CN103151578A - Method for optimization design of cross-coupling band-pass filter and duplexer - Google Patents

Abstract

The invention provides a method for an optimization design of a cross-coupling band-pass filter and a duplexer. The method comprises the steps: firstly, carrying out improvement on the optimization design of a traditional band-pass filter, analyzing a performance index of the filter, building a topological structure model of a cross-coupling network, replacing a traditional low-pass prototyping method through a technology of frequency conversion, and giving a specific element value of a z domain. A simplest coupling matrix can be obtained through optimization, the cross-coupling band-pass filter and the duplexer which are compact in structure and provided with asymmetric ripple waves and plural transmission zeros can be obtained, the problems of overmuch resonance units and overlarge size due to that a direct coupling method is adopted to design the filter and the duplexer are effectively solved, and a passive filter can obtain a best filtering effect.

Description

A kind of cross-coupling band pass filter and duplexer Optimization Design

Technical field

The present invention relates to a kind of cross-couplings passive bandpass filters and duplexer Optimization Design.

Technical background

In the current communications field, undergoing an unusual development of various communication systems is rapid, and filter occupies an important position in communication equipment.Especially along with the development of large scale integrated circuit, require device miniaturization and functional diversities.Cross-coupled filter is compared with the cross-linked filter that do not have of equal performance, although in optimal design and make want relative complex some, have that resonant element is few, volume is little, lightweight advantage, thereby in certain field, very large advantage arranged.Seem extremely important for cross-couplings resonator filter and Multiplexer Theory research and practical application, and the filter that utilizes traditional optimal design method institute optimal design is faced with and has that resonant element is many, bulky problem, the present invention is mainly based on this point, adopt a new filter circuit cross coupling structure, the proportion converter technique has designed a kind of cross-couplings passive bandpass filters and duplexer optimal design algorithm.

In order to obtain best filter effect, draw the simplest coupling matrix by optimization, can obtain asymmetric ripple and multiple transmission zero band pass filter and the duplexer of waiting of compact conformation, effectively overcome and adopted direct coupling method institute's optimal design filter and the duplexer resonant element is too much, volume is excessive problem, can guarantee that passive filter obtains best filter effect.

Summary of the invention

the invention provides a kind of cross-couplings passive bandpass filters and duplexer Optimization Design, at first design improves the method to conventional band-pass filters, the performance index of analysis filter, set up the topological structure model of coupling network, method by frequency translation replaces traditional low-pass prototype method, and provide the concrete component value in z territory, draw the simplest coupling matrix by optimization, can obtain asymmetric ripple and multiple transmission zero band pass filter and the duplexer of waiting of compact conformation, employing direct coupling method institute's optimal design filter and duplexer resonant element have effectively been overcome too much, the problem that volume is excessive, can guarantee that passive filter obtains best filter effect.

The technical scheme concrete steps that the present invention proposes comprise:

The performance index of analysis filter are set up cross-couplings topology of networks model as shown in Figure 1;

Cross-coupled filter can be regarded as a two-port network as shown in Figure 2;

Its input admittance of equal value is;

$Y=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{T^{\left(i\right)}}{p+s{\mathrm{\λ}}_i}---\left(1\right)$

P=sL+1/sC wherein,

T ⁽ⁱ⁾Coupling matrix M=[M _ij] _{N * n}Characteristic value, T ⁽ⁱ⁾That the first row and last column from orthogonal matrix T obtains, T wherein ^tMT=Λ, Λ are diagonal matrix.

