CN111366793B - Planar antenna near field measurement method and system for reducing truncation error - Google Patents

Planar antenna near field measurement method and system for reducing truncation error Download PDF

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CN111366793B
CN111366793B CN202010482038.2A CN202010482038A CN111366793B CN 111366793 B CN111366793 B CN 111366793B CN 202010482038 A CN202010482038 A CN 202010482038A CN 111366793 B CN111366793 B CN 111366793B
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antenna
spectrum
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formula
plane
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CN111366793A (en
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周建华
栗曦
毛小莲
杨林
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Shanghai Hollywell Electronic System Technology Co ltd
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Abstract

The application discloses a plane antenna near field measurement method for reducing truncation errors. And obtaining the plane spectrum output by the probe through inverse Fourier transform according to the electric field received by the probe. And (6) performing probe correction. And calculating the credible spectral domain of the plane spectrum of the antenna to be tested by the emission spectrum and the spectral domain filter function of the antenna to be tested. And obtaining the aperture electric field of the antenna to be measured through Fourier transform of the credible spectral domain of the plane spectrum of the antenna to be measured. And obtaining a scalar form of a plane spectrum of the antenna to be detected and an electric field positioned between the antenna to be detected and the scanning surface by the aperture electric field of the antenna to be detected through inverse Fourier transform. Introducing additional row or column measurements, calculating the electric field at the position of the probe of the additional row or column; each time an additional row or column measurement is made, an iteration error is calculated. And repeating until the iteration error of the nth time is larger than the iteration error of the (n-1) th time, and terminating the iteration. The method and the device realize reduction of truncation errors in plane near-field measurement based on a band-limited function extrapolation algorithm.

Description

Planar antenna near field measurement method and system for reducing truncation error
Technical Field
The present disclosure relates to an antenna measurement technique, and more particularly, to a planar antenna measurement method based on planar near field scanning (planar field scanning) and capable of reducing truncation error.
Background
As can be known from the basic theory of planar near-field measurement, in order to accurately determine a far-field pattern (also called radiation pattern or antenna pattern) of an antenna to be measured, it is required to record the output of a probe (probe) on an infinite plane in front of the antenna to be measured, that is, it is required that a scanning plane (scanning plane) should be infinite. However, in practical measurement, the scanning surface is always limited, and the field outside the limited scanning surface (finite scanning plane) is assumed to be zero, so that errors are necessarily brought when determining the far-field pattern of the antenna by the near-field-far-field transformation. This error due to the limited scan surface is referred to as limited scan surface truncation error, or truncation error for short. The truncation error of the limited scan plane is one of the main error sources affecting the planar near-field measurement accuracy, especially for the planar near-field measurement and error diagnosis of ultra-low sidelobe antennas (ultra-low sidelobe antennas).
Typically the truncation level at the edge of the scan plane requires-40 dB to control the limited scan plane truncation error to a small extent. However, for a large array antenna (array antenna), the scanning area is too large, so that the near field test efficiency is low. For example, when a reflector antenna with an operating frequency of 30GHz and a caliber of 1.5 m is tested, when a scanning surface is a rectangle with a size of 2.4m × 2.4m, a sampling interval is 5mm, and a sampling rate is 80mm/s, 7 hours are consumed, and the efficiency is very low. If the scanning surface is reduced, the truncation error of the limited scanning surface inevitably has a large influence on the measurement result. Therefore, it is important to find a method to solve the truncation error.
Disclosure of Invention
The technical problem to be solved by the application is to provide a plane near-field antenna measuring method, which is based on plane near-field scanning and can reduce the influence of truncation errors on actual measuring results.
In order to solve the technical problem, the application provides a planar antenna near field measurement method for reducing truncation errors, which comprises the following steps. Step S10: the probe is arranged on a scanning surface parallel to the planar antenna, and a planar spectrum output by the probe is obtained through inverse Fourier transform according to an electric field received by the probe. Step S20: and (4) performing probe correction, namely obtaining the emission spectrum of the antenna to be measured by the emission spectrum of the probe and the plane spectrum output by the probe. Step S30: and calculating the credible spectral domain of the plane spectrum of the antenna to be tested by the emission spectrum and the spectral domain filter function of the antenna to be tested. Step S40: and obtaining the aperture electric field of the antenna to be measured through Fourier transform of the credible spectral domain of the plane spectrum of the antenna to be measured. Step S50: and obtaining a scalar form of a plane spectrum of the antenna to be detected and an electric field positioned between the antenna to be detected and the scanning surface by the aperture electric field of the antenna to be detected through inverse Fourier transform. Step S60: arranging a row or a column of probes between the antenna to be measured and the scanning surface, introducing additional row or column measurement, and repeating the steps S10 to S50 to calculate the electric field at the position of the additional row or column probes; each time an additional row or column measurement is made, an iteration error is calculated. Step S70: repeating the step S60 until the iteration error of the nth time is larger than the iteration error of the (n-1) th time, and terminating the iteration; at this time, the scalar form of the plane spectrum of the antenna under test calculated in step S50 is taken as the far-field pattern of the antenna under test. The method realizes the reduction of truncation errors in plane near-field measurement based on a band-limited function extrapolation algorithm.
