CN110988499A - Antenna radiation characteristic obtaining method based on phase-free near field measurement - Google Patents

Antenna radiation characteristic obtaining method based on phase-free near field measurement Download PDF

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CN110988499A
CN110988499A CN201911001780.0A CN201911001780A CN110988499A CN 110988499 A CN110988499 A CN 110988499A CN 201911001780 A CN201911001780 A CN 201911001780A CN 110988499 A CN110988499 A CN 110988499A
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electric field
field
antenna
spherical
coordinate system
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CN110988499B (en
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谢志祥
张云华
何思远
朱国强
王继红
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Wuhan University WHU
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Abstract

The invention discloses an antenna radiation characteristic obtaining method based on phase-free near-field measurement, which comprises the steps of firstly, obtaining electric field amplitude information of all sampling points on a closed curved surface in a near-field area which is not far away from an antenna to be measured, and then establishing two nonlinear relations of electric field distribution on a spherical surface of the near-field area and amplitude data on a measuring surface through a spherical wave expansion theory; finally, the electric field distribution on the target spherical surface of the near field region is 'guessed' by utilizing a genetic algorithm; when the algorithm stops iterative optimization, the tangential electric field distribution of the spherical surface to be guessed is basically close to an ideal result, at the moment, the weighting coefficient on the spherical surface to be optimized is calculated by utilizing a spherical wave mode expansion theory, and the far field is obtained through the near-far field transformation of the spherical surface; the invention provides a measuring technology suitable for antennas of various specifications.

Description

Antenna radiation characteristic obtaining method based on phase-free near field measurement
Technical Field
The invention belongs to the technical field of microwave measurement, and particularly relates to a test method for reconstructing far-field radiation characteristics by using near-field phase-free data.
Background
The antenna measurement technique mainly comprises far-field measurement, near-field measurement and compact field measurementThree methods are adopted. Far-field measurement is a direct measurement that, through some mechanical control, obtains the far-field radiation characteristics of the antenna. The far field region of the antenna has a test distance R
Figure BDA0002241548450000011
λ is the wavelength, D is the maximum size of the antenna; as the size of the antenna increases, it has become impractical to measure the far field directly, especially as the test size increases and the frequency increases, it becomes very difficult to measure the far field, thereby developing antenna near field measurement techniques. The technology has the advantages of all weather, high test precision, good confidentiality and the like, thereby gaining wide attention; the near-field measurement technology is an indirect measurement method, generally, an antenna to be measured is placed in a dark room, then a small probe with known characteristics is used for scanning on an enclosing surface which is 3 to 10 wavelengths away from the antenna to be measured, so that near-field electric field information of the antenna to be measured is obtained once, then, far-field radiation characteristics of the antenna are obtained through strict near-far field transformation, and if mechanical control software can be reasonably designed and various errors can be properly processed, the precision of near-field measurement is better than that of a direct far field.
The near-field measurement technology is roughly divided into plane, cylindrical surface and spherical surface near-field measurement according to different shapes, and the three measurement technologies are derived from Maxwell equations through an equivalent theorem. However, from the programming point of view, the spherical near-field measurement technology is relatively complex, and the plane and cylindrical near-field measurement is relatively simple; from the view of measurement difficulty and probe compensation, the plane and the cylindrical surface are relatively easy in mechanical control, and the measurement cost is low, however, when the near-field measurement of the plane and the cylindrical surface is used for calculating the far-field radiation characteristic, the problems of truncation error and the like exist;
the development of the near-field measurement technology to date has become a very mature and widely applied means, and the near-field measurement technology requires that the amplitude and phase information of an electric field is obtained in a near-field area, but the two methods are not available; however, as the frequency of the antenna increases, it becomes difficult to obtain very fine and accurate phase information, especially in the sub-millimeter wave to millimeter wave bands, errors in the position of the probe antenna, temperature fluctuation of the device during measurement, noise of the test system, coupling effect between the probe and the antenna to be measured, and various artificial factors, etc., so that it becomes difficult to obtain accurate phase information in the near field, even if relatively reliable phase data can be obtained, it is at a very high cost, it requires very precise and expensive instruments, and a general laboratory cannot realize high-precision phase measurement, so that one starts a concept, namely, under the condition of neglecting the phase signal, the very accurate far-field radiation characteristic can still be obtained, which is the phase-free antenna near-field technology with gradually-increased heat.
