阅读说明：本技术 一种声波滤波器带通域直接综合设计方法 (Direct and comprehensive design method for band-pass domain of acoustic wave filter ) 是由 王亚宁 赵洪元 于 2021-06-29 设计创作，主要内容包括：本发明公开一种声波滤波器带通域直接综合设计方法,适合于任意阶数的对称和非对称拓扑结构,属于基本电气元件的技术领域。首先是将切比雪夫多项式由低通变换到带通,再根据带通域切比雪夫多项式推导出传输多项式、反射多项式和分母多项式,并计算输入阻抗和导纳,最后根据输入阻抗和导纳逐阶计算串联谐振器和并联谐振器BVD模型参数,得到声波滤波器设计参数和频率响应曲线,计算过程简洁明了且准确度高。(The invention discloses a direct and comprehensive design method for a band-pass domain of an acoustic wave filter, which is suitable for symmetrical and asymmetrical topological structures with any order and belongs to the technical field of basic electric elements. Firstly, transforming a Chebyshev polynomial from low pass to band pass, deducing a transmission polynomial, a reflection polynomial and a denominator polynomial according to the Chebyshev polynomial in a band pass domain, calculating input impedance and admittance, and finally calculating BVD model parameters of the series resonator and the parallel resonator step by step according to the input impedance and the admittance to obtain design parameters and a frequency response curve of the acoustic wave filter.)

1. A direct comprehensive design method for band-pass domain of acoustic wave filter is characterized in that,

determining the order and the topological structure of the filter according to the index requirement of the acoustic wave filter;

converting the low-pass domain Chebyshev function into a band-pass domain Chebyshev polynomial;

calculating a transmission polynomial and a reflection polynomial according to the zero position of the root band-pass filter and the band-pass domain Chebyshev polynomial, and constructing a denominator polynomial;

calculating the input impedance of the acoustic wave filter according to the transmission polynomial, the reflection polynomial and the denominator polynomial;

extracting BVD model parameters step by step according to the input impedance and the input admittance of the acoustic wave filter;

and simulating a frequency response curve of the acoustic wave filter according to the BVD model parameters obtained by step-by-step extraction.

2. The method according to claim 1, wherein the acoustic filter index requirements include order, center frequency, bandwidth, return loss, and out-of-band zero position.

3. The method according to claim 1, wherein the band-pass domain direct synthesis design method is based on mapping relationship between low-pass and band-passConverting the low-pass domain Chebyshev function into a band-pass domain Chebyshev polynomial, wherein omega is the band-pass domain, omega is the frequency in the low-pass domain, and omega is the frequency in the low-pass domain_LAnd ω_HThe left side band and the right side band of the pass band, omega, of the low-pass domain of the acoustic wave filter respectively_cIs the center frequency of the low-pass domain of the acoustic filter,

4. the direct and comprehensive design method for the band-pass domain of the acoustic wave filter according to claim 3, wherein the band-pass domain chebyshev polynomial is:ω_nis the nth order zero of the band pass filter.

5. The method as claimed in claim 4, wherein the transmission polynomial and the reflection polynomial are based on band-pass domain chebyshev polynomial G (ω) andcalculating, P (omega) is a transmission polynomial, F (omega) is a reflection polynomialThen, a denominator polynomial E (omega) is constructed by using an alternating pole method according to the transmission polynomial and the reflection polynomial.

6. The method as claimed in claim 5, wherein the input impedance z of the acoustic wave filter is_in(ω) is:acoustic wave filter input admittance y_in(ω) is: y is_in(ω)＝1/z_in(ω)，S₁₁(ω) is the reflection coefficient of the filter, θ₁₁Is S₁₁The phase angle of (c).

7. The method according to claim 6, wherein the specific method for extracting BVD model parameters step by step according to input impedance and input admittance of the acoustic wave filter is as follows: for the acoustic wave filter with the first resonator in the equivalent circuit as the series resonator, repeating the step A and the step B from the step A until the iterative calculation of BVD model parameters of each order is completed; for the acoustic wave filter with the first resonator in the equivalent circuit as the parallel resonator, repeating the step B and the step A from the step B until the iterative calculation of BVD model parameters of each order is completed;

step A, according to the transmission zero point omega of the first series resonator₁Impedance z of acoustic wave filter_in(ω) is expressed as:z₁(omega) is equivalent input impedance from the input end position of the first parallel resonator, and L is obtained according to the equivalent impedance of the BVD model of the first series resonator_a1＝1/K₁，C_a1＝ω₁/K₁Then according to the equivalent input impedance z from the position of the input end of the first parallel resonator₁Transmission zero point omega of omega₂Determination of C₀₁＝imag(z_in(ω₂) Therein), wherein，L_a1、C_a1Is the dynamic inductance and capacitance C related to the machine in the BVD model of the first series resonator₀₁Is the static capacitance in the first series resonator BVD model;