Further, in step S10, a plane spectrum of the output of the probe on the scanning surface is calculated by using formula one.
Figure 596896DEST_PATH_IMAGE002
(formula one).
Wherein the content of the first and second substances,
Figure 487492DEST_PATH_IMAGE004
and
Figure 284546DEST_PATH_IMAGE006
respectively outputting an x component and a y component of a plane spectrum for the probe;
Figure 893382DEST_PATH_IMAGE008
and
Figure 129191DEST_PATH_IMAGE010
are respectively a probe at
Figure 139873DEST_PATH_IMAGE012
An x-component and a y-component of the electric field received at the location; k is a radical ofx、ky、kzThe x, y, z components of the wavenumber k, respectively. This is an exemplary implementation of step S10.
Further, k in the formula onex、ky、kzRespectively obtained by a formula II, a formula III and a formula IV.
Figure 107829DEST_PATH_IMAGE014
(formula two).
Figure 266278DEST_PATH_IMAGE016
(formula III))。
Figure 977882DEST_PATH_IMAGE018
(equation four).
Wherein M and N are the number of Fourier transform points along the x direction and the y direction respectively; Δ x and Δ y are the sampling intervals of the x-axis and the y-axis, respectively; and require
Figure 843069DEST_PATH_IMAGE020
. This is an exemplary way of calculating the three parameters.
Further, in step S20, a probe correction is performed using the formula five.
Figure 545709DEST_PATH_IMAGE022
(formula five).
Wherein the content of the first and second substances,
Figure 129137DEST_PATH_IMAGE024
and
Figure 378852DEST_PATH_IMAGE026
respectively in the form of vectors of emission spectra of an antenna to be detected and a probe;
Figure 426443DEST_PATH_IMAGE028
is the plane spectrum of the probe output. This is an exemplary implementation of step S20.
Further, in step S30, the confidence spectrum domain of the plane spectrum of the antenna to be measured is calculated by using the formula six
Figure 736201DEST_PATH_IMAGE030
。
Figure 806926DEST_PATH_IMAGE032
(equation six).
Wherein, URIs a spectral domain filtering function. This is an exemplary implementation of step S30.
Further, in the step S30, the expression of the spectral domain filter function is formula seven.
Figure 922649DEST_PATH_IMAGE034
(formula seven).
Wherein, thetaxAnd thetayRespectively calculating the credible angle domains in the x-axis direction and the y-axis direction according to the caliber of the antenna to be measured; gamma rayxAnd gammayTwo thresholds, γ, representing the x-axis direction and the y-axis directionxAnd gammayAre all greater than 1. This is an exemplary way of calculating a parameter.
Further, in step S40, the probe is calculated by fourier transform from the reliable spectrum domain of the plane spectrum of the antenna to be measured
Figure 762429DEST_PATH_IMAGE036
X and y components of the electric field received at the site, then spatial filtering functions are calculated, and finally the probe is positioned
Figure 243089DEST_PATH_IMAGE036
And calculating the x component and the y component of the aperture electric field of the antenna to be measured by the x component and the y component of the electric field received at the position and the spatial filtering function. This is an exemplary implementation of step S40.
Further, the probe is at
Figure 535530DEST_PATH_IMAGE036
X component of electric field received at location
Figure 454945DEST_PATH_IMAGE038
And the y component
Figure 149231DEST_PATH_IMAGE040
And calculating by adopting a formula eight.
Figure 800792DEST_PATH_IMAGE042
(formula eight).
Wherein the content of the first and second substances,
Figure 406961DEST_PATH_IMAGE044
and
Figure 802170DEST_PATH_IMAGE046
the x component and the y component of the plane wave spectrum of the antenna to be measured are respectively. This is an exemplary way of calculating a parameter.
Further, the spatial filtering function UAUTAnd calculating by adopting a formula nine.
Figure 350963DEST_PATH_IMAGE048
(formula nine).
Wherein N is0Is the number of points located within the antenna aperture; n is a radical ofnIs the number of transition points between the edge of the antenna aperture and the null point; n is a radical of1Is the number of fourier transform points. This is an exemplary way of calculating a parameter.
Further, the x component of the aperture electric field of the antenna to be measured
Figure 501322DEST_PATH_IMAGE050
And the y component
Figure 768355DEST_PATH_IMAGE052
And calculating by adopting a formula ten.
Figure 967255DEST_PATH_IMAGE054
(equation ten). This is an exemplary way of calculating a parameter.
