CN103698616A - Method of determining near-field phase center of antenna with complex structure - Google Patents

Abstract

The invention discloses a method for determining a near-field phase center of an antenna with a complex structure. The method comprises the following steps: 1) performing electromagnetic emulation modeling on the antenna with the complex structure; 2) determining the electromagnetic characteristic of the antenna with the complex structure; 3) determining a field value on a extrapolated boundary surface which encircles the antenna; 4) determining an auxiliary function of a reference observation surface of the phase center; 5) determining the curvature radius of an equiphase surface; 6) determining the near-field phase center of the antenna with the complex structure.

Description

A kind of definite method with labyrinth antenna near-field phase center

Technical field

The present invention relates to a kind of method of antenna near-field phase center evaluation, particularly relate to a kind of method with labyrinth antenna near-field phase center of determining.

Background technology

Due to spaceborne useful load requirement, the cross-sectional sizes in blackbody calibration source is limited, directivity to calibration antenna requires high, the 1/2(that main lobe wave beam drops on the focal radius on reference source adopts the diameter in cycle blackbody calibration source during calibration mode in 300mm-500mm left and right), the spacing in calibration antenna and blackbody calibration source is substantially within the scope of 200mm-700mm, this scope is near for the calibration antenna of the following frequency range of 90GHz, far field transitional region, its phase center can be along with the distance along antenna main lobe direction and observation angle generation marked change, while measuring blackbody calibration source emissivity based on space law, need accurately to determine near, in the transitional region of far field, blackbody calibration source is to the distance of calibration antenna phase center, and then evaluate bright temperature transmission system uncertainty.

Measuring the extensive method adopting of antenna phase center is three point method, and the method is mainly used in the measurement of low-frequency antenna far zone field phase center.For millimeter wave band antenna; while adopting three point method near region; conventionally can introduce the interference of testing apparatus to antenna near field; thereby test result is impacted; and measuring accuracy is all very high to the accuracy requirement of signal source frequency, the reflection of measuring place and environment, survey phase and distance mearuring equipment in test process, brings difficulty to the uncertainty evaluation of experiment test and measurement result.Therefore, for millimeter wave band calibration antenna, based on theory, calculate the evaluation result that provides phase center near, far field zone of transition a kind of effective method of can yet be regarded as.

The traditional antenna phase center theoretical calculation method all far-field region radiation field value based on antenna is determined, because the analytical expression of antenna far region radiation field is easily determined, adopt method or two point methods of in geometry of space, getting second derivative can realize determining of phase center.But, far field transitional region near at antenna, while determining the analytical expression of radiation field, need to assess the impact of propagation distance high-order term, and some antenna structure is complicated, the analytical expression of radiation field itself is just difficult to determine, cannot meet the calculation requirement that needs in the assessment method of conventional phase center obtain the radiation field analytical expression of antenna.

Therefore, need to have that a kind of method can obtain closely comparatively easily, the field value at transitional region observation station place, far field, overcome the difficulty that radiation field of aerial is near, far field transitional region analytical expression is difficult to determine, and determine corresponding phase center computing method, in order to applying by through engineering approaches.

Summary of the invention

For above the deficiencies in the prior art, object of the present invention provides a kind of method with labyrinth antenna near-field phase center of determining.First the method surrounds the field value on the extrapolated boundary of antenna by acquisition, obtain equivalent current and magnetic current on this extrapolated boundary, the vector potential function being represented by free space Green function obtains locating radiation field amplitude and the PHASE DISTRIBUTION on given plane cross section along the arbitrary distance of antenna main lobe direction (comprising near region and far field), utilize the constant phase front of radiation field amplitude and phase place on this planar interface to distribute, finally utilize geometry of space to determine that the method for radius-of-curvature determines the phase center of antenna.

