CN103077264A - Method for designing waveguide filter by medium blocks - Google Patents

Abstract

The invention relates to a method for designing a waveguide filter by medium blocks and belongs to the field of a microwave device. The invention provides a method for efficiently designing the waveguide filter by a substructure assembly method and a precise integration method. The method is used into two conditions that 1, the size and the number of the existing medium blocks are utilized for determining the distance among all medium blocks, and the waveguide filter conforming to the requirements is designed; and 2, the size of the existing medium blocks and the distance among the medium blocks are calculated according to the requirements of a target waveguide filter, and the requirement of the target waveguide filter is met, so the waveguide filter conforming to the requirement is designed. The advantage that the substructure assembly method and the precise integration method can be utilized for efficiently calculating the reflection coefficient and the transmission coefficient of media at various frequencies in the microwave range is utilized by the method, the easy-operation degree for designing the waveguide filter by media is reached, and the goal of efficiently designing the waveguide filter is realized.

Description

A kind of method of utilizing medium block design waveguide filter

Technical field

The invention belongs to the microwave device field, relate to a kind of method of utilizing medium block to pass through minor structure assembly unit method and Precise integration method design waveguide filter.

Background technology

The uncontinuity of waveguide refers to the unevenness of existence in the waveguide or structure or material, or all there are unevenness in structure and material.After adding medium in the waveguide, just make waveguide have dielectric discontinuities, the part of transmission wave reflects in inhomogeneous part, and another part then continues to propagate, and analyzes the energy distribution of reflection and transmission, can effectively instruct the design of microwave device.Various guided wave structure formed many important application that obtained in microwave circuit are such as waveguide filter, circulator, waveguide connector and coupling mechanism etc.Take cavity cascade coupled waveguide filter as example, horizontally set Rectangular Enclosure with Participating Media band in waveguide, the character of media strip, shape, quantity, position and direction have determined that the frequency of filtering is selected and filter effect, and especially the character of medium itself plays Main Function to wave reflection and transmission.

Although utilize the waveguide filter of medium designs simple, effective, utilize at present medium designs waveguide filter or a loaded down with trivial details large order, so utilize the kind of the waveguide filter that medium consists of also very limited.Nowadays more and more effective to the analysis of Waveguide Discontinuities problem, under the help of computing machine, can in seconds analyze in the microwave range reflection coefficient of medium and transmission coefficient under the various frequencies such as minor structure assembly unit and precision integration, comprise that isotropic medium also comprises anisotropic medium.If utilization is carried out the design of waveguide filter to the achievement of the analysis of Waveguide Discontinuities problem, then can greatly improve the efficient of waveguide filter design.

Summary of the invention

In order to improve design waveguide filter efficient, the invention provides a kind of minor structure assembly unit side and Precise integration method of utilizing and obtain the method that the waveguide medium designs waveguide filter to reflection coefficient and the transmission coefficient of microwave.

To achieve these goals, the technical solution used in the present invention is: design a kind of method of utilizing medium block design waveguide filter, plural equidimension medium block is equidistantly arranged the formation waveguide filter along waveguide, be divided into following two kinds of situations according to different condition

(1) cross sectional dimensions of known waveguide, the size of medium block, quantity, and relative dielectric coefficient and the magnetic capacity of this medium block, design the target distance of medium block that can the realize target waveguide filter, its step is as follows: utilize computing machine, size according to waveguide cross-section, the size of medium block, quantity, relative dielectric coefficient and magnetic capacity, use minor structure assembly unit method and Precise integration method to obtain each medium block in 1 millimeter to 20 millimeters scope of spacing, take 1 millimeter as step-length, reflection coefficient and the transmission coefficient of the various frequencies in the microwave range in the medium block different spacing situation, according to each reflection coefficient and the transmission coefficient that obtain, find out with the object wave waveguide filter require the corresponding spacing of immediate frequency band, as described target distance;

(2) cross sectional dimensions of known waveguide, relative dielectric coefficient and the magnetic capacity of medium block, and the frequency band of object wave waveguide filter, design target size and the target distance of medium block that can the realize target waveguide filter, its step is as follows: utilize computing machine, the size of incoming wave conduit xsect, the frequency band requirement of input object wave waveguide filter, relative dielectric coefficient and the magnetic capacity of input media piece; Getting step-length is 1 millimeter, respectively in the length of medium block, wide, progressively increase on the height, wherein, widely and high progressively increase from 1 millimeter cross sectional dimensions to waveguide, long progressively increase from 1 millimeter to the L millimeter, 10＜L＜30 wherein, and the medium block for each size, use minor structure assembly unit method and Precise integration method to obtain two these medium blocks in 1 millimeter to 20 millimeters scope of spacing, take 1 millimeter as step-length, reflection coefficient and the transmission coefficient of the various frequencies in the microwave range in the medium block different spacing situation, thereby draw under the various sizes and various spacings under the microwave range of two medium blocks in reflection coefficient and the transmission coefficient of various frequencies, and utilize computing machine that the frequency band of the above results and object wave waveguide filter is compared, get immediate result, obtain thick size and the target distance of medium block; Then, getting step-length is 0.1 millimeter, respectively in the length of medium block, wide, progressively increase on the height, its scope of progressively increasing is respectively the length from described thick size medium block, wide, height subtracts 1 millimeter to the length of described thick size medium block, wide, height adds 1 millimeter, reflection coefficient and the transmission coefficient of the various frequencies in the microwave range when re-using minor structure assembly unit method and Precise integration method and obtaining that two medium blocks under each size are placed with the gained target distance in new scope, and utilize computing machine that the frequency band of this result and object wave waveguide filter is compared, get immediate result and obtain the target size of medium block, when the wide or tall and big cross sectional dimensions in waveguide of target size, wide or high as target size of cross sectional dimensions wide or high of getting waveguide.

The realization of this programme is mainly by means of the application of minor structure assembly unit and precision integration, minor structure assembly unit and precision integration make efficiently, and reflection coefficient and the transmission coefficient of calculation medium become possibility, " application of Precise integration method in the 1-D photon crystal numerical simulation " that " application of precision integration in the Waveguide Discontinuities problem " delivered such as Beijing University of Technology's journal in 2009 and photon journal in 2012 are delivered wherein describes in detail and utilizes minor structure assembly unit method and Precise integration method to obtain isotropy and anisotropic crystal medium to transmissivity and the reflectivity of microwave signal in the waveguide.Lower mask body introduces that the minor structure assembly unit divides and the concrete application process of Precise integration method, obtains in accordance with the following steps reflection R and the transmission coefficient t of microwave in medium:

Both sides at dielectric are blocked waveguide, and make truncation surface from medium block enough away from, guarantee to be disappeared before arriving truncation surface by the higher mode of dielectric excitation;

Waveguide longitudinally is divided into three minor structures, and three minor structures are respectively, and one contains the minor structure of the inhomogeneous part of dielectric, two respectively minor structures of the truncation surface from the dielectric two ends to correspondence that do not contain dielectric.

