A High-Flatness Filter Optimization Method Based on Lossy Filter Coupling Matrix Synthesis
By constructing the transmission and reflection functions of an Nth-order Chebyshev lossy filter in the complex frequency domain, solving the correlation polynomial, and optimizing the coupling matrix, the problems of passband flatness and loss in miniaturized filters are solved, and high-performance filter design is realized.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- UNIV OF ELECTRONICS SCI & TECH OF CHINA
- Filing Date
- 2026-03-05
- Publication Date
- 2026-06-02
AI Technical Summary
In the prior art, as the filter size decreases, the quality factor (Q) of the resonator decreases, leading to increased passband insertion loss, reduced passband flatness, and distortion of the transmitted signal. Furthermore, existing methods suffer from problems such as complex coupling topology, deteriorated return signal, and poor process compatibility.
By synthesizing lossy filters in the complex frequency domain, the transmission and reflection functions of an Nth-order Chebyshev lossy filter are constructed. The correlation polynomial is solved to construct the filter Y parameter matrix. The coupling matrix is then optimized using a gradient optimization method to obtain a filter coupling matrix with a highly flat response.
The design of miniaturized high-performance filters has been realized, which significantly improves passband flatness, reduces loss, improves signal transmission quality, and maintains out-of-band suppression.
Smart Images
Figure CN122137367A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of wireless communication technology, and particularly relates to a high-flatness filter optimization method based on lossy filter coupling matrix synthesis. Background Technology
[0002] Filters play a crucial role in most RF integrated front-end architectures, with miniaturized, high-performance filters gaining popularity in recent years. However, as filter size decreases, the quality factor (Q) of its resonator drops significantly. This reduction in Q not only increases passband insertion loss but also inevitably reduces passband flatness, leading to severe distortion of the transmitted signal.
[0003] Current design methods for flattened lossy filters include lossy synthesis, predistortion techniques, and non-uniform Q-factor techniques. Lossy synthesis methods result in filter losses primarily concentrated at the port resonators, and distributing losses through matrix rotation complicates the coupling topology. Predistortion techniques, by altering pole positions, severely degrade filter return. Non-uniform Q-factor techniques significantly increase filter losses, and due to the large Q-value differences between resonators, they are difficult to implement on a single fabrication process. Summary of the Invention
[0004] The purpose of this invention is to provide a high-flatness filter optimization method based on the synthesis of lossy filter coupling matrix. By synthesizing a filter coupling matrix that matches the actual circuit response of the lossy filter, gradient optimization is used to obtain a high-flatness lossy filter coupling matrix. This solves the technical problems of complex coupling topology, deteriorated return, increased loss, and process compatibility in existing methods for flattening lossy filters.
[0005] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:
[0006] A method for optimizing highly flat filters based on the synthesis of lossy filter coupling matrices, the method comprising the following steps:
[0007] Step S1: Perform lossy filter synthesis in the complex frequency domain to construct the transmission and reflection functions of the Nth-order Chebyshev lossy filter;
[0008] Step S2: Solve for the polynomials related to the reflection zeros, the transmission zeros, and the poles in the transmission and reflection functions of the Nth-order Chebyshev lossy filter.
[0009] Step S3: Construct the filter Y parameter matrix based on the polynomials related to the reflection zeros, the transmission zeros, and the poles, and finally obtain the lossy filter coupling matrix.
[0010] Step S4: Define the passband flatness of the lossy filter coupling matrix;
[0011] Step S5: Optimize the passband flatness of the lossy filter coupling matrix using gradient optimization to obtain a filter coupling matrix with a highly flat response;
[0012] Step S6: Map the physical structure parameters of the filter based on the high-flatness response filter coupling matrix to guide circuit design.
[0013] Furthermore, in step S1, the reflection and transfer functions of the constructed Nth-order Chebyshev lossy filter are expressed as follows:
[0014]
[0015] in, Indicates the transmission coefficient; Represents a polynomial related to the transmission zero; Represents a polynomial related to the poles; Indicates the reflection coefficient; Represents the polynomial related to the zero point of reflection; and All of these represent normalization constants; Represents a complex frequency variable; ; Represents the imaginary unit; Indicates angular frequency; This represents the dissipation factor.
[0016] Furthermore, in step S4, the passband flatness of the lossy filter coupling matrix is expressed as follows:
[0017]
[0018] Where F represents the passband flatness of the coupling matrix of the lossy filter; The passband of a filter is determined by its center frequency and relative bandwidth. Indicates the transmission coefficient. This indicates that the amplitude of the transmission coefficient is converted into an amplitude value in decibels. This indicates the maximum value of the decibel amplitude within the passband. This indicates the minimum decibel amplitude within the passband.