The present invention adopts following technical proposals:

Determine a method with labyrinth antenna near-field phase center, the method comprises the steps:

1) labyrinth antenna is carried out to electromagnetics simulation modeling, determine the extrapolated boundary of labyrinth antenna, phase center computing reference plane, the observation point in reference planes and be positioned at the source point surrounding on antenna extrapolated boundary, and according to source point S on extrapolated boundary _aelectric field

and magnetic field

obtain the electric current on extrapolated boundary

and magnetic current

2) determine the Electromagnetism Characteristics of described labyrinth antenna;

3) determine the field value on the extrapolated boundary face that surrounds antenna;

4) determine the auxiliary function of the reference inspection surface of phase center;

5) determine constant phase front radius-of-curvature;

6) determine labyrinth antenna near-field phase center.

Electric current on described step 1 extrapolated boundary

and magnetic current for

${\stackrel{\→}{J}}_A={\stackrel{\→}{e}}_n\×{\stackrel{\→}{H}}_A$ With ${\stackrel{\→}{J}}_{\mathrm{mA}}=-{\stackrel{\→}{e}}_n\×{\stackrel{\→}{E}}_A---\left(1\right)$

Wherein,

represent the unit normal vector vertical with plane.

The Electromagnetism Characteristics 3 D auto space Green function of described step 2 labyrinth antenna

for:

$G\left(\stackrel{\→}{r}{,\stackrel{\→}{r}}^{\′}\right)=\frac{\exp (-\mathrm{jk}|\stackrel{\→}{r}-{\stackrel{\→}{r}}^{\′}\left|\right)}{4\mathrm{\π}|\stackrel{\→}{r}-{\stackrel{\→}{r}}^{\′}|}---\left(2\right)$

Wherein,

for the observation point S in phase center computing reference plane (4) _p(5) position vector,

for source point S _aposition vector

Observation point S in described step 3 phase center computing reference plane _pon radiation field intensity

for:

${\stackrel{\→}{E}}_{\mathrm{ij}}=-\▿\×\stackrel{\→}{F}+\frac{1}{\mathrm{j\ω\ϵ}}\▿\×\▿\×\stackrel{\→}{A}=-\▿\×\stackrel{\→}{F}-\mathrm{j\ω\μ}\stackrel{\→}{A}+\frac{1}{\mathrm{j\ω\ϵ}}\▿(\▿\·\stackrel{\→}{A})---\left(6\right)$

Wherein: i and j are S _pthe upper numbering of the discrete point along x and y direction.

Phase face radius-of-curvature in described step 5 is:

${\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA0000441934550000011.png"\; state="\{\{state\}\}">D</figure-callout>}}_2=\frac{a_0{b_0}^{\&prime;\&prime;}-b_0{a_0}^{\&prime;\&prime;}}{k({a_0}^2+{b_0}^2)},$

Wherein:

$a_0=a{|}_{\mathrm{\&theta;}=0}={\&Integral;}_{S_P}A\cos \mathrm{\&alpha;ds}$

$b_0=b{|}_{\mathrm{\&theta;}=0}={\&Integral;}_{S_P}A\sin \mathrm{\&alpha;ds}$

${a_0}^{\&prime;\&prime;}=\frac{d^{2}a}{d{\mathrm{\&theta;}}^2}{|}_{\mathrm{\&theta;}=0}={-\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000441934550000011.png"\; state="\{\{state\}\}">k</figure-callout>}}^2{\&Integral;}_{S_P}A\cos \mathrm{\&alpha;}{(x\cos \mathrm{\&phi;}+y\sin \mathrm{\&phi;})}^2\mathrm{ds}$

${b_0}^{\&prime;\&prime;}=\frac{d^{2}b}{d{\mathrm{\&theta;}}^2}{|}_{\mathrm{\&theta;}=0}={-\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000441934550000011.png"\; state="\{\{state\}\}">k</figure-callout>}}^2{\&Integral;}_{S_P}A\sin \mathrm{\&alpha;}{(x\cos \mathrm{\&phi;}+y\sin \mathrm{\&phi;})}^2\mathrm{ds}.$

The phase center D=D of described labyrinth antenna near-field ₂-D ₁, D ₁for Antenna aperture center is to phase center computing reference plan range.