For one of them minor structure, the z coordinate of establishing two end faces of this minor structure is respectively z _aAnd z _b, consider that homogeneous boundary condition, the functional corresponding with vector wave equation are,

$\mathrm{\&Pi;}\left(E\right)=\frac{1}{2}{\&Integral;}_{z_a}^{z_b}{\&Integral;\&Integral;}_{\mathrm{\&Omega;}}[(\&dtri;\&times;E)\&CenterDot;{\left[\mathrm{\&mu;}\right]}^{-1}\&CenterDot;(\&dtri;\&times;E)-{{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="DEST\_PATH\_HDA00002887468500031.png,DEST\_PATH\_HDA00002887468500033.png"\; state="\{\{state\}\}">k</figure-callout>}}_0}^{2}E\&CenterDot;[\mathrm{\&epsiv;}]\&CenterDot;E]\mathrm{d\&Omega;dz},\mathrm{\&delta;\&Pi;}\left(E\right)=0---\left(1\right)$

Wherein, Π represents functional, and E represents electric field intensity, k ₀Expression free space wave number, Ω represents the transverse cross-sectional area of minor structure, and ε represents relative dielectric coefficient, and μ represents relative permeability, and for anisotropic medium, its relative dielectric coefficient and magnetic capacity tensor representation are

$\left[\mathrm{\&epsiv;}\right]=\left[\begin{array}{ccc}{\mathrm{\&epsiv;}}_x& 0& 0\\ 0& {\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="DEST\_PATH\_HDA00002887468500031.png,DEST\_PATH\_HDA00002887468500033.png"\; state="\{\{state\}\}">y</figure-callout>}}& 0\\ 0& 0& {\mathrm{\&epsiv;}}_z\end{array}\right],$ $\left[\mathrm{\&mu;}\right]=\left[\begin{array}{ccc}{\mathrm{\&mu;}}_x& 0& 0\\ 0& {\mathrm{\&mu;}}_{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="DEST\_PATH\_HDA00002887468500031.png,DEST\_PATH\_HDA00002887468500033.png"\; state="\{\{state\}\}">y</figure-callout>}}& 0\\ 0& 0& {\mathrm{\&mu;}}_z\end{array}\right]---\left(2\right)$

Cross stream component [ε with relative dielectric coefficient and magnetic capacity tensor _t] and [μ _t] expression, namely

$\left[{\mathrm{\&epsiv;}}_t\right]=\left[\begin{array}{cc}{\mathrm{\&epsiv;}}_x& 0\\ 0& {\mathrm{\&epsiv;}}_y\end{array}\right],$ $\left[{\mathrm{\&mu;}}_t\right]=\left[\begin{array}{cc}{\mathrm{\&mu;}}_x& 0\\ 0& {\mathrm{\&mu;}}_y\end{array}\right]---\left(3\right)$

Electric field strength E is split as cross stream component E _tWith longitudinal component E _z, namely

E=E _t+E _z (4)

E wherein _t=E _xX+E _yY, E _z=E _zZ, x, y and z represent the unit vector of three directions;

The vector operator

Also be split into horizontal operator

With vertical operator

, namely

$\&dtri;={\&dtri;}_t+z\stackrel{\&CenterDot;}{\left(\right)}---\left(5\right)$

Wherein ${\&dtri;}_t=x\&PartialD;/\&PartialD;x+y\&PartialD;/\&PartialD;y,$ $z\stackrel{\&CenterDot;}{\left(\right)}=z\frac{\&PartialD;}{\&PartialD;z};$

With (4) and (5) formula substitutions (1) formula, functional is expressed as

$\mathrm{\&Pi;}=\frac{1}{2}{\&Integral;}_{z_a}^{z_b}{\&Integral;}_{\mathrm{\&Omega;}}\left[\begin{array}{c}({\&dtri;}_t\&times;E_t)\&CenterDot;{\left[{\mathrm{\&mu;}}_t\right]}^{-1}\&CenterDot;({\&dtri;}_t\&times;E_t)+\frac{1}{{\mathrm{\&mu;}}_z}\left({\&dtri;}_t{E}_z\right)\&CenterDot;\left({\&dtri;}_t{E}_z\right)\\ +{\stackrel{\&CenterDot;}{E}}_t\&CenterDot;{\left[{\mathrm{\&mu;}}_t\right]}^{-1}\&CenterDot;{\stackrel{\&CenterDot;}{E}}_t-\left({\&dtri;}_t{E}_z\right)\&CenterDot;{\left[{\mathrm{\&mu;}}_t\right]}^{-1}\&CenterDot;{\stackrel{\&CenterDot;}{E}}_t-{\stackrel{\&CenterDot;}{E}}_t\&CenterDot;{\left[{\mathrm{\&mu;}}_t\right]}^{-1}\&CenterDot;\left({\&dtri;}_t{E}_z\right)\\ -{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="DEST\_PATH\_HDA00002887468500031.png,DEST\_PATH\_HDA00002887468500033.png"\; state="\{\{state\}\}">k</figure-callout>}}_0^2{E}_t\&CenterDot;\left[{\mathrm{\&epsiv;}}_t\right]\&CenterDot;E_t-{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="DEST\_PATH\_HDA00002887468500031.png,DEST\_PATH\_HDA00002887468500033.png"\; state="\{\{state\}\}">k</figure-callout>}}_0^2{\mathrm{\&epsiv;}}_z{E}_z\&CenterDot;E_z\end{array}\right]\mathrm{d\&Omega;dz}---\left(6\right)$

Utilize finite element that xsect is dispersed, wherein with the vector base interpolating function transverse electric field is dispersed, with the node base interpolating function longitudinal electric field is dispersed, that is:

$E_t={\left[N_t^e\right]}^T{E}_t^e---\left(7\right)$

$E_z={\left[N_z^e\right]}^T{E}_z^e---\left(8\right)$

Wherein, E _tAnd E _zRepresent respectively the horizontal and vertical electric field intensity in certain unit on the xsect,

With The horizontal and vertical interpolating function that represents respectively the unit,

With

Represent respectively longitudinal electric field on transverse electric field on the element edges and the node;

With (7) and (8) formula substitution formulas (6), and the unary system matrix number on the assembling xsect gets

$\mathrm{\&Pi;}=\frac{1}{2}{\&Integral;}_{z_a}^{z_b}[E_t^T{M}_1{E}_t+E_z^T{M}_2{E}_z+{\stackrel{\&CenterDot;}{E}}_t^T{M}_3{E}_t-{\stackrel{\&CenterDot;}{E}}_t^T{M}_4{E}_z-E_z^T{M}_4{\stackrel{\&CenterDot;}{E}}_t]\mathrm{dz}---\left(9\right)$

Wherein

$M_1=\underset{e=1}{\overset{N}{\mathrm{\&Sigma;}}}{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_e}\left[\frac{1}{{\mathrm{\&mu;}}_z}\right[{\&dtri;}_t\&times;N_t^e]\&CenterDot;{[{\&dtri;}_t\&times;N_t^e]}^T-{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="DEST\_PATH\_HDA00002887468500031.png,DEST\_PATH\_HDA00002887468500033.png"\; state="\{\{state\}\}">k</figure-callout>}}_0^2{N}_t^e\&CenterDot;[{\mathrm{\&epsiv;}}_t]\&CenterDot;{\left[N_t^e\right]}^T]\mathrm{d\&Omega;}---\left(10\right)$

$M_2=\underset{e=1}{\overset{N}{\mathrm{\&Sigma;}}}{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_e}\left[\right[{\&dtri;}_t{N}_z^e]\&CenterDot;{{\left[{\mathrm{\&mu;}}_t\right]}^{-1}\&CenterDot;\left[{\&dtri;}_t{N}_z^e\right]}^T-{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="DEST\_PATH\_HDA00002887468500031.png,DEST\_PATH\_HDA00002887468500033.png"\; state="\{\{state\}\}">k</figure-callout>}}_0^2{{\mathrm{\&epsiv;}}_{z}N}_z^e\&CenterDot;{\left[N_z^e\right]}^T]\mathrm{d\&Omega;}---\left(11\right)$