[0019] Furthermore, in step S5, the passband flatness of the lossy filter coupling matrix is optimized using the following cost function:
[0020]
[0021] in, and It is the frequency point at the edge of the filter's passband; This represents the angular frequency at the zero point of the filter's transmission. Indicates the passband of the filter; Indicates the number of transmission zeros. This represents the S-parameter response calculated from the initial coupling matrix of the lossy filter. and Represents the optimized S-parameter response, RL represents the target return loss, and F... t Indicates the flatness of the target passband.
[0022] Compared with the prior art, the present invention has the following beneficial technical effects:
[0023] 1) This invention proposes a lossy filter synthesis method, in which the lossy filter coupling matrix can accurately reflect the filtering response of the resonator under different Q values.
[0024] 2) Based on the lossy coupling matrix, this invention obtains a passband flat filter coupling matrix through gradient optimization. This coupling matrix can effectively guide the design of miniaturized high-performance filters. Attached Figure Description
[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0026] Figure 1 The characteristic polynomials E(s) and E'(s) of the filter in this invention are * Root distribution plot of (s).
[0027] Figure 2 This is the sixth-order filter topology of the present invention.
[0028] Figure 3 This paper compares the S-parameter responses of the filter with resonator Q=180 before and after optimization of the coupling matrix.
[0029] Figure 4 This paper presents a comparison of the S-parameter responses of the filter with resonator Q=50 before and after optimization of the coupling matrix in this invention.
[0030] Figure 5 The diagram shows the fabrication layout and physical sample of the filter with a resonator Q value of 180 according to the present invention.
[0031] Figure 6 The diagram shows the fabrication layout and physical sample of the filter with a resonator Q value of 50 according to the present invention.
[0032] Figure 7 The measured and simulated results of the initial matrix response, optimized matrix response, and S-parameters of a sixth-order filter with a resonator Q value of 180 are compared.
[0033] Figure 8 The measured and simulated results of the initial matrix response, optimized matrix response, and S-parameters of a sixth-order filter with a resonator Q value of 50 are compared. Detailed Implementation
[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0035] This invention proposes a method for optimizing highly flat filters based on the synthesis of lossy filter coupling matrices. The method includes the following steps:
[0036] Step S1: Perform lossy filter synthesis in the complex frequency domain to construct the transmission and reflection functions of the Nth-order Chebyshev lossy filter.
[0037] Complex frequency domain representation is , Represents a complex frequency variable; Represents the imaginary unit; Indicates angular frequency; This represents the dissipation factor. The dissipation factor is expressed as the quality factor of the resonator. The dissipation factor is calculated as follows:
[0038]
[0039] in, This represents the quality factor of the resonator. This indicates the relative bandwidth of the filter.
[0040] The reflection and transfer functions of the constructed Nth-order Chebyshev lossy filter are expressed as follows:
[0041]
[0042] in, Indicates the transmission coefficient; Represents a polynomial related to the transmission zero; Represents a polynomial related to the poles; Indicates the reflection coefficient; Represents the polynomial related to the zero point of reflection; and All of these represent normalization constants.
[0043] Step S2: Solve for the polynomials related to the reflection zeros, the transmission zeros, and the poles in the transmission and reflection functions of the Nth-order Chebyshev lossy filter.
[0044] Define the transmission zero of the filter as , Indicates the angular frequency at the transmission zero point; The polynomial representing the number of transmission zeros and related to reflection zeros. The root of represents the transmission zero of the filter, therefore It can be represented as:
[0045]
[0046] Since the filter response is a Chebyshev response, the Chebyshev function can be expressed as: , It is a constant. Let N be a Chebyshev polynomial; then We can obtain it through recursion.
[0047] For polynomials , square of amplitude The root cause and The root is composed of, express The complex conjugate, such as Figure 1 As shown, The root of Symmetry, due to The roots are strictly Herwitz type, therefore these are located in The roots of the left half-plane all belong to By selecting the root of the left half-plane, we can construct... Polynomial.
[0048] Step S3: Construct the filter Y parameter matrix based on the polynomials related to the reflection zeros, the transmission zeros, and the poles, and finally obtain the lossy filter coupling matrix.
[0049] First, define the Y parameter matrix as follows:
[0050]
[0051] in , , and For the numerator of the Y-parameter polynomial, The denominator of the Y-parameter polynomial can be obtained by... , and The calculation yielded:
[0052]
[0053] in, express The complex conjugate, express .
[0054] Simultaneously, by performing a partial fractional expansion on the polynomial of the Y-parameter matrix, we obtain the following equation:
[0055]
[0056] In this invention, when the number of filter zeros is less than the number of poles... = 0; The Y parameter matrix represents the eigenvalues of the polynomial; N represents the filter order. , , , Indicates the residue.
