A method for extracting COM parameters of a surface acoustic wave resonator based on polynomial fitting

Abstract

The application relates to the field of semiconductor devices, in particular to a surface acoustic wave resonator COM parameter extraction method based on polynomial fitting, which comprises the following steps: extracting multiple groups of COM parameters by adopting a measured fitting method; centering and scaling each group of COM parameters and corresponding resonant frequencies to obtain centered and scaled COM parameters and centered and scaled resonant frequencies; defining a 9-order polynomial model group and obtaining an optimal 9-order polynomial model group by adopting a weighted residual error optimization method; inputting the target resonant frequency after centering and scaling into the optimal 9-order polynomial model group to obtain target centered and scaled COM parameters; and inputting the target centered and scaled COM parameters into a COM model after restoration to obtain an electroacoustic characteristic curve of the target resonator; and the application can realize rapid and accurate simulation of the surface acoustic wave resonator.

Description

Technical Field

[0001] This invention relates to the field of semiconductor devices, and in particular to a method for extracting COM parameters of a surface acoustic wave resonator based on polynomial fitting. Background Technology

[0002] Surface acoustic wave (SAW) resonators offer numerous advantages, including miniaturization, low cost, high efficiency, and ease of integration. Their applications are widespread, particularly in wireless communication, sensor technology, and signal processing. In wireless communication, SAW resonators are used to design SAW filters, helping to select signals at specific frequencies and improving the accuracy and efficiency of signal processing. They are also used in radio and radar systems to aid in frequency tuning and signal quality enhancement.

[0003] The key to surface acoustic wave (SAW) device design lies in how to perform rapid and accurate device simulation. Currently, methods for simulating SAW resonators mainly focus on the finite element method (FEM) and the coupled-mode model (COM) method. The FEM method has a long computation time; the COM model method is fast, but its simulation accuracy depends on the accuracy of the extracted COM parameters. Currently, methods for extracting COM parameters based on the COM model primarily rely on experimental methods, which are costly and time-consuming. Summary of the Invention

[0004] To address the problems of high cost and long cycle time in existing experimental methods for extracting COM parameters, this invention provides a method for extracting COM parameters of surface acoustic wave resonators based on polynomial fitting, characterized by the following steps:

[0005] S1. Extract multiple sets of COM parameters using an experimental fitting method. The COM parameters include sound velocity, transducer coefficient, reflection coefficient, and static capacitance. S2. Center and scale each set of COM parameters and its corresponding resonant frequency to obtain the corresponding center-scaled COM parameters and center-scaled resonant frequency. The center-scaled COM parameters include center-scaled sound velocity, center-scaled transducer coefficient, center-scaled reflection coefficient, and center-scaled static capacitance. S3. Define a 9th-order polynomial model set between the center-scaled resonant frequency and the center-scaled COM parameters.

[0006] S4. Combining the centered scaling resonant frequency and the centered scaling COM parameter, the weighted residual optimization method is used to process the 9th order polynomial model set to obtain the corresponding optimal 9th ​​order polynomial model set;

[0007] S5. After centering and scaling the target resonant frequency corresponding to the target resonator, input it into the optimal 9th ​​order polynomial model set to obtain the target centered and scaled COM parameters.

[0008] S6. Restore the target COM parameters by centering and scaling the target COM parameters, and substitute the target COM parameters into the COM model to obtain the electroacoustic characteristic curve of the target resonator.

[0009] Furthermore, step S1, which involves extracting a set of COM parameters using a measured fitting method, includes:

[0010] S11. Use the COM model to obtain the simulated impedance curve of an actual fabricated SAW resonator;

[0011] S12. Experimental testing steps: S11 uses the actual fabricated SAW resonator to obtain the actual impedance curve;

[0012] S13. Fit the simulated impedance curve to the actual impedance curve, and extract the COM parameters of the actual fabricated SAW resonator based on the fitting results.