Further, in step S50, the scalar form of the plane spectrum of the antenna under test
Figure 432872DEST_PATH_IMAGE056
And calculating by adopting a formula eleven. This is an exemplary implementation of step S50.
Figure 691815DEST_PATH_IMAGE058
(formula eleven).
Further, in step S50, the electric field located between the antenna to be measured and the scanning surface is located between the antenna to be measured and the scanning surface
Figure 446144DEST_PATH_IMAGE060
Electric field of
Figure 245473DEST_PATH_IMAGE062
And calculating by adopting a formula twelve.
Figure 768858DEST_PATH_IMAGE064
(formula twelve).
Wherein the content of the first and second substances,
Figure 198702DEST_PATH_IMAGE066
；
Figure 738530DEST_PATH_IMAGE068
is the distance between the antenna to be measured and the selected position, and d is the distance between the antenna to be measured and the scanning surface. This is an exemplary implementation of step S50.
Further, in step S60, the error of the nth iteration
Figure 279233DEST_PATH_IMAGE070
And calculating by adopting a formula thirteen.
Figure 922704DEST_PATH_IMAGE072
(equation thirteen).
Wherein the content of the first and second substances,
Figure 320187DEST_PATH_IMAGE074
means that additional rows or columns measure the electric field distribution corrected by the probe, and m is the extrapolated point coordinate. This is an exemplary implementation of step S60.
The application also provides a plane antenna near field measurement system for reducing truncation errors, which comprises a scanning surface plane spectrum calculation unit, a probe correction unit, a reliable spectrum domain calculation unit, an antenna aperture electric field calculation unit, an antenna plane spectrum calculation unit, a line or column measurement unit and an iteration unit. The scanning surface plane spectrum calculating unit is used for arranging the probe on a scanning surface parallel to the plane antenna, and obtaining the plane spectrum output by the probe through inverse Fourier transform according to the electric field received by the probe. The probe correction unit is used for correcting the probe, which means that the emission spectrum of the antenna to be measured is obtained by the emission spectrum of the probe and the plane spectrum output by the probe. The credible spectral domain calculating unit is used for calculating the credible spectral domain of the plane spectrum of the antenna to be measured by the emission spectrum of the antenna to be measured and the spectral domain filtering function. The antenna aperture electric field calculating unit is used for obtaining the aperture electric field of the antenna to be measured through Fourier transform of the credible spectrum domain of the plane spectrum of the antenna to be measured. The antenna plane spectrum calculating unit is used for obtaining a scalar form of a plane spectrum of the antenna to be detected and an electric field located between the antenna to be detected and the scanning surface through inverse Fourier transform of a caliber electric field of the antenna to be detected. The line or column measuring unit is used for arranging a line or column of probes between the antenna to be measured and the scanning surface, introducing additional line or column measurement, and repeating the calculation process of each unit to obtain an electric field at the position of the additional line or column probe; each time an additional row or column measurement is made, an iteration error is calculated. The iteration unit is used for terminating the iteration of the row or column measuring unit when the nth iteration error is larger than the (n-1) th iteration error; and the scalar form of the plane spectrum of the antenna to be tested calculated by the antenna plane spectrum calculating unit is used as the far-field directional diagram of the antenna to be tested.
The method has the technical effects that the truncation error algorithm for plane near-field scanning is reduced based on the band-limited function extrapolation algorithm, and is applied to plane near-field antenna measurement, so that the influence of truncation errors on actual measurement results is reduced, the angle domain can be effectively extrapolated, and the method has great engineering practical value.
In addition, the window function (formula nine) is introduced on the basis of the Gerchberg-Papoulis algorithm, so that the edge level can be preventedAnd (4) suddenly cutting off. For example, respectively taking N in the formula ninenIs 0, 5, 10, with NnThe distortion of the directional diagram of the antenna to be tested is gradually reduced.
In addition, the present application considers the attenuation mode (γ in formula seven)xAnd gammayGreater than 1), the push-back precision of the aperture field is improved. For example, respectively taking gamma in formula sevenx、γyIs 1, 1.25, 1.67 (gamma)x、γyThe same value), with gammax、γyThe value is increased, namely the attenuation mode is considered more fully, and the directional diagram of the antenna to be tested obtained by the method is closer to the theoretical directional diagram.
In addition, the method introduces additional row or column measurement as the reference field distribution of whether the algorithm is converged, so that the iteration can be immediately stopped when the extrapolation error is about to be amplified, and the extrapolation accuracy of the algorithm is improved. Through the three technical means, the precision of the plane near-field near-far-field transformation algorithm can be improved, and the testing precision of the testing system is further improved.
Drawings
Fig. 1 is a simplified model schematic of a planar antenna.
Fig. 2 is a flowchart of a near-field measurement method of a planar antenna with reduced truncation error proposed in the present application.
