WO2023005248A1 - 一种基于谐波的频率响应测量系统及方法 - Google Patents

一种基于谐波的频率响应测量系统及方法 Download PDF

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WO2023005248A1
WO2023005248A1 PCT/CN2022/083899 CN2022083899W WO2023005248A1 WO 2023005248 A1 WO2023005248 A1 WO 2023005248A1 CN 2022083899 W CN2022083899 W CN 2022083899W WO 2023005248 A1 WO2023005248 A1 WO 2023005248A1
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frequency
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square wave
analog
digital converter
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冯向东
赵博
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Zhejiang University ZJU
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  • 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.
  • Linear systems exist widely. Measuring linear system frequency response is important.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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:
  • 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;
  • 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;
  • 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;
  • 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 ).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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:
  • 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;
  • 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;
  • 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;
  • 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 ).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • the spectrum of the signal x(t) has the characteristics that the even harmonic energy is 0, namely
  • 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.
  • the specific measurement process is as follows.
  • 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;
  • 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;
  • 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 ;
  • 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.
  • 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;
  • 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;
  • 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;
  • 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 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.
  • 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.
  • a 555 timer combined with a resistor array is used to replace the sine wave generating circuit, which has the advantage of lower cost.
  • the measurement system and method proposed by the present invention have the advantages of high measurement efficiency and low measurement cost.

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Abstract

一种基于谐波的频率响应测量系统，利用占空比为50％的方波作为测量信号，把测量系统中的模数转换器过采样率设置为半整数，通过数学运算一次得到待测线性系统在多个频点上的频率响应。还公开了一种利用基于谐波的频率响应测量系统进行频率响应测量的方法。测量系统和方法具有测量效率高、测量成本低的优点。

Description

一种基于谐波的频率响应测量系统及方法 技术领域
本发明属于线性系统频率响应测量技术领域，尤其涉及一种基于谐波的频率响应测量系统及方法。
背景技术
线性系统广泛存在。测量线性系统频率响应很重要。
测量线性系统频率响应，常用的方法有点频法、扫频法等。点频法和扫频法都是使用正弦信号作为测量信号输入待测线性系统。施加一次正弦信号进行一次测量，只能得到一个频点上的频率响应。而且，点频法和扫频法都需要正弦波产生电路，而正弦波产生电路比起方波产生电路，具有电路更复杂、成本更高等缺点。
所以，点频法和扫频法存在着测量效率相对较低、测量成本相对较高的问题。它们不能应用在对测量效率或测量成本有高要求的场景。
发明内容
本发明目的在于提供一种基于谐波的频率响应测量系统及方法,以解决点频法和扫频法存在的测量效率相对较低、测量成本相对较高的技术问题。
为解决上述技术问题，本发明的一种基于谐波的频率响应测量系统及方法的具体技术方案如下：
一种基于谐波的频率响应测量系统，包括：
一个频率可控方波生成器，输入是计算控制单元输出的控制信号Ctrl0，输出是方波信号x(t)；
一个待测线性系统，输入是频率可控方波生成器输出的方波x(t)，输出m(t)接入信号调理电路；
一个信号调理电路，输入是待测线性系统的输出m(t)和计算控制单元输出的控制信号Ctrl2，输出y(t)接入模数转换器；
一个模数转换器，输入是信号调理电路的输出y(t)和计算控制单元输出的控制信号Ctrl1，输出码字y(n)接入计算处理单元；
一个计算处理单元，输入是模数转换器输出的码字y(n)，输出控制信号Ctrl0、Ctrl1和Ctrl2分别接入频率可控方波生成器、模数转换器和信号调理电路，并输出测量结果。
本发明还公开了一种基于谐波的频率响应测量方法，包括若干个测量轮次，每个测量轮次包括以下四个步骤：
第一步，根据目标测量频率，计算控制单元设定方波生成器生成的方波频率f 0和方波幅度等参数，设定信号调理电路的低通截止频率f C和模数转换器过采样率OSR，启动方波生成器，其中过采样率OSR是半整数；
第二步，计算处理单元调整信号调理电路的增益A V，保证模数转换器的输入处在接近满量程、未饱和的状态；
第三步，计算处理单元对模数转换器输出的结果y(n)进行K点DFT计算，得到在频率点f 0、3f 0、5f 0、……Mf 0处信号y(t)的频谱数据Y(f 0)、Y(3f 0)、Y(5f 0)、……Y(Mf 0)，其中M是奇数且满足M<OSR；
第四步，计算处理单元用Y(f 0)、Y(3f 0)、Y(5f 0)、……Y(Mf 0)分别除以信号调理电路的增益A V(f 0)、A V(3f 0)、A V(5f 0)、……A V(Mf 0)，再分别除以信号x(t)的K点DFT频谱数据X(f 0)、X(3f 0)、X(5f 0)、……X(Mf 0)，分别得到待测线性系统在频率点f 0、3f 0、5f 0、……Mf 0处的频率响应H(f 0)、H(3f 0)、H(5f 0)、……H(Mf 0)。