At present, there is a commonly used phase-free near-field measurement technique, which is a phase recovery technique, and generally recovers phase data by using one or more sets of amplitude data of a near-field region, and then calculates a far field by using strict mathematical transformation, for example, chinese patent application No. 201710676154.6, and accurately calculates far-field radiation characteristics according to amplitude data of spherical tangential electric fields at two different radii of the near-field region, however, this method is only suitable for the phase-free near-field measurement technique of a regular sampling surface, and amplitude data on two measurement surfaces must be measured; in addition, this method puts high demands on the quality of the initial phase. Chinese patent application No. 201610614730.X provides an arbitrary curved near-field antenna measurement method, however, both amplitude and phase data on discrete grid points must be obtained, and this method will pay extra cost to obtain phase information when the frequency is increased, which will increase the measurement cost.
Disclosure of Invention
The invention aims to provide a phase-free near-field measuring method for any curved surface scanning, which can be applied to a near-field measuring method for any closed curved surface scanning, aims to reconstruct the electric field distribution of an unknown source domain, and then calculates a far field.
The technical scheme adopted by the invention is as follows: an antenna radiation characteristic obtaining method based on phase-free near field measurement is characterized in that: the method comprises the steps that an antenna to be measured is placed on a rotary table, near-field electric field information on one closed curved surface of the antenna is measured in a microwave darkroom through a movable probe, and electric field amplitude data on regular closed curved surfaces #1 and #2 and an Irregular surface Irregular which are composed of two circular planes and a cylindrical surface are obtained respectively;
wherein, grid discretization is carried out on the closed curved surfaces #1 and #2 by adopting uniform sampling; acquired grid point electric field information, which includes: in a cylindrical coordinate system, along
Figure BDA0002241548450000021
Directional electric field component amplitude data;
carrying out grid discretization by adopting non-uniform sampling aiming at Irregular curved surface Irregular; acquired grid point electric field information, which includes: in a cylindrical coordinate system, along
Figure BDA0002241548450000022
Directional electric field component amplitude data;
the electric field amplitude information acquired at each sampling point includes:
Figure BDA0002241548450000023
wherein,
Figure BDA0002241548450000024
respectively representing three polarization components of the electric field under a cylindrical coordinate system, wherein the three polarization components are vectors;
Figure BDA0002241548450000025
the amplitudes of the three polarization components in the cylindrical coordinate system are respectively expressed, and are scalar quantities.
Compared with the prior art, the invention has the beneficial effects that:
firstly, the method comprises the following steps: generally speaking, in near field measurement, amplitude and phase information of any point on a scanning surface need to be measured and obtained in a near field area, and in the invention, very accurate far field radiation characteristics can still be obtained under the condition of neglecting phase signals; for near-field measurement under the condition of no phase, domestic literature is less;
secondly, the method comprises the following steps: in the existing phase-free near-field measurement, amplitude data acquisition is carried out on a plane or a cylindrical surface, however, truncation errors are inevitably generated in the cylindrical surface or plane near-field measurement, and the plane and cylindrical surface near-field measurement is only suitable for a part of antennas. The invention is applicable to any antenna; in addition, the plane and the cylindrical surface are combined to form a closed surface, so that truncation errors are avoided;
thirdly, the method comprises the following steps: in the existing phase-free near-field measurement technology, amplitude data of two or more measurement surfaces away from an antenna to be measured generally need to be acquired, and the measurement surfaces are always regular sampling surfaces such as planes, cylindrical surfaces and spherical surfaces. The required measuring surface can be any irregular curved surface, and the number of the measuring surfaces can be one or more, so that the measuring cost can be greatly reduced, and the application range of the invention is expanded;
fourthly: in the existing phase-free near-field measurement technology, iteration reduction is often performed by using a local optimization algorithm, the method usually requires to obtain a reasonable initial iteration estimation, the quality of the initial iteration estimation directly determines the accuracy of a reconstructed far field, and in the invention, the numerical value of the initial iteration estimation has no any requirement and can be any group of random data;
fifth, the method comprises the following steps: the invention utilizes the spherical wave expansion theory to guess the tangential electric field distribution on a certain spherical surface surrounding the antenna to be measured at the near field; in each iterative optimization and reduction process, the field point calculation is carried out by adopting the theory, so that the time is saved, the program compiling is relatively simple, and the implementation efficiency of the method is improved.
Drawings
FIG. 1 is a schematic diagram of an embodiment of the present invention;
FIG. 2 is a flow chart of genetic algorithm optimization provided by an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of a microstrip antenna;
FIG. 4 is a schematic diagram of the shape of the ruled surfaces #1, #2 according to an embodiment of the invention;
FIG. 5 is a schematic diagram of an embodiment of the present invention providing Irregular surface Irregular shape;
FIG. 6 is a chart of the fitness trend of each iteration;
FIGS. 7 and 8 are graphs of RMSE trend for two components of the far field, respectively;
fig. 9 and 10 show far field patterns of the H and E planes of the microstrip antenna, respectively.
