CN115060355B - A method for measuring the quality factor of resonators based on chirped frequency modulation pulses - Google Patents
A method for measuring the quality factor of resonators based on chirped frequency modulation pulses Download PDFInfo
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Abstract
Description
技术领域Technical field
本发明涉及谐振器件参数测量领域,具体涉及一种基于线性调频脉冲的谐振子品质因数测量方法。The invention relates to the field of resonant device parameter measurement, and specifically relates to a resonator quality factor measurement method based on linear frequency modulation pulses.
背景技术Background technique
品质因数是谐振式器件振动特性的重要参数,对驱动控制和误差机理分析具有重要作用。品质因数的测量方法主要分为时域法和频域法两种。时域法基于自由振荡时的幅值衰减特性,利用振荡幅值在特定时间内的衰减程度及其与Q值之间的对应关系来计算,需要检测瞬态响应的峰值或者幅值包络,相对比较复杂。频域法较为常用,它一般基于幅频特性曲线利用谐振频率和通频带宽来计算,称为半功率带宽法。但当信噪比较低时,半功率带宽法可靠性较低,误差较大。Quality factor is an important parameter for the vibration characteristics of resonant devices and plays an important role in drive control and error mechanism analysis. The measurement methods of quality factor are mainly divided into two types: time domain method and frequency domain method. The time domain method is based on the amplitude attenuation characteristics of free oscillation. It uses the attenuation degree of the oscillation amplitude within a specific time and its correspondence with the Q value to calculate. It needs to detect the peak value or amplitude envelope of the transient response. Relatively complicated. The frequency domain method is more commonly used. It is generally calculated based on the amplitude-frequency characteristic curve using the resonant frequency and passband bandwidth, which is called the half-power bandwidth method. However, when the signal-to-noise ratio is low, the half-power bandwidth method has lower reliability and larger errors.
发明内容Contents of the invention
为解决上述问题,本发明公开了一种基于线性调频脉冲的谐振子品质因数测量方法,以解决低信噪比情况下品质因数测量误差较大的问题。In order to solve the above problems, the present invention discloses a resonator quality factor measurement method based on linear frequency modulation pulses to solve the problem of large quality factor measurement errors under low signal-to-noise ratio conditions.
为了实现上述目的,本发明采用的方案如下:In order to achieve the above object, the scheme adopted by the present invention is as follows:
一种基于线性调频脉冲的谐振子品质因数测量方法,包括以下步骤:A method for measuring the quality factor of a resonator based on chirped frequency modulation pulses, including the following steps:
步骤1:使用chirp信号对谐振子进行扫频激励,得到响应信号s(t);Step 1: Use the chirp signal to sweep the frequency of the resonator and obtain the response signal s(t);
步骤2:对响应信号s(t)进行采样、FFT变换、取模、归一化后得到频谱|S′(n)|;截选扫频范围频谱|S1′(n)|计算得到振频率的估计值 Step 2: Sampling, FFT transform, modulo, and normalize the response signal s(t) to obtain the spectrum |S′(n)|; intercept the frequency sweep range spectrum |S 1 ′(n)| to calculate the vibration Frequency estimate
步骤3:建立洛伦兹曲线模型,针对不同的频率范围,先后进行两次洛伦兹拟合,结合上一步骤求得的谐振频率值获得品质因数。Step 3: Establish a Lorentz curve model, perform Lorentz fitting twice for different frequency ranges, and obtain the quality factor by combining the resonant frequency value obtained in the previous step.
