CN101800360A - Method for accurately obtaining antenna radiating gap active admittance of planar slotted array - Google Patents

Abstract

The invention provides a method for accurately obtaining antenna radiating gap active admittance of a planar slotted array. The method has high obvious admittance extracting efficiency and accurately obtains the active admittance of each gap of an antenna array. The method comprises the following steps of: (1) analyzing and calculating the field distribution of a planar slotted array radiating gap by using a moment vector method, establishing field equations on the upper surface and the lower surface of the gap according to the continuity of a magnetic field, converting an integral equation into a matrix form by using a Rooftop primary function and a pulse verifying function and solving the equation to obtain the distribution condition of the field in the gap position; (2) obtaining the active admittance of the gap by a forward and backward scattered field in the gap position; (3) respectively carrying out simulating analysis on square and circular gaps by adopting HFSS (High Frequency Structure Simulator) software, obtaining an equivalent relation between the square gap and the circular gap, and solving the length correction factor c between the square gap and the circular gap by the following relational expression; and (4) correcting the circular gap length which corresponds to the active admittance and is calculated by using the moment vector method by the solved correction factor c.

Description

The method of accurately obtaining antenna radiating gap active admittance of planar slotted array

Technical field

The invention relates to the method for extracting antenna radiating gap active admittance of planar slotted array.

Background technology

The extraction of antenna radiating gap active admittance of planar slotted array can provide basic data accurately for designing high performance dull and stereotyped crack array antenna.The accuracy of this basic data is the key point of design high-performance Planar Slot Antenna.Three design equations [1 ~ 3] about Planar Slot Antenna that Elliott proposes are to extract the common method that active admittance designs dull and stereotyped crack array antenna, but this method is based upon on the basis of the group of solving an equation, increase along with number of slots, the number of equation becomes the increase of 2 times of number of slots, and contain double integral in the equation, make that the speed of calculating is slower, especially amount of calculation is very big in the battle array of large-scale slit, and it also is huge calculating the used time.Development along with computer, Electromagnetic Simulation software such as HFSS etc. can be by setting up the active admittance that model extracts slit in the array, but this method can only be extracted the admittance value of waveguide port, and then the active admittance mean value in slit in the acquisition waveguide, in fact the slit at diverse location place in the same waveguide, because different its active admittances of suffered coupling are different, the active admittance that therefore this method is extracted is an approximation.In addition, adopt moment method can extract the active admittance [4] in slit in the capable ripple battle array waveguide slotted array, but the active admittance for slit in the standing-wave array is not mentioned, and when moment method is calculated, the termination in slit is square toes, and the actual slit that processes is a round end, therefore need determine the equivalent relation between the two, does not still have accurately to determine the report of this equivalent relation in the existing literature data.

The present invention is further improvement of existing technologies and development.

Summary of the invention

The objective of the invention is the weak point at above-mentioned prior art existence, a kind of admittance extraction efficiency height is provided, computational speed is fast, can accurately obtain the method for each slit active admittance in the aerial array.

Above-mentioned purpose of the present invention can reach by following measure, and a kind of method of accurately obtaining antenna radiating gap active admittance of planar slotted array is characterized in that comprising the steps:

(1) calculates the field distribution of dull and stereotyped crack battle array radiating slot with moment Method Analysis, continuity according to magnetic field, upper and lower surface in the slit is set up field equation, select Rooftop basic function [5] and pulse verification function [6] for use, integral equation is changed into matrix form, and solving equation can obtain the distribution situation of the field at place, slit;

(2) obtain the active admittance in slit by slit place forward direction and back scattering field;

(3) adopt HFSS software respectively square toes and round end slit to be carried out simulation analysis, obtain the equivalent relation between the two, try to achieve length correction factor c between square toes and the round end slit by following relational expression:

$c=\frac{L_y-L_f}{w(1-\mathrm{\π}/4)}---\left(3\right)$

Wherein, L _yBe the length in cup head slit, L _fBe the length in square toes slit, w is the width in slit;

(4) revise the round end gap length of the active admittance correspondence that moment method calculates with the above-mentioned modifying factor c that tries to achieve.

