CN114372365B - Quick analysis method for electromagnetic radiation of antenna array based on DGFM and CMT algorithm - Google Patents
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Abstract
The invention relates to a rapid analysis method for electromagnetic radiation of an antenna array based on DGFM and a CMT algorithm, and belongs to the technical field of electromagnetic simulation. Firstly, grouping antenna arrays into a strong coupling group and a weak coupling group; and then using MoM to calculate the current of the strong coupling group array element, and using DGFM to correct the current of the weak coupling group. And then, constructing an impedance matrix into a characteristic value equation by using CMT, extracting characteristic vectors and characteristic values of a main mode, and calculating to obtain the current distribution of the array elements by linear combination of the characteristic vectors and the characteristic values of the main mode. The invention can rapidly and accurately calculate the electromagnetic radiation characteristics of the antenna array. The method is easy to implement and has the same applicability to dissimilar arrays, so that the method is suitable for processing most of the electromagnetic radiation problems of the antenna array.
Description
Technical Field
The invention belongs to the technical field of electromagnetic simulation, and relates to a rapid analysis method for electromagnetic radiation of an antenna array based on DGFM and a CMT algorithm.
Background
The radiation problem of antenna arrays occurs in numerous fields of practical electronic engineering, such as frequency selective surfaces, metamaterials, etc. With respect to large-scale arrays, the conventional full-wave algorithm solves the electromagnetic radiation problem by converting electromagnetic integration equations into matrix equations by the Method of Moment (MoM). Such methods typically increase system simulation time and consume significant computing resources.
Therefore, the research on a rapid analysis method for calculating the electromagnetic radiation problem of the antenna array is of great significance.
Disclosure of Invention
In view of the above, the present invention aims to provide a rapid analysis method for electromagnetic radiation of an antenna array based on DGFM and CMT algorithms, which can obviously reduce the unknown quantity, so that the system simulation time can be greatly shortened. And the technique has equal applicability to dissimilar antenna arrays.
In order to achieve the above purpose, the present invention provides the following technical solutions:
A rapid analysis method of electromagnetic radiation of an antenna array based on DGFM and CMT algorithm adopts a Domain Green's Function (DGFM) and a moment method (MoM), wherein DGFM evaluates a weak coupling region, and the strong coupling region is calculated by MoM. Furthermore, a characteristic mode theory (CHARACTERISTIC MODES THEORY, CMT) algorithm is further adopted to extract the main radiation mode of the antenna array element, and the technology can obviously reduce the unknown quantity, so that the system simulation time can be greatly shortened. And the technique has equal applicability to dissimilar antenna arrays.
The method specifically comprises the following steps:
s1: firstly, dispersing all array elements of an antenna array by using triangular units to obtain structural information of the antenna array, and constructing RWG (random number generator) basis functions on triangular grids obtained by subdivision; establishing an electric field integral equation according to the boundary condition of the array, and dispersing the established electric field integral equation by utilizing the RWG basis function;
S2: analyzing each array element on the antenna array; grouping the array elements with small spacing into strong coupling groups and grouping the array elements with large spacing into weak coupling groups;
S3: constructing an impedance matrix equation set by the strong coupling set through MoM, and simultaneously correcting current distribution of array elements in the weak coupling set through DGFM;
S4: constructing an impedance matrix Z into a generalized characteristic equation set by using a CMT algorithm, and extracting characteristic values and characteristic vectors;
S5: orthogonalizing the feature vectors and extracting a main mode in the feature modes; solving a final current coefficient by utilizing linear combination of the characteristic value and the characteristic vector;
s6: and (5) according to the result obtained in the step (S5), solving the radiation characteristics of the far zone of the antenna array.
Further, in step S2, according to the positions of the analyzed array elements, the coupling relation of the surrounding array elements is determined, and the coupling relation is grouped into a strong coupling group and a weak coupling group.
Further, the step S3 specifically includes: firstly, calculating the current on the array elements by using the strong coupling group through MoM, and constructing an impedance matrix equation set as follows, assuming that Q array elements in total in the strong coupling group D' have strong coupling effect with the array elements t:
Wherein Z ij is an impedance matrix between the ith and jth array elements in the strong coupling group formed by taking the analysis array element t as a reference array element; j 0t is the current coefficient required in the strong coupling group corresponding to the t-th array element, and V t is the feed voltage information of the t-th array element;
then, for the weakly coupled group, the current of the analytical array element t is corrected by DGFM, expressed as:
wherein J t is the current coefficient on the array element t, and J 0t is the current coefficient in the strong coupling group obtained by MoM; The current coefficient correction term of DGFM for the weak coupling group is used, and N represents the number of RWG basis functions.
Further, in step S4, the CMT algorithm is used to construct the obtained impedance matrix Z into a generalized characteristic equation set, where the expression is:
XJ′m＝λmRJ′m
Wherein z=r+jx, X and R are the imaginary and real parts, respectively, of the impedance matrix Z; j' m and λ m are the characteristic current and the characteristic value of the mth order mode, respectively.