Fig. 3a is a schematic diagram comparing an antenna pattern obtained by a conventional near-field-far-field transformation method with a theoretical pattern.
Fig. 3b is a schematic diagram comparing the antenna pattern obtained by the conventional TGPA method with the theoretical pattern.
Fig. 3c is a schematic diagram comparing the antenna pattern obtained by the IGPA method proposed in the present application with the theoretical pattern.
Fig. 4 is a schematic diagram of the determination of the number of iterations in the IGPA method proposed in the present application.
Fig. 5 is a schematic structural diagram of a near-field measurement system of a planar antenna for reducing truncation errors according to the present application.
The reference numbers in the figures are: the device comprises a scanning plane spectrum calculating unit 10, a probe correcting unit 20, a reliable spectrum domain calculating unit 30, an antenna aperture electric field calculating unit 40, an antenna plane spectrum calculating unit 50, a line or column measuring unit 60 and an iteration unit 70.
Detailed Description
A function of fourier transform of frequency values outside a finite interval range around an origin to zero is called a band-limited function (band-limited function). When the function f (t) satisfies the band-limiting condition, i.e. when w>wcThe frequency spectrum f (w) =0 of f (t), where w represents frequency, w represents frequencycRepresents the boundary frequency of the function f (t). The band-limited function extrapolation algorithm (extrapolation) can recover f (t) from the finite samples of f (t) within a given interval.
For the measurement of the planar near-field antenna, the aperture field (aperturefield) is regarded as zero outside the aperture (aperture) of the antenna to be measured, so that the band-limited condition is met. Thus, the process of determining a plane wave spectrum (plane wave spectrum) from the finite field measured by a planar near-field antenna can be equated with a mathematical model of a band-limited function extrapolation.
Referring to fig. 1, a simplified model of a planar antenna is shown. The antenna to be tested is a planar antenna and is arranged on the xoy plane. The scan plane is perpendicular to the z-axis and parallel to the xoy plane. The distance between the antenna to be measured and the scanning surface is d.
Referring to fig. 2, the present application proposes a modified Gerchberg-Papoulis algorithm (IGPA for short) for near-field measurement of the planar antenna shown in fig. 1, which includes the following steps.
Step S10: the plane spectrum of the probe output is obtained by inverse fourier transform (inverse fourier transform) based on the electric field received by the probe, which is the step in which the probe is located on the scan plane in fig. 1. This step is calculated, for example, using equation one.
Figure 49109DEST_PATH_IMAGE002
(formula one).
In the formula I, the first step is carried out,
Figure 127923DEST_PATH_IMAGE004
and
Figure 688218DEST_PATH_IMAGE006
respectively outputting an x component and a y component of a plane spectrum for the probe;
Figure 194285DEST_PATH_IMAGE008
and
Figure 410503DEST_PATH_IMAGE010
are respectively a probe at
Figure 355325DEST_PATH_IMAGE012
The x-component and the y-component of the electric field received at the location. k is a radical ofx、ky、kzThe x, y, z components of the wavenumber k, respectively.
K in formula onex、ky、kzRespectively obtained by a formula II, a formula III and a formula IV.
Figure 707809DEST_PATH_IMAGE014
(formula two).
Figure 650357DEST_PATH_IMAGE016
(formula three).
Figure 655003DEST_PATH_IMAGE018
(equation four).
In a formula II, a formula III and a formula IV, M and N are Fourier transform points along the x direction and the y direction respectively; Δ x and Δ y are the sampling intervals on the x-axis and y-axis, respectively, which are less than λ/2 according to the Nyquist-Shannon sampling theorem (Nyquist-Shannon sampling theorem), where λ represents the wavelength. When calculating specifically, simultaneously consider
Figure 75620DEST_PATH_IMAGE020
The case of (1), namely the attenuation mode (evanescent mode) is considered.
Step S20: for accurate measurement, probe correction is carried out, which means that the emission spectrum of the antenna to be measured is obtained from the emission spectrum of the probe and the plane spectrum output by the probe. This step is calculated, for example, using equation five.
Figure 548190DEST_PATH_IMAGE022
(formula five).
In the formula five, the first step is carried out,
Figure 458377DEST_PATH_IMAGE024
and
Figure 383608DEST_PATH_IMAGE026
the emission spectra (emission spectra) of the antenna to be measured and the probe, respectively, are in the form of vectors.
Figure 607916DEST_PATH_IMAGE028
Is the plane spectrum of the probe output.
Step S30: calculating reliable spectrum domain (spectral domain) of plane spectrum of the antenna to be measured according to the emission spectrum and the spectrum domain filter function of the antenna to be measured
Figure 997309DEST_PATH_IMAGE030
. This step is calculated, for example, using equation six.
