Improved awe fast sweep method and system in a radio frequency acoustic filter design

Abstract

The application discloses an improved AWE fast sweeping method and system in a radio frequency acoustic filter design, relates to the technical field of simulation of radio frequency acoustic filter devices, and solves the technical problems of low calculation efficiency and poor approximation accuracy in simulation calculation of a SAW resonator by using traditional AWE technology. The application determines a sweeping frequency band and convergence accuracy, performs LU decomposition on a system matrix at a center frequency of the frequency band, solves order and order Taylor expansion and Pad approximation, calculates relative errors and convergence domains of adjacent order waveform asymptotic estimation expansion, adaptively finds conductance error peaks in the convergence domains, improves accuracy by using a Pad rational interpolation algorithm, and re-calculates the convergence domains, and the iteration is performed based on an adaptive window algorithm until the whole frequency band converges. The application can avoid calculation of each frequency point in a frequency band to be studied, ensures accuracy and reliability of simulation results, and significantly improves calculation efficiency under the condition of ensuring calculation accuracy.

Description

Technical Field

[0001] This invention relates to the field of radio frequency acoustic filter device simulation technology, specifically to an improved AWE fast frequency sweep method and system for radio frequency acoustic filter design. Background Technology

[0002] Radio frequency (RF) acoustic filters are currently the mainstream filters in mobile RF front-ends. These include surface acoustic wave (SAW) filters and bulk acoustic wave (BAW) filters, which are electronic devices that utilize the physical phenomenon of sound waves propagating on the surface of a piezoelectric medium to achieve signal processing. With the continuous development of 5G and 6G technologies, and the increasing modularization, integration, and miniaturization of RF front-ends, RF acoustic filters have become indispensable key components.

[0003] Currently, numerical methods such as the Finite Element Method (FEM), Spectral Element Method (SEM), and Finite Difference Method (FDM) offer high accuracy in simulating RF acoustic filters with complex structures. However, the solution time increases significantly with the scale of the structure. This is especially true when analyzing broadband problems, which require solving for each frequency point individually, consuming enormous computational resources.

[0004] Asymptotic Waveform Evaluation (AWE) is a typical fast frequency sweeping method. AWE constructs Padé rational fractions based on the Taylor expansion of admittance curves, achieving high accuracy. Furthermore, by calculating multi-frequency expansion functions using complex frequency hopping (CFH) techniques, it can approximate curves over a wide frequency band. However, applying traditional AWE techniques to the simulation of SAW resonators suffers from low computational efficiency, and the approximate accuracy of AWE techniques on the conductance frequency response curves of SAW resonators is poor. Summary of the Invention

[0005] To address the shortcomings and deficiencies of existing technologies, this invention provides an improved AWE fast frequency sweep method and system for the design of radio frequency acoustic filters that combines simulation accuracy and computational efficiency with adaptive optimization of conductance approximation accuracy.

[0006] To achieve the above objectives, the present invention provides the following technical solution: The improved AWE fast frequency sweep method for RF acoustic filter design provided by the present invention includes the following steps: S1. Model the SAW model, determine the sweep frequency band and convergence accuracy of the RF acoustic filter, and determine the center frequency of the sweep frequency band. Perform LU decomposition on the system matrix of the SAW model; S2. Solve for the system matrix at the center frequency. order and The Taylor expansion of order AWE is approximated by Pad, and the relative error and convergence region of adjacent order AWE expansions are calculated. ; S3. Adaptively find the conductance error peak within the convergence region, optimize the AWE expansion based on Pad's rational interpolation algorithm to improve the approximation accuracy, and recalculate the convergence region after completion. S4. Based on the adaptive window algorithm, iteratively execute steps S1 to S3 on the frequency bands that do not meet the preset convergence accuracy until the entire frequency band of the RF acoustic filter simulation meets the preset convergence accuracy.

[0007] Preferably, in step S1, the center frequency of the frequency sweep band is... The system matrix of the SAW model is decomposed using LU decomposition, specifically including: The system matrix is ​​obtained by combining the mass matrix and stiffness matrix of the SAW model with the piezoelectric coupling equation. The system matrix is ​​decomposed and calculated using LU decomposition preprocessing technology. During decomposition, the Umfpack library in the SuiteSparse package is used to first reorder the system matrix, and then scale the reordered system matrix based on the row scaling factor. After matrix preprocessing, the LU decomposition operation is performed. The decomposed matrix is ​​used to solve the multiple right-hand linear equations, thereby improving the efficiency of coefficient recursion and calculation related to the system matrix.

[0008] Preferably, the specific process for modeling the SAW model is as follows: Configure the parameters of the SAW device model, including setting the model's geometry, material properties, and electrode configuration. Mesh the SAW device model and set a perfectly matched layer (PML) absorbing boundary around the model. Use the finite element method (FEM) to construct the model's stiffness matrix and mass matrix, and assemble them to obtain the system matrix equation. Based on the system matrix equation, obtain the system matrix of the SAW model.