step B, according to the transmission zero point omega of the first parallel resonator₂By introducing the input admittance y of the first parallel resonator₁(ω) is represented byy₂(ω) is from the second resonator circuit element C₀₂Obtaining L according to equivalent admittance of a BVD model of the first parallel resonator_a2＝1/K₂，C_a2＝ω₂/K₂Then according to the static capacitance C from the first parallel resonator BVD model₀₂Input admittance y equivalent to input edge position₂Transmission zero point omega of omega₃Determination of C₀₂＝imag(y₂(ω₃))，L_a2、C_a2The dynamic inductance and the dynamic capacitance related to the machine in the first parallel resonator BVD model.

Technical Field

The invention relates to a filter comprehensive design technology, in particular to a direct comprehensive design method for a band-pass domain of an acoustic wave filter, and belongs to the technical field of basic electrical elements.

Background

The rapid development of communication systems places increasingly higher demands on the size and performance of filters. The film bulk acoustic filter has the advantages of small volume, low insertion loss and high rectangular coefficient, and is widely applied to various communication systems, so that the key is how to design the film bulk acoustic filter efficiently and quickly.

At present, the research on the traditional filter synthesis methods such as cavity, medium, microstrip and the like is quite mature, but the synthesis research on the acoustic wave filter is less. AlfredGimenez et al proposed a Synthesis method of low-pass to band-pass Acoustic Wave Filters in an article "General Synthesis method for the Design of Acoustic Wave Filters and Duplexers" (Synthesis Design method of Acoustic Ladder Filters and Duplexers) in 2018, and the main Design idea is to make the series resonators and the parallel resonators equivalent to non-resonant nodes and give corresponding equivalent circuits, calculate equivalent circuit parameters based on Chebyshev Synthesis, convert the equivalent circuit parameters into low-pass BVD model circuit parameters, and finally convert into band-pass BVD (Butterworth-Van Dyke, Butterworth Vandyk) model circuit parameters, however, in this method, the reactance in the equivalent circuit corresponding to the non-resonant node is a non-frequency-varying element, so the Synthesis result is only near the center frequency f0 with high accuracy and has a large far-band difference. In 2017, IuliiaEvdokomova et al propose a method for directly synthesizing a band-Pass Domain Acoustic wave filter in the Synthesis of Ladder-Type Acoustic Filters in the band-Pass Domain (a band-Pass Domain Synthesis design method of a trapezoidal Acoustic wave filter), and the core of the method is to construct a Chebyshev function suitable for directly synthesizing the band-Pass Domain according to the characteristics of the filter.

In summary, the present invention is directed to a method for directly and comprehensively designing an acoustic wave filter in a band pass domain to meet the circuit parameter design requirements of any order symmetric and asymmetric topological structures.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provide a direct and comprehensive design method for a band-pass domain of an acoustic wave filter.

The invention adopts the following technical scheme for realizing the aim of the invention:

a method for synthesizing an acoustic wave filter specifically comprises the following steps:

(1) selecting filter topology, determining filter order N and passband frequency range [ omega ] according to filter indexes_L,ω_H]Outer zero position omega_n(N-1, 2, 3, …, N being the order of the filter), and return loss RL;

(2) chebyshev polynomial with low-pass domain synthesisAccording to the mapping relationAnd converting to a band pass domain to obtain a band pass domain Chebyshev polynomial:

(3) calculating a transmission polynomial P (omega), a reflection polynomial F (omega) and a denominator polynomial E (omega) according to the zero position of the band-pass filter and the band-pass domain Chebyshev polynomial G (omega) obtained in the step (2); further calculating the input impedance z of the acoustic wave filter_inAnd input admittance y_in；

(4) According to z_inAnd y_inBVD model parameters of the series resonators and the parallel resonators corresponding to the acoustic wave filter are directly calculated step by step, and the method provided by the invention is ensured to be suitable for the synthesis of any order of symmetrical and asymmetrical acoustic wave filters.

By adopting the technical scheme, the invention has the following beneficial effects: the method provided by the invention is directly integrated in a band-pass domain, so that the problem that the integration is only accurate in a narrow band due to the adoption of a non-frequency variable reactance in the low-pass integration process is avoided; the invention calculates the input impedance of the filter according to the transmission polynomial, the reflection polynomial and the denominator polynomial, and then calculates the BVD model parameters of each stage of the resonator step by step, thus the calculation method has the advantage that the method can be suitable for various symmetrical or asymmetrical filter topologies. The method provided by the invention has the advantages of concise and clear calculation process, high accuracy of the calculation result and wide application range.