$M_3=\underset{e=1}{\overset{N}{\mathrm{\&Sigma;}}}{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_e}[N_t^e\&CenterDot;{\left[{\mathrm{\&mu;}}_t\right]}^{-1}\&CenterDot;{\left[N_t^e\right]}^T]\mathrm{d\&Omega;}---\left(12\right)$

$M_4=\underset{e=1}{\overset{N}{\mathrm{\&Sigma;}}}{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_e}[N_t^e\&CenterDot;{\left[{\mathrm{\&mu;}}_t\right]}^{-1}\&CenterDot;{\left[{\&dtri;}_t{N}_z^e\right]}^T]\mathrm{d\&Omega;}---\left(13\right)$

At M ₁, M ₂, M ₃, M ₄In, when each component of relative dielectric coefficient and magnetic capacity tensor equates, just can be transitioned among the waveguide that contains isotropic medium.Wherein, N represents the number of unit on the xsect, and e represents the unit, Ω _eThe expression unit area; To different minor structures, the M that tries to achieve ₁, M ₂, M ₃And M ₄Difference, they are relevant with the magnetic capacity tensor with the relative dielectric coefficient of the size of medium block and medium block, include the size of medium block in the Ω area coordinate, thereby determine everywhere relative dielectric coefficient and magnetic capacity;

(9) formula is to E _zAsk local derviation, can in the hope of

$E_z={M_2}^{-1}{M_4}^t{\stackrel{\&CenterDot;}{E}}_t---\left(14\right)$

Can obtain following variational principle to (14) formula substitution (9) formula

$\mathrm{\&Pi;}=\frac{1}{2}{\&Integral;\&Integral;}_{z_a}^{z_b}[{E_t}^T{K}_{11}{E}_t+{{\stackrel{\&CenterDot;}{E}}_t}^T{K}_{22}{\stackrel{\&CenterDot;}{E}}_t]\mathrm{dz},$ δΠ(E _t)=0 (15)

Wherein

K ₁₁=M ₁,K ₁₂=K ₂₁=0,K ₂₂=M ₃-M ₄M ₂ ^-1M ₄ ^T (16)

K ₁₁, K ₁₂, K ₂₁, K ₂₂Expression variable E _tWith

Matrix of coefficients;

Π is called again the electromagnetism potential energy of minor structure, and minor structure electromagnetism potential energy should be the Quadratic Function Optimization of the tangential electric field in minor structure two ends, establishes the tangential electric field in two ends and is respectively E _TaAnd E _Tb, be

$\mathrm{\&Pi;}(E_{\mathrm{ta}},E_{\mathrm{tb}})=E_{\mathrm{ta}}^T{K}_{\mathrm{aa}}{E}_{\mathrm{ta}}/2+E_{\mathrm{tb}}^T{K}_{\mathrm{ba}}{E}_{\mathrm{ta}}+E_{\mathrm{tb}}^T{K}_{\mathrm{bb}}{E}_{\mathrm{tb}}/2---\left(17\right)$

K wherein _Aa, K _BaAnd K _BbIt is the outlet stiffness matrix of minor structure;

The below utilizes Precise Integration Method to obtain outlet stiffness matrix K under hot system _Aa, K _BaAnd K _Bb, for this reason, introduce dual variable, for

q=E _t， $p={\stackrel{\&CenterDot;}{E}}_t---\left(18\right)$

Then variational principle (15) formula can be write as

$\mathrm{\&Pi;}={\&Integral;}_{z_a}^{z_b}[p^T\stackrel{\&CenterDot;}{q}-H(q,p)]\mathrm{dz},$ δΠ=0 (19)

Wherein,

H(q,p)=p ^TDp/2+p ^TAq-q ^TBq/2 (20)

H (q, p) is Hamiltonian function, is also referred to as the minor structure mixed energy density, wherein

B＝K ₁₁，A＝0，D=K ₂₂ ^-1 (21)

A, B, D representative and K ₁₁, K ₁₂, K ₂₁, K ₂₂Relevant minor structure mixed energy density matrix of coefficients;

Below, by the Legendre transformation to minor structure potential energy, introduce the minor structure mixing energy, the minor structure mixing energy also is the Quadratic Function Optimization of minor structure two ends variable

$\mathrm{\&Gamma;}(q_a,p_b)=-q_z^{T}Q{q}_a/2+p_b^{T}F{q}_a+p_b^{T}G{p}_b/2---\left(22\right)$

Γ (q wherein _a, p _b) be the mixing energy of minor structure, q _a, p _bBe the variable at minor structure two ends, Q, F and G are minor structure mixing energy matrix of coefficients, satisfy Riccati equation between Q, F, G and A, B, the D

$\left\{\begin{array}{c}\mathrm{dF}=\mathrm{d\&eta;}=(A-\mathrm{GB})F=F(A-\mathrm{DQ})\\ \mathrm{dG}/\mathrm{d\&eta;}=D+\mathrm{AG}+{\mathrm{GA}}^T-\mathrm{GBG}={\mathrm{FDF}}^T\\ \mathrm{dQ}=\mathrm{d\&eta;}=F^T\mathrm{BF}=B+A^{T}Q+\mathrm{QA}-\mathrm{QDQ}\end{array}\right.---\left(23\right)$

Wherein Q, F and G are the functions of minor structure length η, and dF/d η, dG/d η and dQ/d η represent the differentiate to section length η,

Minor structure length η is subdivided into 2 again ^MSection, and M＞10, establishing a bit of length after the minor structure segmentation is τ, namely

τ＝η/2 ^M (24)

η is a finite length, and then τ will be a very little amount;

With F, G and Q do Taylor series expansion, obtain

$\left\{\begin{array}{c}F\left(\mathrm{\&tau;}\right)=I+F^{\&prime;}\left(\mathrm{\&tau;}\right),F^{\&prime;}\left(\mathrm{\&tau;}\right)={\mathrm{\&phi;}}_1\mathrm{\&tau;}+{\mathrm{\&phi;}}_2{\mathrm{\&tau;}}^2+{\mathrm{\&phi;}}_3{\mathrm{\&tau;}}^4+{\mathrm{\&phi;}}_4{\mathrm{\&tau;}}^4+O\left({\mathrm{\&tau;}}^5\right)\\ G\left(\mathrm{\&tau;}\right)={\mathrm{\&gamma;}}_1\mathrm{\&tau;}+{\mathrm{\&gamma;}}_2{\mathrm{\&tau;}}^2+{\mathrm{\&gamma;}}_3{\mathrm{\&tau;}}^3+{\mathrm{\&gamma;}}_4{\mathrm{\&tau;}}^4+O\left({\mathrm{\&tau;}}^5\right)\\ Q\left(\mathrm{\&tau;}\right)={\mathrm{\&theta;}}_1\mathrm{\&tau;}+{\mathrm{\&theta;}}_2{\mathrm{\&tau;}}^2+{\mathrm{\&theta;}}_3{\mathrm{\&tau;}}^3+{\mathrm{\&theta;}}_4{\mathrm{\&tau;}}^4+O\left({\mathrm{\&tau;}}^5\right)\end{array}\right.---\left(25\right)$

