Method for Determining Filter Parameters Based on Filter Synthesis and Cubic Spline Interpolation

Abstract

The present invention proposes a method for determining filter parameters based on filter synthesis and cubic spline interpolation, which mainly solves the problem of low efficiency in solving the electromagnetic parameters of filters in the prior art. The solution is as follows: select the geometric model of the filter, set its material and boundary conditions, and generate tetrahedral meshes; use the finite element method to determine the magnitude of the reflection coefficient of the first port at all frequency points of the filter; use the filter synthesis method to determine the Chebyshev polynomial and use it to determine the frequency points at the resonances of the filter; use cubic spline interpolation to determine the real and imaginary parts of the S-parameters at each frequency point of the filter, and determine the magnitude, phase, and the real and imaginary parts, magnitudes, and phases of the Y-parameters and Z-parameters through their real and imaginary parts. The present invention combines filter synthesis and cubic spline interpolation, which can reduce the complexity and storage resources of solving the parameters one by one for multiple frequency points of the filter, improve the efficiency of determining the electromagnetic parameters of the filter, and can be used for determining the electromagnetic parameters of filters with any structure and shape.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless digital communication, and particularly relates to a method for determining filter parameters, which can be used to determine the electromagnetic parameters of filters with arbitrary structures and shapes. Background Art

[0002] In recent years, with the continuous increase in the electrical size and complexity of filters, determining the parameters of a single frequency point of a filter usually requires consuming huge computer and time resources. Taking a large number of sampling points in a wide frequency band to determine the parameters of the filter is often unacceptable for users. With the continuous development of computer technology, numerical calculation plays a crucial role in researching physical problems and simulating engineering and other fields. In the electromagnetic field, computational electromagnetics has become another important research tool after experiments and theoretical analysis. Existing computational electromagnetics methods can already solve electromagnetic simulation problems in many scientific and practical engineering and technical fields. In the finite element numerical method, the frequency-domain integral equation is widely used in solving the electromagnetic response of complex microwave devices due to its high solution accuracy and few unknowns. However, the problem of limited computer memory can never solve the filter model with a large electrical size. Obtaining the parameters of all frequency points of the filter by interpolation in a wide frequency band has been studied by more scholars.

[0003] He Shiquan et al. disclosed a method for solving the electromagnetic characteristics of wide-band targets in their published paper "Wide-band Electromagnetic Numerical Simulation Based on Robust Adaptive Frequency Sampling" (University of Electronic Science and Technology of China, Journal of Radio Science, 2014). The steps of this method are as follows: 1) Establish a geometric model of the radar target to be solved and perform mesh division on the geometric model; 2) Establish two groups of initial sampling sequences and solve the electromagnetic characteristics of the initial sampling sequences by the fast multipole method; 3) Use Stoer-Bilirsch interpolation to interpolate the two groups of sampling sequences respectively, calculate the relative error, and obtain the maximum error point and the maximum error; 4) Add the extreme points that are not sampling points and the maximum error points that do not meet the requirements in the interpolation sequence to the sampling sequence; 5) After bisecting and encrypting the interpolation region, continue to judge the convergence to achieve an increase in the number of samplings and the encryption of the interpolation interval. The deficiencies of this method are as follows: 1. For the characteristics of the radar target, only the interpolation processing of the variation characteristics of the radar cross section (RCS) with frequency is performed, and no rapid determination operation is performed on the parameters of the wide-band filter. 2. Since a relatively accurate unknown curve needs to be fitted with a large number of sampling points, if interpolation operations are performed on multiple curves one by one, it requires huge computational and storage resources. 3. It is sensitive to the selection of the interpolation interval and the convergence accuracy, and cannot well approximate some points with obvious zero depths, and is prone to pseudo-convergence. Summary of the Invention

[0004] The object of the present invention is to propose a method for determining filter parameters based on filter synthesis and cubic spline interpolation in view of the deficiencies in the above technologies, so as to avoid the pseudo-convergence situation in the process of determining filter parameters by determining the approximate resonance point position of the filter through filter synthesis, reduce the huge computing and storage resources required for solving each of multiple frequency points one by one, and improve the efficiency of determining the parameters of wideband filters.

[0005] The technical idea for realizing the object of the present invention is as follows: Utilizing the characteristics of the finite element method, filter design, and cubic spline interpolation method, sampling points are added one by one by means of sub-interval fitting, maximum value judgment, error judgment, extreme value judgment, and judgment of adjacent points on the left and right sides of the extreme value in the case where the port responses of all frequency points in the unknown wideband are not known; determining the electromagnetic parameters of the newly added sampling points of the filter through the finite element method; and reconstructing the electromagnetic response under the wideband with fewer sampling points by combining cubic spline interpolation and filter synthesis.

[0006] According to the above idea, the technical solution of the present invention is as follows:

[0007] (1) Select a filter with electromagnetic characteristics to be solved having a metal-dielectric hybrid structure, and perform geometric modeling on the selected structure according to the design dimensions of the selected structure and the continuity of the interfaces between different structures to obtain a geometric model corresponding to the design requirements.