Beneficial effect of the present invention is as follows:

Adopt Numerical Calculation of Electromagnetic Fields method to obtain the field value on the extrapolated boundary that surrounds antenna, obtain equivalent current and magnetic current on this extrapolated boundary, the vector potential function being represented by free space Green function obtains locating radiation field amplitude and the PHASE DISTRIBUTION on given plane cross section along the arbitrary distance of antenna main lobe direction (comprising near region and far field), utilize the constant phase front of radiation field amplitude and phase place on this planar interface to distribute, finally utilize geometry of space to determine that the method for radius-of-curvature determines the phase center of antenna, radiation field of aerial can be overcome near, the difficulty that far field transitional region analytical expression is difficult to determine, utilize through engineering approaches application.

Accompanying drawing explanation

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in further detail;

Fig. 1 is a kind of main block diagram of ultimate principle that is applicable to have the near filed phase center of labyrinth antenna of patent of the present invention.

Fig. 2 is a kind of algorithm flow chart of determining the near filed phase center method with labyrinth antenna of the present invention.Fig. 3 is that E face phase center value D is with the change curve of observation point D1 and frequency;

Fig. 4 is that H face phase center value D is with the change curve of observation point D1 and frequency.

Embodiment

For understanding better the present invention, below in conjunction with accompanying drawing, by specific embodiment, further illustrate the solution of the present invention, protection scope of the present invention should comprise the full content of claim, but is not limited to this.

If Fig. 1 is a kind of main block diagram of ultimate principle that is applicable to have the near filed phase center of labyrinth antenna of patent of the present invention.The antenna 1 with labyrinth has the extrapolated boundary 2 that surrounds labyrinth antenna, be positioned at the source point 3 surrounding on antenna extrapolated boundary, phase center computing reference plane 4, be positioned at the observation point 5 in phase center computing reference plane, Antenna aperture center is to phase center computing reference plan range 6, the radius-of-curvature 7 that equiphase curved surface is corresponding and antenna phase center 8.

Fig. 2 is a kind of algorithm flow chart of determining the near filed phase center method with labyrinth antenna of the present invention.For the antenna with labyrinth, a kind ofly determine that to have the method for labyrinth antenna near-field phase center specific as follows:

1. pair labyrinth antenna carries out electromagnetics simulation modeling, and calculates and surround the upper source point S in labyrinth antenna (1) extrapolated boundary (2) based on typical electrical the Magnetic Field Numerical Calculation methods such as finite element, Fdtd Method, method of moment _a(3) electric field and magnetic field

according to electric field

and magnetic field

can obtain the electric current on extrapolated boundary

and magnetic current

${\stackrel{\&RightArrow;}{J}}_A={\stackrel{\&RightArrow;}{e}}_n\&times;{\stackrel{\&RightArrow;}{H}}_A$ With ${\stackrel{\&RightArrow;}{J}}_{\mathrm{mA}}=-{\stackrel{\&RightArrow;}{e}}_n\&times;{\stackrel{\&RightArrow;}{E}}_A---\left(1\right)$

2. pair antenna carries out electromagnetics numerical simulation and determines, by the observation point S being positioned in phase center computing reference plane (4) _p(5) position vector

source point S _aposition vector

can obtain 3 D auto space Green function

$G\left(\stackrel{\&RightArrow;}{r}{,\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)=\frac{\exp (-\mathrm{jk}|\stackrel{\&RightArrow;}{r}-{\stackrel{\&RightArrow;}{r}}^{\&prime;}\left|\right)}{4\mathrm{\&pi;}|\stackrel{\&RightArrow;}{r}-{\stackrel{\&RightArrow;}{r}}^{\&prime;}|}---\left(2\right)$

And obtain vector potential function

with

$\stackrel{\&RightArrow;}{A}\left(\stackrel{\&RightArrow;}{r}\right)={\&Integral;}_{S_A}{\stackrel{\&RightArrow;}{J}}_A\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)G(\stackrel{\&RightArrow;}{r},{\stackrel{\&RightArrow;}{r}}^{\&prime;})\mathrm{ds}---\left(3\right)$