The present invention than the beneficial effect of prior art is:

The present invention is based on HFSS emulation and moment Method Analysis active admittance, utilize moment method to extract the active admittance of dull and stereotyped crack battle array radiating slot, analysis from the field, consider the influence of each physical dimension in waveguide and slit and the effect of short circuit face, the more important thing is the mutual coupling effect of considering that the slit is inside and outside, so its result of calculation is accurate.What deserves to be explained is standing-wave array because the existence of short circuit face makes the complicated degree of analysis of each slit forward direction and back scattering field increase greatly than capable ripple battle array, this also is that this paper proposes the difficult point place that the standing-wave array active admittance extracts formula.In addition, moment method can be obtained the active admittance in each slit in the array accurately, and this is more accurate than the active admittance mean value that HFSS emulation obtains in the every waveguide, and is more superior when the array antenna of the high performance dull and stereotyped crack of design.Because moment method can only be extracted the admittance value in square toes slit, the present invention obtains equivalent relation between square toes slit and the round end slit by HFSS emulation, and adopt moment method accurately to extract the active admittance in each square toes slit in the battle array of dull and stereotyped crack, obtain the active admittance in round end slit in conjunction with equivalent relation.Adopt HFSS emulation, this point that the newly measures of the modifying factor in square toes that obtain and round end slit have just in time remedied moment method is not enough.Therefore, the present invention is based on the active admittance method of HFSS emulation and moment Method Analysis, is the higher method of a kind of precision.And the computational process of moment method can realize by computer programming, improved the efficient that admittance is extracted greatly, for the design and the analysis of the dull and stereotyped crack of high-performance array antenna provides accurately effectively means, for the design of dull and stereotyped crack array antenna provides the admittance data that accurately are suitable for.

Description of drawings

The geometric representation that Fig. 1 rooftop basic function is set up at the place, slit

Fig. 2 is the equivalent electric circuit in all slits in the array antenna root waveguide of dull and stereotyped crack

Embodiment

In the equivalent circuit diagram in slit, standing-wave array is got y in certain root waveguide of dull and stereotyped crack array antenna array shown in Figure 2 _l=0.Can try to achieve the forward scattering coefficient Γ at place, m slit according to the field distribution situation at the place, slit that obtains in (1) _mWith backscattering coefficient T _m, the two has all comprised the effect by the mirror image slit of short circuit face equivalence.According to transmission line theory, the seam voltage in m slit is:

$V_m=(1+\underset{i=1}{\overset{m-1}{\mathrm{\Σ}}}{T}_i)e^{-j{\mathrm{\θ}}_m}+(1+\underset{i=m}{\overset{Q_p}{\mathrm{\Σ}}}{\mathrm{\Γ}}_i)e^{{\mathrm{j\θ}}_m}---\left(3\right)$

And the seam voltage in the reflection coefficient at the admittance value in m slit and transmission line plane of reference place and this slit is relevant, and relational expression is:

y _m＝-2Γ _m0/V _m????????????????????????(2)

It should be noted that wherein the backscattering coefficient in slit self is Γ owing to considered the mirror image effect on the short-and-medium road surface of standing-wave array _M0=Γ _m/ 2, Γ _M0Do not comprise the effect of the back scattering field in its mirror image slit.

Calculate the field distribution of dull and stereotyped crack battle array radiating slot with moment Method Analysis.In dull and stereotyped crack battle array, be in the standing-wave array waveguide slotted array, the field of certain slit upper surface, mainly comprise self radiation field and array in the radiation field in other slits in the stack at place, this slit, and the field of lower surface comprises, the scattered field in other slit and mirror image slit thereof is in the stack at this place, slit in the mirror field of in-field, short circuit face, the same waveguide.According to the continuity in magnetic field, set up field equation in the upper and lower surface in slit, select Rooftop basic function (4) formula and pulse verification function (5) formula for use, integral equation is changed into matrix form, solving equation can obtain the distribution situation of the field at place, slit.

Obtain the active admittance in slit by slit place's forward direction and back scattering field.

Coding is finished the extraction of above-mentioned active admittance.