[0008] (2) Mark the material properties corresponding to the actual design requirements of the filter with electromagnetic characteristics to be solved on each geometric body in the selected geometric model, and mark the excitation and boundary conditions corresponding to the actual design of the filter with electromagnetic characteristics on the specially treated geometric surfaces in the selected geometric model.

[0009] (3) Use a mesh generator to perform tetrahedral mesh division on the selected geometric model to generate a tetrahedral mesh of the selected structure.

[0010] (4) Determine the amplitude information of the reflection coefficient S11 of the first port of the filter at all frequency points:

[0011] (4a) Select two groups of initial sampling frequency points within the frequency domain to be solved, and solve the reflection coefficient of the first port of the initial sampling points by using the finite element method.

[0012] (4b) Determine the amplitude information of the reflection coefficient S11 of the first port of the filter at all frequency points through adaptive interpolation processing.

[0013] (4c) Determine the five parameters required for filter synthesis through the amplitude information of the reflection coefficient S11 of the first port, namely the center operating frequency P, bandwidth B, quality factor Q, filter order M, and return loss R.

[0014] (5) Solve the frequency points corresponding to the resonance of the filter.

[0015] (5a) Determine the Chebyshev polynomial F(ω) of the same order as the filter order according to the center operating frequency P, bandwidth B, quality factor Q, filter order M, and return loss R obtained in 4(c), where ω is the frequency point information of the filter, ω = (ω 1 , …, ω i , …, ω M ), where ω i is the i-th frequency point information of the filter, and F(ω) is the ideal value of the reflection coefficient at the first port of the filter;

[0016] (5b) Find the zeros of the Chebyshev polynomial F(ω), which are the frequency points corresponding to the resonances of the filter, and add the obtained frequency points to two groups of sampling sequences;

[0017] (6) Use the finite element method and cubic spline interpolation to determine the real part S r and imaginary part S i information of the S-parameters of the filter through methods such as maximum value judgment, error judgment, extreme value judgment, and judgment of adjacent points on the left and right sides of the extreme value;

[0018] (7) Solve the electromagnetic parameters of the filter using the real part Sr and imaginary part Si information of the S-parameters at all frequency points of the filter:

[0019] (7a) Solve the magnitude S m and phase S a information of the S-parameters of the filter;

[0020] (7b) Solve the real part Y r , imaginary part Y i , magnitude Y m , and phase Y a information of the Y-parameters of the filter;

[0021] (7c) Solve the real part Z r , imaginary part Z i , magnitude Z m , and phase Z a information of the Z-parameters of the filter.

[0022] Compared with the prior art, the present invention has the following advantages:

[0023] 1. Since the present invention uses the method of filter synthesis to determine the frequency points corresponding to the resonances of the filter, and determines the real part S r and imaginary part S iInformation, thus only a small number of frequency points of the filter need to be calculated to fit the information of all frequency points, overcoming the problem in the prior art that the electromagnetic parameter information of all frequency points needs to be calculated, significantly reducing the time required to determine the electromagnetic parameters of the filter, and improving the efficiency of solving the electromagnetic parameters of the filter.

[0024] 2. Since the present invention adaptively interpolates the real part and the imaginary part of the S-parameters in sequence, information such as the amplitude, phase, Y-parameters, and Z-parameters of the S-parameters can be obtained. Compared with the prior art where only the amplitude of the S-parameters can be obtained, the present invention can meet the requirements of actual engineering.

[0025] 3. Since the present invention judges the adjacent points on the left and right sides of the extreme value, some points with obvious zero depths can be well approximated, overcoming the problem in the prior art that due to pseudo-convergence, some points with obvious zero depths cannot be well fitted. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is the overall flowchart for implementing the present invention;

[0027] Figure 2 is the model diagram of the filter to be solved in the present invention;

[0028] Figure 3 is the schematic diagram of the materials, boundary conditions, and excitation settings of the filter to be solved in the present invention;

[0029] Figure 4 is the schematic diagram of the tetrahedral mesh generation of the filter model to be solved in the present invention;

[0030] Figure 5 is the comparison diagram of the results of calculating the electromagnetic parameters of the filter using the finite element method combined with the cubic spline interpolation method in the present invention and the existing finite element method respectively. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0031] The embodiments and effects of the present invention will be further described in detail below with reference to the accompanying drawings.

[0032] Refer to Figure 1 , this example is a method for determining filter parameters based on filter synthesis and cubic spline interpolation, including the determination of the S-parameters, Y-parameters, and Z-parameters of the filter. The specific implementation steps are as follows:

[0033] Step 1, construct a geometric model of the filter.

[0034] Select a filter with a metal-dielectric hybrid structure whose electromagnetic characteristics are to be solved. According to the design dimensions of the selected structure and the continuity of the interfaces between different structures, geometric modeling is performed on the selected structure to obtain a geometric model corresponding to the design requirements, such as Figure 2As shown. An irregular geometric concave body is the cavity structure of the filter, and the cylinder is the coaxial structure for propagating electromagnetic waves.