Wherein, I is unit matrix, F'(τ) be the increment of F (τ),

γ ₁, γ ₂, γ ₃, γ ₄And θ ₁, θ ₂, θ ₃, θ ₄All be the matrix of coefficients of Taylor expansion, O (τ ⁵) represent the error term of omitting, with (25) formula substitution (22) formula, relatively the identical exponent number of equation two ends τ can obtain

γ ₁, γ ₂, γ ₃, γ ₄, and θ ₁, θ ₂, θ ₃, θ ₄, namely obtain F (τ), G (τ) and Q (τ), carry out again section and merge, repeat M time, just can obtain mixing energy matrix Q (η), F (η), the G (η) of minor structure η, recycling Q, F, G and K _Aa, K _Ba, K _BbRelation

K _aa=Q+F ^TG ^-1F，K _ba=-G ^-1F，K _bb=G ^-1 (26)

Obtain respectively the outlet stiffness matrix of three minor structures, then the section that the outlet stiffness matrix that will obtain carries out minor structure merges, be about to the terminal surface of first minor structure and the initial end face combination of second minor structure, with the terminal surface of second minor structure and the initial end face combination of the 3rd minor structure, form the stiffness matrix of an integral body; After two truncation surface places add upper boundary conditions, just can obtain the electric field intensity at two truncation surface places, boundary condition is as follows,

If the coordinate at incident wave truncation surface place is z ₁, resultant field can be expressed as the stack of incident field and mirror field herein, namely

$E(x,y,z_1)=E_0{e}_{10}(x,y)e^{-i{k}_{z10}{z}_1}+{\mathrm{RE}}_0{e}_{10}(x,y)e^{i{k}_{z10}{z}_1}---\left(27\right)$

Wherein, E ₀The constant of representative expression incident field size, R represents reflection coefficient.

If the coordinate at an other truncation surface place is z ₂, only have transmitted field herein, namely

$E(x,y,z_2)={\mathrm{TE}}_0{e}_{10}(x,y)e^{-i{k}_{z10}{z}_2}---\left(28\right)$

Wherein, T represents transmission coefficient.

The expression formula that can be drawn reflection coefficient and transmission coefficient by (27) and (28) formula is

$R=\frac{E(x,y,z_1)-E_0{e}_{10}(x,y)e^{-i{k}_{z10}{z}_1}}{E_0{e}_{10}(x,y)e^{i{k}_{z10}{z}_1}}---\left(29\right)$

$T=\frac{E(x,y,z_2)}{E_0{e}_{10}(x,y)e^{-i{k}_{z10}{z}_2}}---\left(30\right)$

After namely obtaining the field at two ends, (29) and (30) formula of utilization is namely tried to achieve reflection and transmission coefficient.

In the said process, the expression of adding some points above the variable is to the variable differentiate, and subscript-1 represents finding the inverse matrix, the transposition of subscript T representing matrix;

But top process is realized operationalization by programming.

As preferably, described N gets 32.

As preferably, described M gets 20.

The invention has the beneficial effects as follows: this method is utilized minor structure assembly unit method and the laddering precision target waveguide filter of Precise integration method medium size, spacing, can design in a short period of time the object wave waveguide filter.Can in three minutes, obtain the target distance of medium for the first situation; Also can in twenty four hours, obtain target size and the target distance of medium for the second situation.This has been for having reached easy as my eyes degree with the medium designs waveguide filter, makes the simplicity of design, efficient of waveguide filter.

Description of drawings

Fig. 1 is the block diagram that the present invention utilizes the method for medium block design waveguide filter;

But Fig. 2 is the present invention realizes operationalization by programming program file call graph;

Fig. 3 is massive anisotropic dielectric-filled waveguide discontinuity structure;

Fig. 4 is that the discrete minor structure that reaches of the xsect among the present invention is divided schematic diagram;

Fig. 5 is result's diagram relatively of utilizing anisotropic medium reflection coefficient result that the present invention obtains and finite element method to obtain;

Fig. 6 is the periodic structure wave filter that comprises a plurality of anisotropic medium pieces;

Fig. 7 is the diagram of utilizing the result of the reflection coefficient that contains 10 cycle anisotropic medium wave filters that the present invention calculates.

Embodiment

The below utilizes the method for medium block design waveguide filter and minor structure assembly unit method and the Precise integration method that utilizes to elaborate to the present invention.

Reflection coefficient and transmission coefficient that the present invention mainly utilizes minor structure assembly unit method and Precise integration method to obtain waveguide medium piece design waveguide filter.Computer, the establishment corresponding program, the reflection coefficient and the transmission coefficient that obtain waveguide medium piece with minor structure assembly unit method and Precise integration method are very efficient, for the passband of microwave, only need to calculate several seconds.Utilize existing medium block design waveguide filter, mainly contain two kinds of situations:

Situation one, existing medium block, and the cross sectional dimensions of known waveguide, and the size of medium block, quantity, relative dielectric coefficient and magnetic capacity utilize such medium block to design desired waveguide filter.Because the size of medium block, quantity, relative dielectric coefficient and magnetic capacity are fixing, can only change the frequency band that the spacing of each medium block in waveguide of placing at even interval changes waveguide, so the frequency bandwidth characteristics of such wave filter may have with the frequency bandwidth characteristics of the wave filter that requires larger error, but design process is simple, quick.

The size of incoming wave conduit xsect in computing machine, the size of known media piece, quantity and relative dielectric coefficient and magnetic capacity, utilize minor structure assembly unit method and Precise integration method, can calculate reflection coefficient and the transmission coefficient of the various frequencies in the microwave range after this medium block of placing at n interval superposes in several seconds, getting step-length is 1 millimeter, the spacing of each medium block is increased progressively in 1 millimeter to 20 millimeters scope, calculate reflection coefficient and the transmission coefficient of the microwave frequency band under the various spacings, the requirement of this result and target filter is manually compared, get the corresponding spacing of immediate frequency band as target distance, both got design result.

Situation two, existing medium block, and the cross sectional dimensions of known waveguide, relative dielectric coefficient and the magnetic capacity of known media piece require to design target size and the target distance of medium block according to the frequency band of object wave waveguide filter.The size of medium block and spacing all are the factors that affects the waveguide passband, so suitable size and the spacing of medium block can accurately obtain meeting the waveguide passband that target filter requires.If obtain the suitable size of medium block, need on three directions of medium block length, progressively progressively increase and obtain the medium block of various sizes, in order to reduce calculated amount, can select roughly satisfactory thick size with large step-length first, determine simultaneously the target distance of each medium block, and then with little step-length selected thick size is carried out careful division, and select further satisfactory size, namely obtain target size.At first, with 1 millimeter as step-length, respectively in the length of medium block, wide, progressively increase on the height, wherein, widely and high progressively increase from 1 millimeter cross sectional dimensions to waveguide, long progressively increase from 1 millimeter to the L millimeter, 10＜L＜30 wherein, and the medium block for each size, utilize minor structure assembly unit method and Precise integration method to obtain two these medium blocks in 1 millimeter to 20 millimeters scope of spacing, take 1 millimeter as step-length, reflection coefficient and the transmission coefficient of the microwave frequency band in the medium block different spacing situation, thus draw reflection coefficient and the transmission coefficient of microwave frequency band of two these medium blocks of various sizes and various spacings, and under the help of computing machine, the frequency band of the above results and object wave waveguide filter is compared, get immediate result, obtain thick size and the target distance of medium block; Getting step-length is 0.1 millimeter again, respectively in the length of medium block, wide, progressively increase on the height, its scope of progressively increasing is respectively the length from described thick size medium block, wide, height subtracts 1 millimeter to the length of described thick size medium block, wide, height adds 1 millimeter, reflection coefficient and the transmission coefficient of the microwave frequency band when utilizing minor structure assembly unit method and Precise integration method to obtain that two medium blocks under each size are placed with the gained target distance in new scope, and under the help of computing machine, the frequency band of this result and object wave waveguide filter is compared, get immediate result, obtain the target size of medium block, when the wide or tall and big cross sectional dimensions in waveguide of target size, get wide or high as dimensioning of the cross sectional dimensions of waveguide.Because the medium block unit is more, the filtering performance of waveguide is just better, but structure is just larger, therefore needs comprehensive desired properties and structure to consider, so the quantity of medium block can be selected according to actual requirement.Get 20 for the waveguide that meets microwave region and L like this, obtain design result with the computing machine of present speed, need the time to be no more than 20 hours.