[0009] Preferably, in step S2, the system matrix is ​​solved at the center frequency. order and The Taylor expansion of order AWE is approximated by Pad, and the relative error and convergence region of adjacent order AWE expansions are calculated. Specifically, it includes: Calculate the finite-order Taylor expansions of the matrix and vectors at the center frequency, substitute them into the system matrix equations, and rearrange to obtain the finite-order Taylor expansions of the solution vectors. Based on these Taylor expansions, calculate the admittance expression for the SAW resonator; then solve for the admittance expression. order and Taylor expansion of order and Pad approximation; by evaluation order and The relative error between the two is obtained by calculating the expansion of the asymptotic estimation of the first-order waveform near the center frequency. Then, the frequency window with the largest coverage and the relative error that meets the convergence accuracy is determined, and this frequency window is used as the convergence region.

[0010] Preferably, in step S3, adaptively finding the conductance error peak within the convergence region specifically includes: Within the convergence region of the admittance, the relative error of the conductance is calculated. Frequency bands where the relative error of the conductance exceeds a preset threshold are identified as frequency bands with severe fluctuations. The frequency point with the largest error in the frequency band with severe fluctuations is taken as the conductance error peak. If a conductance error peak exists, the admittance value at the frequency point of the error peak is calculated first. Then, the Pad's rational interpolation algorithm is used to optimize the waveform asymptotic estimation expansion to improve accuracy. After completion, the convergence region is recalculated. If no conductance error peak exists, the subsequent steps are executed directly. Improving accuracy using the Pad rational interpolation algorithm specifically includes: using the frequency point of the conductance error peak as the interpolation point, constructing a rational fraction of Pad rational interpolation by combining the admittance value of the interpolation point, establishing a system of equations through moment matching conditions, solving the system of equations after supplementing the interpolation constraints to obtain the unknown coefficients of the rational fraction, and integrating the Pad rational interpolation into the current waveform asymptotic estimation expansion to complete the accuracy optimization of the expansion.

[0011] Preferably, in the rational fraction of the Pad-type rational interpolation, the order of the numerator polynomial and the denominator polynomial are the same as the order of the Taylor expansion. When supplementing the interpolation constraints, a corresponding number of equations are constructed according to the preset number of interpolation frequency points, so that the solution of the equation system can take a unique solution, a minimum norm solution, or a least squares solution according to the relationship between the number of equations and the number of unknown coefficients. When performing Pad approximation on the Taylor expansion, the Pad approximation is expressed as a rational fraction of the numerator and denominator polynomials. A system of linear equations about the unknown coefficients of the rational fractions is established through the moment matching condition. The coefficients of the denominator polynomial are solved first, and then the coefficients of the numerator polynomial are solved by substituting them back to obtain the Pad approximation expansion.

[0012] Preferably, in step S4, steps S1 to S3 are iteratively executed on the unconverged frequency bands based on the adaptive window algorithm. The specific process is as follows: S41. Take the midpoint of the non-converged frequency band as the new expansion frequency, set the initial expansion order, solve the waveform asymptotic estimation expansion of the corresponding order and calculate the relative error of the expansion of adjacent orders to determine the new convergence region. S42. Determine whether the new convergence region completely covers the current non-converged frequency band. (a) If not, increase the expansion order and solve the expansion again, calculate the relative error and determine the region of convergence. If the expansion order reaches the preset maximum order, directly execute step S43. (b) If so, proceed directly to step S43; S43. If there are still some areas in the current non-converged frequency band that are not covered by the convergence domain, treat the uncovered area as a new non-converged frequency band and repeat steps S41 to S43 until all areas of the entire frequency band are covered by the convergence domain and the convergence accuracy is met.

[0013] An improved AWE fast frequency sweep system for RF acoustic filter design includes a model building module for constructing a SAW device model of the RF acoustic filter, configuring model parameters and performing mesh generation, setting a perfectly matched layer absorption boundary, constructing stiffness matrix and mass matrix using the finite element method and assembling them to obtain the system matrix, and performing LU decomposition on the system matrix at the center frequency of the sweep frequency band. The expansion and convergence region calculation module is used to solve the admittance expression for SAW resonators. order and The Taylor expansion of the order is approximated by Pad, and the relative error of the expansion of the asymptotic estimation of the waveform of adjacent order is calculated and the region of convergence is determined. The peak optimization module is used to adaptively find conductance error peaks within the convergence region. If an error peak exists, its admittance value is calculated, and the waveform asymptotic estimation expansion is optimized by Pad's rational interpolation algorithm and the convergence region is recalculated. The iterative convergence module is used to iteratively process the unconverged frequency band using the model construction module, the expansion and convergence domain calculation module, and the peak optimization module based on the adaptive window algorithm until the entire frequency band meets the convergence accuracy.