Detailed Description
In order to facilitate the understanding and implementation of the present invention for those of ordinary skill in the art, the present invention is further described in detail with reference to the accompanying drawings and examples, it is to be understood that the embodiments described herein are merely illustrative and explanatory of the present invention and are not restrictive thereof.
Referring to fig. 1, the present invention provides a method for obtaining antenna radiation characteristics based on phase-free near-field measurement, which is characterized in that: the method comprises the steps that an antenna to be measured is placed on a rotary table, near-field electric field information on one closed curved surface of the antenna is measured in a microwave darkroom through a movable probe, and electric field amplitude data on regular closed curved surfaces #1 and #2 and an Irregular surface Irregular which are composed of two circular planes and a cylindrical surface are obtained respectively; it should be noted that, for the present invention, by using the amplitude information on 1 closed curved surface (whether regular closed curved surface #1 or #2 or Irregular closed curved surface Irregular), the present invention can already obtain more accurate far field radiation characteristics, but the method shown in the general patent requires two or more number of regular measurement surfaces, in order to better verify the effectiveness of the present invention, three test conditions are set, which are respectively a regular closed curved surface #1, two regular closed curved surfaces #1+ #2, and an Irregular closed curved surface Irregular; the present invention will develop all the tests for the above three tests;
wherein, grid discretization is carried out on the closed curved surfaces #1 and #2 by adopting uniform sampling; acquired grid point electric field information, which includes: in a cylindrical coordinate system, along
Figure BDA0002241548450000041
Directional electric field component amplitude data;
to is directed atIrregular curved surface Irregular adopts non-uniform sampling to carry out grid dispersion; acquired grid point electric field information, which includes: in a cylindrical coordinate system, along
Figure BDA0002241548450000042
Directional electric field component amplitude data;
the electric field amplitude information acquired at each sampling point includes:
Figure BDA0002241548450000043
wherein,
Figure BDA0002241548450000044
respectively representing three polarization components of the electric field under the cylindrical coordinate system, wherein the three polarization components are vectors;
Figure BDA0002241548450000045
Figure BDA0002241548450000046
the amplitudes of the three polarization components in the cylindrical coordinate system are respectively expressed, and are scalar quantities.
In the present embodiment, as shown in FIG. 1, the radii are R1A distance height of H1Two circular planes #1-1 and #1-3 with a radius R1Height of H1Cylinder # 1-2; at a radius R2A distance height of H2Two circular planes #2-1, #2-3 with a radius R2Height of H2The amplitude data is measured on the cylindrical surface #2-2 of (1), and for convenience of description, the closed curved surface #1 is regarded as a combination of #1-1, #1-3 and #1-2, and the closed curved surface #2 is regarded as a combination of #2-1, #2-3 and # 2-2. To better illustrate the superiority of the method herein, an Irregular closed surface, tentatively named Irregular, is added.
The data acquisition specifically comprises the following steps:
(1) placing an antenna to be tested (AUT) on a turntable with a probe at
Figure BDA0002241548450000047
First, the probe moves along a straight line parallel to the Z axis to obtain the electric field amplitude data on a cylindrical surface every other time
Figure BDA0002241548450000048
Measuring amplitude data of three column polarization electric fields on the primary circular plane; when sampling on a cylindrical surface, the requirements must be met
Figure BDA0002241548450000051
Figure BDA0002241548450000052
Where R iscylinderThe radius of the cylindrical surface is indicated.
(2) The probe is parallel to the XOY plane and is at a certain height from the XOY plane every other interval
Figure BDA0002241548450000053
Measuring amplitude data of three column polarization electric fields on the primary circular plane; when sampling on a circular plane, it must be satisfied
Figure BDA0002241548450000054
Figure BDA0002241548450000055
Where R isplanarRepresenting the radius of the circular plane.
(3) Repeating the steps (1) and (2) to finish the acquisition of amplitude information on one or two regular closed curved surfaces; for measurements on irregular closed surfaces, the nyquist sampling theorem should be satisfied as much as possible, as the case may be.
(4) After the amplitude data acquisition is completed, the measurement data is stored in the format of table 1 below.