Can draw the admittance matrix in two terminal two-port network z territory by the Darlington program

$\hat{Y}\left(z\right)={\left[{\hat{y}}_{\mathrm{ij}}\left(z\right)\right]}_{2\×2}---\left(2\right)$

By decomposing rational polynominal

Can obtain

${\hat{y}}_{11}\left(z\right){\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">R</figure-callout>}}_1={\hat{y}}_{22}\left(z\right){\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">R</figure-callout>}}_2=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{C_{11}^{\left(i\right)}\sqrt{(1-z^2)({\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}1}^2{z}^2-{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}2}^2)}}{z^2-{\mathrm{\&sigma;}}_i^2}---\left(3\right)$

${\hat{y}}_{12}\left(z\right)\sqrt{R_1{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">R</figure-callout>}}_2}={\hat{y}}_{21}\left(z\right)\sqrt{R_1{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">R</figure-callout>}}_2}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{C_{12}^i\sqrt{(1-z^2)({\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}1}^2{z}^2-{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}2}^2)}}{z^2-{\mathrm{\&sigma;}}_i^2}---\left(4\right)$

R wherein ₁And R ₂Be respectively source internal resistance and load resistance.

The z territory admittance matrix Y (z) of equivalent circuit is

$Y\left(z\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{T^{\left(i\right)}\sqrt{(1-z^2)({\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}1}^2{z}^2-{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}2}^2)}}{[(1+{\mathrm{\&lambda;}}_i){\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}1}^2-{\mathrm{\&omega;}}_0^2]z^2-[(1+{\mathrm{\&lambda;}}_i){\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}2}^2-{\mathrm{\&omega;}}_0^2]}---\left(5\right)$

(3) (4) and the corresponding coefficient of (5) formula are compared, can draw the characteristic value of coupling matrix

${\mathrm{\&lambda;}}_i={\mathrm{\&omega;}}_0^2\frac{{\mathrm{\&sigma;}}_i^2-1}{{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}1}^2{\mathrm{\&sigma;}}_i^2-{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}2}^2}-1---\left(6\right)$

${\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">R</figure-callout>}}_1={\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">R</figure-callout>}}_2=R=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}[(1+{\mathrm{\&lambda;}}_i){\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}1}^2-{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}2}^2]C_{11}^i---\left(7\right)$

$T_{11}^{\left(i\right)}{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">R</figure-callout>}}_1=T_{22}^{\left(i\right)}{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">R</figure-callout>}}_2=[(1+{\mathrm{\&lambda;}}_i){\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}1}^2-{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}2}^2]C_{11}^i---\left(8\right)$

$T_{12}^{\left(i\right)}\sqrt{R_1{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">R</figure-callout>}}_2}=T_{21}^{\left(i\right)}\sqrt{R_1{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">R</figure-callout>}}_2}=[(1+{\mathrm{\&lambda;}}_i){\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}1}^2-{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HSA00000852078400011.png,HSA00000852078400013.png"\; state="\{\{state\}\}">p</figure-callout>}2}^2]C_{12}^i---\left(9\right)$

By T ⁽ⁱ⁾Can derive orthogonal matrix T, can obtain coupling matrix M and be

M＝TΛT ^t (10)

Wherein Δ is diagonal matrix, and its diagonal element is λ _i

Usually can not realize or unwanted coupling by containing in the resulting coupling matrix of said method, in order to eliminate these couplings, need to be to the coupling matrix simplification that circulates, this optimization is all feasible to different filter constructions.

Make that coupling matrix is M ₀, matrix can pass through the following formula conversion

$M_r=R_r\&CenterDot;M_{r-1}{R}_r^t---\left(11\right)$

R wherein _ii=R _jj=cos θ _r, R _ji=-R _ij=sin θ _r, (i, j ≠ 1, N), θ _rIt is the anglec of rotation

In order to solve above-mentioned optimization problem, use least square method, as f (P ₀) reach hour, can obtain best coupling matrix.