[0014] A computing device, comprising: One or more processors; A storage device for storing one or more programs, which, when executed by one or more processors, enable the one or more processors to implement the improved AWE fast frequency sweep method described above.

[0015] A computer-readable storage medium storing a program that, when executed by a processor, implements the improved AWE fast frequency sweep method described above.

[0016] The improved AWE fast frequency sweep method and system for radio frequency acoustic filter design proposed in this invention have the following advantages: (1) The improved AWE fast frequency sweep method in the design of radio frequency acoustic filters of the present invention has both simulation accuracy and computational efficiency, and can adaptively optimize the conductance approximation accuracy, making the simulation results of the entire frequency sweep band more accurate and reliable, and effectively improving the overall accuracy level of radio frequency acoustic filter simulation.

[0017] By adaptively identifying conductance error spikes within the convergence domain and specifically employing the Pad's rational interpolation algorithm to optimize the waveform asymptotic estimation expansion, the convergence domain can be recalculated to achieve accuracy completion. This improves the fitting accuracy of the conductance curve while ensuring that the admittance magnitude fitting effect meets the preset convergence accuracy. Simultaneously, based on the adaptive window algorithm, iterative processing of the non-converged frequency bands allows for adaptive selection of the AWE expansion function order according to the fluctuation degree of the frequency response curve, reducing the overlap rate and unnecessary computation of the AWE expansion and significantly improving the simulation efficiency of the RF acoustic filter.

[0018] (2) The present invention constructs a SAW model of radio frequency acoustic filter based on the finite element method, which is compatible with the existing simulation technology system of radio frequency acoustic filter devices. It has strong compatibility and practicality. At the same time, the improved AWE technology can be directly applied to the design and simulation of mainstream radio frequency acoustic filters such as surface acoustic wave filters. It adapts to the design requirements of radio frequency front-end modularization, integration and miniaturization under the development of 5G and 6G technologies, and provides technical support for the efficient research and development design of radio frequency acoustic filters. Attached Figure Description

[0019] Figure 1 This is a flowchart of the FEM frequency sweep calculation based on the improved AWE fast frequency sweep method in this invention; Figure 2 This is a schematic diagram of the single-port SAW resonator in this invention; Figure 3 This is the IDT structure of the single-port SAW resonator in this invention; Figure 4 This is an enlarged grid diagram of the left-end structure of the resonator in this invention; Figure 5 The curves showing the typical FEM sweep admittance modulus and conductance of the SAW device model in this invention are shown. Figure 6 This is a comparison curve of the admittance characteristics of the improved AWE fast frequency sweep method and the traditional FEM algorithm in Example 2 of this embodiment; Figure 7 This is a comparison chart of the admittance characteristics of the commercial software COMSOL using the AWE and FEM methods in Example 2 of this embodiment. Detailed Implementation

[0020] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Example 1

[0021] like Figure 1 As shown, the improved AWE fast frequency sweep method in the RF acoustic filter design of this embodiment uses a single-port SAW resonator as the SAW device model and improves the traditional AWE fast frequency sweep algorithm to enhance the efficiency of FEM frequency sweep. The steps are as follows: S1. Determine the frequency sweep band and convergence accuracy, and locate the center frequency of the frequency band. The system matrix of the SAW model is decomposed using LU decomposition, specifically including: First, the center frequency of the target frequency band is used as the expansion frequency of the initial AWE expansion function, and the finite element system matrix A at this frequency is assembled. The SAW modeling of the RF acoustic filter includes: configuring the parameters of the SAW device model, including setting the model's geometry, material properties, and electrode configuration; meshing the SAW device model; setting a Perfectly Matched Layer (PML) absorbing boundary around the model; constructing the model's K and mass matrix M using the finite element method (FEM); and assembling the system matrix equations. Based on these system matrix equations, the system matrix A of the SAW model is obtained. After performing LU decomposition on the system matrix A, the Taylor expansion of the SAW device admittance parameter Y11 can be derived, and the Padre approximation can be calculated.