TABLE 1
Figure BDA0002241548450000056
TABLE 1 first, second, and third rows are respectively the arbitrary sampling points along
Figure BDA0002241548450000057
The coordinates of the direction, the last three rows are the amplitude data of the next three components of the column polarization respectively.
During the whole data acquisition process for the regular closed curved surfaces (#1 and #2), the Nyquist theorem must be satisfied, that is, the distance between any adjacent measuring points must be less than lambda/2; for the acquisition condition on the Irregular surface (Irregular), the processing needs to be carried out according to specific conditions, the nyquist sampling theorem is satisfied as much as possible, and if the nyquist sampling theorem cannot be guaranteed, data information of some measurement points needs to be acquired on the Irregular surface as much as possible.
In this embodiment, the radius of the spherical surface surrounding the antenna to be measured is set to Rmin，RminThe minimum spherical radius surrounding the antenna to be measured; selecting a spherical surface #0 surrounding the antenna to be detected in a near field region, wherein the radius of the spherical surface is R0(R0≥Rmin) The tangential electric field on the sphere #0 is taken as the target electric field to be optimized, and the target electric field is composed of four groups of data:
Figure BDA0002241548450000058
and
Figure BDA0002241548450000059
is in the initial size of [0,1 ]]Represents the sum of theta on the sphere to be optimized by random generation
Figure BDA00022415484500000510
Magnitude in direction;
Figure BDA00022415484500000511
and
Figure BDA00022415484500000512
is in the range of-180,180]Represents the sum of theta on the sphere to be optimized by random generation
Figure BDA0002241548450000061
A phase in a direction;
Figure BDA0002241548450000062
representing coordinates at a source point under a spherical coordinate system;
Figure BDA0002241548450000063
representing coordinates at a field point in a spherical coordinate system;
the invention aims to guess the tangential electric field value of the spherical surface to be optimized by utilizing the amplitude on the measuring surface of the near field region:
wherein, the electric field of the spherical theta component to be optimized is:
Figure BDA0002241548450000064
spherical surface to be optimized
Figure BDA0002241548450000065
The electric field of the components is:
Figure BDA0002241548450000066
wherein: j is the basic unit of an imaginary number; theta and
Figure BDA0002241548450000067
step size in direction satisfies
Figure BDA0002241548450000068
Figure BDA0002241548450000069
k is the wave number and pi is the circumferential ratio.
In this embodiment, the spherical wave theory is used to establish the target electric field to be guessed
Figure BDA00022415484500000610
And
Figure BDA00022415484500000611
with three polarization amplitude data | Eρ|、
Figure BDA00022415484500000612
|EzTwo non-linear relationships of |:
Figure BDA00022415484500000613
Figure BDA00022415484500000614
wherein, | Eρ|、
Figure BDA00022415484500000615
|EzL is respectively Ei,ρ、
Figure BDA00022415484500000616
Ei,zIs made use of
Figure BDA00022415484500000617
And
Figure BDA00022415484500000618
calculating the electric field on the obtained #1 or #2 and Irregular; m represents the total number of sampling points on the measuring surface, i represents the index of the ith sampling point on #1 or #2 and Irregular; mi,ρ、
Figure BDA00022415484500000619
Mi,zRepresenting the amplitude information of any point on the #1 or #2 and Irregular on the measuring surface, and representing the amplitude information along the line under the cylindrical coordinate system
Figure BDA00022415484500000620
Directional electric field component amplitude data;
Figure BDA00022415484500000621
and
Figure BDA00022415484500000622
representation utilization
Figure BDA00022415484500000623
And
Figure BDA00022415484500000624
calculating the radius of the surrounding antenna to be measured as R0The tangential electric field of #0 on the sphere of (a),
Figure BDA00022415484500000625
coordinate information of any source point on the spherical surface # 0;
Figure BDA00022415484500000626
coordinate information of any field point on the spherical surface # 0;
setting the number of points to be optimized on the spherical surface as M0A 1 is to f1、f2Combining to obtain an algebraic relation between the tangential electric field to be optimized and the measured amplitude data, which is expressed by the root mean square error RMSE, namely
Figure BDA0002241548450000071
Performing iterative optimization reduction on the average root error RMSE, wherein the RMSE reaches an acceptable range, and the smaller the RMSE value is, the RMSE value is shown to be
Figure BDA0002241548450000072
And
Figure BDA0002241548450000073
the more accurate the guess is; when the algorithm stops iterative optimization, the accurate radius R is obtained0Upper spherical tangential electric field distribution.
