CN101806836A - Method for analyzing MCM+MOM admittance error of plate leaky antenna - Google Patents

Abstract

The invention discloses a method for analyzing an MCM+MOM admittance error of a plate leaky antenna. The method mainly comprises the following steps of: establishing an error analysis mathematical model of relation between radiating slot admittance and each structure parameter error item of an admittance testing piece by using a moment method; selecting a rooftop primary function [1] and a rectangular pulse check function, establishing a field integral equation on an upper surface and a lower surface of a slot, converting the field integral equation into a rectangular form, solving the field distribution of the slot and the reflection coefficient S11[2] of a waveguide port, and solving the admittance y of the slot according to the relation between the admittance and the reflection coefficient, namely y=-2S11/(1+S11), wherein a computer program realizes the established mathematical model by six structure parameter error functions; providing a suitable machining error index; and analyzing errors of a testing apparatus with a MCM to obtain a statistical result of influence of a testing error on the admittance. Compared with the prior art, the method for analyzing the MCM+MOM admittance error of the plate leaky antenna has the advantages of convenience, quickness, accuracy, higher speed than that of a finite element method, and higher efficiency.

Description

Method for analyzing MCM+MOM admittance error of plate leaky antenna

Technical field

The invention relates to when extracting the admittance of Planar Slot Antenna radiating slot, analyze the method for Planar Slot Antenna admittance error.

Background technology

The admittance error analysis of in the past carrying out in theory, usually radiating slot seam length and the influence of biasing have only been analyzed to admittance, and to the size of waveguide, width as broadside, narrow limit and wall thickness and slit is not analyzed, such error analysis is rough, and the radiating slot admittance under high frequency is all very responsive to the size in waveguide dimensions and slit, and at this moment, traditional error analysis method obviously can not meet the demands.

To carry out the extraction of admittance exactly, at first must guarantee the accuracy of admittance test block processing dimension, must analyze each structural parameters of admittance test block (the biasing δ that has comprised waveguide broadside a, Narrow Wall of Waveguide limit b, waveguide wall thickness t, gap length 2l, gap width w and slit) so accurately to the influence of admittance and influence degree separately thereof, thereby propose rational mismachining tolerance requirement.Secondly, also need clearly to know of the influence of test macro error to the admittance extraction.Obtain the total error that experimental method extracts admittance by analysis, instruct the processing and the test thereof of admittance test block thus, guarantee the accuracy of the admittance data that experiment is extracted above error.

Summary of the invention

The present invention is directed to the weak point that above-mentioned prior art exists, provide a kind of more convenient, quick, accurate, the method for the analysis Planar Slot Antenna admittance error that efficient is higher than above-mentioned prior art

Above-mentioned purpose of the present invention can reach by following measure.A kind of method for analyzing MCM+MOM admittance error of plate leaky antenna provided by the invention is characterized in that comprising the steps:

(1) adopt method of moment (MOM) to set up the error analysis mathematical model that concerns between radiating slot admittance and each structural parameters error term of admittance test block;

(2) select rooftop basis function [1] and rect.p. verification function for use, utilize the continuity in magnetic field on the upper and lower surfaces in slit, to set up field equation, and integral equation changed into the form of matrix, and find the solution the field distribution that obtains the slit, obtain the reflection coefficient S of waveguide port ₁₁[2], again according to the y=-2S that concerns of admittance and reflection coefficient ₁₁/ (1+S ₁₁) trying to achieve the admittance y in slit, admittance value y is respectively a and b about the length and width of waveguide, and the wall thickness of waveguide is t, seam is long to be 2l, and stitching wide is w, and the position model that the waveguide core line is departed from the slit is biased to δ, the function of six structural parameters errors is finished and is set up mathematical model.

(3) computer programming is realized the mathematical model in (1).

(4) regard the structural parameters error term in above-mentioned waveguide and slit as obey certain probability distribution stochastic variable, and these variablees are sampled.