[0022] The surface interdigital transducers (IDTs) of the SAW resonator consist of two electrode buses, defined as the positive electrode (labeled 1) and the negative electrode (labeled 2), according to the definition of admittance (Y parameter), as shown in Equation 1: ; Among them, current j is the imaginary unit. Let ω be the angular frequency, W be the device aperture, and Q be the amount of charge accumulated on the surface of the excitation electrode. The Y parameters can be calculated based on different electrical conditions. Taking the calculation of Y11 as an example, the electrical conditions are: a voltage is applied to the positive electrode; for ease of calculation, a voltage of 1V is generally applied (V1 = 1V), and the negative electrode is grounded (V2 = 0V). Consider the matrix equations of the finite element system. : ; Where V1 and V2 are the voltages of the positive electrode (1V) and negative electrode (0V), respectively, and X represents the other degrees of freedom of the entire model, including all displacement degrees of freedom and the potential degree of freedom of the substrate. From the piezoelectric coupling equation, it can be seen that the overall matrix A is calculated from the mass matrix M and the stiffness matrix K. ; Write the unknown X in Taylor expansion form: ; in, Substituting formula (4) into formulas (1), (2), and (3) for Taylor coefficients, we can obtain the Taylor expansion of admittance Y11: ; in: ; coefficient It can be derived recursively from the derivative matrix of matrix A and vector b: ; coefficient The calculation process can be reduced to solving a system of linear equations with multiple right-hand sides, in the form of: ; Wherein, the coefficient matrix Keep constant, right-hand side The computational efficiency varies with the subspace dimension. For this type of problem, LU decomposition preprocessing techniques can significantly improve computational efficiency. ; SuiteSparse, an open-source numerical computation software package, offers high computational efficiency for LU decomposition. It is specifically designed for handling sparse matrix computations and has wide applications in scientific computing, engineering simulation, and machine learning. The Umfpack library within SuiteSparse is a solver for LU decomposition of asymmetric sparse matrices, supporting various cutting-edge methods. Umfpack reorders the matrix before decomposition and scales it based on row scaling factors, significantly improving the computational efficiency of LU decomposition.

[0023] Solve Then, substituting into formula (5), the complete Taylor expansion of the admittance Y11 can be calculated, and the approximate frequency response curve near the center frequency can be obtained. Taylor series expansion has the inherent defect of a limited radius of convergence. Padé approximation can effectively broaden the original region of convergence. Padé approximation can describe a larger range of the original function by taking advantage of the structural flexibility of rational functions and introducing pole distribution. Padé rational fraction can be written in the following form with unknown coefficients: ; in, and The coefficients to be determined are established using the moment matching conditions, and the coefficients to be determined are as follows: ; use Multiply by equation 10, and Expressed using equation (4), and then comparing the coefficients of the same power on both sides of the equation, we obtain the relevant... and A system of linear equations.

[0024] ; The coefficients can be obtained first using the last M equations in the system of equations (12). Then, substitute the coefficients back into the first L+1 equations to find the coefficients. Substituting into equation (11) yields the Padé approximation expansion. .

[0025] S2, Solve order and The Taylor expansion of order A is approximated by Pad's expansion, and the relative error and convergence region of the asymptotic estimation expansion of adjacent order waveforms are calculated. The finite-order Taylor expansions of matrix A and vector b at the center frequency are calculated, and substituted into the system matrix equations to derive the solution vector x. The Taylor expansion with limited order is used to calculate the admittance Y of the SAW resonator based on the Taylor expansion of the solution vector. 11 Expressions; Solve the admittance expressions respectively. order and Taylor expansion of order and Pad approximation; by evaluation order and The calculation results of the asymptotic estimation expansion of the Y11 waveform near the center frequency are obtained, and the relative errors of the adjacent order AWE expansions are obtained. Then, the frequency window with the largest coverage and the relative error satisfying the convergence accuracy is determined, and this frequency window is taken as the convergence region. Specifically, this includes: exist Calculate separately order and AWE expansion and ,exist The results of the two AWE expansions are evaluated nearby, and the relative error between the two expansions is calculated.

[0026] ; Determine the frequency window with the largest coverage area That is, the region of convergence, such that All meet The fluctuation of conductivity with frequency is more pronounced than the fluctuation of the admittance magnitude of the Y parameter.

[0027] S3. Adaptively search for conductance error peaks within the convergence region. Calculate the relative conductance error within the admittance convergence region. Determine frequency bands where the relative conductance error exceeds a preset threshold as volatile frequency bands. Take the frequency point with the largest error in the volatile frequency band as the conductance error peak. If a conductance error peak exists, first calculate the admittance value at the peak frequency, then use the Pad's rational interpolation algorithm to optimize the waveform asymptotic estimation expansion to improve accuracy. After completion, recalculate the convergence region. If no conductance error peak exists, directly execute the subsequent steps.

[0028] Using the frequency point of the conductance error peak as the interpolation point, and combining the admittance value at this interpolation point, a rational fraction of Pad's rational interpolation is constructed. A system of equations is established through moment matching conditions. After supplementing the interpolation constraints, the unknown coefficients of the rational fraction are obtained by solving the system of equations. This Pad's rational interpolation is then incorporated into the current waveform asymptotic estimation expansion to complete the accuracy optimization of the expansion, specifically including: When the algorithm in step S2 above calculates the region of convergence of the admittance... Even when the fitting accuracy of the admittance modulus reaches a set threshold, the fitting accuracy of the conductance curve may still have a significant error. Therefore, the conductance error can be evaluated separately. When the error in a certain frequency band exceeds the set threshold, the frequency response curve near that frequency is considered to fluctuate significantly, exhibiting an "error peak." The frequency point with the largest error is taken as the "interpolation point," and after calculating its Y parameters, a Padé-type rational interpolation algorithm is applied and incorporated into the current AWE expansion. In this process, the curve can be "modified".