[0057] For a transverse network model of a lossy filter, its k-th first-order resonator can be represented as a capacitor (C). k ), a conductance (B) k ) and a resistor (R) k The equivalent circuit in parallel. Therefore, to meet the required Y-parameter matrix, the Y-parameter matrix of the lossy filter transverse network model can be calculated and partially expanded as follows:
[0058]
[0059] in, This indicates the coupling between the input port and the output port. This indicates the coupling between the input port and the k-th resonator. This indicates the coupling between the output port and the k-th resonator.
[0060] pass The circuit parameters of the transverse network model are combined with , , , and One-to-one correspondence yields:
[0061]
[0062] Using these formulas, the coupling matrix of a lossy filter with complex terms can be obtained:
[0063]
[0064] Step S4: Define the passband flatness of the lossy filter coupling matrix.
[0065] The passband flatness of the lossy filter coupling matrix defined in this invention is expressed as follows:
[0066]
[0067] Where F represents the passband flatness of the coupling matrix of the lossy filter; The passband of a filter is determined by its center frequency and relative bandwidth. Indicates the transmission coefficient. This indicates that the amplitude of the transmission coefficient is converted into an amplitude value in decibels. This indicates the maximum value of the decibel amplitude within the passband. This indicates the minimum decibel amplitude within the passband.
[0068] Step S5: Optimize the passband flatness of the lossy filter coupling matrix using gradient optimization to obtain a filter coupling matrix with a highly flat response.
[0069] The cost function used for optimization is as follows:
[0070]
[0071] in and It is the frequency point at the edge of the filter's passband. This represents the S-parameter response calculated from the initial coupling matrix of the lossy filter. and Represents the optimized S-parameter response, RL represents the target return loss, and F... t Indicates the flatness of the target passband.
[0072] This optimization method treats all coupling elements as optimization values and performs iterative optimization using the cost function to obtain a filter coupling matrix with a highly flat response.
[0073] Step S6: Map the physical structure parameters of the filter based on the high-flatness response filter coupling matrix to guide circuit design.
[0074] like Figure 2The diagram shows the sixth-order filter topology designed in this invention. Based on this topology, filters with resonator Q values of 180 and 50 are designed. For the sixth-order filter with a resonator Q value of 180, its center frequency is 0.95 GHz, relative bandwidth is 9.5%, and echo is 20 dB. Calculations show that the dissipation factor σ0 = -0.058, and the transmission zeros are located at (2.28j-0.058) and (-2.43j-0.058), respectively. The characteristic polynomials P(s), F(s), and E(s) of this filter are all obtained in the defined complex frequency domain s = jω-0.058. Subsequently, the initial coupling matrix of the lossy filter can be obtained according to the classical synthesis method. The passband flatness of the filter response of this initial coupling matrix is calculated to be 2.4 dB. This invention defines the target flatness of the filter as 1.2 dB, and the passband flat lossy filter coupling matrix can be obtained through gradient optimization.
[0075] For a sixth-order filter with a resonator Q value of 50, a center frequency of 0.95 GHz, a relative bandwidth of 11%, and an echo of 20 dB, calculations show that the dissipation factor σ0 = -0.18, and the transmission zeros are located at (2.67j - 0.18) and (-2j - 0.18), respectively. The characteristic polynomials P(s), F(s), and E(s) of this filter are all obtained in the defined complex frequency domain s = jω - 0.058. Subsequently, the initial coupling matrix of the lossy filter can be obtained according to the classical synthesis method. The passband flatness of the filter response of this initial coupling matrix is calculated to be 5.8 dB. This invention defines the target flatness of the filter as 3.2 dB, and the passband flat lossy filter coupling matrix can be obtained through gradient optimization.
[0076] Table 1 shows the filter coupling matrices before and after optimization for resonator Q values of 180 and 50, respectively:
[0077] Table 1. Initial and optimized coupling matrices for different resonator Q values.
[0078]
[0079] Figure 3 This shows a comparison of the S-parameter responses of a filter with a resonator Q value of 180 before and after optimization. Figure 4 The comparison of the S-parameter response of the filter before and after optimization with a resonator Q value of 50 is shown. It can be observed that the passband flatness of the filter is significantly improved before and after optimization, while the filter bandwidth and out-of-band rejection remain the same.