所述步骤3包括:The step 3 includes:
步骤3.1:建立洛伦兹曲线模型 是估计的谐振频率,Q是品质因数,设Q最大值为M。若Q=m,绘制L(f)|Q=m的曲线,并进行归一化处理得到L′(f)|Q=m;Step 3.1: Build Lorenz Curve Model is the estimated resonant frequency, Q is the quality factor, and let the maximum value of Q be M. If Q=m, draw the curve of L(f)| Q=m , and perform normalization to obtain L'(f)| Q=m ;
步骤3.2:第一次洛伦兹拟合频率范围Q值范围为1≤Q≤M。将实际频率范围内每一个数据点与拟合曲线所对应的频率点的幅值逐点作差并累加,获得残差error(m);Step 3.2: First Lorentz fitting frequency range The Q value range is 1≤Q≤M. Difference and accumulate the amplitudes of each data point in the actual frequency range and the frequency point corresponding to the fitting curve point by point to obtain the residual error (m);
步骤3.3:索引残差序列error(i)中数值最小的点,序号记为index0,得到第一次估计的品质因数值 Step 3.3: Index the point with the smallest value in the residual sequence error(i), the sequence number is marked as index0, and obtain the first estimated quality factor value.
步骤3.4:第二次洛伦兹拟合f范围在整个扫频域区间f1≤f≤f2,选取Q值范围为重复步骤3.3获得残差序列error(i);Step 3.4: The second Lorentz fitting f range is in the entire frequency sweep domain interval f 1 ≤ f ≤ f 2 , and the Q value range is selected as Repeat step 3.3 to obtain the residual sequence error(i);
步骤3.5:索引残差序列error(i)中数值最小的点,序号记为index1,得到品质因数的最终估计值 Step 3.5: Index the point with the smallest value in the residual sequence error(i). The sequence number is marked as index1 to obtain the final estimate of the quality factor.
本发明的有益效果:不但改进了半功率带宽法在低信噪比环境下会存在的较大误差,还通过两步拟合过程,节约了运算时间,尤其是对于一些高Q值的谐振子优势较为明显。The beneficial effects of the present invention are: it not only improves the large error caused by the half-power bandwidth method in a low signal-to-noise ratio environment, but also saves computing time through a two-step fitting process, especially for some high-Q value resonators. The advantages are obvious.
附图说明Description of drawings
图1是本发明提供的一种基于线性调频脉冲的谐振子品质因数测量方法的流程图;Figure 1 is a flow chart of a resonator quality factor measurement method based on linear frequency modulation pulses provided by the present invention;
图2是半功率带宽法与本发明方法仿真结果相对误差比较。Figure 2 is a comparison of the relative errors of simulation results between the half-power bandwidth method and the method of the present invention.
具体实施方式Detailed ways
下面结合附图和具体实施方式,进一步阐明本发明,应理解下述具体实施方式仅用于说明本发明而不用于限制本发明的范围。需要说明的是,下面描述中使用的词语“前”、“后”、“左”、“右”、“上”和“下”指的是附图中的方向,词语“内”和“外”分别指的是朝向或远离特定部件几何中心的方向。The present invention will be further clarified below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. It should be noted that the words "front", "back", "left", "right", "upper" and "lower" used in the following description refer to the directions in the drawings, and the words "inside" and "outside" ” refers to the direction toward or away from the geometric center of a specific part, respectively.
如图1-2所示,本实施例的一种基于线性调频脉冲的谐振子品质因数测量方法,设置线性调频信号的参数:起始频率f1、终止频率f2、扫频时间T、信号幅度A,生成chirp信号x(t):As shown in Figure 1-2, a resonator quality factor measurement method based on linear frequency modulation pulses in this embodiment sets the parameters of the linear frequency modulation signal: starting frequency f 1 , end frequency f 2 , frequency sweep time T, signal Amplitude A, generate chirp signal x(t):
其中 in
用chirp信号对谐振子进行扫频激励,得到响应信号s(t);Use the chirp signal to sweep the frequency of the resonator and obtain the response signal s(t);
用采样率fs对响应信号s(t)进行采样,然后进行FFT变换并取模得到频谱|S(n)|,长度为N,频谱的分辨率Δf=1/T,对频谱进行归一化后得到|S′(n)|。Use the sampling rate f s to sample the response signal s(t), then perform FFT transformation and take the modulus to obtain the spectrum |S(n)|, the length is N, the resolution of the spectrum Δf=1/T, and normalize the spectrum After transformation, we get |S′(n)|.