[0029] Padé-type rational interpolation has a similar functional form to Padé approximation and can be written in the following form: ; The numerator polynomial in a rational fraction With denominator polynomial The order of all equations is the same as that of the Taylor expansion. The number of unknown coefficients has increased compared to the Padé approximation. Similarly, a system of equations is established using the moment matching condition, and the coefficients to be determined are determined by the following equation: ; Multiplying both formulas By comparing coefficients of the same power, we can obtain: ; For any set It can be solved based on the moment matching equation. However, it is clear that the number of equations (q+1) is less than the number of unknowns (2q+1), and the system is "underdetermined". By adding interpolation constraints, the equations can be completed.

[0030] After calculating the Y parameters at l frequencies, an equation is established with the rational fraction, i.e. ( (abbreviated as fi), where, For the determined l known frequency points, substituting equation (15) into the equation satisfies: ; To solve equation (18), we first substitute equation (17) into the numerator polynomial. In China, utilizing and linear combination of substitution coefficients and according to Simplify polynomials: ; in: ; Will The expanded form and the sorted form Substituting into equation 18, we obtain the following system of equations: ; Because the first term on the left side of the equation The system of equations does not contain any unknown terms, and can be rearranged as terms on the right-hand side. Rearranging the system yields: ; In the rational fractions of the Pad-type rational interpolation, the orders of the numerator and denominator polynomials are the same as the order of the Taylor expansion. When supplementing the interpolation constraints, a corresponding number of equations are constructed according to the preset number of interpolation frequencies, so that the solution of the system of equations takes a unique solution, a minimum norm solution, or a least squares solution according to the relationship between the number of equations and the number of unknown coefficients. When performing Pad approximation on the Taylor expansion, the Pad approximation is expressed as a rational fraction of the numerator and denominator polynomials. A linear system of equations about the unknown coefficients of the rational fraction is established through the moment matching condition. The coefficients of the denominator polynomial are solved first, and then the coefficients of the numerator polynomial are substituted back to solve for the coefficients of the numerator polynomial, thus obtaining the Pad approximation expansion.

[0031] Therefore, the constructed system of equations contains q coefficients to be determined and l equations, and the characteristics of the solution are determined by the number of equations. When the equation has a unique solution, it belongs to a "well-posed system" and strictly satisfies the interpolation conditions; When the number of equations is less than the number of unknowns, it belongs to an "underdetermined system" and has an infinite number of solutions. In this case, the minimum norm solution is used to ensure the stability of the solution. When the number of equations exceeds the number of unknowns, it is considered an "overdetermined system". The equations have no solution. The constraints are approximated by the least squares solution, but the least squares solution does not actually satisfy equation 18, which weakens the interpolation accuracy.

[0032] S4. Based on the Adaptive Window Algorithm (AWA), iteratively execute steps S1 to S3 on the unconverged frequency band until the entire frequency sweep of the RF acoustic filter simulation meets the preset convergence accuracy. The Adaptive Window Algorithm provides a simple and intuitive framework to generate a set of "non-overlapping" frequency windows that can cover a given frequency band, and can adaptively adjust the expansion order according to the fluctuation of the frequency response curve. The frequency window refers to the frequency convergence domain of a certain AWA expansion function. The AWA algorithm is a sequential binary search algorithm; the algorithm first needs to determine the range of the expanded frequency band. Frequency step size of error assessment Range of adaptive expansion order Step size of order change and convergence accuracy : S41. Take the midpoint of the non-converged frequency band as the new expansion frequency, and expand the frequency... Set to a given frequency band Midpoint: Set the initial expansion order. .exist Calculate the m-th and n-th order AWE expansions respectively. and .

[0033] Solve for the waveform asymptotic estimation expansion of the corresponding order and calculate the relative error between adjacent order expansions to determine the new region of convergence; Evaluate the results of the two AWE expansions in the vicinity and calculate the relative error between the two expansions: ; Determine the frequency window with the largest coverage area , making All meet .

[0034] S42. Determine whether the current frequency window completely covers the frequency band. That is, whether the new convergence domain completely covers the current non-converged frequency band.

[0035] (a) If not, increase m and n respectively To increase the order of the expansion, re-solve the expansion, calculate the relative error, and determine the region of convergence. If the expansion order n reaches the preset maximum order... If so, proceed directly to step S43; (b) If so, proceed directly to step S43; S43. If there are still some areas at both ends of the current frequency window and in the non-converged frequency band that are not covered by the convergence domain, then the previous frequency band... To cover the uncovered area or As a new unconverged frequency band Repeat steps S41 to S43 until all regions of the entire frequency sweep are covered by the convergence domain and the convergence accuracy is met.