$\stackrel{\&RightArrow;}{F}\left(\stackrel{\&RightArrow;}{r}\right)={\&Integral;}_{S_A}{\stackrel{\&RightArrow;}{J}}_m\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)G(\stackrel{\&RightArrow;}{r},{\stackrel{\&RightArrow;}{r}}^{\&prime;})\mathrm{ds}---\left(4\right)$

In near, far field transitional region, must provide by strict calculating.And for far-field region

can be by approximate representation:

$|\stackrel{\&RightArrow;}{r}-{\stackrel{\&RightArrow;}{r}}^{\&prime;}|=r-{\stackrel{\&RightArrow;}{r}}^{\&prime;}\&CenterDot;{\stackrel{\&RightArrow;}{e}}_r---\left(5\right)$

Wherein

be

direction vector.

3. determine the field value on the extrapolated boundary face that surrounds antenna, by the Max dimension system of equations of isotropic medium, S _pon radiation field intensity be:

${\stackrel{\&RightArrow;}{E}}_{\mathrm{ij}}=-\&dtri;\&times;\stackrel{\&RightArrow;}{F}+\frac{1}{\mathrm{j\&omega;\&epsiv;}}\&dtri;\&times;\&dtri;\&times;\stackrel{\&RightArrow;}{A}=-\&dtri;\&times;\stackrel{\&RightArrow;}{F}-\mathrm{j\&omega;\&mu;}\stackrel{\&RightArrow;}{A}+\frac{1}{\mathrm{j\&omega;\&epsiv;}}\&dtri;(\&dtri;\&CenterDot;\stackrel{\&RightArrow;}{A})---\left(6\right)$

Wherein: i and j are S _pthe upper numbering of the discrete point along x and y direction.

Complete phase center computing reference face S _pon electric field value calculate after, can by second derivative method, complete the calculating of phase center according to step below.

4. determine the auxiliary function of the reference inspection surface of phase center, suppose phase center reference planes S _pif upper electric field E=Ae ^{j α}, wherein: A is amplitude, α is argument, the auxiliary computing function a of definition and b:

$a={\&Integral;}_{S_P}A\&CenterDot;\cos [\mathrm{\&alpha;}+k(x\cos \mathrm{\&phi;}+y\sin \mathrm{\&phi;})\sin \mathrm{\&theta;}]\mathrm{ds}---\left(7\right)$

$b={\&Integral;}_{S_P}A\&CenterDot;\sin [\mathrm{\&alpha;}+k(x\cos \mathrm{\&phi;}+y\sin \mathrm{\&phi;})\sin \mathrm{\&theta;}]\mathrm{ds}---\left(8\right)$

Wherein: θ, φ is observation point S in phase center reference planes _porientation angles and luffing angle, ds=dxdy, k=2 π/λ, λ is wavelength.

5. determine constant phase front radius-of-curvature D ₂, by phase center computing reference face S _pdistance D to phase center ₂(7) can be calculated as follows by space geometry method:

${\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA0000441934550000011.png"\; state="\{\{state\}\}">D</figure-callout>}}_2=\frac{a_0{b_0}^{\&prime;\&prime;}-b_0{a_0}^{\&prime;\&prime;}}{k({a_0}^2+{b_0}^2)}---\left(9\right)$

Wherein:

$a_0=a{|}_{\mathrm{\&theta;}=0}={\&Integral;}_{S_P}A\cos \mathrm{\&alpha;ds}---\left(10\right)$

$b_0=b{|}_{\mathrm{\&theta;}=0}={\&Integral;}_{S_P}A\sin \mathrm{\&alpha;ds}---\left(11\right)$

${a_0}^{\&prime;\&prime;}=\frac{d^{2}a}{d{\mathrm{\&theta;}}^2}{|}_{\mathrm{\&theta;}=0}={-\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000441934550000011.png"\; state="\{\{state\}\}">k</figure-callout>}}^2{\&Integral;}_{S_P}A\cos \mathrm{\&alpha;}{(x\cos \mathrm{\&phi;}+y\sin \mathrm{\&phi;})}^2\mathrm{ds}---\left(12\right)$

${b_0}^{\&prime;\&prime;}=\frac{d^{2}b}{d{\mathrm{\&theta;}}^2}{|}_{\mathrm{\&theta;}=0}={-\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000441934550000011.png"\; state="\{\{state\}\}">k</figure-callout>}}^2{\&Integral;}_{S_P}A\sin \mathrm{\&alpha;}{(x\cos \mathrm{\&phi;}+y\sin \mathrm{\&phi;})}^2\mathrm{ds}---\left(13\right)$

By to S _pdiscrete electrical E on face _ijintegration can complete a ₀, b ₀, a ₀", b ₀" calculating.