[0080] This invention is achieved using microstrip open-loop resonator technology, with Rogers 6010 substrate material and a thickness of 20 mil. Figure 5Images (a) and (b) show the fabrication layout and actual photograph of the filter with a resonator Q value of 180 in this invention, respectively. The filter consists of six open-circuit resonant rings, and the circuit dimensions are: l1 = 17.6 mm, l2 = 18.6 mm, l... s1 =7mm, l 6L =6mm, w=1.2mm, w1=9.6mm, w2 = 10.6 mm, w3=8.6mm, w4=8.5mm, w5=9.8mm, w6= 9.9mm, s1=1.1mm, s2 = 3.5 mm, s 12 =0.3mm, s 23 =0.5mm, s 13 =2.4mm, s 34 =0.3mm, s 45 =0.45mm, s 56 =0.35 mm, s 46 =0.5mm. Figure 6 Figures (a) and (b) show the fabrication layout of a filter with a resonator Q value of 50 in this invention. The filter consists of an open-circuit resonant ring with six series resistors. The circuit dimensions and resistance values are: l1 = 17.6 mm, l2 = 18.6 mm, l3 = 13.6 mm. s1 =7mm, l 6L =6mm, w=1.2mm, w1=9.6mm, w2 = 10.3 mm, w3=8.6mm,w4=8.5mm, w5=9.8mm, w6= 14mm, s1=1.1mm, s2 =2.5mm, s3=3.5mm, s 12 =0.4mm, s 23 =0.5mm, s 13 =1.6mm, s 34 =0.12mm, s 45 =0.3mm, s 56 = 0.4 mm, s 46 =0.8mm, R1=3Ω, R2=2Ω, R1=3Ω
[0081] Figure 7 The measured and simulated results of the initial matrix response, optimized matrix response, and S-parameters of a sixth-order filter with a resonator Q-value of 180 are compared. The measured center frequency is 0.95 GHz, the relative bandwidth is 9.5%, the passband return loss is better than 15 dB, and the minimum insertion loss is 2.48 dB. It can be seen that the passband flatness is significantly improved from 2.4 dB in the initial synthesized circuit model to 1.32 dB in the measured result, which verifies the effectiveness of the proposed method.
[0082] Figure 8 The measured and simulated results of the initial matrix response, optimized matrix response, and S-parameters of a sixth-order filter with a resonator Q value of 50 are compared. The measured center frequency is 0.96 GHz, the relative bandwidth is 9%, the passband return loss is better than 19 dB, and the minimum insertion loss is 7.26 dB. It can be seen that the passband flatness is significantly improved from 5.8 dB in the initial synthesized circuit model to 1.58 dB in the measured result, which further verifies the effectiveness of the proposed method.
[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for optimizing highly flat filters based on the synthesis of lossy filter coupling matrices, characterized in that, The method includes the following steps: Step S1: Perform lossy filter synthesis in the complex frequency domain to construct the transmission and reflection functions of the Nth-order Chebyshev lossy filter; Step S2: Solve for the polynomials related to the reflection zeros, the transmission zeros, and the poles in the transmission and reflection functions of the Nth-order Chebyshev lossy filter. Step S3: Construct the filter Y parameter matrix based on the polynomials related to the reflection zeros, the transmission zeros, and the poles, and finally obtain the lossy filter coupling matrix. Step S4: Define the passband flatness of the lossy filter coupling matrix; Step S5: Optimize the passband flatness of the lossy filter coupling matrix using gradient optimization to obtain a filter coupling matrix with a highly flat response; Step S6: Map the physical structure parameters of the filter based on the high-flatness response filter coupling matrix to guide circuit design.
2. The high-flatness filter optimization method based on lossy filter coupling matrix synthesis according to claim 1, characterized in that, In step S1, the reflection and transfer functions of the constructed Nth-order Chebyshev lossy filter are expressed as follows: in, Indicates the transmission coefficient; Represents a polynomial related to the transmission zero; Represents a polynomial related to the poles; Indicates the reflection coefficient; Represents the polynomial related to the zero point of reflection; and All of these represent normalization constants; Represents a complex frequency variable; ; Represents the imaginary unit; Indicates angular frequency; This represents the dissipation factor.
3. The high-flatness filter optimization method based on lossy filter coupling matrix synthesis according to claim 1, characterized in that, In step S4, the passband flatness of the lossy filter coupling matrix is expressed as follows: Where F represents the passband flatness of the coupling matrix of the lossy filter; The passband of a filter is determined by its center frequency and relative bandwidth. Indicates the transmission coefficient. This indicates that the amplitude of the transmission coefficient is converted into an amplitude value in decibels. This indicates the maximum value of the decibel amplitude within the passband. This indicates the minimum decibel amplitude within the passband.
4. The high-flatness filter optimization method based on lossy filter coupling matrix synthesis according to claim 1, characterized in that, In step S5, the passband flatness of the lossy filter coupling matrix is optimized using the following cost function: in, and It is the frequency point at the edge of the filter's passband; This represents the angular frequency at the zero point of the filter's transmission. Indicates the passband of the filter; Indicates the number of transmission zeros. This represents the S-parameter response calculated from the initial coupling matrix of the lossy filter. and Represents the optimized S-parameter response, RL represents the target return loss, and F... t Indicates the flatness of the target passband.