进一步地，所述频率可控方波生成器，生成的方波幅度、频率f 0和相位等参数精确定义，方波频率f 0可调，由计算控制单元输出的控制信号Ctrl0 决定。
进一步地，所述信号调理电路，对输入信号m(t)进行线性放大和低通滤波，它的增益A V可调、低通滤波的截止频率f C可调，由计算控制单元输出的控制信号Ctrl2决定。
进一步地，所述模数转换器，其采样频率f s由计算控制单元输出的控制信号Ctrl1决定，与方波频率f 0之间满足f s＝K×f 0，其中K是奇数。
进一步地，所述计算处理单元，可以进行数学运算，可以输出控制信号，可以读取外部数字码字输入，它输出控制信号Ctrl0接入频率可控方波生成器，控制方波频率等参数；输出控制信号Ctrl1接入模数转换器，控制模数转换器采样频率；输出控制信号Ctrl2接入信号调理电路，控制信号调理电路的增益A V和低通截止频率f C；并输出测量结果。
进一步地，所述M＜K/2。
本发明的一种基于谐波的频率响应测量系统及方法具有以下优点：通过一次测量可以得到待测线性系统多个频点上的频率响应；使用方波生成器而不是正弦波产生电路，简化了电路，降低了成本。
附图说明
图1是本发明的一种基于谐波的频率响应测量系统基本框架示意图。
图2是本发明一种基于谐波的频率响应测量方法主要步骤示意图。
图3是本发明具体实施例基本框架示意图。
具体实施方式
为了更好地了解本发明的目的、结构及功能，下面结合附图，对本发明一种基于谐波的频率响应测量系统及方法做进一步详细的描述。
如图1所示，一种基于谐波的频率响应测量系统包括：
一个频率可控方波生成器，输入是计算控制单元输出的控制信号Ctrl0， 输出是方波信号x(t)；
一个待测线性系统，输入是频率可控方波生成器输出的方波x(t)，输出m(t)接入信号调理电路；
一个信号调理电路，输入是待测线性系统的输出m(t)和计算控制单元输出的控制信号Ctrl2，输出y(t)接入模数转换器；
一个模数转换器，输入是信号调理电路的输出y(t)和计算控制单元输出的控制信号Ctrl1，输出码字y(n)接入计算处理单元；
一个计算处理单元，输入是模数转换器输出的码字y(n)，输出控制信号Ctrl0、Ctrl1和Ctrl2分别接入频率可控方波生成器、模数转换器和信号调理电路，并输出测量结果。
如图2所示，本发明的一种基于谐波的频率响应测量方法可以包括若干个测量轮次，每个测量轮次主要包括以下四个步骤：
第一步，根据目标测量频率，计算控制单元设定方波生成器生成的方波频率f 0和方波幅度等参数，设定信号调理电路的低通截止频率f C和模数转换器过采样率OSR，启动方波生成器，其中过采样率OSR是半整数；
第二步，计算处理单元调整信号调理电路的增益A V，保证模数转换器的输入处在接近满量程、未饱和的状态；
第三步，计算处理单元对模数转换器输出的结果y(n)进行K点DFT计算，得到在频率点f 0、3f 0、5f 0、……Mf 0处信号y(t)的频谱数据Y(f 0)、Y(3f 0)、Y(5f 0)、……Y(Mf 0)，其中M是奇数且满足M<OSR；
第四步，计算处理单元用Y(f 0)、Y(3f 0)、Y(5f 0)、……Y(Mf 0)分别除以信号调理电路的增益A V(f 0)、A V(3f 0)、A V(5f 0)、……A V(Mf 0)，再分别除以信号x(t)的K点DFT频谱数据X(f 0)、X(3f 0)、X(5f 0)、……X(Mf 0)，分别得到待测线性系统在频率点f 0、3f 0、5f 0、……Mf 0处的频率响应H(f 0)、 H(3f 0)、H(5f 0)、……H(Mf 0)。
优选地，所述频率可控方波生成器，生成的方波幅度、频率f 0和相位等参数精确定义，方波频率f 0可调，由计算控制单元输出的控制信号Ctrl0决定。
优选地，所述信号调理电路，对输入信号m(t)进行线性放大和低通滤波。它的增益A V可调、低通滤波的截止频率f C可调，由计算控制单元输出的控制信号Ctrl2决定。
优选地，所述模数转换器，其采样频率f s由计算控制单元输出的控制信号Ctrl1决定，与方波频率f 0之间满足f s＝K×f 0，其中K是奇数。
优选地，所述计算处理单元，可以进行数学运算，可以输出控制信号，可以读取外部数字码字输入。它输出控制信号Ctrl0接入频率可控方波生成器，控制方波频率等参数；输出控制信号Ctrl1接入模数转换器，控制模数转换器采样频率；输出控制信号Ctrl2接入信号调理电路，控制信号调理电路的增益A V和低通截止频率f C；并输出测量结果。
优选地，上述测量方法中的参数M是奇数，且满足M＜K/2。
上述测量系统和方法具有如下优点：通过一次测量可以得到待测线性系统多个频点上的频率响应；使用方波生成器而不是正弦波产生电路，简化了电路，降低了成本。
如果需要测量某线性系统许多频点上的频率响应，可以重复上述步骤，每次设定不同的方波频率f 0和低通截止频率f C等参数。