Determine the equivalent factor in square toes slit and round end slit with HFSS emulation.Because moment method can only be calculated the square toes slit when calculating dull and stereotyped crack battle array radiating slot active admittance, this round end slit with actual processing is not inconsistent.Adopt HFSS software respectively simulation analysis to be carried out in square toes and round end slit and obtain equivalent relation between the two, relation can get that length correction factor c is between square toes and the round end slit thus:

$c=\frac{L_y-L_f}{w(1-\mathrm{\π}/4)}---\left(3\right)$

Wherein, L _yBe the length in cup head slit, L _fLong for the seam in square toes slit, w is the width in slit.

The modifying factor C of gained revises the gap length that moment method is calculated above adopting.The seam in round end slit of knowing the active admittance correspondence of being extracted thus is long.

According to top method, be centre frequency with the millimeter wave frequency band frequency, radiating guide is selected non-standard waveguide for use, stitches the wide 0.8mm that all gets.At first adopt moment method to extract the active admittance of radiating slot in 5 * 5 little gust, the resonant slit length that wherein obtains is meant the length in square toes slit.

When table 1 is biased to 0.45mm in the battle array resonance electricity in each slit lead

The position in slit	??1	??2	??3	??4	??5
						??1	??0.2391	??0.2594	??0.248	??0.2596	??0.239
??2	??0.3869	??0.3766	??0.4246	??0.3767	??0.3871
						??3	??0.4805	??0.5364	??0.5101	??0.5352	??0.484
??4	??0.3657	??0.4223	??0.3906	??0.4206	??0.3657
						??5	??0.2491	??0.2428	??0.2632	??0.2424	??0.2484

The resonance length in each slit in battle array when table 2 is biased to 0.45mm

The position in slit	??1	??2	??3	??4	??5
						??1	??4.2138	??4.225	??4.2135	??4.2256	??4.2097
??2	??4.1689	??4.1836	??4.1593	??4.1841	??4.1658
						??3	??4.1744	??4.1654	??4.1678	??4.1659	??4.1716
??4	??4.1837	??4.1583	??4.1855	??4.1587	??4.1804
						??5	??4.2216	??4.2092	??4.2283	??4.2102	??4.2178

Because what moment method was calculated is the length in square toes slit, and the slit of actual processing and fabricating is a round end, adopt the method in the step 4 so, with HFSS difference emulation square toes and round end slit both of these case, be biased to 0.45mm equally, stitch wide when being 0.8mm, the resonance electricity is led and is 0.21, the resonance length in square toes slit is 4.26mm, the resonance length in round end slit is 4.45mm, the modifying factor C that finally obtains square toes and round end gap length is 1.1, and this moment, available this modifying factor C revised the resonance length value that moment method is calculated.

Same, the resonance length and the resonance electricity that can obtain other biasings (comprising 0.25mm, 0.35mm, 0.55mm, 0.65mm, 0.75mm and 0.85mm) are led, because length is limit, enumerate no longer one by one.

In the large-scale dull and stereotyped crack array antenna of design, design according to residing diverse location place, slit in the big battle array, the biasing in the slit in the middle of the battle array and edge diverse location place and seam length can design by the admittance data in the slit at diverse location place in 5 * 5 little battle arrays greatly.

The HFSS software that the present invention adopts is the HFSS11 version that Ansoft company makes, and is bought by electronics ten.

Claims (6)

1. the method for an accurately obtaining antenna radiating gap active admittance of planar slotted array is characterized in that comprising the steps:

(1) calculates the field distribution of dull and stereotyped crack battle array radiating slot with moment Method Analysis, continuity according to magnetic field, upper and lower surface in the slit is set up field equation, select Rooftop basic function and pulse verification function for use, integral equation is changed into matrix form, and solving equation can obtain the distribution situation of the field at place, slit;

(2) obtain the active admittance in slit by slit place forward direction and back scattering field;

(3) adopt HFSS software respectively square toes and round end slit to be carried out simulation analysis, obtain the equivalent relation between the two, try to achieve length correction factor c between square toes and the round end slit by following relational expression:

$c=\frac{L_y-L_f}{w(1-\mathrm{\π}/4)}---\left(3\right)$

Wherein, L _yBe the length in round end slit, L _fBe the length in square toes slit, w is the width in slit;

(4) revise the round end gap length of the active admittance correspondence that moment method calculates with the above-mentioned modifying factor c that asks.