[0013] Furthermore, step S2 centers and scales each set of COM parameters and its corresponding resonant frequency, as follows:

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] Among them, f i Let f(i) represent the resonant frequency of the i-th actual SAW resonator, mean(f) represent the mean resonant frequency of the actual SAW resonator, and std(f) represent the standard deviation of the resonant frequency of the actual SAW resonator. This represents the centered scaled resonant frequency corresponding to the resonant frequency of the i-th actual fabricated SAW resonator; v i Let v represent the speed of sound at the i-th position, mean(v) represent the mean speed of sound, and std(v) represent the standard deviation of the speed of sound. a represents the centered scaled sound velocity corresponding to the i-th sound velocity; i Let represent the i-th transducer, mean(a) represent the mean of the transducers, and std(a) represent the standard deviation of the transducers. k represents the centered scaled transducer corresponding to the i-th transducer; i Let represent the i-th reflection coefficient, mean(k) represent the mean of the reflection coefficients, and std(k) represent the standard deviation of the reflection coefficients. c represents the centered scaled reflection coefficient corresponding to the i-th reflection coefficient; i Let represent the i-th static capacitance, mean(c) represent the mean of the static capacitance, and std(c) represent the standard deviation of the static capacitance. This represents the centralized scaled static capacitor corresponding to the i-th static capacitor.

[0020] Furthermore, the 9th-order polynomial model set mentioned in step S3 includes 9th-order polynomial models relating the centrally scaled resonant frequency to the centrally scaled sound velocity, the centrally scaled transducer, the centrally scaled reflection coefficient, and the centrally scaled static capacitance, respectively; wherein, the 9th-order polynomial model relating the centrally scaled resonant frequency to the centrally scaled sound velocity is expressed as:

[0021] v_scaled(f_scaled,p)=p1×f_scaled 9 +p2×f_scaled 8 +p3×f_scaled 7

[0022] +p4×f_scaled 6 +p5×f_scaled 5 +p6×f_scaled 4

[0023] +p7×f_scaled 3 +p8×f_scaled 2 +p9×f_scaled+p

[0024] Where p = [p, p1, ..., p9] are the parameters of the polynomial, f_scaled represents the center-scaled resonant frequency, and v_scaled(f_scaled, p) represents the polynomial-defined speed of sound.

[0025] Furthermore, for the 9th-order polynomial model between the centrally scaled resonant frequency and the centrally scaled sound velocity, a weighted residual optimization method is used to obtain the corresponding optimal 9th-order polynomial model, including:

[0026] S41. Obtain the polynomial-defined sound velocity through a 9th-order polynomial model, and calculate the sound velocity residual between the polynomial-defined sound velocity and the centered scaled sound velocity.

[0027] S42. Calculate the weight values ​​of the sound velocity residual using a robust Bisquare weighting function;

[0028] S43. Construct a sound velocity optimization objective function based on the weight values ​​of the sound velocity residual;

[0029] S44. Iteratively optimize the 9th-order polynomial model using the nonlinear least squares method and the Levenberg-Marquardt algorithm until the sound speed optimization objective function satisfies the convergence condition, and output the optimal 9th-order polynomial model.

[0030] Furthermore, step S42 uses a robust Bisquare weighting function to calculate the weight values ​​of the sound velocity residual, expressed as:

[0031]

[0032] Where b represents the scale parameter, r i w(r) represents the difference in sound speed between the i-th polynomial-defined sound speed and the i-th centered scaled sound speed. i ) represents the weight corresponding to the i-th sound speed residual.

[0033] Furthermore, in step S43, the weighted values ​​of the sound velocity residual are combined with the sound velocity residual to construct the sound velocity optimization objective function F(p), which is expressed as:

[0034]

[0035] Where n represents the number of observations, y i Let x represent the actual value of the i-th observation. i f(x) represents the value of the independent variable corresponding to the actual value of the i-th observation, p represents the parameter vector of the polynomial, and f(x) i (p) represents a 9th-order polynomial model defined using the parameter vector p with respect to x. i The predicted value.

[0036] The beneficial effects of this invention are:

[0037] This invention obtains the polynomial relationship between the resonant frequency of a surface acoustic wave (SAW) resonator and its four corresponding COM parameters: sound velocity, transduction coefficient, reflection coefficient, and static capacitance, through polynomial fitting. This invention can, to some extent, solve the problems of long periods and high costs associated with extracting COM parameters from SAW resonators using on-chip experimental methods. The COM parameters obtained by this invention, when input into the COM equation, enable rapid and accurate simulation of the SAW resonator. Attached Figure Description

[0038] Figure 1 This is a flowchart of the method of the present invention;

[0039] Figure 2 This is a schematic diagram of polynomial fitting curve fitting in an embodiment of the present invention;

[0040] Figure 3 This is a comparison chart of the measured impedance and the predicted impedance in an embodiment of the present invention. Detailed Implementation

[0041] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] Traditionally, obtaining the COM parameters of a resonator using experimental methods involves fabricating a physical resonator and then combining a COM model with actual testing to derive the COM parameters. The advantage of this method is that the extracted COM parameters take into account factors such as manufacturing processes and external influences; however, this method is costly and time-consuming. Therefore, this invention provides a method for extracting COM parameters of a surface acoustic wave resonator based on polynomial fitting. By using polynomial fitting to obtain the relationship between the resonant frequency and the COM parameters, the COM parameters can be obtained without actually fabricating the resonator. Figure 1 As shown, it includes the following steps:

[0043] S1. The COM parameters of a small number of actual fabricated SAW resonators are extracted using the experimental fitting method. The COM parameters include sound velocity, transduction coefficient, reflection coefficient and static capacitance.