|S(n)|=|X(n)|·|G(n)| (2)|S(n)|=|X(n)|·|G(n)| (2)
其中|X(n)|是chirp在频域的频谱;|G(n)|是谐振子幅频特性的模;n=1、2、…、N;Among them, |
截选|S′(n)|内扫频范围为f1≤f≤f2内的频谱|S1′(n)|,f1对应的谱线序号为N1、f2对应的谱线序号为N2,即|S1′(n)|=|S′(n)|,N1≤n≤N2:Intercept the spectrum |S 1 ′(n)| within the sweep range of f 1 ≤ f ≤ f 2 in |S ′ (n)|, and the spectral line numbers corresponding to f 1 are N 1 and the spectral lines corresponding to f 2 The sequence number is N 2 , that is, |S 1 ′(n)|=|S′(n)|, N 1 ≤n≤N 2 :
对|S1′(n)|进行谱峰索引,谱峰对应的谱线序号为k0,谱峰幅度为|S1′(k0)|,得到谐振频率的估计值 Index the spectral peaks of |S 1 ′(n)|. The spectral line number corresponding to the spectral peak is k 0 , and the spectral peak amplitude is |S 1 ′(k 0 )| to obtain the estimated value of the resonant frequency.
建立洛伦兹曲线模型L(f):Establish Lorenz curve model L(f):
是估计的谐振频率,设Q最大值为M。 is the estimated resonant frequency, and let the maximum value of Q be M.
若Q=m,绘制L(f)|Q=m的曲线,并进行归一化处理得到L′(f)|Q=m;If Q=m, draw the curve of L(f)| Q=m , and perform normalization to obtain L'(f)| Q=m ;
第一次洛伦兹拟合频率f范围在Q值范围为1≤Q≤M。The range of the first Lorentz fitting frequency f is The Q value range is 1≤Q≤M.
该频率范围对应的频谱序列为将实际频率范围内每一个数据点与拟合曲线所对应的频率点的幅值逐点作差并累加,获得残差error(m):The spectrum sequence corresponding to this frequency range is the difference and accumulation of the amplitudes of each data point in the actual frequency range and the frequency point corresponding to the fitting curve point by point to obtain the residual error (m):
索引残差序列error(i)中数值最小的点,序号记为index0,得到第一次估计的品质因数值 Index the point with the smallest value in the residual sequence error(i), the sequence number is recorded as index0, and the first estimated quality factor value is obtained.
第二次洛伦兹拟合f范围在整个扫频域区间f1≤f≤f2,选取Q值范围为重复步骤3.3获得残差序列error(i):The second Lorentz fitting f range is in the entire frequency sweep domain interval f 1 ≤ f ≤ f 2 , and the Q value range is selected as Repeat step 3.3 to obtain the residual sequence error(i):
索引残差序列error(i)中数值最小的点,序号记为index1,得到品质因数的最终估计值 Index the point with the smallest value in the residual sequence error(i), the sequence number is recorded as index1, and the final estimated value of the quality factor is obtained.
由于半功率带宽法只利用了响应信号频谱的三个点进行计算,而洛伦兹拟合则运用了有效频率范围内的所有点,所以对于低信噪比的信号来说可以减小误差;相比只进行一次洛伦兹拟合,两步拟合更能节约运算时间,尤其是对于一些高Q值的谐振子。Since the half-power bandwidth method only uses three points of the response signal spectrum for calculation, while the Lorentz fitting uses all points within the effective frequency range, the error can be reduced for signals with low signal-to-noise ratio; Compared with only one Lorentz fitting, the two-step fitting can save computing time, especially for some resonators with high Q values.
本发明方案所公开的技术手段不仅限于上述实施方式所公开的技术手段,还包括由以上技术特征任意组合所组成的技术方案。The technical means disclosed in the solution of the present invention are not limited to the technical means disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features.
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