ and phase are precisely defined, and the square wave frequency f ₀ is adjustable, determined by the control signal Ctrl0 output by the calculation control unit.

Preferably, the signal conditioning circuit performs linear amplification and low-pass filtering on the input signal m(t). Its gain A _V is adjustable, and the cut-off frequency f _C of the low-pass filter is adjustable, which is determined by the control signal Ctrl2 output by the calculation control unit.

Preferably, the sampling frequency f _s of the analog-to-digital converter is determined by the control signal Ctrl1 output by the calculation control unit, and the square wave frequency f ₀ satisfies f _s =K×f ₀ , where K is an odd number.

Preferably, the calculation and processing unit can perform mathematical operations, output control signals, and read external digital code input. It outputs the control signal Ctrl0 to access the frequency-controllable square wave generator to control parameters such as the frequency of the square wave; the output control signal Ctrl1 to access the analog-to-digital converter to control the sampling frequency of the analog-to-digital converter; the output control signal Ctrl2 to access the signal conditioning circuit , control the gain A _V and the low-pass cut-off frequency f _C of the signal conditioning circuit; and output the measurement results.

Preferably, the parameter M in the above measuring method is an odd number and satisfies M<K/2.

The above measurement system and method have the following advantages: the frequency response at multiple frequency points of the linear system to be tested can be obtained through one measurement; the use of a square wave generator instead of a sine wave generating circuit simplifies the circuit and reduces the cost.

If you need to measure the frequency response of a linear system at many frequency points, you can repeat the above steps, and set different parameters such as square wave frequency f ₀ and low-pass cut-off frequency f _C each time.

The principle that the above measurement system and method can measure the frequency response at multiple frequency points of the linear system to be tested at one time is that based on the superposition theorem of the linear circuit and the spectrum characteristics of the square wave with a duty cycle of 50%, the fundamental wave of the square wave is used and low-order harmonics to measure the system frequency response, and eliminate possible high-order harmonic spectrum aliasing by setting the oversampling rate of the analog-to-digital converter.

Denote the frequency response of the linear system to be tested as H(f), denote the Fourier coefficients of the signals x(t) and y(t) at the frequency point jf ₀ as X(jf ₀ ), Y(jf ₀ ) respectively, denote The gain of the signal conditioning circuit at the frequency point jf ₀ is A _V (jf ₀ ), where j=1,2,...M. X(jf ₀ ), Y(jf ₀ ), and A _V (jf ₀ ) are complex numbers and include amplitude and phase. have

Y(jf ₀ )＝A _V (jf ₀ )X(jf ₀ )H(jf ₀ )

Among them, j=1, 2, ... M (formula 1)

The result after recording y(n) as K-point DFT calculation is Y _F (jf ₀ ), j=1, 2,...M.

So there is

Since we limit the duty cycle of the measured signal x(t) to 50%, the spectrum of the signal x(t) has the characteristics that the even harmonic energy is 0, namely

X(mf ₀ )=0, m=2, 4, . . . ∞ (Formula 5)

Combining Equation 1 and Equation 5, we can get that the even harmonic energy of the signal y(t) is also 0, that is

Y(mf ₀ )=0, m=2, 4, . . . ∞ (Formula 6)

Since both K and M are set to be odd numbers, even harmonic energies such as K-1, K+1, 3K-1, 3K+1 in y(t) are 0. So there is

Similarly, there are

According to formula 1, it can be obtained

Since the duty cycle of the measurement signal x(t) is set to 50%, according to the signal and system knowledge, we can get

Due to low-pass filtering, |A _V ((2·i·K-1)f ₀ )|<<|A _V (f ₀ )|, and the ratio in formula 11 is a very small number, so in formula 10 ratio is close to 0. Therefore, 2K-1, 2K+1 and higher odd harmonics of y(t) in Formula 7 can be ignored. Similarly, the odd harmonics in Equation 8 and Equation 9 can also be ignored.

Therefore, the influence of spectral aliasing can be neglected.

So there is

Then use the following formula 15 to obtain the frequency response of the linear system to be tested.

Wherein, j=1, 2, ... M (formula 15)

In this embodiment, we test the frequency response of a linear system within 1kHz-10kHz. The system structure block diagram of the embodiment is shown in FIG. 3 . The frequency controllable square wave generator is realized by using a 555 timer combined with a resistor array; the signal conditioning circuit uses a program-controlled amplifier and a program-controlled filter, and the calculation control unit uses a stm32 single-chip microcomputer.