(5) carry out statistical computation in the mathematical model program with sample value substitution error,, propose suitable mismachining tolerance index according to result of calculation;

(6) with MCM the error of testing tool is analyzed, the error of testing tool promptly is the test error of scattering parameter S parameter.Regard the amplitude and the phase error of S parameter as obey certain probability distribution stochastic variable, it is carried out sample calculation, obtain the statistics of test error the admittance influence;

(7) total error that experimental method extracts the radiating slot admittance is proposed.

The present invention has following beneficial effect than prior art:

MCM+MOM admittance error analysis method utilizes method of moment to set up mathematical model, and the parameter of obeying certain probability distribution is carried out random sampling, with the simulation real physical process, and last statistical model output result's error profile.

When experimental method extracts the admittance of Planar Slot Antenna radiating slot, error is extracted in admittance be divided into two class errors: the mismachining tolerance of test block and instrument test error.Calculate above two class errors respectively with Monte Carlo method (MCM), at last two class errors are synthesized, obtain testing the total error of extracting the radiating slot admittance, instruct the processing and the test thereof of admittance test block with this.

The present invention compares more convenient, quick, accurate with error analysis method in the past, consideration to the structural parameters error that influences admittance is more comprehensive, because this method can be analyzed the width in waveguide length and width, wall thickness and slit, this be in the past the error analysis method can not finish.Therefore this analytical approach is more pressed close to the process that actual processing produces error.In addition, the mathematical model of this method is set up with the MOM method and is realized that with computer program speed is fast, the efficient height.And in the admittance of high bands such as millimeter wave is extracted, its advantage also is very tangible, because the radiating slot admittance is more responsive to each structural parameters error of test block under the high frequency, must know influence and the influence degree thereof of each error term to admittance so accurately, the accurately comprehensive error analysis that MCM+MOM error analysis method provides just in time can well be finished such work.

Description of drawings

Fig. 1 is a Planar Slot Antenna gap waveguide synoptic diagram.

Fig. 2 is the vertical view in Planar Slot Antenna slit.

The geometric representation that Fig. 3 rooftop basis function is set up at the place, slit.

Embodiment

At first set up the mathematical model of error analysis at the radiating slot place of waveguide leaky antenna according to the inventive method.Adopt method of moment (MOM) to set up the mathematical model of error analysis, promptly set up the relation between each structural parameters error term of radiating slot admittance and admittance test block.Length and width by Fig. 1, waveguide shown in Figure 2 are respectively a and b, and the wall thickness of waveguide is t, and seam is long to be 2l, stitchs wide w of being and slit and depart from the position of waveguide core line and promptly be biased to δ.Adopt MOM to analyze, select rooftop basis function [1] and rect.p. verification function [2] for use, utilize the continuity in magnetic field on the upper and lower surfaces in slit, to set up field equation, and integral equation is changed into the form of matrix, find the solution the field distribution that obtains the slit, thereby can obtain the reflection coefficient S of waveguide port ₁₁[2], again according to the y=-2S that concerns of admittance and reflection coefficient ₁₁/ (1+S ₁₁) can be in the hope of the admittance y in slit:

$y=\frac{-2\frac{j{(\mathrm{\π}/a)}^2}{\mathrm{\π\ω}{\mathrm{\μ}}_0{\mathrm{\β}}_{10}^{3}h}\cos \left[\frac{\mathrm{\π}}{a}(\frac{a}{2}+{\mathrm{\δ}}^{\′})\right]\sin (\frac{\mathrm{\π}}{a}\×\frac{w}{2})[1-\cos \left({\mathrm{\β}}_{10}h\right)]\underset{j=1}{\overset{N-1}{\mathrm{\Σ}}}{a}_j{e}^{-j{\mathrm{\β}}_{10}{\mathrm{\ζ}}_j}}{1-\frac{j{(\mathrm{\π}/a)}^2}{\mathrm{\π\ω}{\mathrm{\μ}}_0{\mathrm{\β}}_{10}^{3}h}\cos \left[\frac{\mathrm{\π}}{a}(\frac{a}{2}+\mathrm{\δ})\right]\sin (\frac{\mathrm{\π}}{a}\×\frac{w}{2})[1-\cos \left({\mathrm{\β}}_{10}h\right)]\underset{j=1}{\overset{N-1}{\mathrm{\Σ}}}{a}_j{e}^{-j{\mathrm{\β}}_{10}{\mathrm{\ζ}}_j}}---\left(1\right)$

This admittance value is a function about waveguide and gap structure parameter.