Drawings

Fig. 1 is a flow chart of the band-pass domain direct synthesis design of the acoustic wave filter of the present invention.

Fig. 2 is an equivalent circuit diagram of a seventh-order acoustic wave filter according to an embodiment of the present invention.

Fig. 3 is an equivalent circuit diagram of an eighth-order acoustic wave filter according to an embodiment of the present invention.

Fig. 4 is a schematic diagram of a BVD circuit according to an embodiment of the present invention.

Fig. 5 is a frequency response curve of an acoustic wave filter according to a first embodiment of the present invention.

Fig. 6 is a frequency response curve of an acoustic wave filter according to a second embodiment of the present invention.

Detailed Description

The method for directly integrating the band pass domains of the acoustic wave filter is described in detail below with reference to the accompanying drawings.

The variable symbols used in the present invention are not limited to those used in the present invention. If other variable symbols are adopted to replace the variable symbols adopted in the direct synthesis method of the band-pass domain of the acoustic wave filter of the invention, the technical scheme of replacing other variable symbols is considered to fall into the protection scope of the invention.

The specification and drawings of the present invention illustratively describe specific embodiments of the present invention. The invention only considers the situation of lossless, fig. 1 is a flow chart of the direct synthesis method of the band-pass domain of the acoustic wave filter, which specifically comprises the following 6 steps.

Step 1) selecting filter order N and topological structure according to filter index requirements

FIG. 2 is a schematic diagram of a symmetrical topology, and FIG. 3 is a schematic diagram of an asymmetrical topology, which defines the pass band frequency range [ omega ] of the filter_L,ω_H]，ω_LAnd ω_HUpper and lower sidebands of the acoustic wave filter, respectively, the filter center frequencyPosition omega of out-of-band zero point_n(N is 1, 2, 3, …, N being the order of the filter), passband echo RL.

Step 2) converting the Chebyshev function from a low-pass domain to a band-pass domain

The chebyshev function is:

wherein the content of the first and second substances,in the formula, omega_n(N is 1, 2, 3, …, N) is the zero point for each order of the band pass filter transitions to the zero point for the low pass, and the function X is_n(Ω) satisfies the condition:

1) when Ω is Ω_nWhen, X_n(Ω) ± ∞, wherein Ω_nZero points of the finger band-pass filter are transformed to zero points corresponding to low pass;

2) in the pass band having X_n(±Ω_H)＝-X_n(±Ω_L) Is-1, wherein Ω_HAnd Ω_LTransforming the band pass filter passband boundary to a low pass value;

3) when the frequency satisfies the condition of omega ═ omega_HAnd Ω ═ Ω_LWhen 1 is not less than X_n(Ω)≥-1。

According to the mapping relationship between the low-pass domain and the band-pass domain,converting the Chebyshev function to obtain a band-pass-domain Chebyshev polynomial, comprising:

step 3) calculating transmission polynomial, reflection polynomial and denominator polynomial

According to the zero position of the band-pass filter(2) Corrected band-pass domain Chebyshev polynomialAnd calculating a transmission polynomial P (omega) and a reflection polynomial F (omega), and constructing a denominator polynomial E (omega) by using an alternating pole method.

Step 4) calculating the input impedance z of the filter_in

Calculating the input impedance z of the filter according to the transmission polynomial P (omega), the reflection polynomial F (omega) and the denominator polynomial E (omega)_in(omega) and input admittance y_in(ω)：

y_in(ω)＝1/z_in(ω)。

Wherein S is₁₁(ω) is the reflection coefficient of the filter, θ₁₁Represents S₁₁The phase angle of (c).

Step 5) according to the input impedance z_in(omega) and input admittance y_in(omega) recursively calculating BVD model parameters

5-a) first extract the relevant parameters of the first series resonator BVD model: according to the first series resonator at ω₁Has a transmission zero point, the filter can be input with an impedance z_in(ω) is expressed as:

wherein the content of the first and second substances,z₁and (ω) is the input impedance equivalent to the position of the input end of the second resonator, i.e. the input impedance of the second resonator.

According to fig. 4, the BVD model equivalent impedance of a single series resonator, resineries 1, may be represented by L_a1、C_a1、C₀₁Expressed as:then there are:

then at ω according to the series resonator 1₁Has a transmission zero point at which L can be obtained_a1＝1/K₁，C_a1＝ω₁/K₁. For circuit parameter C₀₁According to the remaining part z of the impedance₁(omega) at frequency omega₂There is a transmission zero, and the zero is located outside the right band of the filter, then C₀₁Is z_inAt ω₂The imaginary part of (i.e. C)₀₁＝imag(z_in(ω₂))。L_a1、C_a1Is dynamic inductance and dynamic capacitance related to the machine in the BVD model, C₀₁Static capacitance in the BVD model.