[0035] Step 2: Set the filter material, boundary conditions, and excitation attributes.

[0036] Mark the material attributes corresponding to the actual design requirements of the filter for which the electromagnetic characteristics are to be solved on each geometric body in the selected geometric model, and mark the boundary conditions corresponding to the actual design of the filter for which the electromagnetic characteristics are to be solved on the geometric surfaces that should be specially treated, such as Figure 3 As shown, where mark 1 represents a homogeneous dielectric material, mark 2 represents that the coaxial inner core is an ideal electric conductor material, mark 3 represents that the two coaxial bottom surfaces are excited by coaxial wave ports, and mark 4 represents that the outermost side of the geometric structure is the Prefect E boundary condition.

[0037] Step 3: Perform tetrahedral mesh division on the selected geometric model to generate a tetrahedral mesh.

[0038] For Figure 2 different material regions of the cavity filter geometric model shown, different treatments are carried out, that is, the region where the dielectric structure of the geometric model is located is filled with tetrahedrons, and the region of the ideal electric conductor structure of the geometric model is not filled with regions to generate a tetrahedral mesh, such as Figure 4 As shown. The size of this tetrahedral mesh is determined according to the severity of the filter current change. The more severe the current change, the smaller the mesh division size, and vice versa, the larger the mesh division size.

[0039] Step 4: Use the finite element method to determine the amplitude information of the first-port reflection coefficient S11 at the initial sampling frequency.

[0040] 4.1) Select two groups of initial sampling frequency sequences d1 and d2:

[0041] d 1 =(Fmax - Fmin) / (n - 1),

[0042] d 2 =(Fmax - Fmin) / (2n - 1),

[0043] where Fmin is the minimum frequency within the wide frequency band of the filter, Fmax is the maximum frequency within the wide frequency band of the filter, and n is the number of sampling points in the first group of sampling sequences;

[0044] 4.2) Create an em file to store the filter frequency information, input the two groups of initial sampling sequences d1 and d2 into the em file in sequence, read the em file and solve it by the finite element method, and respectively output the real part, imaginary part, and amplitude information of the first-port reflection coefficient S11 and transmission coefficient S21 of these two groups of initial sampling sequences.

[0045] Step 5: Determine the amplitude information of the first-port reflection coefficient S11 at all frequency points of the filter using adaptive interpolation.

[0046] 5.1) Determine two groups of interpolation sampling frequency sequences d3 and d4:

[0047] d3 = (Fmax - Fmin) / (N - 1),

[0048] d4 = (Fmax - Fmin) / (N - 1),

[0049] where N is the number of sampling points of the interpolation sampling sequence, Fmin is the minimum frequency within the wide frequency band of the filter, and Fmax is the maximum frequency within the wide frequency band of the filter;

[0050] 5.2) Use piecewise fitting of cubic spline interpolation to determine the amplitude information of the first-port reflection coefficient S11 of the first group of interpolation sampling sequence d3 from the first group of initial sampling sequence d1;

[0051] 5.3) Use piecewise fitting of cubic spline interpolation to determine the amplitude information of the first-port reflection coefficient S11 of the second group of interpolation sampling sequence d4 from the second group of initial sampling sequence d2;

[0052] 5.4) Determine whether the frequency points corresponding to the minimum and maximum values of the amplitude information of the first-port reflection coefficient S11 of the second group of interpolation sampling sequence d4 exist in the two groups of sampling sequences d1 and d2:

[0053] If not, add the corresponding frequency points to the two groups of initial sampling sequences d1 and d2;

[0054] If so, execute 5.5);

[0055] 5.5) Calculate the relative error e between the two groups of interpolation sampling sequences d3 and d4:

[0056]

[0057] where R n represents the amplitude information of the first-port reflection coefficient S11 of the first group of interpolation sampling sequence d3, and R 2n represents the amplitude information of the first-port reflection coefficient S11 of the second group of interpolation sampling sequence d4;

[0058] 5.6) Set the error threshold ε to 0.4 and determine whether e < ε holds:

[0059] If not, add the frequency point corresponding to the maximum relative error reflection coefficient amplitude information to the two groups of initial sampling sequences d1 and d2;

[0060] If it holds, then execute 5.7);

[0061] 5.7) Determine whether the extreme value of the magnitude information of the first-port reflection coefficient S11 of the second interpolation sampling sequence d4 and the frequency points corresponding to the adjacent points on the left and right sides of the extreme value already exist in the two sampling sequences d1 and d2:

[0062] If not, add the corresponding frequency points to the two initial sampling sequences d1 and d2;

[0063] If so, execute 5.8);

[0064] 5.8) Use piecewise fitting by cubic spline interpolation for the second initial sampling sequence d2 to determine the magnitude information of the first-port reflection coefficient S11 of the second interpolation sampling sequence d4.

