CN102411676A - Surface exciting method applicable to calculation of direction diagrams of waveguides in different shapes - Google Patents

Abstract

The invention provides a surface exciting method applicable to calculation of direction diagrams of waveguides in different shapes. The method comprises the following steps of: 1, setting an exciting surface of a shape corresponding to the shape of the cross section of a waveguide according to the the shape of the cross section of a waveguide; 2, dividing the exciting surface into even two-dimensional meshes, wherein an equivalent electric dipole source and a magnetic dipole source are arranged in the center of each mesh; 3, obtaining electric current of all the equivalent electric dipole sources and magnetic current of all the magnetic dipole sources on the exciting surface according to an equivalence principle, wherein an electromagnetic filed on the exciting surface is a main mode in which electromagnetic wave spreads in the waveguide; 4, carrying out mesh generation on the surface of the waveguide by virtue of triangular binning so as to obtain radiation fields generated by all the equivalent electric dipole sources, wherein the radiation fields serve as exciting fields of the surface of the waveguide; establishing an electric filed integral equation according to boundary conditions of the surface of the waveguide and obtaining the induction current of the surface of the waveguide by solving the equation according to a moment method; and 5, calculating the scattering direction diagram of the waveguide according to the induction current. Waveguides in different structures and shapes can be excited by the method provided by the invention instead of different methods separately.

Description

A kind of face motivational techniques that are applicable to that difformity wave guide direction figure calculates

Technical field

The invention belongs to the electromagnetic compatibility field, relate to a kind of face motivational techniques that are applicable to that difformity wave guide direction figure calculates.

Background technology

Electromagnetic horn is the simplest and one of the most widely used microwave antenna.The structure of electromagnetic horn generally is divided into waveguide part and flare.Waveguide is the main incentive structure of electromagnetic horn.Modal waveguide has circular waveguide, rectangular waveguide, coaxial waveguide etc.Except the waveguide of these regular shapes, the waveguide of one type of special construction is a ridge waveguide, promptly adds ridge structure in waveguide and flare, comes widening frequency band.The general wired excitation of the energisation mode of waveguide, port excitation etc.For such irregularly shaped of ridge waveguide, the field distribution in the waveguide is very complicated, has only employing face energisation mode to combine method of moment, or finite element method.And finite element method need be separated into the three dimensions in the waveguide tetrahedral grid one by one when calculating, and when the face energisation mode combines method of moment to calculate, only needs the subdivision waveguide surface, and required unknown quantity of finding the solution is big, and the computer resource that takies is many.

The Feko of typical commercial simulation software also only has the face energisation mode to circle, rectangle, coaxial waveguide, in redaction in 2009, has just added the finite element method account form to abnormally-structured waveguide such as ridge waveguide.Energisation mode is the basis of analyzing the aerial radiation characteristic, and the radiation characteristic of analysis antenna is significant for antenna arrangement and platform electromagnetic Compatibility Design.Face excitation is a kind of novelty and widely applicable energisation mode, not only can be used as the excitation of waveguide, behind the feed structure of waveguide as electromagnetic horn, also can calculate the radiation field of electromagnetic horn and paraboloidal-reflector antenna.

Summary of the invention

The technical matters that the present invention will solve is: a kind of face motivational techniques that are applicable to that difformity wave guide direction figure calculates are provided.

The present invention solves the problems of the technologies described above the technical scheme of being taked to be: a kind of face motivational techniques that are applicable to that difformity wave guide direction figure calculates, and it is characterized in that: it may further comprise the steps:

1) perturbed surface of correspondingly-shaped is set according to the waveguide cross-section shape;

2) perturbed surface is divided into uniform two-dimensional grid, the center of each grid is the position of equivalent electric dipole source and Magnetic Dipole Source;

3) electromagnetic field on the perturbed surface is the holotype of propagation of electromagnetic waves in the waveguide, obtains the electric current of all equivalent electric dipole sources on the perturbed surface and the magnetic current of all equivalent Magnetic Dipole Source according to equivalence principle;

4) utilize the triangle bin to carry out mesh generation to waveguide surface, obtain the exciting field of the radiation field of all equivalent source generations as waveguide surface; Set up the field integral equation according to the waveguide surface boundary condition, obtain the induction current of waveguide surface with the method for moment solving equation;

5) calculate the scattering directional diagram of waveguide according to induction current.