In this embodiment, the electric field of the grid point is calculated by using the electromagnetic field equivalent theorem and the spherical wave expansion correlation theory, and the specific implementation process is as follows:
the vector spherical wave function for any simple harmonic electromagnetic field in the passive region is known
Figure BDA0002241548450000074
And
Figure BDA0002241548450000075
expressed as:
Figure BDA0002241548450000076
wherein N and m are variables, and N represents the order of the highest mode in the antenna field expansion formula and is represented by a positive integer; a ismnAnd bmnIs a mode expansion coefficient, also called weighting coefficient;
Figure BDA0002241548450000077
representing the coordinates of any field point in the spherical coordinate system; the larger N is, the larger the order of the weighting coefficient is, and the calculation efficiency is greatly reduced, so that in the implementation of the present invention, the value of N should be reduced as much as possible, and specifically, the geometric center of the antenna should be matched with the origin of the coordinate system as much as possible.
Figure BDA0002241548450000078
Figure BDA0002241548450000079
Wherein,
Figure BDA00022415484500000710
representing a second class of spherical Hankel functions;
Figure BDA00022415484500000711
Figure BDA00022415484500000712
wherein,
Figure BDA0002241548450000081
denotes the associated legendre function, k is the wave number;
Figure BDA0002241548450000082
Figure BDA0002241548450000083
S′mn(theta) is Smn(theta), j is the basic unit of an imaginary number,
Figure BDA0002241548450000084
representing the coordinates at the field point in a spherical coordinate system, r representing the radial distance of the field point from the origin of the coordinate system, theta representing the magnitude of the angle along the pitch angle,
Figure BDA0002241548450000085
represents the magnitude of the angle along the azimuth;
therefore, in a spherical coordinate system, the electric field at any point in space surrounding the minimum spherical surface of the antenna to be measured is represented as:
Figure BDA0002241548450000086
Figure BDA0002241548450000087
Figure BDA0002241548450000088
Figure BDA0002241548450000089
Figure BDA00022415484500000810
Figure BDA00022415484500000811
Figure BDA00022415484500000812
then the electric field in the spherical coordinate system is converted into the electric field in the cylindrical coordinate system, and the expression is:
Figure BDA00022415484500000813
Figure BDA00022415484500000814
Figure BDA00022415484500000815
wherein, N represents the coefficient of expansion of the highest mode of the antenna, and is in direct proportion to the minimum spherical radius surrounding the antenna to be measured and the working frequency of the antenna.
Referring to fig. 2, in the embodiment, the initial data of the sphere to be guessed is optimized by the fitness function of the genetic algorithm, and in each iteration, the value of f is smaller and smaller, and the smaller the value of f is, the sphere to be guessed is
Figure BDA0002241548450000091
And
Figure BDA0002241548450000092
the closer the complex field will be to the exact value; after a certain number of iterations, the algorithm converges, and the solution of the last iteration is calculated by using the spherical wave theory to obtain an accurate weighting coefficient so as to obtain a far field.
The genetic algorithm is a search algorithm for solving optimization in computational mathematics, and belongs to a global algorithm. The algorithm was originally developed by using some phenomena in evolutionary biology, including inheritance, mutation, natural selection, and hybridization. It simulates the "superior-inferior" of the natural life rule and is widely applied in the fields of electromagnetism and other interdiscipline.
Each chromosome in the genetic algorithm corresponds to a solution of the genetic algorithm, and the fitness function (fitness function) is generally used to measure the quality of the solution. Therefore, fitness from a genome to its solution forms a map. The process of genetic algorithm can be regarded as a process of finding the optimal solution in the multivariate function. It can be imagined that there are numerous "peaks" in the multidimensional surface, and the peaks correspond to the local optimal solution. And the altitude of a peak is the highest, so that the solution is the global optimal solution. The task of the genetic algorithm is to climb to the highest peak rather than collapse on some small mountains. It should be noted that the genetic algorithm does not necessarily need to find the "highest peak", and if the fitness evaluation of the problem is smaller and better, the global optimal solution is the minimum value of the function, and correspondingly, the genetic algorithm needs to find the "deepest valley". Generally, the longer the chromosome length, the more parameters (genes) to be optimized, the lower the probability that the genetic algorithm will find the global optimum, and the large scale of optimization and the time consumed are increased.
The core of the genetic algorithm is a fitness function which establishes an algebraic relation between a decision variable (chromosome) to be optimized and known data, and in the invention, the smaller the fitness, the better the fitness is required, because the smaller the fitness, the closer the spherical tangential electric field to be optimized is to a true value; in the optimization process of the genetic algorithm, the optimization is mainly completed through three operators of selection, intersection and mutation, the solution space to be searched by the algorithm is closer to the real solution when the algorithm is iterated once, and the searched solution space is basically stable when the algorithm is converged.