[0044] Specifically, step S1 involves extracting a set of COM parameters using a measured fitting method, including:

[0045] S11. Use the COM model to obtain the simulated impedance curve of an actual fabricated SAW resonator;

[0046] S12. Experimental Measurement Steps: S11 uses the actual fabricated SAW resonator to obtain the actual impedance curve;

[0047] S13. Fit the simulated impedance curve to the actual impedance curve, and extract the COM parameters of the actual fabricated SAW resonator based on the fitting results.

[0048] S2. The resonant frequency and COM parameters of each actual fabricated SAW resonator are centered and scaled to obtain the corresponding centered and scaled resonant frequency and centered and scaled COM parameters; the centered and scaled COM parameters include centered and scaled sound velocity, centered and scaled transducer coefficient, centered and scaled reflection coefficient, and centered and scaled static capacitance.

[0049] Specifically, step S2 centers and scales the resonant frequency and COM parameters of the actual fabricated SAW resonator, as shown below:

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] Among them, f i Let f(i) represent the resonant frequency of the i-th actual fabricated SAW resonator, mean(f) represent the mean resonant frequency of the actual fabricated SAW resonator, and std(f) represent the standard deviation of the resonant frequency of the actual fabricated SAW resonator. This represents the centered scaled resonant frequency corresponding to the resonant frequency of the i-th actual fabricated SAW resonator; v i Let v represent the speed of sound at the i-th position, mean(v) represent the mean speed of sound, and std(v) represent the standard deviation of the speed of sound. a represents the centered scaled sound velocity corresponding to the i-th sound velocity; i Let represent the i-th transducer, mean(a) represent the mean of the transducers, and std(a) represent the standard deviation of the transducers. k represents the centered scaled transducer corresponding to the i-th transducer; i Let represent the i-th reflection coefficient, mean(k) represent the mean of the reflection coefficients, and std(k) represent the standard deviation of the reflection coefficients. c represents the centered scaled reflection coefficient corresponding to the i-th reflection coefficient; i Let represent the i-th static capacitance, mean(c) represent the mean of the static capacitance, and std(c) represent the standard deviation of the static capacitance. This represents the centralized scaled static capacitor corresponding to the i-th static capacitor.

[0056] The purpose of centering and scaling the resonant frequency and the extracted measured COM parameters is to eliminate the differences between features. This invention mainly achieves this by subtracting the mean of the features and then dividing by the standard deviation of the features.

[0057] S3. Define a set of 9th-order polynomial models between the centrally scaled resonant frequency and the centrally scaled COM parameters.

[0058] Specifically, the 9th-order polynomial model set in step S3 includes 9th-order polynomial models relating the centralized scaled resonant frequency to the centralized scaled sound velocity, the centralized scaled transducer, the centralized scaled reflection coefficient, and the centralized scaled static capacitance.

[0059] The 9th-order polynomial model between the centrally scaled resonant frequency and the centrally scaled speed of sound is expressed as:

[0060] v_scaled(f_scaled,p)=p1×f_scaled9 +p2×f_scaled 8 +p3×f_scaled 7

[0061] +p4×f_scaled 6 +p5×f_scaled 5 +p6×f_scaled 4

[0062] +p7×f_scaled 3 +p8×f_scaled 2 +p9×f_scaled+p

[0063] Where p = [p, p1, ..., p9] are the parameters of the polynomial, f_scaled represents the center-scaled resonant frequency, and v_scaled(f_scaled, p) represents the polynomial-defined speed of sound.

[0064] The 9th-order polynomial model relating the centered-scaling resonant frequency and the centered-scaling transduction coefficient is expressed as:

[0065] a_scaled(f_scaled,p)=l1×f_scaled9+l2×f_scaled8+l3×f_scaled7

[0066] +l4×f_scaled6+l5×f_scaled5+l6×f_scaled4

[0067] +l7×f_scaled3+l8×f_scaled2+l9×f_scaled+l

[0068] Where l = [l, l1, ..., l9] are the parameters of the polynomial, and a_scaled(f_scaled, p) represents the polynomial-defined transduction coefficient.