Figure 281660DEST_PATH_IMAGE032
(equation six).
In the sixth formula, URThe expression of the spectral domain filter function is calculated by using a formula seven.
Figure 694187DEST_PATH_IMAGE034
(formula seven).
In the seventh formula, thetaxAnd thetayThe confidence angle domains (angular domains) in the x-axis direction and the y-axis direction are respectively calculated according to the aperture of the antenna to be measured. Gamma rayxAnd gammayTwo thresholds, γ, representing the x-axis direction and the y-axis directionxAnd gammayBoth must be greater than 1 to account for the attenuation modes.
Step S40: reliable spectral domain of the plane spectrum of the antenna to be measured
Figure 518923DEST_PATH_IMAGE030
And obtaining the x component and the y component of the aperture electric field of the antenna to be measured through Fourier transform.
First, the probe is calculated in
Figure 700506DEST_PATH_IMAGE036
X component of electric field received at location
Figure 155758DEST_PATH_IMAGE038
And the y component
Figure 619362DEST_PATH_IMAGE040
For example, the formula eight is used for calculation.
Figure 185473DEST_PATH_IMAGE042
(formula eight).
In the formula eight, the first step is,
Figure 221562DEST_PATH_IMAGE044
and
Figure 910032DEST_PATH_IMAGE046
the x component and the y component of the plane wave spectrum of the antenna to be measured are respectively.
Then, a spatial filtering function U is calculatedAUTFor example, the formula nine is used for calculation.
Figure 297151DEST_PATH_IMAGE048
(formula nine).
In the formula nine, N0Is the number of points located within the antenna aperture; n is a radical ofnIs the number of transition points between the edge of the antenna aperture and the null point; n is a radical of1The number of Fourier transform points is M or N in formula two and formula three.
Finally, calculating the x component of the aperture electric field of the antenna to be measured
Figure 401374DEST_PATH_IMAGE050
And the y component
Figure 619865DEST_PATH_IMAGE052
For example, the formula ten is used for calculation.
Figure 416920DEST_PATH_IMAGE054
(equation ten).
Step S50: by x-component of electric field of aperture of antenna to be measured
Figure 25756DEST_PATH_IMAGE050
And the y component
Figure 261565DEST_PATH_IMAGE052
Obtaining scalar form of plane spectrum of antenna to be measured through inverse Fourier transform
Figure 272247DEST_PATH_IMAGE056
For example, the formula eleven is used for calculation.
Figure 240203DEST_PATH_IMAGE058
(formula eleven).
This step is also calculated at
Figure 897187DEST_PATH_IMAGE060
Electric field of
Figure 343211DEST_PATH_IMAGE062
For example, the formula twelve is used for calculation.
Figure 473978DEST_PATH_IMAGE064
(formula twelve).
In the formula twelve, the first and second parameters are,
Figure 612836DEST_PATH_IMAGE068
is located at a selected distance between the antenna to be measured and the scan surface, as shown in figure 1,
Figure 258581DEST_PATH_IMAGE066
。
step S60: at a distance d '< d (i.e. between the antenna to be measured and the scanning surface) an additional row (row) or column (column) measurement is introduced, i.e. an additional row or column of probes is provided at the position d'. Repeating steps S10 through S50 calculates the electric field at additional row or column probe locations.
Step S70: step S60 is repeated, with only the Z position being changed for each iteration, and iterative error calculations being performed each time an additional row or column measurement is made. Error of nth iteration
Figure 508296DEST_PATH_IMAGE070
For example, using equation thirteen. The probe is in position d' in fig. 1 in this step.
Figure 493570DEST_PATH_IMAGE072
(equation thirteen).
In the formula thirteen, the first and second formulas,
Figure 865646DEST_PATH_IMAGE074
the electric field distribution of extra row or column measurement after probe correction is obtained by actual measurement; and m is the extrapolated point coordinate.
This step is up to
Figure 936370DEST_PATH_IMAGE076
The iteration terminates. In this case, the scalar form of the plane spectrum of the antenna under test calculated in step S50
Figure 989776DEST_PATH_IMAGE056
It is used as far field directional diagram of the antenna to be tested.
Suppose the antenna under test shown in FIG. 1 is an array antenna consisting of Nx×NyAn electric dipole (electric dipole) antenna unit, the distance between the antenna units on the x-axis and the y-axis is dxAnd dyThe amplitude distribution is-25 dB side lobe Taylor distribution (Taylor distribution) in the azimuth dimension (azimuth dimension) and-35 dB side lobe Taylor distribution in the pitch dimension (elevation dimension). In order to enable the antenna to be measured to radiate along the positive Z-axis direction, two units are arranged along the Z-axis, and the phase difference is 90 degrees. The distance between the scanning surface and the antenna to be measured is d, and the credible angle domains in the x-axis direction and the y-axis direction are theta respectivelyxAnd thetayThe sampling intervals in the x-axis direction and the y-axis direction are Δ x and Δ y. The detailed parameters of the antenna to be tested are shown in table 1.