In step S5, the generalized characteristic equation set obtained in step S4 is filtered to obtain a first M-order principal mode, and the current coefficient of the array element is obtained by linear combination of the eigenvalue and the eigenvector, where the current coefficient is as follows:
Then, the current coefficient on the analysis array element t can be obtained efficiently and accurately through the steps S3 to S5, and the current coefficient is as follows:
The invention has the beneficial effects that:
(1) The invention can reduce the time required for calculation in the analysis of the radiation characteristics of the antenna array.
(2) The method is particularly suitable for solving the electromagnetic radiation problem of the antenna array, and the memory consumption of a computer can be greatly reduced by using the algorithm, so that the calculation time is saved.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objects and other advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out in the specification.
Drawings
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in the following preferred detail with reference to the accompanying drawings, in which:
Fig. 1 is a schematic grouping diagram of an antenna array;
FIG. 2 is a schematic diagram of a 10-element similar antenna array arrangement;
FIG. 3 is a diagram showing the far field radiation contrast of a 10-element similar antenna array;
FIG. 4 is a schematic diagram of a 10-element dissimilar butterfly array arrangement;
Fig. 5 is a diagram of 10-element dissimilar butterfly array far field radiation contrast.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the illustrations provided in the following embodiments merely illustrate the basic idea of the present invention by way of illustration, and the following embodiments and features in the embodiments may be combined with each other without conflict.
Referring to fig. 1 to 5, the invention provides a rapid analysis method for electromagnetic radiation of an antenna array based on DGFM and CMT algorithms, which specifically comprises the following steps:
the first step: the surface of the antenna array is discretized by a triangular patch, wherein the average side length of the triangular patch is 0.02λ, and λ is the wavelength. Then, an electric field integral equation is established between the antenna arrays:
where J is the current density, divergence operator Acting on the source point vector r'; /(I)Is the wave impedance of the medium space,/>The wave number of the medium space, f represents the frequency of the electromagnetic wave; volume fraction represents the contributions of the current source and the charge source everywhere within the volume v to the wave function at the field point r; mu is magnetic permeability, epsilon is dielectric constant; e represents an electric field. Where G (R) is a green's function in free space, and r= |r-R' | represents the distance from the source point to the field point. J is then discretized with RWG basis functions, the current density of the antenna array of which can be spread out as:
Wherein f n is the nth RWG basis function, and α n is the coefficient corresponding to the nth basis function; adopting a gamma method, taking RWG basis function as a test function, further writing the formula (1) into a matrix form of ZI=V, wherein Z represents a matrix of N by N's moment method ' impedance '; i and V are each column vectors of N1, representing the "current" vector and the "voltage" vector, respectively, of the moment method. The impedance elements of Z and V are respectively
In the method, in the process of the invention,Is the source triangle pair where the nth basis function f n (r') is located,/>Is the field triangle pair where the mth test function f m (r) is located, s and s' represent the closed faces of the discrete field triangle patch and the source triangle patch, respectively.
And a second step of: each element on the antenna array is analyzed.
As shown in fig. 1, array elements with small pitches are grouped into strong coupling groups and array elements with large pitches are grouped into weak coupling groups by grouping.
And a third step of: the invention uses analysis array element t as reference array element, and calculates and corrects the current of array element t through DGFM for the coupling effect of array element in weak coupling group to t.
Wherein DGFM is an approximation technique, i.e. assuming that the currents on all parallel arranged elements have the same or proportional coefficient characteristics, this can be expressed as
Jk(r+rkt)≈αktJt(r) (5)
Wherein a kt is a complex proportionality coefficient, which represents the relation of current coefficients of array elements k and t, namely
Wherein J 0k、J0t is the current coefficient of array elements k and t when the coupling effect independently exists without consideration. Therefore, the characteristic of DGFM is utilized, and the ZI=V impedance matrix equation set obtained in the first step is combined. The current coefficient at element t can be expressed as
For the array elements in the strong coupling group, the current on the array elements is accurately calculated by the strong coupling group through MoM, and the assumption is that Q array elements and t array elements in the strong coupling group D' have strong coupling effect. Then a set of impedance matrix equations may be established as:
wherein J 0t is the current coefficient of the array element t considering only the influence of the strong coupling group. Then, through the influence in the weak coupling group, namely the combination (7), the current coefficient of t under the influence of all antenna array elements on t can be accurately obtained, wherein the current coefficient of t is as follows:
fourth step: constructing the impedance matrix Z in (8) and (9) into a generalized set of characteristic equations, i.e
XJ′m＝λmRJ′m (10)
Wherein X and R are the imaginary and real parts of the impedance matrix Z (z=r+jx), respectively; j' m and λ m are feature currents and feature values of the mth order in the feature mode and extract feature values and feature vectors.