[0036] The improved AWE fast frequency sweep method of this invention not only significantly improves the accuracy of conductance curve fitting and ensures the fitting effect of admittance magnitude by adaptively identifying conductance error peaks within the convergence domain and optimizing the expansion formula and recalculating the convergence domain using the Pad's rational interpolation algorithm, making the frequency sweep simulation results of RF acoustic filters more accurate and reliable, but also relies on the adaptive window algorithm to iteratively process the non-converged frequency bands and adaptively select the AWE expansion order according to the fluctuation of the frequency response curve, reducing the amount of computation and the overlap rate of the expansion formula, avoiding solving for each frequency point in a wide bandwidth, and significantly improving the simulation calculation efficiency and reducing the consumption of computing resources. At the same time, this method is based on the finite element method to construct the SAW model, which is compatible with the existing simulation technology system, has strong compatibility and practicality, and the improved AWE technology can be directly applied to the design simulation of mainstream RF acoustic filters, adapting to the design requirements of modularization, integration and miniaturization of RF front-end under 5G and 6G, providing strong technical support for the efficient R&D and design of RF acoustic filters. Example 2

[0037] This invention uses a single-port SAW resonator as the SAW device model. The structure of the single-port SAW resonator is as follows: Figure 2 As shown, the performance of the improved AWE fast frequency sweep method is verified through simulation experiments from the two dimensions of accuracy and efficiency.

[0038] The IDT structure of a single-port SAW resonator is as follows: Figure 3 As shown, the structural parameters of its IDT basic unit are shown in Table 1, and its partial structural mesh division is shown in Table 1. Figure 4 As shown, an equidistant grid density distribution is used on the piezoelectric substrate from the surface to the bottom (y-direction). The piezoelectric material of the resonator substrate is set to LT-42, using aluminum electrodes, with 20 short-circuit reflective grating fingers of the same period on each side. The frequency sweep range is 1.8GHz~2.15GHz, and the frequency sweep step size is 2MHz.

[0039] Table 1: Structural Parameters of IDT Basic Unit

[0040] When excitation signals of different frequencies are applied to the electrodes of the SAW device model, frequency response analysis is performed on the SAW device model to obtain the Y-parameter admittance curve. The typical FEM swept frequency admittance magnitude versus conductance curves of the SAW device model are shown below. Figure 6 As shown, the Y-parameter curves can be used to analyze the resonant and anti-resonant frequencies of the device, as well as the frequency response information of other frequencies.

[0041] To verify the accuracy of the improved AWE algorithm in this invention, this embodiment compares its simulation results with those of the traditional finite element method (FEM). All simulation verifications were performed on a dedicated workstation configured with an 11th Gen Intel® Core™ i9-11900K @ 3.50GHz, 3504MHz, 8 cores, and 16 logic processor. The testing environment was standardized, professional, and representative.

[0042] Figure 6 This is a comparison curve of the admittance characteristics of the improved AWE technique and the traditional FEM algorithm in this invention. As can be seen from the figure, the simulation curves of the two methods highly overlap, show good agreement in details, and have no significant deviations, proving that the improved AWE algorithm of this invention can maintain the same frequency sweep simulation accuracy as the traditional FEM method.

[0043] Meanwhile, this invention also conducted comparative experiments on the simulation results of the traditional AWE method and the FEM method in the commercial software COMSOL. Figure 7 The figure compares the admittance characteristics of the commercial software COMSOL using the AWE and FEM methods. It can be seen from the figure that the conductance curve of the traditional AWE method has a significant fitting error compared to the FEM reference curve, especially in the frequency band with severe fluctuations such as the resonance peak. The improved AWE algorithm of this invention, by adaptively finding the conductance error peak and combining it with the Pad's rational interpolation algorithm for optimization, solves the problem of the conductance approximation accuracy deficiency of the traditional AWE method. Its simulation results are completely consistent with the FEM reference.

[0044] To further quantify the frequency sweep efficiency improvement effect of the present invention, Table 2 summarizes the frequency sweep time data of the traditional FEM method, the traditional AWE method used in the commercial software COMSOL, and the improved AWE method of the present invention under the same simulation conditions: Table 2 compares the time consumption of two frequency sweeping methods: traditional FEM and FEM based on improved AWE technology.