上述测量系统和方法能一次测出待测线性系统多个频点上频率响应的原理是，基于线性电路的叠加定理和占空比为50％的方波的频谱特点，利用方波的基波和低次谐波来测量系统频率响应，通过对模数转换器过采样率的设置来消除可能的高次谐波频谱混叠。
记待测线性系统频率响应为H(f)，记信号x(t)、y(t)在频率点jf 0处的傅里叶系数分别为X(jf 0)、Y(jf 0)，记信号调理电路在频率点jf 0处的增益为A V(jf 0)，其中j＝1,2,……M。X(jf 0)、Y(jf 0)、A V(jf 0)是复数，包含幅度和相位。有
Y(jf 0)＝A V(jf 0)X(jf 0)H(jf 0)
其中，j＝1，2，......M(公式1)
记y(n)作K点DFT计算之后的结果是Y F(jf 0)，j＝1，2，......M。
于是有
Figure PCTCN2022083899-appb-000001
由于我们限定测量信号x(t)的占空比为50％，信号x(t)的频谱具有偶次谐波能量为0的特点，即
X(mf 0)＝0，m＝2，4，...∞(公式5)
联立公式1和公式5，我们可以得到信号y(t)的偶数次谐波能量也为0，即
Y(mf 0)＝0，m＝2，4，...∞(公式6)
由于设定K和M都是奇数，所以y(t)中的K-1、K+1、3K-1、3K+1等偶次谐波能量为0。于是有
Figure PCTCN2022083899-appb-000002
Figure PCTCN2022083899-appb-000003
类似地，有
Figure PCTCN2022083899-appb-000004
根据公式1可得
Figure PCTCN2022083899-appb-000005
由于设定测量信号x(t)的占空比为50％，根据信号与系统知识，我们可以得到
Figure PCTCN2022083899-appb-000006
由于低通滤波，|A V((2·i·K-1)f 0)|＜＜|A V(f 0)|，且公式11中的比值是一个很小的数，于是公式10中的比值接近于0。于是公式7中y(t)的2K-1、2K+1以及更高次的奇数次谐波可以忽略。类似的，公式8和公式9中的奇数次谐波也可以忽略。
所以，频谱混叠带来的影响可以忽略不记。
于是有
Figure PCTCN2022083899-appb-000007
Figure PCTCN2022083899-appb-000008
于是利用以下公式15即可求得待测线性系统的频率响应。
Figure PCTCN2022083899-appb-000009
其中，j＝1，2，......M(公式15)
本实施例中，我们测试一个线性系统在1kHz-10kHz内的频率响应。实施例的系统结构框图如图3所示。频率可控方波生成器采用555定时器结合电阻阵列来实现；信号调理电路采用程控放大器和程控滤波器，计算控制单元采用stm32单片机。
使用本发明提出的测量系统和方法，具体测量过程如下。
第一轮：
第一步，stm32单片机设定方波生成器生成的方波频率为1kHz，设定程控滤波器低通截止频率为33kHz，设定模数转换器过采样率为49.5，启动方波生成器；
第二步，stm32单片机调整程控放大器的增益，保证模数转换器处在接近满量程、未饱和的状态，记录此时程控放大器和程控滤波器的级联增益A V；
第三步，stm32单片机对数字信号y(n)做99点DFT，得到y(t)在1kHz、3kHz、5kHz、7kHz、9kHz这5个频率点上的频谱数据Y 1、Y 3、Y 5、Y 7、Y 9；
第四步，stm32单片机用Y 1、Y 3、Y 5、Y 7、Y 9分别除以程控放大器和程控滤波器在1kHz、3kHz、5kHz、7kHz、9kHz这5个频率点上的级联增益A V1、A V3、A V5、A V7、A V9，再分别除以对x(t)作99点DFT得到的在1kHz、3kHz、5kHz、7kHz、9kHz这5个频率点上x(t)的频谱数据X 1、X 3、X 5、X 7、X 9，分别得到待测线性系统在频率点1kHz、3kHz、5kHz、7kHz、9kHz这5个频率点处的频率响应H 1、H 3、H 5、H 7、H 9。
第二轮：
第一步，stm32单片机设定方波生成器生成的方波频率为2kHz，设定程控滤波器低通截止频率为66kHz，设定模数转换器过采样率为49.5，启动方波生成器；
第二步，stm32单片机调整程控放大器的增益，保证模数转换器处在接近满量程、未饱和的状态，记录此时程控放大器和程控滤波器的级联增益A V；
第三步，stm32单片机对数字信号y(n)做99点DFT，得到y(t)在2kHz、6kHz、10kHz这3个频率点上的频谱数据Y 2、Y 6、Y 10；
第四步，stm32单片机用Y 2、Y 6、Y 10分别除以程控放大器和程控滤波器在2kHz、6kHz、10kHz这3个频率点上的级联增益A V2、A V6、A V10，再分别除以对x(t)作99点DFT得到的在2kHz、6kHz、10kHz这3个频率点上x(t)的频谱数据X 2、X 6、X 10,分别得到待测线性系统在频率点2kHz、6kHz、10kHz这3个频率点处的频率响应H 2、H 6、H 10。