Press such scheme, the radiation far field that said step 5) waveguide surface induction current produces adds the antenna pattern that is waveguide behind the radiation far field that equivalent source produces on the perturbed surface.

Press such scheme, said step 3) obtains the electric current of eelctric dipole component according to equivalence principle:

${\stackrel{\→}{J}}^{\mathrm{eq}}\left({\stackrel{\→}{r}}^{\′}\right)=\hat{n}\×\stackrel{\→}{H}\left({\stackrel{\→}{r}}^{\′}\right)---\left(1\right),$

The magnetic current of Magnetic Dipole Source is:

${\stackrel{\→}{M}}^{\mathrm{eq}}\left({\stackrel{\→}{r}}^{\′}\right)=-\hat{n}\×\stackrel{\→}{E}\left({\stackrel{\→}{r}}^{\′}\right)---\left(2\right),$

is the unit normal vector of perturbed surface along direction of wave travel in the waveguide;

is the trivector coordinate of each eelctric dipole component and Magnetic Dipole Source, is positioned on the perturbed surface;

is the magnetic field on the perturbed surface;

is the electric field on the perturbed surface; Be the electromagnetic expression formula of the holotype of propagating in the waveguide, and

according to the electromagnetic pattern decision of propagating in waveguide cross-section size and the waveguide; Subscript eq representes equivalence.

Press such scheme, said step 4) is carried out subdivision with waveguide surface s with the triangle bin,

The direction that makes the eelctric dipole component is along the z axle, and it at the radiated electric field that free space produces is:

${\stackrel{\&RightArrow;}{E}}^{{\stackrel{\&RightArrow;}{J}}^{\mathrm{eq}}}\left(\stackrel{\&RightArrow;}{r}\right)=\frac{J^{\mathrm{eq}}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)}{2\mathrm{\&pi;}}{\mathrm{\&eta;e}}^{-{\mathrm{jk}}_{0}R}(\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000103931900000013.png"\; state="\{\{state\}\}">R</figure-callout>}}^2}+\frac{1}{{\mathrm{jk}}_0{R}^3})\cos \mathrm{\&theta;}\hat{r}+\frac{J^{\mathrm{eq}}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)}{4\mathrm{\&pi;}}{\mathrm{\&eta;e}}^{{-\mathrm{jk}}_{0}R}(\frac{{\mathrm{jk}}_0}{R}+\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000103931900000013.png"\; state="\{\{state\}\}">R</figure-callout>}}^2}+\frac{1}{{\mathrm{jk}}_0{R}^3})\sin \mathrm{\&theta;}\widehat{\mathrm{\&theta;}}---\left(3\right),$

In the formula (3)

Be the distance between an equivalent electric dipole and the point, the field point is positioned at waveguide surface, promptly Be positioned at perturbed surface, and Be positioned at waveguide surface; θ is a vector

With the angle of z axle, k ₀Be wave number, η is the free space wave impedance, and j is a plural number,

For what obtain in the formula (1)

Amplitude;

For in the spherical coordinates along the unit vector of radius vector;

The radiated electric field that the free space magnetic dipole produces is:

${\stackrel{\&RightArrow;}{E}}^{{\stackrel{\&RightArrow;}{M}}^{\mathrm{eq}}}\left(\stackrel{\&RightArrow;}{r}\right)={\stackrel{\&RightArrow;}{M}}^{\mathrm{eq}}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)\&times;{\&dtri;g}_0(\stackrel{\&RightArrow;}{r},{\stackrel{\&RightArrow;}{r}}^{\&prime;})---\left(4\right),$

is the free space Green function in the formula (4); is the position of magnetic dipole on the perturbed surface, and

is positioned at waveguide surface;

sets up the field integral equation according to the waveguide surface boundary condition, that is:

$[{\stackrel{\&RightArrow;}{E}}^i\left(\stackrel{\&RightArrow;}{r}\right)+{\stackrel{\&RightArrow;}{E}}^s\left(\stackrel{\&RightArrow;}{r}\right)]{|}_{\max }=0---\left(5\right),$

is positioned on the waveguide surface in the formula (5); The total electric field that

locates for point

, i.e. exciting field and scattered field sum;

In the formula (5); According to formula (3) and formula (4), total exciting field that all electric dipoles and Magnetic Dipole Source produce on the perturbed surface is:

${\stackrel{\&RightArrow;}{E}}^i\left(\stackrel{\&RightArrow;}{r}\right)=(\underset{p=-M}{\overset{M}{\mathrm{\&Sigma;}}}\underset{q=-N}{\overset{N}{\mathrm{\&Sigma;}}}{\stackrel{\&RightArrow;}{E}}_{p,q}^{{\stackrel{\&RightArrow;}{J}}^{\mathrm{eq}}}\left(\stackrel{\&RightArrow;}{r}\right)+\underset{p=-M}{\overset{M}{\mathrm{\&Sigma;}}}\underset{q=-N}{\overset{N}{\mathrm{\&Sigma;}}}{\stackrel{\&RightArrow;}{E}}_{p,q}^{{\stackrel{\&RightArrow;}{M}}^{\mathrm{eq}}}\left(\stackrel{\&RightArrow;}{r}\right))\mathrm{\&Delta;s}---\left(6\right),$

Wherein

locates in order to be positioned at, label is (p, the radiated electric field that q) equivalent electric dipole source produces;

locates in order to be positioned at

, label is (p, the radiated electric field that equivalent Magnetic Dipole Source q) produces; Δ s is the area of each sub-grid on the perturbed surface;

is positioned at perturbed surface, and

is positioned at waveguide surface;

and

is respectively by formula; (3) and likes; (4) obtain;

Perturbed surface is divided into (2M+1) * (2N+1) individual grid with long limit a of waveguide cross-section and waveguide cross-section minor face b, and M, N are integer; Label is (p; Q) the equivalent electric dipole source and the coordinate of equivalent Magnetic Dipole Source be

wherein the span of p for [M; M]; The span of q is [N; N], and the value of p and q makes its coordinate be positioned on the perturbed surface; Label is that the eelctric dipole component and the magnetic dipole source of (0,0) promptly is positioned at perturbed surface center, just true origin; Label is that the eelctric dipole component and the magnetic dipole source of (1,1) is positioned at its upper right corner;

Scattered field in the formula (5)

is the field that the induction current of waveguide surface produces, and is expressed as:

Ds is in the waveguide surface upper integral in the formula (7), and

and

all is positioned on the waveguide surface at this moment;

The available current known basis function of the induction current of waveguide surface launches:

$\stackrel{\&RightArrow;}{J}\left(\stackrel{\&RightArrow;}{r}\right)=\underset{n=1}{\overset{N_s}{\mathrm{\&Sigma;}}}{I}_n^s{\stackrel{\&RightArrow;}{\mathrm{\&Lambda;}}}_n^s\left(\stackrel{\&RightArrow;}{r}\right)---\left(8\right),$

Wherein

Be current coefficient to be found the solution,

Be RWG electric current basis function, N _sThe number of all triangle bin common edge on the expression waveguide surface;

With formula (6), (7), (8) substitution formula (5); Utilize the Jia Lvejin method of moment that formula (5) is converted into matrix equation; Find the solution obtain unknown current coefficient

thus obtain the induction current of waveguide surface and then can calculate the scattered field of waveguide according to formula (8) according to formula (7);

that promptly produces by

just in this up-to-date style (7)

be positioned on the waveguide surface and

any to be calculated position of putting that be free space.

If perturbed surface is the ridge waveguide perturbed surface, then the long limit a of waveguide cross-section is I-shaped length, and waveguide cross-section minor face b is I-shaped height.

If perturbed surface is the rectangular waveguide perturbed surface, then the long limit a of waveguide cross-section is the length of rectangle, and waveguide cross-section minor face b is the wide of rectangle.