[0045] As shown in Table 2, the traditional FEM method takes 696 seconds to sweep the frequency, the traditional AWE method built into the commercial software COMSOL takes 746 seconds, while the improved AWE method of this invention takes only 321 seconds. In comparison, the improved AWE method of this invention improves the frequency sweep calculation efficiency by 53.88% compared to the traditional FEM method, effectively solving the problem of long calculation time and frequency-point-by-frequency calculation in the traditional FEM method for wideband frequency sweep. It also overcomes the dual technical defects of the traditional AWE method, which has no efficiency improvement and poor accuracy in approximate conductance frequency response, ultimately achieving dual optimization of accuracy and efficiency in RF acoustic filter simulation. Example 3

[0046] The improved AWE fast frequency sweep system for RF acoustic filter design provided in this embodiment specifically includes: The model building module is used to build the SAW device model of the radio frequency acoustic filter, configure the model parameters and perform mesh generation, set the absorption boundary of the perfectly matched layer, use the finite element method to construct the stiffness matrix and mass matrix and assemble them to obtain the system matrix, and perform LU decomposition on the system matrix at the center frequency of the swept frequency band. The expansion and convergence region calculation module is used to solve the admittance expression for SAW resonators. order and The Taylor expansion of the order is approximated by Pad, and the relative error of the expansion of the asymptotic estimation of the waveform of adjacent order is calculated and the region of convergence is determined. The peak optimization module is used to adaptively find conductance error peaks within the convergence region. If an error peak exists, its admittance value is calculated, and the waveform asymptotic estimation expansion is optimized by Pad's rational interpolation algorithm and the convergence region is recalculated. The iterative convergence module is used to iteratively process the unconverged frequency band using the model construction module, the expansion and convergence domain calculation module, and the peak optimization module based on the adaptive window algorithm until the entire frequency band meets the convergence accuracy.

[0047] It should be noted that this system is a system corresponding to the above method. All implementation methods in the above method embodiments are applicable to this embodiment and can achieve the same technical effect.

[0048] Embodiments of the present invention also provide a computing device, including: a processor and a memory storing a computer program, wherein the computer program, when executed by the processor, performs the method described above. All implementations in the above method embodiments are applicable to this embodiment and can achieve the same technical effects.

[0049] Embodiments of the present invention also provide a computer-readable storage medium storing instructions that, when executed on a computer, cause the computer to perform the method described above. All implementations in the above method embodiments are applicable to this embodiment and can achieve the same technical effects.

[0050] The above are preferred embodiments of the present invention. It should be noted that those skilled in the art can make various equivalent modifications or substitutions without departing from the principle of the present invention. These possible changes and substitutions also fall within the scope of protection covered by the present invention.

Claims

1. An improved AWE fast frequency sweep method for radio frequency acoustic filter design, characterized in that, The steps include the following: S1. Model the SAW model, determine the sweep frequency band and convergence accuracy of the RF acoustic filter, and determine the center frequency of the sweep frequency band. Perform LU decomposition on the system matrix of the SAW model; S2. Solve for the system matrix at the center frequency. order and The Taylor expansion of order AWE is approximated by Pad, and the relative error and convergence region of adjacent order AWE expansions are calculated. ; S3. Adaptively find the conductance error peak within the convergence region, optimize the AWE expansion based on the Pad rational interpolation algorithm to improve the approximation accuracy, and recalculate the convergence region after completion. S4. Based on the adaptive window algorithm, iteratively execute steps S1 to S3 on the frequency bands that do not meet the preset convergence accuracy until the entire frequency band of the RF acoustic filter simulation meets the preset convergence accuracy.

2. The improved AWE fast frequency sweep method in the design of radio frequency acoustic filters according to claim 1, characterized in that, In step S1, at the center frequency of the frequency sweep band The system matrix of the SAW model is decomposed using LU decomposition, specifically including: The system matrix is ​​obtained by combining the mass matrix and stiffness matrix of the SAW model with the piezoelectric coupling equation. The system matrix is ​​decomposed and calculated using LU decomposition preprocessing technology. During decomposition, the Umfpack library in the SuiteSparse package is used to first reorder the system matrix, and then scale the reordered system matrix based on the row scaling factor. After matrix preprocessing, the LU decomposition operation is performed. The decomposed matrix is ​​used to solve the multiple right-hand linear equations, thereby improving the efficiency of coefficient recursion and calculation related to the system matrix.

3. The improved AWE fast frequency sweep method in the design of radio frequency acoustic filters according to claim 2, characterized in that, The specific process of modeling a SAW model is as follows: Configure the parameters of the SAW device model, including setting the model's geometry, material properties, and electrode configuration. Mesh the SAW device model and set a perfectly matched layer (PML) absorbing boundary around the model. Use the finite element method (FEM) to construct the model's stiffness matrix and mass matrix, and assemble them to obtain the system matrix equation. Based on the system matrix equation, obtain the system matrix of the SAW model.

4. The improved AWE fast frequency sweep method in the design of radio frequency acoustic filters according to claim 1, characterized in that, In step S2, the system matrix at the center frequency is solved. order and The Taylor expansion of order AWE is approximated by Pad, and the relative error and convergence region of adjacent order AWE expansions are calculated. Specifically, it includes: Calculate the finite-order Taylor expansions of the matrix and vectors at the center frequency, substitute them into the system matrix equations, and rearrange to obtain the finite-order Taylor expansions of the solution vectors. Based on these Taylor expansions, calculate the admittance expression for the SAW resonator; then solve for the admittance expression. order and Taylor expansion of order and Pad approximation; by evaluation order and The relative error between the two is obtained by calculating the expansion of the asymptotic estimation of the first-order waveform near the center frequency. Then, the frequency window with the largest coverage and the relative error that meets the convergence accuracy is determined, and this frequency window is used as the convergence region.