[0069] The 9th-order polynomial model relating the centered scaled resonant frequency and the centered scaled reflection coefficient is expressed as:

[0070] k_scaled(f_scaled,p)=s1×f_scaled 9 +s2×f_scaled 8 +s3×f_scaled 7

[0071] +s4×f_scaled 6 +s5×f_scaled 5 +s6×f_scaled 4

[0072] +s7×f_scaled 3 +s8×f_scaled 2 +s9×f_scaled+s

[0073] Where s = [s, s1, ..., s9] are the parameters of the polynomial, and k_scaled(f_scaled, p) represents the polynomial-defined reflection coefficient.

[0074] The 9th-order polynomial model representing the relationship between the centered scaled resonant frequency and the centered scaled static capacitance is as follows:

[0075] c_scaled(f_scaled,p)=h1×f_scaled 9 +h2×f_scaled 8 +h3×f_scaled 7

[0076] +h4×f_scaled 6 +h5×f_scaled 5 +h6×f_scaled 4

[0077] +h7×f_scaled 3 +h8×f_scaled 2 +h9×f_scaled+h

[0078] Where h = [h, h1, ..., h9] are the parameters of the polynomial, and c_scaled(f_scaled, p) represents the polynomial definition of the static capacitance.

[0079] S4. Combining the centered scaling resonant frequency and the centered scaling COM parameter, the weighted residual optimization method is used to process the 9th order polynomial model set to obtain the corresponding optimal 9th ​​order polynomial model set.

[0080] Specifically, for the 9th-order polynomial model between the centrally scaled resonant frequency and the centrally scaled sound velocity, a weighted residual optimization method is used to obtain the corresponding optimal 9th-order polynomial model, including:

[0081] S41. Obtain the polynomial-defined sound velocity through a 9th-order polynomial model, and calculate the sound velocity residual between the polynomial-defined sound velocity and the centered scaled sound velocity.

[0082] S42. The weight values ​​of the sound velocity residuals are calculated using a robust Bisquare weighting function, expressed as follows:

[0083]

[0084] Where b represents the scale parameter, r i w(r) represents the difference in sound speed between the i-th polynomial-defined sound speed and the i-th centered scaled sound speed. i ) represents the weight corresponding to the i-th sound speed residual.

[0085] S43. Construct the sound speed optimization objective function F(p) based on the weight values ​​of the sound speed residual, which is expressed as:

[0086]

[0087] Where n represents the number of observations (specifically, the n sound velocity parameters obtained from n actual fabricated SAW resonators), y i x represents the actual value of the i-th observation (i.e., the sound velocity parameter obtained from the i-th actual fabrication SAW resonator), i f(x) represents the value of the independent variable (resonant frequency) corresponding to the actual value of the i-th observation, p represents the parameter vector of the polynomial, p = (p0, p1, p2, ..., pn), and f(x) i (p) represents a 9th-order polynomial model defined using the parameter vector p with respect to x. i The predicted value.

[0088] S44. Use the nonlinear least squares method and the Levenberg-Marquardt algorithm to iteratively optimize the 9th-order polynomial model until the convergence condition is met (i.e., the sound speed optimization objective function F(p) reaches its minimum or the maximum number of iterations is reached), and output the optimal 9th-order polynomial model.

[0089] Following the above method, the optimal 9th-order polynomial model corresponding to the other 9th-order polynomial models can be obtained similarly.

[0090] S5. After centering and scaling the target resonant frequency corresponding to the target resonator, input it into the optimal 9th ​​order polynomial model set to obtain the target centered and scaled COM parameters.

[0091] S6. Restore the target COM parameters by centering and scaling the target to obtain the original scale target COM parameters, and substitute the target COM parameters into the COM model to obtain the electroacoustic characteristic curve of the target resonator.

[0092] In one embodiment, the resonant frequency range of the SAW resonator is 500MHz-3GHz. Fifty sets of COM parameters are extracted within this resonant frequency range as training data for the polynomial model. Then, the above method is used to obtain the optimal 9th-order polynomial model set.