The cross-couplings resonator filter can be by electric capacity, and the equivalent circuit model that electric capacity and LC resonator consist of is as shown in Figure 2. in analysis below, suppose that all capacitor C of resonator are identical, simultaneously i resonator branch road inductance L _i=L+M _ii, wherein

M _iiThe self-induction of i resonator, ω ₀Resonance center frequeH, L, C draws with following formula

$C=\frac{\mathrm{\&Delta;\&omega;}}{{\mathrm{\&omega;}}_0^2},$ $L=\frac{1}{\mathrm{\&Delta;\&omega;}}=\frac{1}{{\mathrm{\&omega;}}_0^{2}C}---\left(12\right)$

Wherein Δ ω is the band pass filter bandwidth. by optimization method, obtain the coupling matrix M that simplifies most _ij, namely can obtain coupling factor K _ij

$K_{\mathrm{ij}}=\frac{M_{\mathrm{ij}}}{\sqrt{L_i{L}_j}},i,j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n,i\&NotEqual;j---\left(13\right)$

$L_{\mathrm{ij}}=\frac{L}{K_{\mathrm{ij}}}---\left(14\right)$

Suppose that inductance all in the resonator of filter is identical,

Can obtain coupling factor, with coupling matrix all elements M _ijBecome-M _ij, the performance of its filter is constant

$C_{\mathrm{Mij}}=\frac{1}{{\mathrm{\&omega;}}_0^2{M}_{\mathrm{ij}}}---\left(15\right)$

$K_{\mathrm{ij}}=\frac{C_{\mathrm{Mij}}}{\sqrt{(C_i+C_{\mathrm{Mij}})(C_j+C_{\mathrm{Mij}})}},i,j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n,i\&NotEqual;j---\left(16\right)$

C _ij＝K _ijC (17)

$C_i=C-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{C}_{\mathrm{ij}},i,j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;n,i\&NotEqual;j---\left(18\right)$

According to above-mentioned theory, the cross-couplings resonator filter of institute's optimal design is carried out parallel connection by matching capacitance or inductance, can obtain needed target duplexer.

Utilize said frequencies converter technique algorithm and formula, finally can determine institute's optimal design band pass filter and each component value of duplexer.

Technique effect of the present invention: the present invention proposes based on frequency transform techniques Design of Bandpass technical scheme, set up cross-couplings topology of networks model, can obtain more compact asymmetric ripple and multiple transmission zero band pass filter and the duplexer of waiting of structure, effectively overcome employing direct coupling method filter and the duplexer resonant element is many, the problem that volume is excessive, and the volume of circuit reaches minimum, can guarantee that passive filter obtains best filter effect.

Description of drawings

Fig. 1 is cross-coupled filter circuit topological structure figure after improving; Equivalence two port cross-couplings networks;

Fig. 2 is equivalent two port cross-couplings networks;

Fig. 3 is cross-coupled filter circuit theory diagrams in embodiment 1;

Fig. 4 is insertion loss and the return loss performance plot of cross-coupled filter in embodiment 1;

Fig. 5 is cross-couplings duplexer circuit schematic diagram in embodiment 2;

Fig. 6 is insertion loss and the return loss performance plot of cross-couplings duplexer in embodiment 2;

Embodiment

Embodiment 1:

Design cross capacitance coupled resonator filter, band is logical is 1703.4-1787.3MHz, its return loss is 20dB.

Utilize above-mentioned algorithm, designed cross-coupled filter as shown in Figure 3; Its insertion loss and return loss characteristic are as shown in Figure 4;

As can be seen from Figure 4, its band is logical is 1703.4-1787.3MHz, and its amplitude characteristic is good, and stopband attenuation is large, and designed filter satisfies index request fully;

Embodiment 2:

The design duplexer, its centre frequency is respectively 1747.5MHz, 1842.5MHz, its three dB bandwidth is 75MHz

Utilize above-mentioned algorithm, designed duplexer as shown in Figure 5; Its insertion loss and return loss characteristic are as shown in Figure 6;

As can be seen from Figure 6, designed duplexer, its amplitude characteristic is good, and stopband attenuation is large;

Oneself successfully is used for certain pulse receiver filter and duplexer, and through the modulation and demodulation of FSK, Output rusults is good.Use result to show that this device has good inhibition degree to receiver modulating pulse and noise level, effectively overcome and adopted direct coupling method filter and the duplexer resonant element is too much, volume is excessive problem, can guarantee that passive filter and duplexer obtain best filter effect.