Using the measurement system and method proposed by the present invention, the specific measurement process is as follows.

first round:

In the first step, the stm32 microcontroller sets the frequency of the square wave generated by the square wave generator to 1kHz, sets the low-pass cut-off frequency of the program-controlled filter to 33kHz, sets the oversampling rate of the analog-to-digital converter to 49.5, and starts the square wave generator;

In the second step, the stm32 single-chip microcomputer adjusts the gain of the program-controlled amplifier to ensure that the analog-to-digital converter is in a state close to full scale and unsaturated, and records the cascaded gain A _V of the program-controlled amplifier and the program-controlled filter at this time;

In the third step, the stm32 single-chip microcomputer performs 99-point DFT on the digital signal y(n), and obtains the spectrum data Y ₁ , Y ₃ , Y ₅ of y(t) at five frequency points of 1kHz, 3kHz, 5kHz, 7kHz, and 9kHz , Y ₇ , Y ₉ ;

In the fourth step, the stm32 MCU divides Y ₁ , Y ₃ , Y ₅ , Y ₇ , and Y ₉ by the cascaded gain of the programmable amplifier and the programmable filter at the five frequency points of 1kHz, 3kHz, 5kHz, 7kHz, and 9kHz, respectively. A _V1 , A _V3 , A _V5 , A _V7 , A _V9 , and then divided by x(t) at 5 frequency points of 1kHz, 3kHz, 5kHz, 7kHz, and 9kHz obtained by performing 99-point DFT on x(t) Spectrum data X ₁ , X ₃ , X ₅ , X ₇ , X ₉ , respectively obtain the frequency responses H ₁ , H ₃ , H ₅ , H ₇ , H ₉ .

second round:

In the first step, the stm32 microcontroller sets the frequency of the square wave generated by the square wave generator to 2kHz, sets the low-pass cut-off frequency of the program-controlled filter to 66kHz, sets the oversampling rate of the analog-to-digital converter to 49.5, and starts the square wave generator;

In the second step, the stm32 single-chip microcomputer adjusts the gain of the program-controlled amplifier to ensure that the analog-to-digital converter is in a state close to full scale and unsaturated, and records the cascaded gain A _V of the program-controlled amplifier and the program-controlled filter at this time;

In the third step, the stm32 single-chip microcomputer performs 99-point DFT on the digital signal y(n), and obtains the spectrum data Y ₂ , Y ₆ , and Y ₁₀ of y(t) at the three frequency points of 2kHz, 6kHz, and 10kHz;

In the fourth step, the stm32 MCU divides Y ₂ , Y ₆ , and Y ₁₀ by the cascaded gains A _V2 , A _V6 , and A _V10 of the program-controlled amplifier and the program-controlled filter at the three frequency points of 2kHz, 6kHz, and 10kHz, respectively, and then Divide by the spectral data X ₂ , X ₆ , and X ₁₀ of x(t) at the three frequency points of 2kHz, 6kHz, and 10kHz obtained by performing 99-point DFT on x(t), respectively, to obtain the linear system to be tested at frequency Frequency responses H ₂ , H ₆ , and H ₁₀ at three frequency points of 2 kHz, 6 kHz, and 10 kHz.

The above two rounds of measurements obtained the frequency response of the linear system to be tested at 8 frequency points of 1kHz, 2kHz, 3kHz, 5kHz, 6kHz, 7kHz, 9kHz, and 10kHz.

Using the measuring system and method shown in the present invention, the frequency response at 8 frequency points can be obtained only by 2 measurements. According to the traditional measurement method, it needs to be measured 8 times. In this example, the efficiency of the measurement system and method proposed by the present invention is 4 times that of the traditional point frequency method and frequency sweep method. At the same time, in this embodiment, a 555 timer combined with a resistor array is used to replace the sine wave generating circuit, which has the advantage of lower cost.

It can be seen from the above embodiments that the measurement system and method proposed by the present invention have the advantages of high measurement efficiency and low measurement cost.

It can be understood that the present invention is described through some embodiments, and those skilled in the art know that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, the features and embodiments may be modified to adapt a particular situation and material to the teachings of the invention without departing from the spirit and scope of the invention. Therefore, the present invention is not limited by the specific embodiments disclosed here, and all embodiments falling within the scope of the claims of the present application belong to the protection scope of the present invention.