[0065] Step 6, determine the parameters required for filter synthesis.

[0066] There are 5 parameters required for filter synthesis, and the specific determination methods are as follows:

[0067] 6.1) Determine the center operating frequency P according to the filter frequency information:

[0068] P = (Fmin + Fmax) / 2

[0069] where Fmin is the minimum frequency within the wide frequency band of the filter, and Fmax is the maximum frequency within the wide frequency band of the filter;

[0070] 6.2) Determine the bandwidth B according to the magnitude information of the first-port reflection coefficient S11 of the second interpolation sampling sequence d4:

[0071] B = F2 -3dB -F1 -3dB

[0072] where F2 -3dB is the frequency corresponding to the -3dB magnitude information closest to Fmax, and F1 -3dB is the frequency corresponding to the -3dB magnitude information closest to Fmin;

[0073] 6.3) Determine the filter order M according to the number of minimum points within the frequency range where the bandwidth B is located for the filter;

[0074] 6.4) Determine the return loss R according to the magnitude information of the first-port reflection coefficient S11 corresponding to the maximum value within the frequency range where the bandwidth B is located for the filter;

[0075] 6.5) Determine the quality factor Q, which characterizes the ability of the filter to filter out interference signals, and its value ranges from 5000 to 10000.

[0076] Step 7, determine the Chebyshev polynomial F(ω) equivalent to the filter order.

[0077] 7.1) Define the first characteristic polynomial:

[0078]

[0079] where ω is the frequency point information of the filter, ω = (ω 1 , …, ω i , …, ω M ), where ω i is the i-th frequency point information of the filter, i = 1...M, and M is the filter order;

[0080] 7.2) Define the first recurrence polynomial:

[0081]

[0082] 7.3) Define the recurrence relations of M characteristic polynomials U M (ω) and M recurrence polynomials V M (ω), and M - 1 characteristic polynomials U M-1 (ω) and M - 1 recurrence polynomials V M-1 (ω):

[0083]

[0084]

[0085] 7.4) Recursively calculate the first characteristic polynomial U 1 (ω) and the first recurrence polynomial V 1 (ω) M times to obtain M characteristic polynomials U M (ω) and M recurrence polynomials V M (ω);

[0086] 7.5) Use the M characteristic polynomials U M (ω) as the Chebyshev polynomial: F(ω) = U M (ω).

[0087] Step 8, use the finite element method and cubic spline interpolation to determine the real and imaginary part information of the first port reflection coefficient S11 and the second port transmission coefficient S21 of the filter S-parameters through the methods of maximum value judgment, error judgment, extreme value judgment, and judgment of adjacent points on the left and right sides of the extreme value, respectively.

[0088] 8.1) Let F(ω) = 0, solve for the corresponding angular frequency ω, obtain the zeros of the Chebyshev polynomial F(ω), and add the obtained zeros to two groups of initial sampling sequences d1 and d2;

[0089] 8.2) Use the piecewise fitting of cubic spline interpolation for the first group of initial sampling sequences d1 to respectively determine the real and imaginary part information of the first port reflection coefficient S11 and the second port transmission coefficient S21 of the first group of interpolated sampling sequences d3;

[0090] 8.3) Use the piecewise fitting of cubic spline interpolation for the second group of initial sampling sequences d2 to respectively determine the real and imaginary part information of the first port reflection coefficient S11 and the second port transmission coefficient S21 of the second group of interpolated sampling sequences d4;

[0091] 8.4) Respectively determine whether the frequency points corresponding to the minimum and maximum values of the real and imaginary part information of the first port reflection coefficient S11 and the second port transmission coefficient S21 of the second group of interpolated sampling sequences d4 exist in the two groups of initial sampling sequences d1 and d2:

[0092] If not, add the corresponding frequency points to the two groups of initial sampling sequences d1 and d2;

[0093] If so, execute 8.5);

[0094] 8.5) Calculate the relative error e between the two groups of interpolated sampling sequences d3 and d4:

[0095] e = |(R n - R 2n ) / R 2n |

[0096] where, R n represents the real and imaginary part information of the first port reflection coefficient S11 and the second port transmission coefficient S21 of the first group of interpolated sampling sequences d3, and R 2n represents the real and imaginary part information of the first port reflection coefficient S11 and the second port transmission coefficient S21 of the second group of interpolated sampling sequences d4;

[0097] 8.6) Set the error threshold ε to 0.04 and determine whether e < ε holds:

[0098] If not, add the frequency points corresponding to the real and imaginary part information of the first port reflection coefficient S11 and the second port transmission coefficient S21 with the maximum relative error to the two groups of initial sampling sequences d1 and d2;

[0099] If so, execute 8.7);

[0100] 8.7) Respectively determine whether the extreme values of the real and imaginary part information of the first port reflection coefficient S11 and the second port transmission coefficient S21 of the second group of interpolated sampling sequences d4 and the frequency points corresponding to the adjacent points on the left and right sides of the extreme values exist in the two groups of initial sampling sequences d1 and d2:

[0101] If it does not exist, add the corresponding frequency point to the two groups of initial sampling sequences d1 and d2;

[0102] If it exists, execute 8.8);

[0103] 8.8) Use piecewise fitting of cubic spline interpolation for the second group of initial sampling sequences d2 to respectively determine the real part S of the first-port reflection coefficient S11 and the second-port transmission coefficient S21 of the second group of interpolated sampling sequences d4 r and the imaginary part information S i .