2. the method for accurately obtaining antenna radiating gap active admittance of planar slotted array as claimed in claim 1 is characterized in that, described Rooftop basic function is

Wherein used symbol is seen shown in Figure 1, and h is a step-length, ζ ₀, ζ ₁... ζ _NBe node, ζ _j=-l+jh.

3. the method for accurately obtaining antenna radiating gap active admittance of planar slotted array as claimed in claim 1 is characterized in that, described pulse verification function is

Wherein, ${\mathrm{\ζ}}_i^{+}={\mathrm{\ζ}}_i+h/2,{\mathrm{\ζ}}_i^{-}={\mathrm{\ζ}}_i-h/2.$

4. the method for accurately obtaining antenna radiating gap active admittance of planar slotted array as claimed in claim 1 is characterized in that, described field equation is

Get the field equation of setting up at the upper and lower surface place in pq slit as follows respectively:

${\stackrel{v}{H}}_{\mathrm{pq},s1}^{s1}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})+{\stackrel{v}{H}}_{\mathrm{pq},s2}^{s1}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})={\stackrel{v}{H}}_{\mathrm{pq},\mathrm{\ζ}}^{\mathrm{inc}}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})+{\stackrel{v}{H}}_{\mathrm{pq},\mathrm{\ζ}}^{\mathrm{scat}}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})+$

$\underset{k=1,k\≠q}{\overset{Q_p}{\mathrm{\Σ}}}{\stackrel{V}{H}}_{\mathrm{pk},\mathrm{\ζ}}^{\mathrm{int}}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})---\left(6\right)$

${\stackrel{V}{H}}_{\mathrm{pq},s1}^{s2}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})+{\stackrel{V}{H}}_{\mathrm{pq},s2}^{s2}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})={\stackrel{V}{H}}_{\mathrm{pq},\mathrm{\ζ}}^{\mathrm{rad}}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})+\underset{k=11,k\≠\mathrm{pq}}{\overset{{\mathrm{PQ}}_p}{\mathrm{\Σ}}}{\stackrel{V}{H}}_{k,\mathrm{\ζ}}^{\mathrm{ext}}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})---\left(7\right)$

Wherein, ζ _i ^Pq, ξ _i ^PqThe coordinate of representing pq i the node of slit in local coordinate.

The inboard magnetic current of two bore faces up and down that is pq slit respectively is in the inboard magnetic field, seam chamber that produces of the lower surface in slit;

The inboard magnetic current of two bore faces up and down that is pq slit respectively is in the inboard magnetic field, seam chamber that produces of the upper surface in slit;

It is the exciting field of the lower surface outside generation in q the slit of p root waveguide in this waveguide;

Be the scattered field of the lower surface outside electric current in pq slit and its mirror image slit in this slit lower surface generation;

Be the magnetic field of all slits in the waveguide of p root and mirror image slit lower surface thereof outside magnetic current in the lower surface outside generation in pq slit;

It is the radiation field that the upper surface outside, pq slit magnetic current produces in this upper surface outside, slit;

The magnetic field that expression other slits except that pq slit produce in the upper surface outside in this slit.

5. the method for accurately obtaining antenna radiating gap active admittance of planar slotted array as claimed in claim 1 is characterized in that, described integral equation is

Get the field integral equation of setting up at the upper and lower surface place in pq slit as follows respectively:

$\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{a}_j\underset{\mathrm{spq}1}{\∫\∫}{q}_i({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})\left[\underset{\mathrm{spq}1}{\∫\∫}\right[G^{s1}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}},{{\mathrm{\ζ}}^{\′}}_{\mathrm{pq}},{{\mathrm{\ξ}}^{\′}}_{\mathrm{pq}})+G^{\mathrm{scat}}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}},{{\mathrm{\ζ}}^{\′}}_{\mathrm{pq}},{{\mathrm{\ξ}}^{\′}}_{\mathrm{pq}})\left]f_i({{\mathrm{\ζ}}^{\′}}_{\mathrm{pq}},{{\mathrm{\ξ}}^{\′}}_{\mathrm{pq}})\mathrm{ds}\right]\mathrm{ds}+$