Fifth step: because X and R are real symmetric Hermitian matrices, J' m and λ m are normalized to have orthogonalization, i.e.:
wherein δmn is 1 when m=n, otherwise 0. Then the current density J is expanded to be by the eigenvector
Jt＝βmJ′m (12)
Wherein beta m is a weight pattern coefficient, and the same can be obtained by using a gamma method
Then, J' m and lambda m are linearly combined, and only the principal mode is selected, assuming that the M-order principal mode is shared, J 0t can be obtained as
The third, fourth and fifth steps, namely the utilization of (8), (9) and (14), can efficiently and accurately obtain the current coefficient of the array element t as
Sixth step: and according to the result obtained in the fifth step, solving the radiation characteristic of the far zone of the antenna array.
The process according to the invention is further illustrated by the following two specific examples:
Example 1:
And calculating a dipole array with 10 elements arranged in parallel, wherein the interval between the array elements is lambda/2, the length of the array elements is lambda/2, the width of the array elements is lambda/200, the frequency range is 2GHz to 4GHz, the center frequency is 3GHz, and according to the first step, dispersing the array to obtain 620 RWG basis functions. Then according to 2-6 steps, the calculation time of the original algorithm can be greatly reduced by using the CMT algorithm. Fig. 3 is a comparison chart of far field radiation fields (phi=90° theta= -180) of an antenna array calculated by several methods, and the correctness of the method is verified. Tables 1 and 2 show the comparison of the computational resources and unknowns of the inventive method with conventional computational methods.
Table 1 calculation of time contrast
Table 2 calculation of unknown quantity contrast
Example 2:
A 10-element non-parallel array of butterfly antennas is calculated, the spacing between the array elements is λ/2, the length of the array elements is λ/2, and the width is λ/3, as shown in fig. 4, and in order to make the calculation example more general, each antenna is randomly rotated in space. According to the first step, the array is discretized to obtain 420 triangles, so that there are 490 RWG basis functions. The simulation frequency was 300MHz. As shown in fig. 5, two methods are shown to calculate the far field radiation contrast of the butterfly antenna array, which verifies that the present invention is also applicable to the radiation analysis of dissimilar arrays.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the claims of the present invention.
Claims (2)
1. A rapid analysis method for electromagnetic radiation of an antenna array based on DGFM and CMT algorithms is characterized by comprising the following steps:
s1: firstly, dispersing all array elements of an antenna array by using triangular units to obtain structural information of the antenna array, and constructing RWG (random number generator) basis functions on triangular grids obtained by subdivision; establishing an electric field integral equation according to the boundary condition of the array, and dispersing the established electric field integral equation by utilizing the RWG basis function;
S2: analyzing each array element on the antenna array; grouping the array elements with small spacing into strong coupling groups and grouping the array elements with large spacing into weak coupling groups;
s3: constructing an impedance matrix equation set by the strong coupling set through MoM, and simultaneously correcting current distribution of array elements in the weak coupling set through DGFM; wherein MoM represents a moment method and DGFM represents a domain green function method;
S4: constructing an impedance matrix Z into a generalized characteristic equation set by using a CMT algorithm, and extracting characteristic values and characteristic vectors; wherein CMT represents the eigenmode theory;
S5: orthogonalizing the feature vectors and extracting a main mode in the feature modes; solving a final current coefficient by utilizing linear combination of the characteristic value and the characteristic vector;
S6: according to the result obtained in the step S5, solving the radiation characteristics of the far zone of the antenna array;
The step S3 specifically comprises the following steps: firstly, calculating the current on the array elements by using the strong coupling group through MoM, and constructing an impedance matrix equation set as follows, assuming that Q array elements in total in the strong coupling group D' have strong coupling effect with the array elements t:
Wherein Z ij is an impedance matrix between the ith and jth array elements in the strong coupling group formed by taking the analysis array element t as a reference array element; j 0t is the current coefficient required in the strong coupling group corresponding to the t-th array element, and V t is the feed voltage information of the t-th array element;
then, for the weakly coupled group, the current of the analytical array element t is corrected by DGFM, expressed as:
Wherein J t is the current coefficient at element t, The current coefficient correction term of DGFM on the weak coupling group is utilized, and N represents the number of RWG basis functions;
In step S4, the CMT algorithm is used to construct the obtained impedance matrix Z into a generalized characteristic equation set, where the expression is:
XJ'm＝λmRJ'm
Wherein z=r+jx, X and R are the imaginary and real parts, respectively, of the impedance matrix Z; j' m and λ m are the characteristic current and the characteristic value of the mth order mode, respectively;
in step S5, the generalized characteristic equation set obtained in step S4 is screened out to obtain the front M-order principal mode, and the current coefficient of the array element is obtained by linear combination of the eigenvalue and the eigenvector, where:
Then, the current coefficient on the analysis array element t is obtained through the steps S3 to S5:
2. The method according to claim 1, wherein in step S2, the coupling relation of surrounding array elements is determined according to the positions of the analyzed array elements, and the array elements are grouped into a strong coupling group and a weak coupling group.
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