[0104] Step 9, solve for the magnitude S m and phase S a information of the filter S-parameters according to the real and imaginary part information of the first-port reflection coefficient S11 and the second-port transmission coefficient S21. The formulas are as follows:

[0105]

[0106] S a = arctan(S r / S i )

[0107] where S r is the real part information of the filter S-parameters, and S i is the imaginary part information of the filter S-parameters.

[0108] Step 10, solve for the real part Y r and imaginary part Y i , magnitude Y m and phase Y a information of the filter Y-parameters.

[0109] 10.1) According to the characteristic impedance matrix Z 0 of the filter ports, the characteristic admittance matrix G of the filter ports, and the unit diagonal matrix E, solve for the real part Y r and imaginary part Y i of the filter Y-parameters:

[0110] Y r = Re[G -1 ·(S·Z 0 + Z 0 * ) -1 ·(E - S)·G]

[0111] Y i = Im[G -1 ·(S·Z 0 + Z 0 * )-1 ·(E - S)·G]

[0112] Among them, S represents the S-parameters of the filter, which include the real and imaginary part information of the reflection coefficient S11 at the first port and the transmission coefficient S21 at the second port;

[0113] 10.2) Solve for its magnitude Y r and phase Y i from the real part Y m and imaginary part Y a of the filter Y-parameters:

[0114]

[0115] Y a = arctan(Y r / Y i ).

[0116] Step 11, solve for the real part Z r , imaginary part Z i , magnitude Z m , and phase Z a information of the filter Z-parameters.

[0117] 11.1) Solve for the real part Z 0 and imaginary part Z r of the filter Z-parameters according to the characteristic impedance matrix Z i at the filter ports, the characteristic admittance matrix G at the filter ports, the identity diagonal matrix E, and the S-parameters:

[0118] Z r = Re[G -1 ·(E - S) -1 ·(S·Z 0 + Z 0 * )·G]

[0119] Z i = Im[G -1 ·(E - S) -1 ·(S·Z 0 + Z 0 * )·G]

[0120] 11.2) Solve for its magnitude Z r and phase Z i from the real part Z m and imaginary part Z a of the filter Z-parameters:

[0121]

[0122] Za = arctan(Z r / Z i ).

[0123] The technical effects of the present invention are further described through simulation experiments as follows:

[0124] 1. Simulation experiment conditions:

[0125] The hardware platform for the simulation experiment of the present invention is: a 32-core Intel(R) Xeon(R) Gold 5215 CPU with a main frequency of 2.50 GHz and 1 TB of memory.

[0126] The software platform for the simulation experiment of the present invention is: Windows 10 operating system and Visual Studio 2017.

[0127] The filter selected for the simulation experiment of the present invention is Figure 2 the cavity filter shown in the figure. The relative dielectric constant of the dielectric material is 20.79, the frequency sweep range is 2.2 - 3.0 GHz, and the number of frequency sweep points is 401.

[0128] 2. Simulation content and result analysis:

[0129] In Simulation 1, the electromagnetic parameters of the cavity filter model are calculated using the method of the present invention and the existing finite element method respectively. The results are as Figure 2 shown in the figure. Among them: Figure 5

[0130] Figure 5 (a) is a comparison chart of the real part information of the S parameters of the cavity filter calculated using the method of the present invention and the existing finite element method respectively;

[0131] Figure 5 (b) is a comparison chart of the imaginary part information of the S parameters of the cavity filter calculated using the method of the present invention and the existing finite element method respectively;

[0132] Figure 5 (c) is a comparison chart of the amplitude information of the S parameters of the cavity filter calculated using the method of the present invention and the existing finite element method respectively;

[0133] Figure 5 (d) is a comparison chart of the phase information of the S parameters of the cavity filter calculated using the method of the present invention and the existing finite element method respectively;

[0134] Figure 5 (e) is a comparison chart of the amplitude information of the Y parameters of the cavity filter calculated using the method of the present invention and the existing finite element method respectively;

[0135] Figure 5 (f) is a comparison chart of the amplitude information of the Z parameters of the cavity filter calculated using the method of the present invention and the existing finite element method respectively;​

[0136] From Figure 5 the comparison results, it can be seen that the calculation results of the method of the present invention are in good agreement with the calculation results of the existing finite element method, verifying the calculation accuracy of the present invention.