Beneficial effect of the present invention is:

1, this method adopts the face energisation mode to realize the excitation to arbitrary structures, difformity waveguide, need not to select diverse ways to encourage to the shape of waveguide, and is convenient feasible.

2, after waveguide is as feed, also can realizes excitation, and then calculate the nearly far field of radiation of electromagnetic horn and reflector antenna, and can be used as a kind of antenna design method electromagnetic horn and paraboloidal-reflector antenna.

3, the induction current that adopts equivalent electromagnetic current method and method of moment to find the solution waveguide surface avoids adopting body subdivision and finite element method, and it is few to occupy computer resource, calculates faster.

Description of drawings

Fig. 1 is the perturbed surface of one embodiment of the invention.

Fig. 2 is the shape assumption diagram of one embodiment of the invention.

Fig. 3 is the scattering directional diagram of one embodiment of the invention on the xoz plane.

Fig. 4 is the scattering directional diagram of one embodiment of the invention on the xoy plane.

Fig. 5 is the shape assumption diagram of another embodiment of the present invention.

Fig. 6 is the I-shaped perturbed surface of another embodiment of the present invention.

Fig. 7 is the scattering directional diagram of another embodiment of the present invention on the xoz plane.

Fig. 8 is the scattering directional diagram of another embodiment of the present invention on the xoy plane.

Embodiment

Further specify embodiments of the invention below in conjunction with accompanying drawing.

Embodiment one:

Rectangular waveguide as shown in Figure 2, the waveguide endcapped, an end opening, its perturbed surface is as shown in Figure 1, is positioned at the yoz plane, and the center is an initial point.Perturbed surface is divided into (2M+1) * (2N+1) individual grid, M, N are integer, and equivalent electric dipole source and equivalent Magnetic Dipole Source are positioned at the center of each grid.Label is (p; Q) the equivalent electric dipole source and the coordinate of equivalent Magnetic Dipole Source are

wherein a be the long limit of waveguide cross-section; B is the waveguide cross-section minor face, and the span of p is [M, M]; The span of q is [N, N].

The long limit of rectangular waveguide is a=0.15m, and broadside is b=a/2, i.e. propagate TE in the waveguide ₁₀Ripple.The long l=0.15m of waveguide (along the x axle), the closed end of waveguide is positioned at x=-0.05m.Waveguide wall thickness 3mm.Calculated rate 1.2GHz.

Electromagnetic field expressions on the perturbed surface is:

$\stackrel{\&RightArrow;}{E}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)=\hat{z}{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="HDA0000103931900000013.png,HDA0000103931900000023.png"\; state="\{\{state\}\}">E</figure-callout>}}_0\cos \left(\frac{{\mathrm{\&pi;y}}^{\&prime;}}{a}\right)---\left(9\right),$

$\stackrel{\&RightArrow;}{H}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)=\hat{y}\frac{E_0}{Z_{\mathrm{TE}}}\cos \left(\frac{{\mathrm{\&pi;y}}^{\&prime;}}{a}\right)---\left(10\right),$

E in the following formula ₀Be electric field amplitude, Z _TEBe wave impedance,

ω=2 π f are angular frequency, and f is a calculated rate, μ ₀Be permeability of free space, β is a phase velocity,

α is the long limit of waveguide cross-section, and y ' is the y coordinate of each eelctric dipole component and Magnetic Dipole Source,

Trivector coordinate for each eelctric dipole component and Magnetic Dipole Source is positioned on the perturbed surface,

For in the rectangular coordinate system along the axial unit vector of y,

For in the rectangular coordinate system along the axial unit vector of z.

According to equivalence principle, the expression formula of electric current is on the electric dipole:

${\stackrel{\&RightArrow;}{J}}^{\mathrm{eq}}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)=\hat{n}\&times;\stackrel{\&RightArrow;}{H}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)---\left(1\right),$

The expression formula of magnetic current is on the magnetic dipole:

${\stackrel{\&RightArrow;}{M}}^{\mathrm{eq}}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)=-\hat{n}\&times;\stackrel{\&RightArrow;}{E}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)---\left(2\right),$

is the unit normal vector of perturbed surface along direction of wave travel in the waveguide, i.e.