When producing error in the process, x=x ₀+ Δ x.Wherein x represents a, δ, and t, w, the Design Theory value of any one among 2l and the δ, Δ x represents the error term Δ a corresponding with their theoretical value, Δ b, Δ t, Δ w, among Δ 2l and the Δ δ one.Admittance value y about the function of these six structural parameters errors is so:

y＝f(Δa，Δb，Δt，Δw，Δ2l，Δδ)???????????(2)

$y=\frac{-2\frac{j{(\mathrm{\π}/a^{\′})}^2}{\mathrm{\π\ω}{\mathrm{\μ}}_0{\mathrm{\β}}_{10}^3{h}^{\′}}\cos \left[\frac{\mathrm{\π}}{a^{\′}}(\frac{a^{\′}}{2}+{\mathrm{\δ}}^{\′})\right]\sin (\frac{\mathrm{\π}}{a^{\′}}\×\frac{w^{\′}}{2})[1-\cos \left({\mathrm{\β}}_{10}{h}^{\′}\right)]\underset{j=1}{\overset{N-1}{\mathrm{\Σ}}}{a}_j{e}^{-j{\mathrm{\β}}_{10}{{\mathrm{\ζ}}_j}^{\′}}}{1-\frac{j{(\mathrm{\π}/a^{\′})}^2}{\mathrm{\π\ω}{\mathrm{\μ}}_0{\mathrm{\β}}_{10}^3{h}^{\′}}\cos \left[\frac{\mathrm{\π}}{a^{\′}}(\frac{a^{\′}}{2}+{\mathrm{\δ}}^{\′})\right]\sin (\frac{\mathrm{\π}}{a^{\′}}\×\frac{w^{\′}}{2})[1-\cos \left({\mathrm{\β}}_{10}{h}^{\′}\right)]\underset{j=1}{\overset{N-1}{\mathrm{\Σ}}}{a}_j{e}^{-j{\mathrm{\β}}_{10}{{\mathrm{\ζ}}_j}^{\′}}}---\left(3\right)$

A '=a+ Δ a wherein, δ '=δ+Δ δ, w '=w+ Δ w, h '=(2l+ Δ 2l)/N,

A wherein _jBe the coefficient factor of finding the solution the electric field of field equation gained, used Narrow Wall of Waveguide limit b ' in the solution procedure=b+ Δ b, wall thickness t '=t+ Δ t.Admittance y is about error term Δ a so, Δ b, and Δ t, Δ w, the mathematical model of Δ 2l and Δ δ is set up and is finished.Wherein to error term Δ a, Δ b, Δ t, Δ w, when Δ 2l and Δ δ carried out sample calculation, available computers produced the random number of Normal Distribution and simulates.

Realize the computational analysis of above-mentioned mathematical model by computer programming.

Regard the structural parameters error term in waveguide and slit as obey certain probability distribution stochastic variable, and these variablees are sampled.

Carry out statistical computation in the mathematical model program with sample value substitution error.Go on foot comprising two: at first be difference Analysis of Waveguide and gap structure parameter error item Δ a, secondly Δ b, Δ t, Δ w, Δ 2l and Δ δ are that these error terms are done the influence of time spent to admittance simultaneously to the influence of admittance and influence degree separately thereof.

Wherein the error of some structural parameters is bigger to the influence of admittance, broadside a as waveguide, stitch long 2l, biasing δ, mismachining tolerance to these structural parameters requires carry strictlyer so, and some error influences small construction parameter such as narrow limit b to admittance, stitches wide w and waveguide wall thickness t, then can suitably relax its mismachining tolerance index.