[0137] Simulation 2, respectively using the present invention and the existing finite element method for Figure 2 the cavity filter, under different theoretical solution frequency points, solve the required actual calculation points and calculation time, and the results are shown in Table 1:

[0138] Table 1 Comparison of frequencies and times calculated by the present invention and the existing method under different theoretical solution frequency points

[0139]

[0140] From the comparison data in Table 1, it can be seen that the present invention greatly reduces the number of calculation frequency points required to solve the filter compared with the prior art, significantly reduces the calculation time for solving the electromagnetic parameters of the filter, thereby improving the simulation efficiency of the filter.

[0141] The description of determining the electromagnetic parameters of the above cavity filter is for the convenience of those skilled in the art to understand and apply the technology of the present invention, and does not constitute any limitation to the present invention. Obviously, for those skilled in the art, filters of any structure can be replaced without creative labor. However, these replacements or improvements based on the disclosure of the present invention all fall within the protection scope of the present invention.

Claims

1. A method for determining filter parameters based on filter synthesis and cubic spline interpolation, characterized in that, it includes the following steps: (1) Select a filter with electromagnetic characteristics to be solved in a metal-dielectric hybrid structure. According to the design dimensions of the selected structure and the continuity of the interfaces between different structures, perform geometric modeling on the selected structure to obtain a geometric model corresponding to the design requirements; (2) Mark the material properties corresponding to the actual design requirements of the filter with electromagnetic characteristics to be solved on each geometric body in the selected geometric model, and mark the excitation and boundary conditions corresponding to the actual design of the filter with electromagnetic characteristics to be solved on the specially processed geometric surfaces in the selected geometric model; (3) Use a mesh generator to perform tetrahedral mesh division on the selected geometric model to generate a tetrahedral mesh of the selected structure; (4) Determine the amplitude information of the first-port reflection coefficient S11 at all frequency points of the filter: (4a) Select two groups of initial sampling frequency points within the frequency range to be solved, and use the finite element method to solve the reflection coefficient of the first port at the initial sampling points; (4b) Determine the amplitude information of the first-port reflection coefficient S11 at all frequency points of the filter through adaptive interpolation processing; (4c) Determine the five parameters required for filter synthesis, namely the center operating frequency P, bandwidth B, quality factor Q, filter order M, and return loss R, based on the amplitude information of the first-port reflection coefficient S11; (5) Solve the frequency points corresponding to the resonances of the filter: (5a) Determine the Chebyshev polynomial F(ω) equivalent to the filter order based on the center operating frequency P, bandwidth B, quality factor Q, filter order M, and return loss R obtained from 4(c), where ω is the frequency point information of the filter, ω = (ω 1 , …, ω i , …, ω M ), where ω i is the i-th frequency point information of the filter, and F(ω) is the ideal value of the reflection coefficient at the first port of the filter; (5b) Solve the zeros of the Chebyshev polynomial F(ω), which are the frequency points corresponding to the resonances of the filter, and add the obtained frequency points to the two groups of sampling sequences; (6) Determine the real part S r and the imaginary part S i of the filter S-parameters by means of the finite element method and cubic spline interpolation through maximum value judgment, error judgment, extreme value judgment, and judgment of adjacent points on the left and right sides of the extreme value; (7) Solve the electromagnetic parameters of the filter using the real part Sr and imaginary part Si information of the S parameters at all frequency points of the filter; (7a) Solve for the magnitude S of the filter S-parameters m and the phase S a information; (7b) Solve for the real part Y r and the imaginary part Y i , the magnitude Y m , and the phase Y a information; (7c) Solve for the real part $Z_{re}$ of the filter Z-parameter r , the imaginary part $Z_{im}$ i , the magnitude $Z_{mag}$ m , and the phase $Z_{phase}$ a information.

2. The method according to claim 1, characterized in that, in step (2), marking the material properties corresponding to the actual design requirements of the filter with electromagnetic characteristics to be solved on each geometric body in the selected geometric model is to set the main structure of the filter as a homogeneous dielectric material and set the coaxial inner core structure as an ideal conductor material.

3. The method according to claim 1, characterized in that, in step (2), marking the excitation and boundary conditions corresponding to the actual design of the filter with electromagnetic characteristics to be solved on the specially processed geometric surfaces in the selected geometric model is to set the two coaxial bottom surfaces as coaxial wave port excitations, and set the outermost side of the geometric structure and the inner and outer sides of the coaxial structure as PrefectE boundary conditions.

4. The method according to claim 1, characterized in that, in step (3), performing tetrahedral mesh division on the selected geometric model to generate a tetrahedral mesh of the selected structure is to perform different treatments on different material regions of the geometric model, that is, filling the region where the dielectric structure of the geometric model is located with tetrahedrons, and not filling the region of the ideal conductor structure of the geometric model, to generate a tetrahedral mesh of the selected filter structure.