Referring to fig. 2, in this embodiment, a genetic algorithm is used to perform iterative optimization reduction on the root mean square error RMSE, and the specific implementation process includes the following sub-steps:
step 1: by using
Figure BDA0002241548450000093
And
Figure BDA0002241548450000094
calculating amplitude information of any point on one or two closed surfaces, and comparing the amplitude information with the measured amplitude data
Figure BDA0002241548450000095
And
Figure BDA0002241548450000096
performing subtraction; then utilize
Figure BDA0002241548450000097
And
Figure BDA0002241548450000098
calculating the tangential electric field of the spherical surface to be guessed
Figure BDA0002241548450000101
And
Figure BDA0002241548450000102
will be provided with
Figure BDA0002241548450000103
And
Figure BDA0002241548450000104
performing absolute value operation to obtain
Figure BDA0002241548450000105
And
Figure BDA0002241548450000106
then use the two variables and
Figure BDA0002241548450000107
and
Figure BDA0002241548450000108
subtracting the absolute values of;
step 2: evaluating the root mean square error f by using a selection operator of the genetic algorithm, respectively calculating the root mean square error of a far field from the optimal solution in the genetic algorithm population, and paying attention to: the optimal solution is the group of data with the minimum f, and the population number is set to be 24 in the invention;
and step 3: crossover and mutation operator pairs using genetic algorithms
Figure BDA0002241548450000109
Figure BDA00022415484500001010
Performing a related algebraic operation on
Figure BDA00022415484500001011
Figure BDA00022415484500001012
Once conversion is carried out; every time the transformation is performed, the four items are closer to the value which is wanted;
and 4, step 4: repeating the steps 1-3 until the genetic algorithm is converged, and setting the maximum iteration number of the genetic algorithm as a termination condition.
The invention has no requirement on the shape and the number (one or more) of the measuring surface, and the measuring surface can be any regular or irregular surface as long as the measuring surface can surround the antenna to be measured, and the coordinate of any discrete point on the measuring surface is in the range of a near field region; in addition, at the time of sampling, the nyquist sampling theorem does not necessarily need to be satisfied.
To better illustrate the effectiveness of the method herein, the algorithm will calculate, at each iteration, the fitness value and the root mean square error RMSE of the far field in order to better observe the convergence characteristics of the algorithm and the degree of agreement with the target far field, and specific measurement embodiments are given below.
As shown in fig. 3, the operating frequency f of the microstrip antenna is 10.0GHz, and the wavelength λ is 30 mm.
The sampling range and step size of the regular closed curved surfaces #1 and #2 and specific parameters are as shown in fig. 4 and table 2, and field amplitude information of 5063 and 6527 points is collected respectively.
Sample range and step size settings of tables 2#1 and #2
Figure BDA0002241548450000111
Irregular closed surface Irregular sampling range and step size and specific parameters are shown in FIG. 5, field amplitude information of 7391 points is respectively collected, and it can be seen from the figure that the sampling interval of some points is larger than λ/2, and the sampling interval between some points is smaller than λ/2.
The optimization flow chart of the genetic algorithm is shown in FIG. 2; in the calculation example of the present invention, the crossover probability Pc is 0.95, the variation probability Pm is 0.001, and the population number PS is 24; the maximum number of iterations for a regular closed surface is set to 91650, while the example for an irregular surface is set to 231720;
the radius of the electric field selection distance coordinate to be optimized is R0On a sphere of 1.5 λ, the step sizes in the theta and phi directions are both 6 °, and the total number of parameters to be optimized is 31 × 61 × 4.
As can be seen from fig. 6, 7, and 8, the algorithm basically converges at approximately 3 ten thousand iterations, and as the iterations progress, the root mean square error of both the fitness value and the far field becomes smaller.
For comparison with the invention of the present disclosure, the FEKO measurement using the electromagnetic simulation software results in far-field radiation characteristics, and as can be seen from fig. 9 and 10, whether it is one or two regular closed curved surfaces or one irregular measurement surface, the result of the near-far-field transformation matches well with the far-field result (see reference in the example) obtained by the probe test; as can also be seen from fig. 9 and 10, the results of the near-far field transformation and the results of the actual probe test and FEKO measurement agree well with each other, thereby confirming the effectiveness of the present invention.
