CN115060355B - A method for measuring the quality factor of resonators based on chirped frequency modulation pulses - Google Patents

Abstract

The invention provides a method for measuring quality factor of harmonic oscillator based on linear frequency modulation pulse signal, which comprises the steps of firstly using the linear frequency modulation pulse signal to carry out sweep frequency excitation on the harmonic oscillator to obtain a response signalThe method comprises the steps of carrying out a first treatment on the surface of the Responsive to a response signalSampling, FFT, modulo, normalizing to obtain frequency spectrumThe method comprises the steps of carrying out a first treatment on the surface of the Frequency spectrum of frequency sweeping range is cut offCalculating to obtain the estimated value of the vibration frequencyThe method comprises the steps of carrying out a first treatment on the surface of the Establishing a Lorentz curve model, and fitting the frequency range of the first LorentzQ value range 1 Q M，Performing first estimation on the quality factor; combining the first estimateIn the whole domain of sweep frequencyQ value rangeAnd (5) performing second Lorentz fitting to obtain a final quality factor estimated value. The method not only improves larger errors of the half-power bandwidth method in a low signal-to-noise ratio environment, but also saves operation time through a two-step fitting process, and particularly has obvious advantages for some high-Q-value resonators.

Description

A method for measuring the quality factor of resonators based on chirped frequency modulation pulses

Technical field

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.

Background technique

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.

Contents of the invention

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.

In order to achieve the above object, the scheme adopted by the present invention is as follows:

A method for measuring the quality factor of a resonator based on chirped frequency modulation pulses, including the following steps:

Step 1: Use the chirp signal to sweep the frequency of the resonator and obtain the response signal s(t);

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

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.

The step 3 includes:

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 ;

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);

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.

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);

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.

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.

Description of drawings

Figure 1 is a flow chart of a resonator quality factor measurement method based on linear frequency modulation pulses provided by the present invention;

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.

Detailed ways

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.

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):

in

Use the chirp signal to sweep the frequency of the resonator and obtain the response signal s(t);

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)

Among them, |

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 :

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.

Establish Lorenz curve model L(f):

is the estimated resonant frequency, 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 ;

The range of the first Lorentz fitting frequency f is The Q value range is 1≤Q≤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):

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.

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):

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.

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.

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.

Claims (1)

1. A method for measuring a quality factor of a harmonic oscillator based on a chirp pulse, the method comprising the steps of:

step 1: using chirp signals to carry out sweep frequency excitation on the harmonic oscillator to obtain response signals s (t);

step 2: sampling, FFT (fast Fourier transform), modulo, and normalizing the response signal S (t) to obtain a frequency spectrum |S' (n) |; cut off frequency spectrum |S of sweep frequency range ₁ 'n' is calculated to obtain the estimated value of the vibration frequency

Step 3: establishing a Lorentz curve model, and obtaining a frequency range of a first Lorentz fitting by using a half-power bandwidth methodPerforming first estimation on the quality factor; combining the first estimateIn the sweep frequency domain f ₁ ≤f≤f ₂ ，/>Performing second Lorentz fitting to obtain a final quality factor estimated value; setting parameters of the chirp signal in the step 1: initial frequency f ₁ Termination frequency f ₂ Generating a chirp signal x (T):

wherein the method comprises the steps ofSweeping excitation is carried out on the harmonic oscillator by using a chirp signal, so as to obtain a response signal s (t); the step 2: by sampling rate f _s Sampling a response signal S (T), performing FFT (fast Fourier transform) and taking a modulus to obtain a frequency spectrum |S (N) |, wherein the length is N, the resolution Deltaf=1/T of the frequency spectrum, and normalizing the frequency spectrum to obtain |S' (N) |;

|S(n)|＝|X(n)|·|G(n)| (2)

where |x (n) | is the spectrum of chirp in the frequency domain; the I G (n) I is a mode of amplitude-frequency characteristics of the harmonic oscillator; n=1, 2, …, N;

cut off the sweep frequency range in |S' (n) | to be f ₁ ≤f≤f ₂ Spectrum |S in ₁ ′(n)|，f ₁ Corresponding spectral line number N ₁ 、f ₂ Corresponding spectral line number N ₂ I.e. |S ₁ ′(n)|＝|S′(n)|，N ₁ ≤n≤N ₂ ：

For |S ₁ ' (n) | carrying out spectrum peak index, wherein the spectral line serial number corresponding to the spectrum peak is k ₀ Spectral peak amplitude is |S ₁ ′(k ₀ ) I, obtain an estimate of the resonant frequencyThe step 3 comprises the following steps:

step 3.1:

establishing Lorentz curve model Is the estimated resonant frequency, Q is the quality factor, and the maximum value of Q is set to M; if q=m, draw L (f) | _Q＝m And normalized to obtain L' (f) | _Q＝m ；

Step 3.2: the first Lorentz fitting frequency f ranges fromQ is more than or equal to 1 and less than or equal to M; the amplitude of each data point in the actual frequency range and the frequency point corresponding to the fitting curve are subjected to point-by-point difference and accumulated to obtain a residual sequence error (m);

step 3.3: indexing the point with the minimum value in the residual error sequence error (m), and marking the sequence number as index0 to obtain the quality factor value estimated for the first time

Step 3.4: the second Lorentz fitting f range is in the whole sweep frequency domain interval, and the Q value range is selected asRepeating the step 3.3 to obtain a residual sequence error (i); error (i):

step 3.5: indexing the point with the minimum value in the residual error sequence error (i), and marking the sequence number as index1 to obtain the final estimated value of the quality factor