[0093] a_scaled = 0.072429 x 9 -0.24617 x 8 -0.11169 x7 +0.78901 x 6 +0.12245 x 5

[0094] -0.99542 x 4 +0.30371 x 3 -0.53967 x 2 -0.46579 x+0.88926

[0095] v_scaled=0-0.019579 x 9 +0.05498 x 8 +0.071905 x 7 -0.23612 x 6 -0.11483 x 5

[0096] +0.38952 x 4 -0.14011 x 3 +0.072369 x 2 -0.69713 x-0.20712

[0097] c_scaled=0.016921 x 9 -0.065206 x 8 +0.0025907 x 7 +0.19491 x 6 -0.095394 x 5

[0098] -0.13304 x 4 +0.025157 x 3 +0.23102 x 2 -1.0137 x-0.22175

[0099] k_scaled=0.01001 x 9 -0.023827 x 8 -0.061947 x 7 +0.12196 x 6 +0.15901 x 5

[0100] -0.19927 x 4 -0.017188 x 3 +0.16824 x 2 +0.66768 x-0.13864

[0101] Where x is the target-centered scaled resonant frequency variable; a_scaled is the target-centered scaled transducer coefficient; v_scaled is the target-centered scaled sound velocity; c_scaled is the target-centered scaled static capacitance; and k_scaled is the target-centered scaled reflection coefficient. The corresponding polynomial fitting curve is shown below. Figure 2 As shown.

[0102] To illustrate the technical effects of this invention, five sets of COM parameters were selected and compared with the predicted COM parameters of this invention. Table 1 shows the measured COM parameters, and Table 2 shows the predicted COM parameters. Figure 3 The measured and predicted impedance curves of the resonator are shown. The comparison reveals that the predicted COM parameters output by the polynomial model constructed in this invention are in good agreement with the COM parameters extracted from the actual fabricated SAW resonator. Furthermore, the measured and predicted impedance curves also show a high degree of fit. In summary, the polynomial-fit-based COM parameter extraction method for surface acoustic wave resonators proposed in this invention can achieve accurate simulation of unfabricated SAW resonators.

[0103] Table 1 Measured COM Parameters

[0104] resonant frequency Speed ​​of sound Transduction coefficient static capacitor Reflectance coefficient 2286 3948.33 0.000873 7.75E-16 31.5864 2839 3884.16 0.000835 6.62E-16 40.3735 1795 3983.19 0.000908 9.58E-16 27.968 1455 4008.3 0.000912 1.12E-15 26.0821 960 4104.63 0.000861 1.45E-15 22.9964

[0105] Table 2 Predicted COM Parameters

[0106] resonant frequency Speed ​​of sound Transduction coefficient static capacitor Reflectance coefficient 2286 3946.21 0.000879 7.83E-16 31.713 2839 3884.87 0.000830 6.51E-16 40.279 1795 3981.09 0.000907 9.55E-16 27.966 1455 4009.31 0.000913 1.11E-15 26.154 960 4103.72 0.000862 1.46E-15 22.872

[0107] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "setting," "connection," "fixing," "rotation," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal connection of two components or the interaction between two components. Unless otherwise explicitly limited, those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0108] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for extracting COM parameters of a surface acoustic wave resonator based on polynomial fitting, characterized in that, Includes the following steps: S1. Multiple sets of COM parameters are extracted using the measured fitting method. The COM parameters include sound velocity, transduction coefficient, reflection coefficient, and static capacitance. S2. Center and scale each set of COM parameters and its corresponding resonant frequency to obtain the corresponding center-scaled COM parameters and center-scaled resonant frequency; the center-scaled COM parameters include center-scaled sound velocity, center-scaled transducer coefficient, center-scaled reflection coefficient, and center-scaled static capacitance; S3. Define a 9th-order polynomial model set between the centrally scaled resonant frequency and the centrally scaled COM parameter; S4. Combining the centered scaling resonant frequency and the centered scaling COM parameter, the weighted residual optimization method is used to process the 9th order polynomial model set to obtain the corresponding optimal 9th ​​order polynomial model set; Step S3 describes a 9th-order polynomial model set comprising 9th-order polynomial models relating the centrally scaled resonant frequency to the centrally scaled sound velocity, the centrally scaled transducer, the centrally scaled reflection coefficient, and the centrally scaled static capacitance; wherein the 9th-order polynomial model relating the centrally scaled resonant frequency to the centrally scaled sound velocity is expressed as follows: v_scaled(f_scaled,p) = p1×f_scaled 9 + p2×f_scaled 8 + p3× f_scaled 7 + p4×f_scaled 6 + p5×f_scaled 5 + p6× f_scaled 4 + p7×f_scaled 3 + p8× f_scaled 2 + p9× f_scaled + p, Where p=[p,p1,···,p9] are the parameters of the polynomial, f_scaled represents the center-scaled resonant frequency, and v_scaled(f_scaled,p) represents the polynomial-defined speed of sound; For the 9th-order polynomial model between the centrally scaled resonant frequency and the centrally scaled sound velocity, a weighted residual optimization method is used to obtain the corresponding optimal 9th-order polynomial model, including: S41. Obtain the polynomial-defined sound velocity through a 9th-order polynomial model, and calculate the sound velocity residual between the polynomial-defined sound velocity and the centered scaled sound velocity. S42. Calculate the weight values ​​of the sound velocity residual using a robust Bisquare weighting function; S43. Construct a sound velocity optimization objective function based on the weight values ​​of the sound velocity residual; S44. Iteratively optimize the 9th-order polynomial model using the nonlinear least squares method and the Levenberg-Marquardt algorithm until the sound speed optimization objective function satisfies the convergence condition, and output the optimal 9th-order polynomial model; S5. After centering and scaling the target resonant frequency corresponding to the target resonator, input it into the optimal 9th ​​order polynomial model set to obtain the target centered and scaled COM parameters. S6. Restore the target COM parameters by centering and scaling the target COM parameters, and substitute the target COM parameters into the COM model to obtain the electroacoustic characteristic curve of the target resonator.