Claims (7)

A frequency response measurement system based on harmonics, characterized in that it comprises: A frequency controllable square wave generator, the input is the control signal Ctrl0 output by the computing control unit, and the output is a square wave signal x(t); A linear system to be tested, the input is a square wave x(t) output by a frequency controllable square wave generator, and the output m(t) is connected to a signal conditioning circuit; A signal conditioning circuit, the input is the output m(t) of the linear system to be tested and the control signal Ctrl2 output by the calculation control unit, and the output y(t) is connected to the analog-to-digital converter; An analog-to-digital converter, the input is the output y(t) of the signal conditioning circuit and the control signal Ctrl1 output by the calculation control unit, and the output code word y(n) is connected to the calculation processing unit; A calculation processing unit, the input is the code word y(n) output by the analog-to-digital converter, the output control signals Ctrl0, Ctrl1 and Ctrl2 are respectively connected to the frequency controllable square wave generator, the analog-to-digital converter and the signal conditioning circuit, and output measurement results. A method utilizing the frequency response measurement system based on harmonics as claimed in claim 1 to carry out frequency response measurement, characterized in that, comprising several measurement rounds, each measurement round comprising the following four steps: In the first step, according to the target measurement frequency, the calculation control unit sets the square wave frequency f ₀ and the square wave amplitude and other parameters generated by the square wave generator, and sets the low-pass cut-off frequency f _C of the signal conditioning circuit and the analog-to-digital converter pass Sampling rate OSR, start the square wave generator, where the oversampling rate OSR is a half integer; In the second step, the calculation processing unit adjusts the gain A _V of the signal conditioning circuit to ensure that the input of the analog-to-digital converter is in a state close to full scale and not saturated; In the third step, the calculation processing unit performs K-point DFT calculation on the result y(n) output by the analog-to-digital converter, and obtains the frequency spectrum of the signal y(t) at the frequency points f ₀ , 3f ₀ , 5f ₀ , ... Mf ₀ Data Y(f ₀ ), Y(3f ₀ ), Y(5f ₀ ), ... Y(Mf ₀ ), where M is odd and M<OSR; In the fourth step, the calculation processing unit divides Y(f ₀ ), Y(3f ₀ ), Y(5f ₀ ), ... Y(Mf ₀ ) by the gain A _V (f ₀ ) and A _V of the signal conditioning circuit respectively (3f ₀ ), A _V (5f ₀ ), ... A _V (Mf ₀ ), and then divided by the K-point DFT spectrum data X(f ₀ ), X(3f ₀ ), X( 5f ₀ ),...X(Mf ₀ ), respectively obtain the frequency responses H( _{f 0} ), H(3f _{0 )} , H(3f _{0 )} , H(5f ₀ ), ... H(Mf ₀ ). The frequency response measurement method based on harmonics according to claim 2, characterized in that, the frequency controllable square wave generator, parameters such as square wave amplitude, frequency f ₀ and phase are precisely defined, square wave frequency f ₀ is adjustable, determined by the control signal Ctrl0 output by the computing control unit. The method for measuring frequency response based on harmonics according to claim 2, wherein the signal conditioning circuit performs linear amplification and low-pass filtering on the input signal m (t), and its gain A _V is adjustable, low The cut-off frequency f _C of the pass filter is adjustable and is determined by the control signal Ctrl2 output by the calculation control unit. The method for measuring frequency response based on harmonics according to claim 2, wherein, for the analog-to-digital converter, its sampling frequency f _s is determined by the control signal Ctrl1 output by the calculation control unit, which is between the square wave frequency f ₀ satisfy f _s =K×f ₀ , where K is an odd number. The method for measuring frequency response based on harmonics according to claim 2, wherein the calculation processing unit can perform mathematical operations, can output control signals, can read external digital code word input, and it outputs control signal Ctrl. Access frequency controllable square wave generator, control parameters such as square wave frequency; output control signal Ctrl1 access analog-to-digital converter, control the sampling frequency of analog-digital converter; output control signal Ctrl2 access signal conditioning circuit, control signal conditioning circuit Gain A _V and low-pass cutoff frequency f _C ; and output the measurement results. The method for measuring frequency response based on harmonics according to claim 2, wherein said M<K/2.

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