Adopt Monte Carlo method (MCM) that the error of testing tool is analyzed.The basis of admittance is extracted in experiment, is the measurement to the S parameter, and the error of testing tool promptly is a S parameter testing error so.Can regard the amplitude and the phase error of S parameter as obey certain probability distribution stochastic variable, it is carried out sample calculation, can obtain the statistics of test error equally the admittance influence.

The total error of experimental technique extraction admittance is determined jointly by the test error of mismachining tolerance and S scattering parameter.According to Can obtain the total error that experimental method extracts admittance, wherein σ _cFor the total error root-mean-square value of admittance, σ are extracted in experiment _jBe mismachining tolerance, σ _sMeasuring error for the S parameter.

Suppose that selecting centre frequency is a certain frequency of Ka wave band, waveguide is the standard waveguide a * b=7.112mm * 3.556mm of Ka wave band.The influence that the error of each structural parameters of considering waveguide and slit is at first respectively led resonance frequency and resonance electricity in ± 0.02mm scope the time.

The mismachining tolerance of each structural parameters of table 1 all gets ± during 0.02mm to the influence of resonance frequency

Structural parameters (mm)	??a	??b	??t	??w	??2l	??δ
							The mean square deviation (10 of resonance frequency 6Hz)	??2.156	??6.822	??6.371	??9.700	??34.225	??4.6518
The number percent of resonance frequency error (%)	??0.0187	??0.0592	??0.0552	??0.0841	??0.2968	??0.0403

The machining tolerance of each structural parameters of table 2 all gets ± influence the resonance electricity led during 0.02mm

Structural parameters (mm)	??a	??b	??t	??w	??2l	??δ
							The intermediate value that the resonance electricity is led	??0.1023	??0.1022	??0.1023	??0.1022	??0.1023	??0.1022
The mean square deviation (10 that the resonance electricity is led -4)	??5.1946	??0.7134	??0.7114	??1.5544	??4.8634	??11.85
							The percentage error that the resonance electricity is led (%)	??1.5233	??0.2094	??0.2086	??0.4563	??1.4262	??3.4785

What as can be seen resonance frequency and electric conductivity value precision are had the greatest impact according to the result of table 1 and table 2 so is gap length and slit biasing.Therefore adjust the error range of each parameter according to above result, the error range of 2l and δ is taken as ± 0.02mm, and the error range of b and t is got ± 0.03mm, and the error range of a and w is still got ± 0.02mm.When calculating these errors and existing simultaneously the resonance electricity is led influence with resonance frequency, shown in table 3,4:

The adjusted mismachining tolerance of table 3 is to the influence of resonance frequency

Biasing (mm)	??0.4	??0.7	??1.0	??1.3	??1.6	??1.9	??2.2	??2.5	??2.8
										Resonance frequency mean square deviation (10 7)	??2.9254	??2.8437	??3.0196	??2.8013	??2.8725	??2.9081	??2.8583	??2.8526	??2.7828
The number percent of resonance frequency error (%)	??0.2558	??0.2477	??0.2618	??0.2415	??0.2465	??0.2488	??0.2444	??0.2445	??0.2397

The influence that the adjusted mismachining tolerance of table 4 is led the resonance electricity

Biasing (mm)

??0.4

??0.7

??1.0

??1.3

??1.6

??1.9

??2.2

??2.5

??2.8

The intermediate value that the resonance electricity is led

??0.0184

??0.0535

??0.1018

??0.1579

??0.2178

??0.2798

??0.3434

??0.4086

??0.4744

The mean square deviation (10 that the resonance electricity is led -3)

??0.3179

??0.5829

??0.8751

??1.1886

??1.45

??1.759

??2.022

??2.415

??2.725

The percentage error that the resonance electricity is led (%)

??5.183

??3.2686

??2.5789

??2.259

??1.9972

??1.886

??1.7665

??1.7731

??1.7232

According to above calculating, obtained the index request of machining precision as follows:

The error range of 2l and δ is taken as ± 0.02mm, and the error range of b and t is got ± 0.03mm, and the error range of a and w is got ± 0.02mm.