It should be understood that parts of the specification not set forth in detail are prior art; the above description of the preferred embodiments is intended to be illustrative, and not to be construed as limiting the scope of the invention, which is defined by the appended claims, and all changes and modifications that fall within the metes and bounds of the claims, or equivalences of such metes and bounds are therefore intended to be embraced by the appended claims.

Claims (4)

1. An antenna radiation characteristic obtaining method based on phase-free near field measurement is characterized in that: the method comprises the steps that an antenna to be measured is placed on a rotary table, near-field electric field information on one closed curved surface of the antenna is measured in a microwave darkroom through a movable probe, and electric field amplitude data on regular closed curved surfaces #1 and #2 and an Irregular surface Irregular which are composed of two circular planes and a cylindrical surface are obtained respectively;
wherein, grid discretization is carried out on the closed curved surfaces #1 and #2 by adopting uniform sampling; acquired grid point electric field information, which includes: in a cylindrical coordinate system, along
Figure FDA0002241548440000011
Directional electric field component amplitude data;
carrying out grid discretization by adopting non-uniform sampling aiming at Irregular curved surface Irregular; the acquired grid point electric field information, which is included in the cylindrical coordinate system, along the grid point
Figure FDA0002241548440000012
Directional electric field component amplitude data; the electric field amplitude information acquired at each sampling point includes:
Figure FDA0002241548440000013
wherein,
Figure FDA0002241548440000014
respectively representing three polarization components of the electric field under a cylindrical coordinate system, wherein the three polarization components are vectors;
Figure FDA0002241548440000015
the amplitudes of the three polarization components in the cylindrical coordinate system are respectively expressed, and are scalar quantities.
2. The method for obtaining the radiation characteristics of the antenna based on the phase-free near-field measurement as claimed in claim 1, wherein the method comprisesIn the following steps: setting the radius of the spherical surface surrounding the antenna to be measured to be Rmin，RminThe minimum spherical radius surrounding the antenna to be measured; selecting a spherical surface #0 surrounding the antenna to be detected in a near field region, wherein the radius of the spherical surface is R0，R0≥Rmin(ii) a Taking the tangential electric field on the spherical surface #0 as a target electric field to be optimized, wherein the target electric field consists of four groups of data:
Figure FDA0002241548440000016
wherein,
Figure FDA0002241548440000017
and
Figure FDA0002241548440000018
is in the initial size of [0,1 ]]Represents the sum of theta on the sphere to be optimized by random generation
Figure FDA0002241548440000019
Magnitude in direction;
Figure FDA00022415484400000110
and
Figure FDA00022415484400000111
is in the range of-180,180]Represents the sum of theta on the sphere to be optimized by random generation
Figure FDA00022415484400000112
A phase in a direction;
Figure FDA00022415484400000113
representing coordinates at a source point under a spherical coordinate system;
Figure FDA00022415484400000114
representing coordinates at a field point in a spherical coordinate system;
then, the electric field of the spherical θ component to be optimized is:
Figure FDA00022415484400000115
spherical surface to be optimized
Figure FDA00022415484400000116
The electric field of the components is:
Figure FDA0002241548440000021
wherein j is the basic unit of an imaginary number; theta andstep size in direction satisfies
Figure FDA0002241548440000023
Figure FDA0002241548440000024
k is the wave number, and π is the circumferential ratio;
establishing a target electric field to be guessed through a spherical wave theory
Figure FDA0002241548440000025
And
Figure FDA0002241548440000026
with three polarization amplitude data | Eρ|、
Figure FDA0002241548440000027
|EzAnd two non-linear relationships of the electric field of the sphere itself to be guessed:
Figure FDA0002241548440000028
Figure FDA0002241548440000029
wherein, | Eρ|、
Figure FDA00022415484400000210
|EzL is respectively Ei,ρ、
Figure FDA00022415484400000211
Ei,zIs made use of
Figure FDA00022415484400000212
And
Figure FDA00022415484400000213
calculating electric fields on #1, #2 and Irregular, wherein M represents the total number of sampling points on the measuring surface, and i represents the index of the ith sampling point on the closed curved surfaces #1, #2 and Irregular; mi,ρ、
Figure FDA00022415484400000214
Mi,zShowing the amplitude information of any point on the closed curved surfaces #1, #2 and Irregular along the cylindrical coordinate system
Figure FDA00022415484400000215
Directional electric field component amplitude data;
Figure FDA00022415484400000216
and
Figure FDA00022415484400000217
representation utilization
Figure FDA00022415484400000218
And
Figure FDA00022415484400000219
calculating the radius of the surrounding antenna to be measured as R0The tangential electric field distribution on the sphere #0 of (a),
Figure FDA00022415484400000220
is the coordinate of any point on the sphere # 0;
setting the number of points to be optimized on the spherical surface as M0A 1 is to f1、f2Combining to obtain an algebraic relation between the tangential electric field to be optimized and the measured amplitude data, which is expressed by the root mean square error RMSE, namely
Figure FDA00022415484400000221
The average root error RMSE is subjected to iterative optimization reduction, the size of the RMSE reaches an acceptable range, and the smaller the value of the RMSE is, the indication is that
Figure FDA00022415484400000222
And
Figure FDA00022415484400000223
the more accurate the guess is; when the algorithm stops iterative optimization, the accurate radius R is obtained0Tangential electric field distribution on the sphere.