2. The method for extracting COM parameters of a surface acoustic wave resonator based on polynomial fitting according to claim 1, characterized in that, Step S1 involves extracting a set of COM parameters using the experimental fitting method, including: S11. Use the COM model to obtain the simulated impedance curve of an actual fabricated SAW resonator; S12. Experimental testing steps: S11 uses the actual fabricated SAW resonator to obtain the actual impedance curve; S13. Fit the simulated impedance curve to the actual impedance curve, and extract the COM parameters of the actual fabricated SAW resonator based on the fitting results.

3. The method for extracting COM parameters of a surface acoustic wave resonator based on polynomial fitting according to claim 1, characterized in that, Step S2 centers and scales each set of COM parameters and its corresponding resonant frequency, as follows: ， ， ， ， ， Among them, f i Let f(i) represent the resonant frequency of the i-th actual fabricated SAW resonator, mean(f) represent the mean resonant frequency of the actual fabricated SAW resonator, and std(f) represent the standard deviation of the resonant frequency of the actual fabricated SAW resonator. This represents the centered scaled resonant frequency corresponding to the resonant frequency of the i-th actual fabricated SAW resonator; v i Let v represent the speed of sound at the i-th position, mean(v) represent the mean speed of sound, and std(v) represent the standard deviation of the speed of sound. a represents the centered scaled sound velocity corresponding to the i-th sound velocity; i Let represent the i-th transducer, mean(a) represent the mean of the transducers, and std(a) represent the standard deviation of the transducers. k represents the centered scaled transducer corresponding to the i-th transducer; i Let represent the i-th reflection coefficient, mean(k) represent the mean of the reflection coefficients, and std(k) represent the standard deviation of the reflection coefficients. c represents the centered scaled reflection coefficient corresponding to the i-th reflection coefficient; i Let represent the i-th static capacitance, mean(c) represent the mean of the static capacitance, and std(c) represent the standard deviation of the static capacitance. This represents the centralized scaled static capacitor corresponding to the i-th static capacitor.

4. The method for extracting COM parameters of a surface acoustic wave resonator based on polynomial fitting according to claim 1, characterized in that, Step S42 uses a robust Bisquare weighting function to calculate the weight values ​​of the sound velocity residual, expressed as: ， Where b represents the scale parameter, r i This represents the difference in sound speed between the i-th polynomial-defined sound speed and the i-th centered scaled sound speed. This represents the weight corresponding to the i-th sound speed residual.

5. The method for extracting COM parameters of a surface acoustic wave resonator based on polynomial fitting according to claim 1, characterized in that, Step S43 combines the weight values ​​of the sound velocity residual with the sound velocity residual to construct the sound velocity optimization objective function F(p), which is expressed as: ， Where n represents the number of observations, y i Let x represent the actual value of the i-th observation. i This represents the value of the independent variable corresponding to the actual value of the i-th observation. The parameter vector of the polynomial, This represents a 9th-order polynomial model defined using the parameter vector p with respect to x. i The predicted value.

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