上述两轮测量，得到了待测线性系统在1kHz、2kHz、3kHz、5kHz、6kHz、7kHz、9kHz、10kHz这8个频率点上的频率响应。
使用本发明所示测量系统和方法，只需2次测量即可获得8个频率点上的频率响应。按照传统测量方法，需要测8次。本例中，本发明提出的测量系统和方法效率是传统点频法、扫频法的4倍。同时，本实施例中用555定时器结合电阻阵列取代正弦波生成电路，具有成本更低的优点。
由以上实施例可以看出，本发明提出的测量系统和方法，具有测量效率高、测量成本低的优势。
可以理解，本发明是通过一些实施例进行描述的，本领域技术人员知悉的，在不脱离本发明的精神和范围的情况下，可以对这些特征和实施例进行各种改变或等效替换。另外，在本发明的教导下，可以对这些特征和实施例 进行修改以适应具体的情况及材料而不会脱离本发明的精神和范围。因此，本发明不受此处所公开的具体实施例的限制，所有落入本申请的权利要求范围内的实施例都属于本发明所保护的范围内。

Claims (7)

  1. 一种基于谐波的频率响应测量系统，其特征在于，包括：
    一个频率可控方波生成器，输入是计算控制单元输出的控制信号Ctrl0，输出是方波信号x(t)；
    一个待测线性系统，输入是频率可控方波生成器输出的方波x(t)，输出m(t)接入信号调理电路；
    一个信号调理电路，输入是待测线性系统的输出m(t)和计算控制单元输出的控制信号Ctrl2，输出y(t)接入模数转换器；
    一个模数转换器，输入是信号调理电路的输出y(t)和计算控制单元输出的控制信号Ctrl1，输出码字y(n)接入计算处理单元；
    一个计算处理单元，输入是模数转换器输出的码字y(n)，输出控制信号Ctrl0、Ctrl1和Ctrl2分别接入频率可控方波生成器、模数转换器和信号调理电路，并输出测量结果。
  2. 一种利用如权利要求1所述的基于谐波的频率响应测量系统进行频率响应测量的方法，其特征在于，包括若干个测量轮次，每个测量轮次包括以下四个步骤：
    第一步，根据目标测量频率，计算控制单元设定方波生成器生成的方波频率f 0和方波幅度等参数，设定信号调理电路的低通截止频率f C和模数转换器过采样率OSR，启动方波生成器，其中过采样率OSR是半整数；
    第二步，计算处理单元调整信号调理电路的增益A V，保证模数转换器的输入处在接近满量程、未饱和的状态；
    第三步，计算处理单元对模数转换器输出的结果y(n)进行K点DFT 计算，得到在频率点f 0、3f 0、5f 0、……Mf 0处信号y(t)的频谱数据Y(f 0)、Y(3f 0)、Y(5f 0)、……Y(Mf 0)，其中M是奇数且满足M<OSR；
    第四步，计算处理单元用Y(f 0)、Y(3f 0)、Y(5f 0)、……Y(Mf 0)分别除以信号调理电路的增益A V(f 0)、A V(3f 0)、A V(5f 0)、……A V(Mf 0)，再分别除以信号x(t)的K点DFT频谱数据X(f 0)、X(3f 0)、X(5f 0)、……X(Mf 0)，分别得到待测线性系统在频率点f 0、3f 0、5f 0、……Mf 0处的频率响应H(f 0)、H(3f 0)、H(5f 0)、……H(Mf 0)。
  3. 根据权利要求2所述的基于谐波的频率响应测量方法，其特征在于，所述频率可控方波生成器，生成的方波幅度、频率f 0和相位等参数精确定义，方波频率f 0可调，由计算控制单元输出的控制信号Ctrl0决定。
  4. 根据权利要求2所述的基于谐波的频率响应测量方法，其特征在于，所述信号调理电路，对输入信号m(t)进行线性放大和低通滤波，它的增益A V可调、低通滤波的截止频率f C可调，由计算控制单元输出的控制信号Ctrl2决定。
  5. 根据权利要求2所述的基于谐波的频率响应测量方法，其特征在 于，所述模数转换器，其采样频率f s由计算控制单元输出的控制信号Ctrl1决定，与方波频率f 0之间满足f s＝K×f 0，其中K是奇数。
  6. 根据权利要求2所述的基于谐波的频率响应测量方法，其特征在于，所述计算处理单元，可以进行数学运算，可以输出控制信号，可以读取外部数字码字输入，它输出控制信号Ctrl0接入频率可控方波生成器，控制方波频率等参数；输出控制信号Ctrl1接入模数转换器，控制模数转换器采样频率；输出控制信号Ctrl2接入信号调理电路，控制信号调理电路的增益A V和低通截止频率f C；并输出测量结果。
  7. 根据权利要求2所述的基于谐波的频率响应测量方法，其特征在于，所述M＜K/2。
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