Figure 891873DEST_PATH_IMAGE077
Table 1: detailed parameters of the antenna to be tested.
From the previous analysis, efficiency and accuracy, γ, were taken into accountxAnd gammayThe selection was 1.25. N is a radical ofnChosen to be 10 to avoid distortion, αxAnd αySet to 0.6, a new angle of trust domain is derived from equations fourteen and fifteen.
Figure 372533DEST_PATH_IMAGE079
(formula fourteen).
Figure 664974DEST_PATH_IMAGE081
(equation fifteen).
In formula fourteen and formula fifteen, αxAnd αyRespectively representing the ratio of the angle of confidence to the scan angle, thetax' and thetay' is a new angular domain of confidence for reducing the effect of truncation errors.
Errors were introduced in the simulation with amplitude errors of random distribution between-0.5 dB to 0.5dB and phase errors of random distribution between-5 ° and 5 °.
Please refer to fig. 3a, which is a schematic diagram of a conventional near-field to far-field transformation method. The abscissa is angle and the ordinate is amplitude. The solid line is a theoretical directional diagram of the antenna to be measured, and the dotted line is a directional diagram of the antenna to be measured obtained by a traditional near field-far field transformation method. It can be seen that the two agree well within the confidence angle domain. However, the directional pattern obtained by the conventional near-field-far-field transformation method is only well matched with the theoretical directional pattern of the antenna to be tested in a small range near the credible angle domain, and is obviously different from the theoretical directional pattern of the antenna to be tested in other angles.
Please refer to fig. 3b, which is a schematic diagram of the conventional Gerchberg-Papoulis algorithm (abbreviated as TGPA). The abscissa is angle and the ordinate is amplitude. The solid line is the theoretical directional diagram of the antenna to be measured, and the dotted line is the directional diagram of the antenna to be measured obtained by the TGPA method. It can be seen that the two agree well within the confidence angle domain. Comparing fig. 3a and fig. 3b, it can be known that the pattern obtained by the TGPA method fits well with the theoretical pattern of the antenna to be measured in a larger range near the trusted angular domain, and is therefore better than the pattern obtained by the conventional near-field-far-field transformation method.
Please refer to fig. 3c, which is a schematic diagram of the improved Gerchberg-Papoulis algorithm (IGPA) proposed in the present application. The abscissa is angle and the ordinate is amplitude. The solid line is the theoretical directional diagram of the antenna to be measured, and the dotted line is the directional diagram of the antenna to be measured obtained by the IGPA method. It can be seen that the two agree well within the confidence angle domain. Comparing fig. 3b and fig. 3c, it can be known that the directional pattern obtained by the IGPA method is in good agreement with the theoretical directional pattern of the antenna to be measured in a wider range near the trusted angular domain, and therefore is superior to the directional pattern obtained by the TGPA method. This indicates that the IGPA method has a better extrapolation area. However, far from the trusted area, the IGPA method yields patterns that have reduced consistency with the theoretical pattern of the antenna under test.
Fig. 4 shows the iteration error calculated by equation thirteen and the variation of the error with the number of iterations. The iteration of the IGPA method proposed by the present application ends at step 33 because the error at step 34 is larger than the error at step 33.
Referring to fig. 5, the near-field measurement system for a planar antenna with reduced truncation error includes a scan plane spectrum calculation unit 10, a probe modification unit 20, a reliable spectrum domain calculation unit 30, an antenna aperture electric field calculation unit 40, an antenna plane spectrum calculation unit 50, a line or column measurement unit 60, and an iteration unit 70.
The scanning surface plane spectrum calculating unit 10 is used for arranging the probe on a scanning surface parallel to the plane antenna, and obtaining the plane spectrum output by the probe through inverse Fourier transform according to the electric field received by the probe.
The probe correction unit 20 is used for performing probe correction, which means that the emission spectrum of the antenna to be measured is obtained from the emission spectrum of the probe and the plane spectrum output by the probe.
The reliable spectral domain calculating unit 30 is used for calculating the reliable spectral domain of the plane spectrum of the antenna to be measured by the emission spectrum of the antenna to be measured and the spectral domain filtering function.
The antenna aperture electric field calculating unit 40 is used for obtaining the aperture electric field of the antenna to be measured through fourier transform of the reliable spectrum domain of the plane spectrum of the antenna to be measured.
The antenna plane spectrum calculating unit 50 is configured to obtain a scalar form of a plane spectrum of the antenna to be measured and an electric field located between the antenna to be measured and the scanning surface from the aperture electric field of the antenna to be measured through inverse fourier transform.