The direction of eelctric dipole component is along the z axle, and it at the radiated electric field that free space produces is:

${\stackrel{\&RightArrow;}{E}}^{{\stackrel{\&RightArrow;}{J}}^{\mathrm{eq}}}\left(\stackrel{\&RightArrow;}{r}\right)=\frac{J^{\mathrm{eq}}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)}{2\mathrm{\&pi;}}{\mathrm{\&eta;e}}^{-{\mathrm{jk}}_{0}R}(\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000103931900000013.png"\; state="\{\{state\}\}">R</figure-callout>}}^2}+\frac{1}{{\mathrm{jk}}_0{R}^3})\cos \mathrm{\&theta;}\hat{r}+\frac{J^{\mathrm{eq}}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)}{4\mathrm{\&pi;}}{\mathrm{\&eta;e}}^{{-\mathrm{jk}}_{0}R}(\frac{{\mathrm{jk}}_0}{R}+\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000103931900000013.png"\; state="\{\{state\}\}">R</figure-callout>}}^2}+\frac{1}{{\mathrm{jk}}_0{R}^3})\sin \mathrm{\&theta;}\widehat{\mathrm{\&theta;}}---\left(3\right),$

In the following formula

Be the distance between the point of equivalent electric dipole source to field,

Be the position in equivalent electric dipole source on the perturbed surface, and a point

Be positioned at waveguide surface, θ is a vector

With the angle of z axle, k ₀Be wave number, η is the free space wave impedance, and j is a plural number, j ²=-1,

For in the spherical coordinates along the unit vector of radius vector;

is the amplitude by the eelctric dipole component of formula (1) decision.

The radiated electric field that the free space magnetic dipole produces is:

${\stackrel{\&RightArrow;}{E}}^{{\stackrel{\&RightArrow;}{M}}^{\mathrm{eq}}}\left(\stackrel{\&RightArrow;}{r}\right)={\stackrel{\&RightArrow;}{M}}^{\mathrm{eq}}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)\&times;{\&dtri;g}_0(\stackrel{\&RightArrow;}{r},{\stackrel{\&RightArrow;}{r}}^{\&prime;})---\left(4\right),$

is the free space Green function in the following formula;

is the position of magnetic dipole on the perturbed surface, and

is positioned at waveguide surface.

The resultant field that each equivalent electric dipole source and Magnetic Dipole Source on the perturbed surface are produced utilizes the boundary condition

of conductive surface to set up the field integral equation as the exciting field

of waveguide surface, that is:

$[{\stackrel{\&RightArrow;}{E}}^i\left(\stackrel{\&RightArrow;}{r}\right)+{\stackrel{\&RightArrow;}{E}}^s\left(\stackrel{\&RightArrow;}{r}\right)]{|}_{\max }=0---\left(5\right),$

is positioned on the waveguide surface in the following formula.

Total exciting field that all electric dipoles and Magnetic Dipole Source produce on the perturbed surface is:

${\stackrel{\&RightArrow;}{E}}^i\left(\stackrel{\&RightArrow;}{r}\right)=(\underset{p=-M}{\overset{M}{\mathrm{\&Sigma;}}}\underset{q=-N}{\overset{N}{\mathrm{\&Sigma;}}}{\stackrel{\&RightArrow;}{E}}_{p,q}^{{\stackrel{\&RightArrow;}{J}}^{\mathrm{eq}}}\left(\stackrel{\&RightArrow;}{r}\right)+\underset{p=-M}{\overset{M}{\mathrm{\&Sigma;}}}\underset{q=-N}{\overset{N}{\mathrm{\&Sigma;}}}{\stackrel{\&RightArrow;}{E}}_{p,q}^{{\stackrel{\&RightArrow;}{M}}^{\mathrm{eq}}}\left(\stackrel{\&RightArrow;}{r}\right))\mathrm{\&Delta;s}---\left(6\right),$

Wherein

locates for being positioned at

; Label is (p; Q) radiated electric field that equivalent electric dipole produces;

locates for being positioned at

; Label is (p; Q) radiated electric field that equivalent magnetic dipole produces; Δ s is the area of each sub-grid on the perturbed surface;

is positioned at perturbed surface, and

is positioned at waveguide surface.

and

is respectively by formula; (3) and likes; (4) obtain.