3. The antenna radiation characteristic acquisition method based on the phase-free near-field measurement according to claim 2, characterized in that: the electric field at the grid point is calculated by utilizing the electromagnetic field equivalent theorem and the spherical wave expansion correlation theory, and the specific implementation process is as follows:
the vector spherical wave function for any simple harmonic electromagnetic field in the passive region is known
Figure FDA0002241548440000031
And
Figure FDA0002241548440000032
expressed as:
Figure FDA0002241548440000033
wherein N and m are variables, and N represents the order of the highest mode in the antenna field expansion formula and is represented by a positive integer; a ismnAnd bmnIs a mode expansion coefficient, also called weighting coefficient;
Figure FDA0002241548440000034
representing the coordinates of any field point in the spherical coordinate system;
Figure FDA0002241548440000035
Figure FDA0002241548440000036
wherein,
Figure FDA0002241548440000037
representing a second class of spherical Hankel functions;
Figure FDA0002241548440000038
Figure FDA0002241548440000039
wherein,
Figure FDA00022415484400000310
denotes the associated legendre function, k is the wave number;
Figure FDA00022415484400000311
Figure FDA00022415484400000312
S′mn(theta) is Smn(theta), j is the basic unit of an imaginary number,
Figure FDA00022415484400000313
representing the coordinates at the field point in a spherical coordinate system, r representing the radial distance between the field point and the origin of the coordinate system, theta representing the angular magnitude of the pitch angle,
Figure FDA00022415484400000314
an angular magnitude representing an azimuth;
therefore, in a spherical coordinate system, the electric field at any point in space surrounding the minimum spherical surface of the antenna to be measured is represented as:
Figure FDA00022415484400000315
Figure FDA00022415484400000316
Figure FDA0002241548440000041
Figure FDA0002241548440000042
Figure FDA0002241548440000043
Figure FDA0002241548440000044
Figure FDA0002241548440000045
then the electric field in the spherical coordinate system is converted into the electric field in the cylindrical coordinate system, and the expression is:
Figure FDA0002241548440000046
Figure FDA0002241548440000047
Figure FDA0002241548440000048
wherein, N represents the coefficient of expansion of the highest mode of the antenna, and is in direct proportion to the minimum spherical radius surrounding the antenna to be measured and the working frequency of the antenna.
4. The antenna radiation characteristic acquisition method based on the phase-free near-field measurement according to claim 2, characterized in that: the iterative optimization reduction of the root mean square error RMSE comprises the following specific implementation processes:
step 1: by using
Figure FDA0002241548440000049
And
Figure FDA00022415484400000410
calculating amplitude information of any point on one or two closed surfaces, and comparing the amplitude information with the measured amplitude data
Figure FDA00022415484400000411
And
Figure FDA00022415484400000412
performing subtraction; then utilize
Figure FDA00022415484400000413
And
Figure FDA00022415484400000414
calculating the tangential electric field distribution of the spherical surface to be guessed
Figure FDA00022415484400000415
And
Figure FDA00022415484400000416
finally, will
Figure FDA00022415484400000417
And
Figure FDA00022415484400000418
performing absolute value operation to obtain
Figure FDA00022415484400000419
And
Figure FDA00022415484400000420
then use the two variables and
Figure FDA00022415484400000421
and
Figure FDA00022415484400000422
subtracting the absolute values of;
step 2: evaluating the root mean square error f by using a selection operator of the genetic algorithm, and respectively calculating the root mean square error of a far field from the optimal solution in the genetic algorithm population;
and step 3: crossover and mutation operator pairs using genetic algorithms
Figure FDA0002241548440000051
Figure FDA0002241548440000052
Performing a related algebraic operation on
Figure FDA0002241548440000053
Figure FDA0002241548440000054
Once conversion is carried out;
and 4, step 4: repeating the steps 1-3 until the genetic algorithm converges.
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