The below elaborates to minor structure assembly unit method and the Precise integration method of using in the design waveguide filter method.

In general, for dielectric loaded waveguide, suppose that waveguide is operated in a certain frequency, and only have main mould TE ₁₀Ripple can zero-decremently transmit.Both sides at medium block are blocked waveguide, truncation surface from medium block enough away from, the higher mode by medium block excitation is disappeared before arriving truncation surface.Waveguide longitudinally is divided into three minor structures, and inhomogeneous part that contains medium block and two divide the uniform parts that is clipped to corresponding truncation surface from the medium block two ends.On xsect, we carry out finite element discretization.What of discrete unit can come value according to needed precision, and in general, it is thinner that grid is divided, and precision is higher, but calculated amount will increase.

For one of them minor structure, the z coordinate of establishing two end faces of this minor structure is respectively z _aAnd z _b, η is the distance between two end faces of minor structure.Consider homogeneous boundary condition, the variational principle corresponding with vector wave equation is

$\mathrm{\&Pi;}\left(E\right)=\frac{1}{2}{\&Integral;}_{z_a}^{z_b}{\&Integral;\&Integral;}_{\mathrm{\&Omega;}}[(\&dtri;\&times;E)\&CenterDot;{\left[\mathrm{\&mu;}\right]}^{-1}\&CenterDot;(\&dtri;\&times;E)-{{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="DEST\_PATH\_HDA00002887468500031.png,DEST\_PATH\_HDA00002887468500033.png"\; state="\{\{state\}\}">k</figure-callout>}}_0}^{2}E\&CenterDot;[\mathrm{\&epsiv;}]\&CenterDot;E]\mathrm{d\&Omega;dz},$ δΠ(E)=0 (1)

Wherein, Π represents functional, and E represents electric field intensity, k ₀Expression free space wave number, Ω represents the minor structure transverse cross-sectional area, for anisotropic medium, its relative dielectric coefficient and relative permeability tensor can be expressed as

$\left[\mathrm{\&epsiv;}\right]=\left[\begin{array}{ccc}{\mathrm{\&epsiv;}}_x& 0& 0\\ 0& {\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="DEST\_PATH\_HDA00002887468500031.png,DEST\_PATH\_HDA00002887468500033.png"\; state="\{\{state\}\}">y</figure-callout>}}& 0\\ 0& 0& {\mathrm{\&epsiv;}}_z\end{array}\right],$ $\left[\mathrm{\&mu;}\right]=\left[\begin{array}{ccc}{\mathrm{\&mu;}}_x& 0& 0\\ 0& {\mathrm{\&mu;}}_{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="DEST\_PATH\_HDA00002887468500031.png,DEST\_PATH\_HDA00002887468500033.png"\; state="\{\{state\}\}">y</figure-callout>}}& 0\\ 0& 0& {\mathrm{\&mu;}}_z\end{array}\right]---\left(2\right)$

Cross stream component [ε with relative dielectric coefficient and magnetic capacity tensor _t] and [μ _t] expression, namely

$\left[{\mathrm{\&epsiv;}}_t\right]=\left[\begin{array}{cc}{\mathrm{\&epsiv;}}_x& 0\\ 0& {\mathrm{\&epsiv;}}_y\end{array}\right],$ $\left[{\mathrm{\&mu;}}_t\right]=\left[\begin{array}{cc}{\mathrm{\&mu;}}_x& 0\\ 0& {\mathrm{\&mu;}}_y\end{array}\right]---\left(3\right)$

The variable electric field strength E is split as cross stream component E _tWith longitudinal component E _z, namely

E=E _t+E _z (4)

E wherein _t=E _xX+E _yY, E _z=E _zZ, x, y and z represent the unit vector of three directions.

The vector operator

Also can be split into horizontal operator

With vertical operator

, namely

$\&dtri;={\&dtri;}_t+z\stackrel{\&CenterDot;}{\left(\right)}---\left(5\right)$

Wherein ${\&dtri;}_t=x\&PartialD;/\&PartialD;x+y\&PartialD;/\&PartialD;y,$ $z\stackrel{\&CenterDot;}{\left(\right)}=z\frac{\&PartialD;}{\&PartialD;z}.$

With (4) and (5) formula substitutions (1) formula, functional can be expressed as again

$\mathrm{\&Pi;}=\frac{1}{2}{\&Integral;}_{z_a}^{z_b}{\&Integral;}_{\mathrm{\&Omega;}}\left[\begin{array}{c}({\&dtri;}_t\&times;E_t)\&CenterDot;{\left[{\mathrm{\&mu;}}_t\right]}^{-1}\&CenterDot;({\&dtri;}_t\&times;E_t)+\frac{1}{{\mathrm{\&mu;}}_z}\left({\&dtri;}_t{E}_z\right)\&CenterDot;\left({\&dtri;}_t{E}_z\right)\\ +{\stackrel{\&CenterDot;}{E}}_t\&CenterDot;{\left[{\mathrm{\&mu;}}_t\right]}^{-1}\&CenterDot;{\stackrel{\&CenterDot;}{E}}_t-\left({\&dtri;}_t{E}_z\right)\&CenterDot;{\left[{\mathrm{\&mu;}}_t\right]}^{-1}\&CenterDot;{\stackrel{\&CenterDot;}{E}}_t-{\stackrel{\&CenterDot;}{E}}_t\&CenterDot;{\left[{\mathrm{\&mu;}}_t\right]}^{-1}\&CenterDot;\left({\&dtri;}_t{E}_z\right)\\ -{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="DEST\_PATH\_HDA00002887468500031.png,DEST\_PATH\_HDA00002887468500033.png"\; state="\{\{state\}\}">k</figure-callout>}}_0^2{E}_t\&CenterDot;\left[{\mathrm{\&epsiv;}}_t\right]\&CenterDot;E_t-{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="DEST\_PATH\_HDA00002887468500031.png,DEST\_PATH\_HDA00002887468500033.png"\; state="\{\{state\}\}">k</figure-callout>}}_0^2{\mathrm{\&epsiv;}}_z{E}_z\&CenterDot;E_z\end{array}\right]\mathrm{d\&Omega;dz}---\left(6\right)$

Utilize finite element that xsect is dispersed, wherein disperse with the transverse electric field of vector base interpolating function to its xsect, with the node base interpolating function the longitudinally electric field on the xsect is dispersed, that is:

$E_t={\left[N_t^e\right]}^T{E}_t^e---\left(7\right)$

$E_z={\left[N_z^e\right]}^T{E}_z^e---\left(8\right)$

Wherein, E _tAnd E _zHorizontal and vertical electric field intensity on the expression xsect in certain unit,

With The horizontal and vertical interpolating function that represents respectively the unit,

With Represent respectively transverse electric field on the element edges and the longitudinal electric field on the node, the transposition of subscript T representing matrix.