Next be analysis to the testing tool error.Suppose the S of the biasing 1.0mm that HFSS emulation obtains ₁₁Value is S parameter value (the also S that can select for use MOM to calculate ₁₁), then change around this parameter value of test error.Each calculating 10,000 times, statistical computation is average and mean square deviation as a result, and 3 times of mean square deviation as error amount.

Getting range error is: ± 0.1dB, and phase error is: ± 1 °, the test error of gained is as shown in table 5:

Table 5 testing tool error is led influence with resonance frequency to the resonance electricity

Resonance frequency (mean square deviation GHz)	??0.0119
		Resonance frequency (error GHz)	??0.0357(0.10％)
The resonance electricity is led (HFSS calculated value)	??0.1019
		The resonance electricity is led (mean value GHz)	??0.1018
The resonance electricity is led (mean square deviation)	??7.0913e-004
		The resonance electricity is led (error)	??21.27e-004(2.09％)

So, the testing total error is:

The resonance electricity that table 6 method of testing obtains is led and resonance frequency error

Resonance frequency (error)	??±0.1％
		The resonance electricity is led (error)	??±1.0％

Can carry out detail analysis to the error that the experimental method admittance is extracted according to above-mentioned error analysis step, instrument can not propose suitable mismachining tolerance index, and can know the accuracy rating of measured admittance.This provides accurate error analysis data for experimental method extracts admittance, and especially its advantage is very outstanding in the admittance of high band is extracted.

The concrete form of rooftop basis function [1] and rect.p. verification function [2] is as follows:

[1] Rooftop basis function

Wherein h is a step-length, and w is wide for seam,

Be node,

2l is long for seam;

[2] pulse verification function is

Wherein used symbol is seen shown in Figure 3,

H is a step-length,

Be node.

The HFSS software that the present invention adopts is the HFSS11 version that Ansoft company makes.

Claims (4)

1. a method for analyzing MCM+MOM admittance error of plate leaky antenna is characterized in that comprising the steps:

(1) adopt method of moment (MOM) to set up the error analysis mathematical model that concerns between radiating slot admittance and each structural parameters error term of admittance test block;

(2) select rooftop basis function [1] and rect.p. verification function for use, utilize the continuity in magnetic field, on the upper and lower surfaces in slit, set up an integral equation, and integral equation is changed into the form of matrix, find the solution the field distribution that obtains the slit and the reflection coefficient S of waveguide port ₁₁[2], again according to the relational expression y=-2S of admittance and reflection coefficient ₁₁/ (1+S ₁₁) trying to achieve the admittance y in slit, admittance value y is respectively a and b about the length and width of waveguide, and the wall thickness of waveguide is t, seam is long to be 2l, and stitching wide is w, and the position model that the waveguide core line is departed from the slit is biased to δ, by the function of above-mentioned six structural parameters errors, set up and finish mathematical model;

(3) mathematical model in the computer programming performing step (1);

(4) regard the structural parameters error term in above-mentioned waveguide and slit as obey certain probability distribution stochastic variable, and these variablees are sampled;

(5) carry out statistical computation in the mathematical model program with above-mentioned sample value substitution error,, propose suitable mismachining tolerance index then according to the result of calculation in the step (4);

(6) with MCM the error of testing tool is analyzed, the error of testing tool promptly is the test error of scattering parameter S parameter; With the amplitude and the phase error of scattering parameter S parameter, regard the stochastic variable of obeying certain probability distribution as, it is carried out sample calculation, obtain the statistics of test error to the admittance influence;

(7) in the experimental method of above-mentioned steps (6), the total error of proposed radiation seam admittance.