$\underset{k=1,k\≠q}{\overset{Q_p}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{a}_j^{\mathrm{pk}}\underset{\mathrm{spq}1}{\∫\∫}{q}_i({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})\left[\underset{\mathrm{spk}1}{\∫\∫}{G}^{\mathrm{scat}}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}},{{\mathrm{\ζ}}^{\′}}_{\mathrm{pk}},{{\mathrm{\ξ}}^{\′}}_{\mathrm{pk}})f_j({{\mathrm{\ζ}}^{\′}}_{\mathrm{pk}},{{\mathrm{\ξ}}^{\′}}_{\mathrm{pk}})\mathrm{ds}\right]+$

$\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{b}_j^{\mathrm{pq}}\underset{\mathrm{spq}1}{\∫\∫}{q}_i({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})\left[\underset{\mathrm{spq}2}{\∫\∫}{G}^{s2}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}},{{\mathrm{\ζ}}^{\′}}_{\mathrm{pq}},{{\mathrm{\ξ}}^{\′}}_{\mathrm{pq}})f_j({{\mathrm{\ζ}}^{\′}}_{\mathrm{pq}},{{\mathrm{\ξ}}^{\′}}_{\mathrm{pq}})\mathrm{ds}\right]\mathrm{ds}$

$=\underset{s1}{\∫\∫}{q}_i({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})H_{\mathrm{\ζ}}^{\mathrm{inc}}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})\mathrm{ds}---\left(8\right)$

$\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{a}_j^{\mathrm{pq}}\underset{\mathrm{spq}2}{\∫\∫}{q}_i({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})\left[\underset{\mathrm{spq}1}{\∫\∫}{G}^{s2}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}},{{\mathrm{\ζ}}^{\′}}_{\mathrm{pq}},{{\mathrm{\ξ}}^{\′}}_{\mathrm{pq}})f_j({{\mathrm{\ζ}}^{\′}}_{\mathrm{pq}},{{\mathrm{\ξ}}^{\′}}_{\mathrm{pq}})\mathrm{ds}\right]\mathrm{ds}+$

$\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{b}_j^{\mathrm{pq}}\underset{\mathrm{spq}2}{\∫\∫}{q}_i({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})\left[\underset{\mathrm{spq}2}{\∫\∫}\right[G^{s1}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}},{{\mathrm{\ζ}}^{\′}}_{\mathrm{pq}},{{\mathrm{\ξ}}^{\′}}_{\mathrm{pq}})+G^{\mathrm{rad}}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}},{{\mathrm{\ζ}}^{\′}}_{\mathrm{pq}},{{\mathrm{\ξ}}^{\′}}_{\mathrm{pq}})\left]f_i({{\mathrm{\ζ}}^{\′}}_{\mathrm{pq}},{{\mathrm{\ξ}}^{\′}}_{\mathrm{pq}})\mathrm{ds}\right]\mathrm{ds}+$

$\underset{k=11,k\≠\mathrm{pq}}{\overset{\mathrm{PQp}}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{b}_j^k\underset{\mathrm{spp}2}{\∫\∫}{q}_i({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}})\left[\underset{\mathrm{sk}2}{\∫\∫}{G}^{\mathrm{rad}}({\mathrm{\ζ}}_{\mathrm{pq}},{\mathrm{\ξ}}_{\mathrm{pq}},{{\mathrm{\ζ}}^{\′}}_{\mathrm{pq}},{{\mathrm{\ξ}}^{\′}}_{\mathrm{pq}})f_j({{\mathrm{\ζ}}^{\′}}_{\mathrm{pq}},{{\mathrm{\ξ}}^{\′}}_{\mathrm{pq}})\mathrm{ds}\right]\mathrm{ds}=0---\left(9\right)$

Wherein, G ^ScatIt is the Green's function of opening the endless waveguide of longitudinal joint on the broadside; G ^S1Be that magnetic current on the bore face produces the Green's function in the chamber, slit in magnetic field on this magnetic current face; G ^S2Be that magnetic current on the bore face produces the Green's function in the chamber, slit in magnetic field on another bore face; G ^RadIt is the Green's function of the radiation space outside the slit.

6. the method for accurately obtaining antenna radiating gap active admittance of planar slotted array as claimed in claim 1 is characterized in that, described matrix form is

[Y][x]＝[F]

Wherein, [Y] is the admittance matrix of broad sense, and [x] is the coefficient matrix that will find the solution, and [F] is the matrix relevant with excitation factor.

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