With (7) and (8) formula substitution formulas (6), and the unary system matrix number on the assembling xsect gets

$\mathrm{\&Pi;}=\frac{1}{2}{\&Integral;}_{z_a}^{z_b}[E_t^T{M}_1{E}_t+E_z^T{M}_2{E}_z+{\stackrel{\&CenterDot;}{E}}_t^T{M}_3{E}_t-{\stackrel{\&CenterDot;}{E}}_t^T{M}_4{E}_z-E_z^T{M}_4{\stackrel{\&CenterDot;}{E}}_t]\mathrm{dz}---\left(9\right)$

Put a spot on letter, representative is to its represented variable differentiate (lower same).Wherein

$M_1=\underset{e=1}{\overset{N}{\mathrm{\&Sigma;}}}{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_e}\left[\frac{1}{{\mathrm{\&mu;}}_z}\right[{\&dtri;}_t\&times;N_t^e]\&CenterDot;{[{\&dtri;}_t\&times;N_t^e]}^T-{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="DEST\_PATH\_HDA00002887468500031.png,DEST\_PATH\_HDA00002887468500033.png"\; state="\{\{state\}\}">k</figure-callout>}}_0^2{N}_t^e\&CenterDot;[{\mathrm{\&epsiv;}}_t]\&CenterDot;{\left[N_t^e\right]}^T]\mathrm{d\&Omega;}---\left(10\right)$

$M_2=\underset{e=1}{\overset{N}{\mathrm{\&Sigma;}}}{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_e}\left[\right[{\&dtri;}_t{N}_z^e]\&CenterDot;{{\left[{\mathrm{\&mu;}}_t\right]}^{-1}\&CenterDot;\left[{\&dtri;}_t{N}_z^e\right]}^T-{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="DEST\_PATH\_HDA00002887468500031.png,DEST\_PATH\_HDA00002887468500033.png"\; state="\{\{state\}\}">k</figure-callout>}}_0^2{{\mathrm{\&epsiv;}}_{z}N}_z^e\&CenterDot;{\left[N_z^e\right]}^T]\mathrm{d\&Omega;}---\left(11\right)$

$M_3=\underset{e=1}{\overset{N}{\mathrm{\&Sigma;}}}{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_e}[N_t^e\&CenterDot;{\left[{\mathrm{\&mu;}}_t\right]}^{-1}\&CenterDot;{\left[N_t^e\right]}^T]\mathrm{d\&Omega;}---\left(12\right)$

$M_4=\underset{e=1}{\overset{N}{\mathrm{\&Sigma;}}}{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_e}[N_t^e\&CenterDot;{\left[{\mathrm{\&mu;}}_t\right]}^{-1}\&CenterDot;{\left[{\&dtri;}_t{N}_z^e\right]}^T]\mathrm{d\&Omega;}---\left(13\right)$

At M ₁, M ₂, M ₃, M ₄In, when each component of relative dielectric coefficient and magnetic capacity tensor equates, just can be transitioned among the waveguide that contains isotropic medium.Wherein, N represents the number of unit on the xsect, and e represents the unit, Ω _eThe expression unit area; To different minor structures, the M that tries to achieve ₁, M ₂, M ₃And M ₄Different, they are relevant with the magnetic capacity tensor with the relative dielectric coefficient of the size of medium block and medium block, include the size of medium block in the Ω area coordinate, thereby determine everywhere relative dielectric coefficient and magnetic capacity, in the place that does not have medium, dielectric coefficient and magnetic capacity are 1 relatively.

In the superincumbent derivation, when each component of relative dielectric coefficient and magnetic capacity tensor equates, just be transitioned into the situation of isotropic medium.(9) do not have in the formula

Derivative term, can be to E _zVariation finds the solution out in advance.(9) formula is to E _zAsk local derviation, can in the hope of

$E_z={M_2}^{-1}{M_4}^t{\stackrel{\&CenterDot;}{E}}_t---\left(14\right)$

Can obtain following variational principle to (14) formula substitution (9) formula

$\mathrm{\&Pi;}=\frac{1}{2}{\&Integral;\&Integral;}_{z_a}^{z_b}[{E_t}^T{K}_{11}{E}_t+{{\stackrel{\&CenterDot;}{E}}_t}^T{K}_{22}{\stackrel{\&CenterDot;}{E}}_t]\mathrm{dz},\mathrm{\&delta;\&Pi;}\left(E_t\right)=0---\left(15\right)$

Wherein

K ₁₁=M ₁,K ₁₂=K ₂₁=0,K ₂₂=M ₃-M ₄M ₂ ^-1M ₄ ^T (16)

K ₁₁, K ₁₂, K ₂₁, K ₂₂Expression variable E _tWith Matrix of coefficients.Subscript-1 expression finding the inverse matrix (lower same), the transposition of subscript T representing matrix (lower same).

Π is called again the electromagnetism potential energy of minor structure, and minor structure electromagnetism potential energy should be the Quadratic Function Optimization of the tangential electric field in minor structure two ends, establishes the tangential electric field in two ends and is respectively E _TaAnd E _Tb, be

$\mathrm{\&Pi;}(E_{\mathrm{ta}},E_{\mathrm{tb}})=E_{\mathrm{ta}}^T{K}_{\mathrm{aa}}{E}_{\mathrm{ta}}/2+E_{\mathrm{tb}}^T{K}_{\mathrm{ba}}{E}_{\mathrm{ta}}+E_{\mathrm{tb}}^T{K}_{\mathrm{bb}}{E}_{\mathrm{tb}}/2---\left(17\right)$

K wherein _Aa, K _BaAnd K _BbIt is the outlet stiffness matrix of minor structure.

The below utilizes Precise Integration Method to obtain outlet stiffness matrix K under hot system _Aa, K _BaAnd K _Bb, for this reason, we introduce dual variable, wherein

q=E _t， $p={\stackrel{\&CenterDot;}{E}}_t---\left(18\right)$

Then variational principle (15) formula can be write as

$\mathrm{\&Pi;}={\&Integral;}_{z_a}^{z_b}[p^T\stackrel{\&CenterDot;}{q}-H(q,p)]\mathrm{dz},$ δΠ=0 (19)

Wherein

H(q,p)=p ^TDp/2+p ^TAq-q ^TBq/2 (20)

H (q, p) is Hamiltonian function, is also referred to as the minor structure mixed energy density, wherein

B=K ₁₁，A=0，D=K ₂₂ ^-1 (21)

A, B, D representative and K ₁₁, K ₁₂, K ₂₁, K ₂₂Relevant minor structure mixed energy density matrix of coefficients.