2. method for analyzing MCM+MOM admittance error of plate leaky antenna as claimed in claim 1 is characterized in that, the admittance y in slit:

$y=\frac{-2\frac{j{(\mathrm{\π}/a)}^2}{{\mathrm{\π\ω\μ}}_0{\mathrm{\β}}_{10}^{3}h}\cos \left[\frac{\mathrm{\π}}{a}(\frac{a}{2}+{\mathrm{\δ}}^{\′})\right]\sin (\frac{\mathrm{\π}}{a}\×\frac{w}{2})[1-\cos \left({\mathrm{\β}}_{10}h\right)]\underset{j=1}{\overset{N-1}{\mathrm{\Σ}}}{a}_j{e}^{-j{\mathrm{\β}}_{10}{\mathrm{\ζ}}_j}}{1-\frac{{j(\mathrm{\π}/a)}^2}{{\mathrm{\π\ω\μ}}_0{\mathrm{\β}}_{10}^{3}h}\cos \left[\frac{\mathrm{\π}}{a}(\frac{a}{2}+\mathrm{\δ})\right]\sin (\frac{\mathrm{\π}}{a}\×\frac{w}{2})[1-\cos \left({\mathrm{\β}}_{10}h\right)]\underset{j=1}{\overset{N-1}{\mathrm{\Σ}}}{a}_j{e}^{-j{\mathrm{\β}}_{10}{\mathrm{\ζ}}_j}}---\left(1\right)$

This admittance value is a function about waveguide and gap structure parameter.A wherein, b is respectively the length and width of waveguide, the wall thickness of t waveguide, 2l is long for seam, and w is wide for seam, and δ is that β is promptly setovered in the position that the waveguide core line is departed from the slit ₁₀Be TE ₁₀The propagation coefficient of mould, the step-length when h is gap scatter, μ ₀Be magnetic permeability, ω is an angular frequency, J section center is to the distance of true origin, a when becoming the N section for gap scatter _jElectric field coefficient for the place, slit.

3. method for analyzing MCM+MOM admittance error of plate leaky antenna as claimed in claim 2 is characterized in that when producing error in the process x=x ₀+ Δ x.Wherein x represents a, b, and t, w, the Design Theory value of any one among 2l and the δ, Δ x represents the error term Δ a corresponding with their theoretical value, Δ b, Δ t, Δ w, among Δ 2l and the Δ δ one.Admittance value y about the function of these six structural parameters errors is so:

y＝f(Δa，Δb，Δt，Δw，Δ2l，Δδ)????(2)

$y=\frac{-2\frac{j{(\mathrm{\π}/a^{\′})}^2}{{\mathrm{\π\ω\μ}}_0{\mathrm{\β}}_{10}^3{h}^{\′}}\cos \left[\frac{\mathrm{\π}}{a^{\′}}(\frac{a^{\′}}{2}+{\mathrm{\δ}}^{\′})\right]\sin (\frac{\mathrm{\π}}{a^{\′}}\×\frac{w^{\′}}{2})[1-\cos \left({\mathrm{\β}}_{10}{h}^{\′}\right)]\underset{j=1}{\overset{N-1}{\mathrm{\Σ}}}{a}_j{e}^{-j{\mathrm{\β}}_{10}{{\mathrm{\ζ}}_j}^{\′}}}{1-\frac{{j(\mathrm{\π}/a^{\′})}^2}{{\mathrm{\π\ω\μ}}_0{\mathrm{\β}}_{10}^3{h}^{\′}}\cos \left[\frac{\mathrm{\π}}{a^{\′}}(\frac{a^{\′}}{2}+{\mathrm{\δ}}^{\′})\right]\sin (\frac{\mathrm{\π}}{a^{\′}}\×\frac{w^{\′}}{2})[1-\cos \left({\mathrm{\β}}_{10}{h}^{\′}\right)]\underset{j=1}{\overset{N-1}{\mathrm{\Σ}}}{a}_j{e}^{-j{\mathrm{\β}}_{10}{{\mathrm{\ζ}}_j}^{\′}}}---\left(3\right)$

A '=a+ Δ a wherein, δ '=δ+Δ δ, w '=w+ Δ w, h '=(2l+ Δ 2l)/N,

A wherein _jBe the coefficient factor of finding the solution the electric field of field equation gained, used Narrow Wall of Waveguide limit b ' in the solution procedure=b+ Δ b, wall thickness t '=t+ Δ t.

4. method for analyzing MCM+MOM admittance error of plate leaky antenna as claimed in claim 1 is characterized in that, the total error of experimental technique extraction admittance is determined jointly by the test error of mismachining tolerance and scattering parameter S parameter.

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