5. An improved AWE fast frequency sweep method in the design of radio frequency acoustic filters according to claim 4, characterized in that, In step S3, adaptively searching for conductance error peaks within the convergence region specifically includes: Within the convergence region of the admittance, the relative error of the conductance is calculated. Frequency bands where the relative error of the conductance exceeds a preset threshold are identified as frequency bands with severe fluctuations. The frequency point with the largest error in the frequency band with severe fluctuations is taken as the conductance error peak. If the conductance error peak exists, the admittance value at the frequency point of the error peak is calculated first. Then, the Pad's rational interpolation algorithm is used to optimize the waveform asymptotic estimation expansion to improve accuracy. After completion, the convergence region is recalculated. If the conductance error peak does not exist, the subsequent steps are executed directly. Improving accuracy using the Pad rational interpolation algorithm specifically includes: using the frequency point of the conductance error peak as the interpolation point, constructing a rational fraction of Pad rational interpolation by combining the admittance value of the interpolation point, establishing a system of equations through moment matching conditions, solving the system of equations after supplementing the interpolation constraints to obtain the unknown coefficients of the rational fraction, and integrating the Pad rational interpolation into the current waveform asymptotic estimation expansion to complete the accuracy optimization of the expansion.

6. The improved AWE fast frequency sweep method in the design of radio frequency acoustic filters according to claim 5, characterized in that, In the rational fraction of the Pad-type rational interpolation, the order of the numerator polynomial and the denominator polynomial are the same as the order of the Taylor expansion. When supplementing the interpolation constraints, a corresponding number of equations are constructed according to the preset number of interpolation frequency points, so that the solution of the system of equations takes a unique solution, a minimum norm solution, or a least squares solution according to the relationship between the number of equations and the number of unknown coefficients. When performing Pad approximation on the Taylor expansion, the Pad approximation is expressed as a rational fraction of the numerator and denominator polynomials. A system of linear equations about the unknown coefficients of the rational fractions is established through the moment matching condition. The coefficients of the denominator polynomial are solved first, and then the coefficients of the numerator polynomial are solved by substituting them back to obtain the Pad approximation expansion.

7. An improved AWE fast frequency sweep method in the design of radio frequency acoustic filters according to claim 6, characterized in that, In step S4, steps S1 to S3 are iteratively executed on the unconverged frequency bands based on the adaptive window algorithm. The specific process is as follows: S41. Take the midpoint of the non-converged frequency band as the new expansion frequency, set the initial expansion order, solve the waveform asymptotic estimation expansion of the corresponding order and calculate the relative error of the expansion of adjacent orders to determine the new convergence region. S42. Determine whether the new convergence region completely covers the current non-converged frequency band. (a) If not, increase the expansion order and solve the expansion again, calculate the relative error and determine the region of convergence. If the expansion order reaches the preset maximum order, directly execute step S43. (b) If so, proceed directly to step S43; S43. If there are still some areas in the current non-converged frequency band that are not covered by the convergence domain, treat the uncovered area as a new non-converged frequency band and repeat steps S41 to S43 until all areas of the entire frequency band are covered by the convergence domain and the convergence accuracy is met.

8. An improved AWE fast frequency sweep system for radio frequency acoustic filter design, characterized in that, The improved AWE fast frequency sweep method according to any one of claims 1-7 specifically includes: The model building module is used to build a SAW device model of the radio frequency acoustic filter, configure model parameters and perform mesh generation, set the absorption boundary of the perfectly matched layer, construct the stiffness matrix and mass matrix using the finite element method and assemble them to obtain the system matrix, and perform LU decomposition on the system matrix at the center frequency of the swept frequency band. The expansion and convergence region calculation module is used to solve the admittance expression for SAW resonators. order and The Taylor expansion of the order is approximated by Pad, and the relative error of the expansion of the asymptotic estimation of the waveform of adjacent order is calculated and the region of convergence is determined. The peak optimization module is used to adaptively find conductance error peaks within the convergence region. If an error peak exists, its admittance value is calculated, and the waveform asymptotic estimation expansion is optimized by Pad's rational interpolation algorithm and the convergence region is recalculated. The iterative convergence module is used to iteratively process the unconverged frequency band using the model construction module, the expansion and convergence domain calculation module, and the peak optimization module based on the adaptive window algorithm until the entire frequency band meets the convergence accuracy.

9. A computing device, characterized in that, include: One or more processors; A storage device for storing one or more programs, which, when executed by one or more processors, cause the one or more processors to implement the improved AWE fast frequency sweep method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program that, when executed by a processor, implements the improved AWE fast frequency sweep method as described in any one of claims 1-7.

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