Below, by the Legendre transformation to minor structure potential energy, introduce the minor structure mixing energy, the minor structure mixing energy also is the Quadratic Function Optimization of minor structure two ends variable

$\mathrm{\&Gamma;}(q_a,p_b)=-q_z^{T}Q{q}_a/2+p_b^{T}F{q}_a+p_b^{T}G{p}_b/2---\left(22\right)$

Γ (q wherein _a, p _b) be the mixing energy of minor structure, q _a, p _bBe the variable at minor structure two ends, Q, F and G are minor structure mixing energy matrix of coefficients.

Q, F and G can be by A, and B and D obtain by the method for integration, satisfy Riccati equation between them

$\left\{\begin{array}{c}\mathrm{dF}=\mathrm{d\&eta;}=(A-\mathrm{GB})F=F(A-\mathrm{DQ})\\ \mathrm{dG}/\mathrm{d\&eta;}=D+\mathrm{AG}+{\mathrm{GA}}^T-\mathrm{GBG}={\mathrm{FDF}}^T\\ \mathrm{dQ}=\mathrm{d\&eta;}=F^T\mathrm{BF}=B+A^{T}Q+\mathrm{QA}-\mathrm{QDQ}\end{array}\right.---\left(23\right)$

Wherein Q, F and G are the functions of minor structure length η, and dF/d η, dG/d η and dQ/d η representative are to the differentiate of section length η.

Seek matrix Q, F and G below by the method for precise integration.

We are subdivided into 2 again with minor structure length η ^MSection, establishing a bit of length after the minor structure segmentation is τ, that is:

τ＝η/2 ^M (24)

η is a finite length, and then τ will be a very little amount, gets generally speaking M=20 and just can satisfy accuracy requirement fully, this moment 2 ^M=1048576.

With F, G and Q do Taylor series expansion, and we can obtain

$\left\{\begin{array}{c}F\left(\mathrm{\&tau;}\right)=I+F^{\&prime;}\left(\mathrm{\&tau;}\right),F^{\&prime;}\left(\mathrm{\&tau;}\right)={\mathrm{\&phi;}}_1\mathrm{\&tau;}+{\mathrm{\&phi;}}_2{\mathrm{\&tau;}}^2+{\mathrm{\&phi;}}_3{\mathrm{\&tau;}}^4+{\mathrm{\&phi;}}_4{\mathrm{\&tau;}}^4+O\left({\mathrm{\&tau;}}^5\right)\\ G\left(\mathrm{\&tau;}\right)={\mathrm{\&gamma;}}_1\mathrm{\&tau;}+{\mathrm{\&gamma;}}_2{\mathrm{\&tau;}}^2+{\mathrm{\&gamma;}}_3{\mathrm{\&tau;}}^3+{\mathrm{\&gamma;}}_4{\mathrm{\&tau;}}^4+O\left({\mathrm{\&tau;}}^5\right)\\ Q\left(\mathrm{\&tau;}\right)={\mathrm{\&theta;}}_1\mathrm{\&tau;}+{\mathrm{\&theta;}}_2{\mathrm{\&tau;}}^2+{\mathrm{\&theta;}}_3{\mathrm{\&tau;}}^3+{\mathrm{\&theta;}}_4{\mathrm{\&tau;}}^4+O\left({\mathrm{\&tau;}}^5\right)\end{array}\right.---\left(25\right)$

Wherein, I is unit matrix, F'(τ) be the increment of F (τ),

γ ₁, γ ₂, γ ₃, γ ₄And θ ₁, θ ₂, θ ₃, θ ₄All be the matrix of coefficients of Taylor expansion, O (τ ⁵) the representative error term of omitting.With (25) formula substitution (22) formula, relatively the identical exponent number of equation two ends τ can obtain

γ ₁, γ ₂, γ ₃, γ ₄, and θ ₁, θ ₂, θ ₃, θ ₄At this moment, obtained F (τ), G (τ) and Q (τ), we carry out the formula that is merged to 2 τ sections by two τ sections again, repeat M=20 time, just integration step can be merged into initial length by τ.After merging, can obtain mixing energy matrix Q (η), F (η), the G (η) of minor structure.Utilize Q, F, G and K _Aa, K _Ba, K _BbRelation

K _aa=Q+F ^TG ^-1F，K _ba=-G ^-1F，K _bb=G ^-1 (26)

Obtain respectively the outlet stiffness matrix of three minor structures, then the section that the outlet stiffness matrix that will obtain carries out minor structure merges, be about to the terminal surface of first minor structure and the initial end face combination of second minor structure, with the terminal surface of second minor structure and the initial end face combination of the 3rd minor structure, form the stiffness matrix of an integral body.Two truncation surface places add upper boundary conditions after, just can obtain the electric field intensity at two truncation surface places, boundary condition is as follows:

If the coordinate at incident wave truncation surface place is z ₁, resultant field can be expressed as the stack of incident field and mirror field herein, namely

$E(x,y,z_1)=E_0{e}_{10}(x,y)e^{-i{k}_{z10}{z}_1}+{\mathrm{RE}}_0{e}_{10}(x,y)e^{i{k}_{z10}{z}_1}---\left(27\right)$

Wherein, E ₀The constant of representative expression incident field size, R represents reflection coefficient.

If the coordinate at an other truncation surface place is z ₂, only have transmitted field herein, namely

$E(x,y,z_2)={\mathrm{TE}}_0{e}_{10}(x,y)e^{-i{k}_{z10}{z}_2}---\left(28\right)$

Wherein, T represents transmission coefficient.

The expression formula that can be drawn reflection coefficient and transmission coefficient by (27) and (28) formula is

$R=\frac{E(x,y,z_1)-E_0{e}_{10}(x,y)e^{-i{k}_{z10}{z}_1}}{E_0{e}_{10}(x,y)e^{i{k}_{z10}{z}_1}}---\left(29\right)$

$T=\frac{E(x,y,z_2)}{E_0{e}_{10}(x,y)e^{-i{k}_{z10}{z}_2}}---\left(30\right)$

After namely obtaining the field at two ends, (29) and (30) formula of utilization is namely tried to achieve reflection and transmission coefficient.

Above process is programmed, utilizes computing machine to realize, with the Matlab software programming of top process, the call relation of program as shown in Figure 2, wherein,

1, input parameter: all parameters that will need comprise the size (the wide a of being, height is b) of xsect, the size of medium block (wide is c, and height is b, and long is l), and the inputs such as relative dielectric constant and magnetic capacity.

2, grid division: waveguide longitudinally is divided into three minor structures (as shown in Figure 3), then carries out discrete (as shown in Figure 4) of xsect at xsect, each unit and node are numbered, form a matrix.

3, obtain a mouthful stiffness matrix: at first with matrix M 1, M2, M3, M4 according to parameter utilize program to obtain, matrix A, B and D can be obtained by matrix M 1, M2, M3, M4, and matrix Q, F and G can be by matrix A, B and D obtain by precise integration, outlet stiffness matrix K _Aa, K _Ba, K _BbCan be obtained by matrix Q, F, G.

4, add upper boundary conditions: boundary condition is added on the outlet stiffness matrix, just can obtains electric field intensity.

5, negate and penetrate coefficient and transmission coefficient: by formula (29), (30) that top process provides, obtain reflection coefficient and transmission coefficient.