6. determine labyrinth antenna near-field phase center, D ₁for Antenna aperture center is to phase center computing reference plan range, the phase center 8D of antenna can obtain by following formula:

D=D ₂-D ₁ （14）

In the time need to calculating respectively the E face of antenna and H face phase center, the integration of formula (7) and (8) needs respectively along E face and S _pand H face and S _pintersection carry out.

Below illustrate the method with labyrinth antenna near-field phase center of determining.

As shown in Figure 1, for the antenna (1) with labyrinth, millimeter band corrugated horn antenna as shown in Figure 3, as spaceborne radiometer Feed Horn antenna, this corrugated horn working frequency range is 50GHz～65GHz, corrugated horn and blackbody calibration spacing be from carry out optimum experimental between 200mm～700mm, therefore need to be near at it, calculate its phase center in the zone of transition of far field, for the demarcation of radiometer.

Based on the inventive method, first antenna is carried out to electromagnetics simulation modeling, adopt typical Numerical Calculation of Electromagnetic Fields method, as Finite-Difference Time-Domain Method, determine the electric field on the extrapolated boundary face (2) that surrounds this antenna, then determine phase center computing reference face (4), if the distance of phase center computing reference face and Antenna aperture (6) is the value between 200mm～700mm, application of formula (1)-formula (6) completes the calculating of electromagnetic field magnitude and phase value on phase center computing reference face, by space geometry method, obtain the radius-of-curvature of phase center computing reference face, while being 200mm～700mm as can be calculated the distance of out of phase center calculation reference surface and Antenna aperture by second derivative method, the radius-of-curvature (7) of phase center computing reference face, thereby application of formula (14) can obtain the phase center value of this corrugated horn under different frequency out of phase center calculation reference surface, as shown in Figure 3-4, visible this corrugated horn is near, the following characteristic of far field zone of transition phase center value:

1, for steady job Frequency point, with observation point distance D ₁increase (changing to 700mm from 200mm), E face and H face phase center reduce.For example: at 60GHz, work as D ₁while changing to 700mm from 200mm, E face phase center D reduces to 29.4mm from 41.2mm;

2, for fixing observation point distance D ₁, the increase from 50GHz to 65GHz is approximated to linear change with frequency for E face and H face phase center D;

3, at D ₁during≤400mm (close near region time), E face and H face phase center D approximately equal, work as D ₁during>=400mm (close to far field time), E face and H face phase center D are along with the D of observation point distance ₁increase and difference becomes large.

Obviously; the above embodiment of the present invention is only for example of the present invention is clearly described; and be not the restriction to embodiments of the present invention; for those of ordinary skill in the field; can also make other changes in different forms on the basis of the above description; here cannot give all embodiments exhaustive, every still row in protection scope of the present invention of apparent variation that technical scheme of the present invention extends out or change that belong to.

Claims (6)

1. determine a method with labyrinth antenna near-field phase center, it is characterized in that, the method comprises the steps:

1) labyrinth antenna is carried out to electromagnetics simulation modeling, determine the extrapolated boundary of labyrinth antenna, phase center computing reference plane, the observation point in reference planes and be positioned at the source point surrounding on antenna extrapolated boundary, and according to source point S on extrapolated boundary _aelectric field

and magnetic field

obtain the electric current on extrapolated boundary

and magnetic current

2) determine the Electromagnetism Characteristics of described labyrinth antenna;

3) determine the field value on the extrapolated boundary face that surrounds antenna;

4) determine the auxiliary function of the reference inspection surface of phase center;

5) determine constant phase front radius-of-curvature;

6) determine labyrinth antenna near-field phase center.