5. The method according to claim 1, characterized in that, in step (4a), determining the amplitude information of the first-port reflection coefficient S11 at the initial sampling frequency using the finite element method is implemented as follows: (4a1) Select two groups of initial sampling frequency sequences d1 and d2: d 1 = (Fmax - Fmin) / (n - 1), d 2 = (Fmax - Fmin) / (2n - 1), Where, Fmin is the minimum frequency within the wide frequency band of the filter, Fmax is the maximum frequency within the wide frequency band of the filter, and n is the number of sampling points of the first group of sampling sequences; (4a2) Create an em file to store the filter frequency information, sequentially input the two groups of initial sampling sequences d1 and d2 into the em file, read the em file and solve it by the finite element method, and respectively output the real part, imaginary part, and amplitude information of the first port reflection coefficient S11 and transmission coefficient S21 of these two groups of initial sampling sequences.

6. The method according to claim 1, characterized in that, In step (4b), to determine the amplitude information of the first port reflection coefficient S11 of all frequency points of the filter by adaptive interpolation processing, it is implemented as follows: (4b1) Determine two groups of interpolation sampling frequency sequences d3 and d4: d3 = (Fmax - Fmin) / (N - 1), d4 = (Fmax - Fmin) / (N - 1), where, N is the number of sampling points of the interpolation sampling sequence, Fmin is the minimum frequency within the wide frequency band of the filter, and Fmax is the maximum frequency within the wide frequency band of the filter; (4b2) Use piecewise fitting of cubic spline interpolation for the first group of initial sampling sequences d1 to determine the amplitude information of the first port reflection coefficient S11 of the first group of interpolation sampling sequences d3; (4b3) Use piecewise fitting of cubic spline interpolation for the second group of initial sampling sequences d2 to determine the amplitude information of the first port reflection coefficient S11 of the second group of interpolation sampling sequences d4; (4b4) Determine whether the frequency points corresponding to the minimum and maximum values of the amplitude information of the first port reflection coefficient S11 of the second group of interpolation sampling sequences d4 exist in the two groups of sampling sequences d1 and d2: If not, add the corresponding frequency points to the two groups of initial sampling sequences d1 and d2; If so, execute (4b5); (4b5) Calculate the relative error e of the two groups of interpolation sampling sequences d3 and d4; e = |(R n - R 2n ) / R 2n | Among them, R n represents the amplitude information of the first port reflection coefficient S11 of the first group of interpolation sampling sequences d3, and R 2n represents the amplitude information of the first port reflection coefficient S11 of the second group of interpolation sampling sequences d4; (4b6) Set the error threshold ε to 0.4, and determine whether e < ε holds: If not, add the frequency point corresponding to the maximum relative error reflection coefficient amplitude information to the two groups of initial sampling sequences d1 and d2; If so, execute (4b7); (4b7) Determine whether the extreme values of the amplitude information of the first port reflection coefficient S11 of the second group of interpolation sampling sequences d4 and the frequency points corresponding to the adjacent points on the left and right sides of the extreme values exist in the two groups of sampling sequences d1 and d2: If not, add the corresponding frequency points to the two groups of initial sampling sequences d1 and d2; If so, execute (4b8); (4b8) Use piecewise fitting of cubic spline interpolation for the second group of initial sampling sequences d2 to determine the amplitude information of the first port reflection coefficient S11 of the second group of interpolation sampling sequences d4.

7. The method according to claim 1, characterized in that, In step (4c), to determine the 5 parameters required for filter synthesis by the amplitude information of the first port reflection coefficient S11 of the second group of interpolation sampling sequences d4, it is implemented as follows: Determine the center operating frequency: P = (Fmin + Fmax) / 2, where Fmin is the minimum frequency within the wide frequency band of the filter, and Fmax is the maximum frequency within the wide frequency band of the filter; Determine the bandwidth B: It is the frequency difference at -3 dB of the amplitude information of the first-port reflection coefficient S11 of the second set of interpolated sampling sequences d4; Determine the quality factor Q, which characterizes the ability of the filter to filter out interference signals, and its value ranges from 5000 to 10000; Determine the filter order M, which is the number of minimum points of the filter within the frequency range where the bandwidth B is located; Determine the return loss R, which is the amplitude information of the first-port reflection coefficient S11 corresponding to the maximum value within the frequency range where the bandwidth B is located.

8. The method according to claim 1, characterized in that, in step (5a), determining the Chebyshev polynomial F(ω) equivalent to the filter order is achieved as follows: (5a1) Define the first characteristic polynomial: (5a2) Define the first recursive polynomial: (5a3) Define M characteristic polynomials U M (ω) and M recursive polynomials V M (ω) and M - 1 characteristic polynomials U M-1 (ω) and M - 1 recursive polynomials V M-1 (ω) Recursive relation: (5a4) Through the first characteristic polynomial U 1 (ω) and the first recursive polynomial V 1 (ω), after recursively operating M times, M characteristic polynomials U M (ω) and M recursive polynomials V M (ω) are obtained, where M is the filter order; (5a5) Take the M-th characteristic polynomial U M (ω) as the Chebyshev polynomial: F(ω) = U M (ω).