The line or column measuring unit 60 is used to set a line or column of probes between the antenna to be measured and the scanning surface, introduce additional line or column measurements, and repeat the above calculation process of each unit to obtain the electric field at the position of the additional line or column probe; each time an additional row or column measurement is made, an iteration error is calculated.
The iteration unit 70 is used for terminating the iteration of the row or column measurement unit 60 when the iteration error of the nth time is larger than the iteration error of the (n-1) th time; at this time, the scalar form of the plane spectrum of the antenna to be measured calculated by the antenna plane spectrum calculating unit 50 is used as the far-field pattern of the antenna to be measured.
The above are merely preferred embodiments of the present application and are not intended to limit the present application. Various modifications and changes may occur to those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims (14)

1. A plane antenna near field measurement method for reducing truncation errors is characterized by comprising the following steps;
step S10: the probe is arranged on a scanning surface parallel to the planar antenna, and a planar spectrum output by the probe is obtained through inverse Fourier transform according to an electric field received by the probe;
step S20: performing probe correction, namely obtaining the emission spectrum of the antenna to be measured by the emission spectrum of the probe and the plane spectrum output by the probe;
step S30: calculating a reliable spectrum domain of a plane spectrum of the antenna to be detected by using the emission spectrum and the spectrum domain filter function of the antenna to be detected;
step S40: obtaining the aperture electric field of the antenna to be measured through Fourier transform of a reliable spectrum domain of a plane spectrum of the antenna to be measured;
step S50: obtaining a scalar form of a plane spectrum of the antenna to be detected and an electric field positioned between the antenna to be detected and a scanning surface by the aperture electric field of the antenna to be detected through inverse Fourier transform;
step S60: arranging a row or a column of probes between the antenna to be measured and the scanning surface, introducing additional row or column measurement, and repeating the steps S10 to S50 to calculate the electric field at the position of the additional row or column probes; each time an additional row or column measurement is made, an iteration error is calculated;
step S70: repeating the step S60 until the iteration error of the nth time is larger than the iteration error of the (n-1) th time, and terminating the iteration; at this time, the scalar form of the plane spectrum of the antenna under test calculated in step S50 is taken as the far-field pattern of the antenna under test.
2. The method for near-field measurement of a planar antenna with reduced truncation error as claimed in claim 1, wherein in step S10, the plane spectrum outputted from the probe positioned on the scanning surface is calculated by formula one;
Figure DEST_PATH_IMAGE002
(formula one);
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE004
and
Figure DEST_PATH_IMAGE006
respectively outputting an x component and a y component of a plane spectrum for the probe;
Figure DEST_PATH_IMAGE008
and
Figure DEST_PATH_IMAGE010
are respectively a probe at
Figure DEST_PATH_IMAGE012
An x-component and a y-component of the electric field received at the location; k is a radical ofx、ky、kzThe x, y, z components of the wavenumber k, respectively.
3. The near field measurement method of planar antenna with reduced truncation error as claimed in claim 2, wherein k in the formula onex、ky、kzRespectively obtaining a formula II, a formula III and a formula IV;
Figure DEST_PATH_IMAGE014
(formula two);
Figure DEST_PATH_IMAGE016
(formula three);
Figure DEST_PATH_IMAGE018
(formula four);
wherein M and N are the number of Fourier transform points along the x direction and the y direction respectively; Δ x and Δ y are dividedSampling intervals of the x-axis and the y-axis, respectively; and require
Figure DEST_PATH_IMAGE020
。
4. The near-field measurement method of a planar antenna with reduced truncation error of claim 2, wherein in step S20, probe correction is performed by using formula five;
Figure DEST_PATH_IMAGE022
(formula five);
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE024
and
Figure DEST_PATH_IMAGE026
respectively in the form of vectors of emission spectra of an antenna to be detected and a probe;
Figure DEST_PATH_IMAGE028
is the plane spectrum of the probe output.
5. The method as claimed in claim 4, wherein in step S30, the confidence spectrum domain of the plane spectrum of the antenna under test is calculated by formula VI
Figure DEST_PATH_IMAGE030
；
Figure DEST_PATH_IMAGE032
(formula six);
wherein, URIs a spectral domain filtering function.
6. The near-field measurement method of a planar antenna with reduced truncation error as claimed in claim 5, wherein in the step S30, the expression of the spectral domain filter function is formula seven;
Figure DEST_PATH_IMAGE034
(formula seven);
wherein, thetaxAnd thetayRespectively calculating the credible angle domains in the x-axis direction and the y-axis direction according to the caliber of the antenna to be measured; gamma rayxAnd gammayTwo thresholds, γ, representing the x-axis direction and the y-axis directionxAnd gammayAre all greater than 1.