Above-described embodiment is only for example of the present invention clearly is described, and be not to be restriction to embodiments of the present invention, for those of ordinary skill in the field, can also make other changes in different forms on the basis of the above description.

Claims (10)

1. a cross-couplings passive bandpass filters and duplexer Optimization Design, it is characterized in that: at first the method is that the conventional band-pass filters structure is improved, the performance index of analysis filter, set up cross-couplings topology of networks model, method by frequency translation replaces traditional low-pass prototype method, and provide the concrete component value in z territory, draw the simplest coupling matrix by optimization, can obtain asymmetric ripple and multiple transmission zero band pass filter and the duplexer of waiting of compact conformation, effectively overcome employing direct coupling method filter and the duplexer resonant element is too much, the problem that volume is excessive.

2. method according to claim 1, is characterized in that, cross-coupled filter can be regarded as a two-port network, and its input admittance of equal value is;

P=sL+1/sC wherein,

T ⁽ⁱ⁾Coupling matrix M=[M _ij] _{N * n}Characteristic value, T ⁽ⁱ⁾That the first row and last column from orthogonal matrix T obtains, T wherein ^tMT=Λ, Λ are diagonal matrix.

3. method according to claim 1, is characterized in that, can draw two terminal two-port networks by the Darlington program, the admittance matrix in z territory

。

4. method according to claim 1, is characterized in that, by decomposing rational polynominal Can obtain

R wherein ₁And R ₂Be respectively source internal resistance and load resistance.

5. method according to claim 1, is characterized in that, the z territory admittance matrix Y (z) of equivalent circuit is

(3), the corresponding coefficient of (4) and (5) formula are compared, can draw the characteristic value of coupling matrix

By T ⁽ⁱ⁾Can derive orthogonal matrix T, can obtain coupling matrix M and be

M＝TΛT ^t (10)

Wherein Δ is diagonal matrix, and its diagonal element is λ _i

6. method according to claim 1, is characterized in that, makes that coupling matrix is M ₀, matrix can pass through the following formula conversion

R wherein _ii=R _jj=cos θ _r, R _ji=-R _ij=sin θ _r, (i, j ≠ 1, N), θ _rIt is the anglec of rotation.

7. method according to claim 1, it is characterized in that, usually can not realize or unwanted coupling by containing in the resulting coupling matrix of said method, in order to eliminate these couplings, need to be to the coupling matrix simplification that circulates, this optimization is all feasible to different filter constructions.In order to solve above-mentioned optimization problem, use least square method, as f (P ₀) reach hour, can obtain best coupling matrix M.

8. method according to claim 1, is characterized in that, the cross-couplings resonator filter can be by electric capacity, the equivalent circuit model that electric capacity and LC resonator consist of.In analysis below, suppose that all capacitor C of resonator are identical, simultaneously i resonator branch road inductance L _i=L+M _ii, wherein

M _iiThe self-induction of i resonator, ω ₀Resonance center frequeH, L, C draws with following formula

Wherein Δ ω is the band pass filter bandwidth. by optimization method, obtain the coupling matrix M that simplifies most _ij, namely can obtain coupling factor K _ij

。

9. method according to claim 1, is characterized in that, supposes that inductance all in the resonator of filter is identical,

Can obtain coupling factor, with coupling matrix all elements M _ijBecome-M _ij, the performance of its filter is constant,

C _ij＝K _ijC (17)

。

10. method according to claim 1, is characterized in that, according to above-mentioned theory, the cross-couplings resonator filter of institute's optimal design carried out parallel connection by matching capacitance or inductance, can obtain needed target duplexer.

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