Scattered field in the formula (5) is the field that the unknown induction current

of waveguide surface produces, and is expressed as:

Ds is in the waveguide surface upper integral in the following formula, and and

all is positioned on the waveguide surface at this moment.

Waveguide surface s is carried out subdivision with the triangle bin, and the available current known basis function of the induction current of waveguide surface

launches:

$\stackrel{\&RightArrow;}{J}\left(\stackrel{\&RightArrow;}{r}\right)=\underset{n=1}{\overset{N_s}{\mathrm{\&Sigma;}}}{I}_n^s{\stackrel{\&RightArrow;}{\mathrm{\&Lambda;}}}_n^s\left(\stackrel{\&RightArrow;}{r}\right)---\left(8\right),$

Wherein

Be current coefficient to be found the solution,

Be RWG electric current basis function, N _sThe number of all triangle bin common edge on the expression waveguide surface.

With formula (6), (7), (8) substitution formula (5); Utilize the Jia Lvejin method of moment that formula (5) is converted into matrix equation; Find the solution and obtain the unknown current coefficient; Thereby obtain the induction current

of waveguide surface and then can calculate the scattered field of waveguide according to formula (7) according to formula (8); that promptly produces by

just in this up-to-date style (7) be positioned on the waveguide surface and

any to be calculated position of putting that be free space.

According to said method and parameter, rectangular waveguide shown in Figure 2 has been carried out calculating and compares with the result of business simulation software Feko: the scattering directional diagram

of

this rectangular waveguide is as shown in Figure 3 with the curve that angle θ changes on the xoz plane; On the xoy plane (θ=90 °), the scattering directional diagram of this rectangular waveguide

is as shown in Figure 4 with the curve that angle changes.The result that can find out present embodiment result of calculation and business software Feko among Fig. 3, Fig. 4 coincide finely, explains that this method is feasible.

Embodiment two:

The present embodiment method is identical with embodiment one, and its difference is the shape and the parameter of perturbed surface.Fig. 5 is the geometric model of the ridge waveguide of both ends open, and end is positioned at the yoz plane, and its perturbed surface is as shown in Figure 6, is positioned at the yoz plane, and the center is an initial point.Long limit a=18mm, broadside b=8mm, the long l=30mm of waveguide (along the x axle), waveguide wall thickness 0.5mm, calculated rate 10GHz.

During calculating, because the long limit a of waveguide cross-section is I-shaped length, waveguide cross-section minor face b is I-shaped height, so p and q should be positioned on the perturbed surface with its coordinate when value and be as the criterion, and need remove part not overlapping with perturbed surface in the grid.

Perhaps the I shape perturbed surface is divided into and superposes after three rectangles calculate respectively.

Figure 5 shows the open ends of the ridge waveguide to be calculated: in the plane xoz

The ridge waveguide scattering pattern

with angle θ curve shown in Figure 7; in xoy plane (θ = 90 °), the ridge waveguide scattering pattern

with angle The curve shown in Figure 8.

Claims (6)

1. face motivational techniques that are applicable to that difformity wave guide direction figure calculates, it is characterized in that: it may further comprise the steps:

1) perturbed surface of correspondingly-shaped is set according to the waveguide cross-section shape;

2) perturbed surface is divided into uniform two-dimensional grid, the center of each grid is the position of equivalent electric dipole source and Magnetic Dipole Source;

3) electromagnetic field on the perturbed surface is the holotype of propagation of electromagnetic waves in the waveguide, obtains the electric current of all equivalent electric dipole sources on the perturbed surface and the magnetic current of all equivalent Magnetic Dipole Source according to equivalence principle;

4) utilize the triangle bin to carry out mesh generation to waveguide surface, obtain the exciting field of the radiation field of all equivalent source generations as waveguide surface; Set up the field integral equation according to the waveguide surface boundary condition, obtain the induction current of waveguide surface with the method for moment solving equation;

5) calculate the scattering directional diagram of waveguide according to induction current.