7. The method as claimed in claim 2, wherein in step S40, the probe is first calculated by fourier transform from the reliable spectrum domain of the plane spectrum of the antenna to be measured
Figure DEST_PATH_IMAGE036
X and y components of the electric field received at the site, then spatial filtering functions are calculated, and finally the probe is positioned
Figure 409283DEST_PATH_IMAGE036
And calculating the x component and the y component of the aperture electric field of the antenna to be measured by the x component and the y component of the electric field received at the position and the spatial filtering function.
8. The near field measurement method of planar antenna with reduced truncation error of claim 7, wherein the probe is at
Figure 326423DEST_PATH_IMAGE036
X component of electric field received at location
Figure DEST_PATH_IMAGE038
And the y component
Figure DEST_PATH_IMAGE040
Calculating by adopting a formula eight;
Figure DEST_PATH_IMAGE042
(formula eight);
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE044
and
Figure DEST_PATH_IMAGE046
the x component and the y component of the plane wave spectrum of the antenna to be measured are respectively.
9. The near-field measurement method for planar antenna with reduced truncation error of claim 8, wherein the spatial filtering function U isAUTCalculating by adopting a formula nine;
Figure DEST_PATH_IMAGE048
(formula nine);
wherein N is0Is the number of points located within the antenna aperture; n is a radical ofnIs the number of transition points between the edge of the antenna aperture and the null point; n is a radical of1Is the number of fourier transform points.
10. The near-field measurement method for planar antenna with reduced truncation error of claim 9, wherein the x component of the aperture electric field of the antenna under test
Figure DEST_PATH_IMAGE050
And the y component
Figure DEST_PATH_IMAGE052
Calculating by adopting a formula decimal line;
Figure DEST_PATH_IMAGE054
(equation ten).
11. According to claim 10The method for measuring the near field of the planar antenna with reduced truncation error is characterized in that in the step S50, the planar spectrum of the antenna to be measured is in scalar form
Figure DEST_PATH_IMAGE056
Calculating by adopting a formula eleven;
Figure DEST_PATH_IMAGE058
(formula eleven);
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE060
is the x component or the y component of the aperture electric field of the antenna to be measured.
12. The method as claimed in claim 11, wherein in step S50, the electric field between the antenna to be measured and the scan plane is located at a position corresponding to the position of the scan plane
Figure DEST_PATH_IMAGE062
Electric field of
Figure DEST_PATH_IMAGE064
Calculating by adopting a formula twelve;
Figure DEST_PATH_IMAGE066
(formula twelve);
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE068
；
Figure DEST_PATH_IMAGE070
is the distance between the antenna to be measured and the selected position, and d is the distance between the antenna to be measured and the scanning surface.
13. According to the claimsThe method for near-field measurement of a planar antenna with reduced truncation error of step S12 is characterized in that, in step S60, the error of the nth iteration
Figure DEST_PATH_IMAGE072
Calculating by adopting a formula thirteen;
Figure DEST_PATH_IMAGE074
(formula thirteen);
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE076
means that additional rows or columns measure the electric field distribution corrected by the probe, and m is the extrapolated point coordinate.
14. A plane antenna near field measurement system for reducing truncation errors is characterized by comprising a scanning surface plane spectrum calculation unit, a probe correction unit, a credible spectrum domain calculation unit, an antenna aperture electric field calculation unit, an antenna plane spectrum calculation unit, a line or column measurement unit and an iteration unit;
the scanning surface plane spectrum calculating unit is used for arranging the probe on a scanning surface parallel to the plane antenna and obtaining a plane spectrum output by the probe through inverse Fourier transform according to an electric field received by the probe;
the probe correction unit is used for correcting the probe, which means that the emission spectrum of the antenna to be measured is obtained by the emission spectrum of the probe and the plane spectrum output by the probe;
the credible spectral domain calculating unit is used for calculating the credible spectral domain of the plane spectrum of the antenna to be measured by the emission spectrum and the spectral domain filtering function of the antenna to be measured;
the antenna aperture electric field calculation unit is used for obtaining the aperture electric field of the antenna to be detected through Fourier transform of a reliable spectrum domain of a plane spectrum of the antenna to be detected;
the antenna plane spectrum calculating unit is used for obtaining a scalar form of a plane spectrum of the antenna to be detected and an electric field positioned between the antenna to be detected and a scanning surface through inverse Fourier transform of a caliber electric field of the antenna to be detected;
the line or column measuring unit is used for arranging a line or column of probes between the antenna to be measured and the scanning surface, introducing additional line or column measurement, and repeating the calculation process of each unit to obtain an electric field at the position of the additional line or column probe; each time an additional row or column measurement is made, an iteration error is calculated;
the iteration unit is used for terminating the iteration of the row or column measuring unit when the nth iteration error is larger than the (n-1) th iteration error; and the scalar form of the plane spectrum of the antenna to be tested calculated by the antenna plane spectrum calculating unit is used as the far-field directional diagram of the antenna to be tested.
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