2. a kind of method with labyrinth antenna near-field phase center of determining according to claim 1, is characterized in that the electric current on described step 1 extrapolated boundary

and magnetic current

for

${\stackrel{\&RightArrow;}{J}}_A={\stackrel{\&RightArrow;}{e}}_n\&times;{\stackrel{\&RightArrow;}{H}}_A$ With ${\stackrel{\&RightArrow;}{J}}_{\mathrm{mA}}=-{\stackrel{\&RightArrow;}{e}}_n\&times;{\stackrel{\&RightArrow;}{E}}_A---\left(1\right)$

Wherein,

represent the unit normal vector vertical with plane.

3. a kind of method with labyrinth antenna near-field phase center of determining according to claim 1, is characterized in that the Electromagnetism Characteristics 3 D auto space Green function of described step 2 labyrinth antenna

for:

$G\left(\stackrel{\&RightArrow;}{r}{,\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)=\frac{\exp (-\mathrm{jk}|\stackrel{\&RightArrow;}{r}-{\stackrel{\&RightArrow;}{r}}^{\&prime;}\left|\right)}{4\mathrm{\&pi;}|\stackrel{\&RightArrow;}{r}-{\stackrel{\&RightArrow;}{r}}^{\&prime;}|}---\left(2\right)$

Wherein,

for the observation point S in phase center computing reference plane (4) _p(5) position vector,

for source point S _aposition vector

4. a kind of method with labyrinth antenna near-field phase center of determining according to claim 1, is characterized in that the observation point S in described step 3 phase center computing reference plane _pon radiation field intensity

for:

${\stackrel{\&RightArrow;}{E}}_{\mathrm{ij}}=-\&dtri;\&times;\stackrel{\&RightArrow;}{F}+\frac{1}{\mathrm{j\&omega;\&epsiv;}}\&dtri;\&times;\&dtri;\&times;\stackrel{\&RightArrow;}{A}=-\&dtri;\&times;\stackrel{\&RightArrow;}{F}-\mathrm{j\&omega;\&mu;}\stackrel{\&RightArrow;}{A}+\frac{1}{\mathrm{j\&omega;\&epsiv;}}\&dtri;(\&dtri;\&CenterDot;\stackrel{\&RightArrow;}{A})---\left(6\right)$

Wherein: i and j are S _pthe upper numbering of the discrete point along x and y direction.

5. a kind of method with labyrinth antenna near-field phase center of determining according to claim 1, is characterized in that, the phase face radius-of-curvature in described step 5 is:

$D_2=\frac{a_0{b_0}^{\&prime;\&prime;}-b_0{a_0}^{\&prime;\&prime;}}{k({a_0}^2+{b_0}^2)},$

Wherein:

$a_0=a{|}_{\mathrm{\&theta;}=0}={\&Integral;}_{S_P}A\cos \mathrm{\&alpha;ds}$

$b_0=b{|}_{\mathrm{\&theta;}=0}={\&Integral;}_{S_P}A\sin \mathrm{\&alpha;ds}$

${a_0}^{\&prime;\&prime;}=\frac{d^{2}a}{d{\mathrm{\&theta;}}^2}{|}_{\mathrm{\&theta;}=0}={-k}^2{\&Integral;}_{S_P}A\cos \mathrm{\&alpha;}{(x\cos \mathrm{\&phi;}+y\sin \mathrm{\&phi;})}^2\mathrm{ds}$

${b_0}^{\&prime;\&prime;}=\frac{d^{2}b}{d{\mathrm{\&theta;}}^2}{|}_{\mathrm{\&theta;}=0}={-k}^2{\&Integral;}_{S_P}A\sin \mathrm{\&alpha;}{(x\cos \mathrm{\&phi;}+y\sin \mathrm{\&phi;})}^2\mathrm{ds}.$

6. a kind of method with labyrinth antenna near-field phase center of determining according to claim 1, is characterized in that the phase center D=D of described labyrinth antenna near-field ₂-D ₁, D ₁for Antenna aperture center is to phase center computing reference plan range.

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