2. a kind of face motivational techniques that are applicable to that difformity wave guide direction figure calculates according to claim 1 is characterized in that: the radiation far field that said step 5) waveguide surface induction current produces adds the antenna pattern that is waveguide behind the radiation far field that equivalent source produces on the perturbed surface.

3. a kind of face motivational techniques that are applicable to that difformity wave guide direction figure calculates according to claim 1 and 2, it is characterized in that: said step 3) obtains the electric current of eelctric dipole component according to equivalence principle:

${\stackrel{\&RightArrow;}{J}}^{\mathrm{eq}}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)=\hat{n}\&times;\stackrel{\&RightArrow;}{H}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)---\left(1\right),$

The magnetic current of Magnetic Dipole Source is:

${\stackrel{\&RightArrow;}{M}}^{\mathrm{eq}}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)=-\hat{n}\&times;\stackrel{\&RightArrow;}{E}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)---\left(2\right),$

is the unit normal vector of perturbed surface along direction of wave travel in the waveguide;

is the trivector coordinate of each eelctric dipole component and Magnetic Dipole Source, is positioned on the perturbed surface;

is the magnetic field on the perturbed surface;

is the electric field on the perturbed surface; Be the electromagnetic expression formula of the holotype of propagating in the waveguide,

and

according to the electromagnetic pattern decision of propagating in waveguide cross-section size and the waveguide; Subscript eq representes equivalence.

4. a kind of face motivational techniques that are applicable to that difformity wave guide direction figure calculates according to claim 3, it is characterized in that: said step 4) is carried out subdivision with waveguide surface s with the triangle bin,

The direction that makes the eelctric dipole component is along the z axle, and it at the radiated electric field that free space produces is:

${\stackrel{\&RightArrow;}{E}}^{{\stackrel{\&RightArrow;}{J}}^{\mathrm{eq}}}\left(\stackrel{\&RightArrow;}{r}\right)=\frac{J^{\mathrm{eq}}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)}{2\mathrm{\&pi;}}{\mathrm{\&eta;e}}^{-{\mathrm{jk}}_{0}R}(\frac{1}{R^2}+\frac{1}{{\mathrm{jk}}_0{R}^3})\cos \mathrm{\&theta;}\hat{r}+\frac{J^{\mathrm{eq}}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)}{4\mathrm{\&pi;}}{\mathrm{\&eta;e}}^{{-\mathrm{jk}}_{0}R}(\frac{{\mathrm{jk}}_0}{R}+\frac{1}{R^2}+\frac{1}{{\mathrm{jk}}_0{R}^3})\sin \mathrm{\&theta;}\widehat{\mathrm{\&theta;}}---\left(3\right),$

In the formula (3) Be the distance between an equivalent electric dipole and the point, the field point is positioned at waveguide surface, promptly Be positioned at perturbed surface, and

Be positioned at waveguide surface; θ is a vector

With the angle of z axle, k ₀Be wave number, η is the free space wave impedance, and j is a plural number, j ²=-1;

For what obtain in the formula (1)

Amplitude;

In the spherical coordinates along the unit vector of radius vector; The radiated electric field that the free space magnetic dipole produces is:

${\stackrel{\&RightArrow;}{E}}^{{\stackrel{\&RightArrow;}{M}}^{\mathrm{eq}}}\left(\stackrel{\&RightArrow;}{r}\right)={\stackrel{\&RightArrow;}{M}}^{\mathrm{eq}}\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)\&times;{\&dtri;g}_0(\stackrel{\&RightArrow;}{r},{\stackrel{\&RightArrow;}{r}}^{\&prime;})---\left(4\right),$

is the free space Green function in the formula (4);

is the position of magnetic dipole on the perturbed surface, and

is positioned at waveguide surface;

sets up the field integral equation according to the waveguide surface boundary condition, that is:

$[{\stackrel{\&RightArrow;}{E}}^i\left(\stackrel{\&RightArrow;}{r}\right)+{\stackrel{\&RightArrow;}{E}}^s\left(\stackrel{\&RightArrow;}{r}\right)]{|}_{\max }=0---\left(5\right),$

is positioned on the waveguide surface in the formula (5); The total electric field that

locates for point

, i.e. exciting field and scattered field sum;

In the formula (5); According to formula (3) and formula (4), total exciting field

that all electric dipoles and Magnetic Dipole Source produce on the perturbed surface is:

${\stackrel{\&RightArrow;}{E}}^i\left(\stackrel{\&RightArrow;}{r}\right)=(\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\stackrel{\&RightArrow;}{E}}_{p,q}^{{\stackrel{\&RightArrow;}{J}}^{\mathrm{eq}}}\left(\stackrel{\&RightArrow;}{r}\right)+\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\stackrel{\&RightArrow;}{E}}_{p,q}^{{\stackrel{\&RightArrow;}{M}}^{\mathrm{eq}}}\left(\stackrel{\&RightArrow;}{r}\right))\mathrm{\&Delta;s}---\left(6\right),$

Wherein

locates, label is (p in order to be positioned at; Q) radiated electric field that equivalent electric dipole source produces;

locates, label is (p in order to be positioned at

; Q) radiated electric field that equivalent Magnetic Dipole Source produces; Δ s is the area of each sub-grid on the perturbed surface;

is positioned at perturbed surface, and

is positioned at waveguide surface;

and

is respectively by formula; (3) and likes; (4) obtain;

Perturbed surface is divided into (2M+1) * (2N+1) individual grid with long limit a of waveguide cross-section and waveguide cross-section minor face b, and M, N are integer; Label is (p; Q) the equivalent electric dipole source and the coordinate of equivalent Magnetic Dipole Source be

wherein the span of p for [M; M]; The span of q is [N; N], and the value of p and q makes its coordinate be positioned on the perturbed surface; Label is that the eelctric dipole component and the magnetic dipole source of (0,0) promptly is positioned at perturbed surface center, just true origin; Label is that the eelctric dipole component and the magnetic dipole source of (1,1) is positioned at its upper right corner;

Scattered field in the formula (5)

is the field that the induction current

of waveguide surface produces, and is expressed as:

Ds is in the waveguide surface upper integral in the formula (7), and

and

all is positioned on the waveguide surface at this moment;

The available current known basis function of the induction current of waveguide surface

launches:

$\stackrel{\&RightArrow;}{J}\left(\stackrel{\&RightArrow;}{r}\right)=\underset{n=1}{\overset{N_s}{\mathrm{\&Sigma;}}}{I}_n^s{\stackrel{\&RightArrow;}{\mathrm{\&Lambda;}}}_n^s\left(\stackrel{\&RightArrow;}{r}\right)---\left(8\right),$

Wherein

Be current coefficient to be found the solution,

Be RWG electric current basis function, N _sThe number of all triangle bin common edge on the expression waveguide surface;

With formula (6), (7), (8) substitution formula (5); Utilize the Jia Lvejin method of moment that formula (5) is converted into matrix equation; Find the solution obtain unknown current coefficient

thus obtain the induction current

of waveguide surface and then can calculate the scattered field of waveguide according to formula (8) according to formula (7);

that promptly produces by just in this up-to-date style (7) be positioned on the waveguide surface and

any to be calculated position of putting that be free space.

5. a kind of face motivational techniques that are applicable to that difformity wave guide direction figure calculates according to claim 4; It is characterized in that: if perturbed surface is the ridge waveguide perturbed surface; Then the long limit a of waveguide cross-section is I-shaped length, and waveguide cross-section minor face b is I-shaped height.

6. a kind of face motivational techniques that are applicable to that difformity wave guide direction figure calculates according to claim 4 is characterized in that: if perturbed surface is the rectangular waveguide perturbed surface, then the long limit a of waveguide cross-section is the length of rectangle, and waveguide cross-section minor face b is the wide of rectangle.

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