The below utilizes above-mentioned program to calculate the waveguide that contains a square anisotropic medium, as shown in Figure 3.The cross sectional dimensions of waveguide is a=2cm, b=1cm; Medium block wherein is of a size of c=0.888cm, d=0.399cm, l=0.8cm, the medium block size is an example here, for the first situation among the present invention, this size is a definite value, for the second situation among the present invention, this size is a variate, and c and d progressively increase from 1 millimeter cross sectional dimensions to waveguide, l progressively increases from 1 millimeter to the L millimeter, wherein 10＜L＜30; Relative dielectric coefficient and the magnetic capacity of medium block are respectively

$\left[\mathrm{\&epsiv;}\right]=\left[\begin{array}{ccc}5& 0& 0\\ 0& 6& 0\\ 0& 0& 7\end{array}\right],$ $\left[\mathrm{\&mu;}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]---\left(31\right)$

(31) be relative dielectric coefficient and the magnetic capacity of anisotropic medium, when each component of relative dielectric coefficient and magnetic capacity tensor equates, just can be transitioned into isotropic medium.

In principal function, at first all Frequency points in the computer capacity are formed a column matrix, comprise initial frequency 8GHz, step-length 0.05GHz and stop frequency 13GHz, then call subroutine, by Frequency point of the each calculating of step-length, the transmission coefficient that calculates is formed the another one column matrix, can make transmission coefficient with the variation diagram of frequency with two matrixes at last.Regard to down the subfunction that principal function calls and describe,

1, parameter input subroutine: the parameter that input needs, the size a=2cm, the b=1cm that comprise xsect, the size c=0.888cm of medium block, d=0.399cm, l=0.8cm, medium block to two truncation surface apart from 0.8cm, and relatively dielectric coefficient and magnetic capacity tensor.Wherein, the dimensional accuracy of medium block is got 0.01cm and just can be satisfied actual needs when the design waveguide filter.

2, grid is divided subroutine: waveguide longitudinally is divided into three minor structures (as shown in Figure 3), then divide 8 * 4 unit at xsect, be N=32, carry out discrete (as shown in Figure 4) of xsect, each unit and node are numbered, these numberings are formed a matrix, the media property of each unit is also formed a matrix.

3, obtain a mouthful stiffness matrix subfunction: call unit stiffness matrix subroutine at first, namely utilize the matrix that forms in (10)-(13) formula and the second step with matrix M ₁, M ₂, M ₃, M ₄Obtain, matrix A, B and D can be by (15) and (20) formula by matrix M ₁, M ₂, M ₃, M ₄Obtain, matrix Q, F and G can be by (22) formula by matrix A, and B and D obtain by the precise integration subroutine, outlet stiffness matrix K _Aa, K _Ba, K _BbCan be obtained by matrix Q, F, G by (26) formula.Then carry out the merging of three sections, obtain whole stiffness matrix.

4, boundary condition (27) and (28) are added on the whole stiffness matrix, carry out finding the solution of finite element, just can obtain the electric field intensity at two ends.

5, electric field intensity substitution (29) and (30) formula, obtain reflection coefficient and transmission coefficient.

Its result of calculation as shown in Figure 5.Solid line is the curve that adopts the method for this paper to obtain among the figure, and thin dotted line is the curve that adopts the method for three-dimensional hexahedral element to obtain, and close dotted line is the curve that adopts the method for the hexahedral element of encrypting to obtain.As can be seen from the figure, only need to disperse to xsect in this method, this routine used number of nodes only has 90, and adopts when the discrete case finite element method identical with this method disperses on the xsect, and number of nodes is 585, when dispersing with the finite element method of encrypting, number of nodes has reached 2241, and therefore, this method is discrete easy, calculated amount is little, thereby computing velocity is fast.

Upper routine periodicity is increased to 10, and namely evenly 10 same anisotropic medium pieces are placed at the interval, as shown in Figure 6.At this moment, an outlet Stiffness Matrix that needed obtain upper the 3rd step of example merges 9 times, and soon 10 cycles are merged together, and form new global stiffness matrix, and then just can find the solution reflection coefficient and transmission coefficient in conjunction with boundary condition.

Analog result forbidden band district clearly occurred as shown in Figure 7 as we can see from the figure in the frequency range of simulation.Can find from two kinds of situation contrasts, behind the increase periodicity, the filtering performance of wave filter is significantly improved.Be Intel (R) Core (TM) 2Duo with CPU, dominant frequency is 2.79GHz, in save as 2G computing machine simulate, the time spent is 96.54 seconds when only having one-period, after minor structure length increased to 10, the time spent was 97.66 seconds, and only increased by 1.16% computing time.Thereby this method has very high efficient during the periodic structure of waveguide filter have to(for) design.

Claims (1)

1. a method of utilizing medium block design waveguide filter is equidistantly arranged the formation waveguide filter along waveguide with plural equidimension medium block, is divided into following two kinds of situations according to different condition:

(1) cross sectional dimensions of known waveguide, the size of medium block, quantity, and relative dielectric coefficient and the magnetic capacity of this medium block, design the target distance of medium block that can the realize target waveguide filter, its step is as follows: utilize computing machine, size according to waveguide cross-section, the size of medium block, quantity, relative dielectric coefficient and magnetic capacity, use minor structure assembly unit method and Precise integration method to obtain each medium block in 1 millimeter to 20 millimeters scope of spacing, take 1 millimeter as step-length, reflection coefficient and the transmission coefficient of the various frequencies in the microwave range in the medium block different spacing situation, according to each reflection coefficient and the transmission coefficient that obtain, find out with the object wave waveguide filter require the corresponding spacing of immediate frequency band, as described target distance;

(2) cross sectional dimensions of known waveguide, relative dielectric coefficient and the magnetic capacity of medium block, and the frequency band of object wave waveguide filter, design target size and the target distance of medium block that can the realize target waveguide filter, its step is as follows: utilize computing machine, the size of incoming wave conduit xsect, the frequency band requirement of input object wave waveguide filter, relative dielectric coefficient and the magnetic capacity of input media piece; Getting step-length is 1 millimeter, respectively in the length of medium block, wide, progressively increase on the height, wherein, widely and high progressively increase from 1 millimeter cross sectional dimensions to waveguide, long progressively increase from 1 millimeter to the L millimeter, 10＜L＜30 wherein, and the medium block for each size, use minor structure assembly unit method and Precise integration method to obtain two these medium blocks in 1 millimeter to 20 millimeters scope of spacing, take 1 millimeter as step-length, reflection coefficient and the transmission coefficient of the various frequencies in the microwave range in the medium block different spacing situation, thereby draw under the various sizes and various spacings under the microwave range of two medium blocks in reflection coefficient and the transmission coefficient of various frequencies, and utilize computing machine that the frequency band of the above results and object wave waveguide filter is compared, get immediate result, obtain thick size and the target distance of medium block; Then, getting step-length is 0.1 millimeter, respectively in the length of medium block, wide, progressively increase on the height, its scope of progressively increasing is respectively the length from described thick size medium block, wide, height subtracts 1 millimeter to the length of described thick size medium block, wide, height adds 1 millimeter, reflection coefficient and the transmission coefficient of the various frequencies in the microwave range when re-using minor structure assembly unit method and Precise integration method and obtaining that two medium blocks under each size are placed with the gained target distance in new scope, and utilize computing machine that the frequency band of this result and object wave waveguide filter is compared, get immediate result, obtain the target size of medium block, when the wide or tall and big cross sectional dimensions in waveguide of target size, wide or high as target size of cross sectional dimensions wide or high of getting waveguide.

Images