5-b) extracting relevant parameters of the BVD model of the first parallel resonator: according to parallel resonators in omega₂Has a transmission zero point, the input from the second resonator can be admittance y₁(ω) is expressed as:

wherein the content of the first and second substances,y₂(ω) is from the second resonator circuit element C₀₂The input end positions the equivalent input admittance, i.e. the input admittance of the third resonator.

According to FIG. 4, L_a2And C_a2Admittance of the series circuit beingThen there are:

according to the first parallel resonator at ω₂There is transmission zero point, L can be obtained_a2＝1/K₂，C_a2＝ω₂/K₂。

For circuit parameter C₀₂According to the remaining part y of the impedance₂At ω₃There is a transmission zero and this zero is located outside the left band of the filter. Then C is₀₂Is y₂At ω₃The imaginary part of (i.e. C)₀₂＝imag(y₂(ω₃))。

And repeating the steps a) and b) in the step 5) for the filter with the order greater than 2, so that the BVD model parameters of the series resonators and the parallel resonators with any order and any topology can be sequentially extracted.

Similarly, when the first resonator of the filter is a parallel resonator and the second resonator is a parallel resonator, the step b) and the step a) are exchanged, and the BVD model parameter of each resonator is calculated in a recursive mode in order.

Step 6) simulating to obtain a frequency response curve of the acoustic wave filter according to the extracted BVD parameter

The invention is further illustrated by the following specific examples of acoustic wave filter synthesis.

Example 1:

by adopting the topology shown in fig. 2, the order N of the filter is 7, the passband frequency range is [2402MHz, 2482MHz ], the out-of-band zero positions are [2510MHz, 2350MHz, 2525MHz, 2359MHz, 2525MHz, 2350MHz, 2510MHz ], and the return loss IL is 18 dB.

The transmission polynomial P (ω), the reflection polynomial F (ω), and the denominator polynomial E (ω) are calculated from the band-pass-domain chebyshev polynomial:

F(ω)＝ω⁷-0.508ω⁶+1.78ω⁵-0.81jω⁴+0.91ω³-0.34jω²+0.1163ω-0.0236j，

P(ω)＝ω⁷-0.798ω⁶+11.8ω⁵-11.04jω⁴+46.8322ω³-49.29jω²+61.75ω-71.524j，

E(ω)＝ω⁷+(1.958-0.508j)ω⁶+(3.699-1.011j)ω⁵+(4.04-1.82j)ω⁴+(3.569-1.921j)ω³+(2.1149-1.5558j)ω²+(0.848-0.803j)ω+(0.1602-j0.2385)。

further, the filter input impedance is calculated according to F (omega), P (omega) and E (omega)And then calculating BVD model parameters of each series-parallel resonator:

finally, the filter frequency response curves simulated according to the BVD model parameters in the table are shown in fig. 5.

Example 2:

by adopting the topological structure shown in fig. 3, the filter order N is 8, the passband frequency range is [2496MHz, 2690MHz ], the out-of-band zero positions are [2450MHz, 2750MHz, 2460MHz, 2740MHz, 2465MHz, 2745MHz, 2455MHz, and the return loss IL is 18 dB.

The transmission polynomial P (ω), the reflection polynomial F (ω), and the denominator polynomial E (ω) are calculated from the band-pass-domain chebyshev polynomial:

F(ω)＝ω⁹+0.724ω⁸-2.365jω⁷-1.6387jω⁶+1.8781ω⁵+1.2127jω⁴-0.5531ω³-0.3114jω²+0.042ω+0.0152，

P(ω)＝ω⁹+0.6432ω⁸-9.2767jω⁷-6.7157jω⁶+32.3605ω⁵+25.8206jω⁴-50.2854jω³-43.4729jω²+29.3552ω+27.1307，

E(ω)＝ω⁹+(1.0237-0.037j)ω⁸+(0.9425+0.128j)ω⁷+(0.739-0.265j)ω⁶+(0.326-0.427j)ω⁵+(0.246-0.426j)ω⁴+(0.658-0.268j)ω³+(0.868-0.141j)ω²+(1.012-0.019j)ω+(0.970-0.066j)。

further, the filter input impedance is calculated according to F (omega), P (omega) and E (omega)And then calculating BVD model parameters of each series-parallel resonator:

finally, the filter frequency response curves simulated according to the BVD model parameters in the table are shown in fig. 6.

The above description is only a preferred embodiment of the present invention and does not limit the present invention in any way. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.