9. The method according to claim 1, characterized in that, In step (6), the real part information S of the first-port reflection coefficient S11 of the filter S-parameters is determined by using the finite element method and cubic spline interpolation through maximum value judgment, error judgment, extreme value judgment, and judgment of adjacent points on the left and right sides of the extreme value r and the imaginary part information S i , which is implemented as follows: (6a1) Use piecewise fitting by cubic spline interpolation on the first set of initial sampling sequences d1 to respectively determine the real part information and imaginary part information of the first-port reflection coefficient S11 of the first set of interpolated sampling sequences d3; (6a2) Use piecewise fitting by cubic spline interpolation on the second set of initial sampling sequences d2 to respectively determine the real part information and imaginary part information of the first-port reflection coefficient S11 of the second set of interpolated sampling sequences d4; (6a3) Determine whether the frequency points corresponding to the minimum and maximum values of the real and imaginary parts S of the reflection coefficient S11 of the first port of the second group of interpolation sampling sequences d4 exist in the two groups of sampling sequences d1 and d2 respectively: i ​ If not, add the corresponding frequency points to the two sets of initial sampling sequences d1 and d2; If so, execute (6a4); (6a4) Calculate the relative error e between the two sets of interpolated sampling sequences d3 and d4: e = |(R n - R 2n ) / R 2n | Among them, R n represents the real part information and the imaginary part information S of the first port reflection coefficient S11 of the first group of interpolation sampling sequences d3 i , R 2n represents the real part information and the imaginary part information S of the first port reflection coefficient S11 of the second group of interpolation sampling sequences d4 i ; (6a5) Set the error threshold ε to 0.04 and determine whether e < ε holds: If it does not hold, the real part information of the maximum relative error reflection coefficient S11 and the imaginary part information S i The corresponding frequency points are added to the two groups of initial sampling sequences d1 and d2; If it holds, execute (6a6); (6a6) Respectively determine whether the extreme values of the real part information and imaginary part information of the first-port reflection coefficient S11 of the second set of interpolated sampling sequences d4 and the frequency points corresponding to the adjacent points on the left and right sides of the extreme values exist in the two sets of sampling sequences d1 and d2: If not, add the corresponding frequency points to the two sets of initial sampling sequences d1 and d2; If so, execute (6a7); (6a7) Use interval fitting by cubic spline interpolation for the second group of initial sampling sequences d2 to respectively determine the real part information S of the reflection coefficient S11 at the first port of the second group of interpolated sampling sequences d4 r and the imaginary part information S i .

10. The method according to claim 1, characterized in that, Solve for the magnitude S and phase S of the filter S-parameters in step (7a), the formula is as follows: m and phase S a information, the formula is as follows: S a = arctan(S r / S i ) Among them, S r is the real part information of the reflection coefficient S11 of the first port of the filter S-parameters, and S i is the imaginary part information of the reflection coefficient S11 of the first port of the filter S-parameters.

11. The method according to claim 1, characterized in that, In step (7b), for the real part Y of the solution filter Y parameter r , the imaginary part Y i , the amplitude Y m , the phase Y a information, the implementation is as follows: (7b1) Solve for the real part Y r and the imaginary part Y i of the filter Y-parameters. The formula is as follows: Y r = Re[G -1 ·(S·Z 0 + Z 0 * ) -1 ·(E - S)·G] Y i = Im[G -1 ·(S·Z 0 +Z 0 * ) -1 ·(E - S)·G] Among them, Z 0 is the characteristic impedance matrix of the filter ports, G is the characteristic admittance matrix of the filter ports, and E is the unit diagonal matrix; (7b2) Real part Y of the tool Y parameter r and imaginary part Y i Solve for its amplitude Y m and phase Y a : Y a = arctan(Y r / Y i ).

12. The method according to claim 1, characterized in that, Solving for the real part \(Z_{re}\), imaginary part \(Z_{im}\), magnitude \(Z_{mag}\), and phase \(Z_{phase}\) of the filter Z-parameters in step (7c) is achieved as follows: r imaginary part \(Z_{im}\) i magnitude \(Z_{mag}\) m phase \(Z_{phase}\) a information is as follows: (7c1) Solve for the real part $Z_{re}$ and the imaginary part $Z_{im}$ of the filter Z-parameters. The formulas are as follows: r and i respectively, and the formulas are as follows: Z r = Re[G -1 ·(E - S) -1 ·(S·Z 0 + Z 0 * )·G] Z i = Im[G -1 ·(E - S) -1 ·(S·Z 0 + Z 0 * )·G] Among them, Z 0 is the characteristic impedance matrix of the filter ports, G is the characteristic admittance matrix of the filter ports, and E is the unit diagonal matrix; (7c2) According to the real part $Z_{Re}$ of the Z-parameters of the filter r and the imaginary part $Z_{Im}$ i solve for its magnitude $Z_{Mag}$ m and phase $Z_{Phase}$ a : Z a = arctan(Z r / Z i ).

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