CN110750929B - Antenna radiation and scattering characteristic analysis method based on characteristic mode theory - Google Patents

Antenna radiation and scattering characteristic analysis method based on characteristic mode theory Download PDF

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CN110750929B
CN110750929B CN201910978908.2A CN201910978908A CN110750929B CN 110750929 B CN110750929 B CN 110750929B CN 201910978908 A CN201910978908 A CN 201910978908A CN 110750929 B CN110750929 B CN 110750929B
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陈益凯
邓轩
杨仕文
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University of Electronic Science and Technology of China
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Abstract

The invention discloses an antenna radiation and scattering characteristic analysis method based on a characteristic mode theory, which comprises the following implementation steps: solving an impedance matrix according to a moment method; calculating a characteristic model according to a characteristic model analysis method; calculating an excitation vector according to the type of the analysis problem; expanding the magnetic current coefficient by a characteristic mode, and establishing a new matrix equation related to the characteristic mode weighting coefficient; solving an approximate solution of an original moment method matrix equation solution by the mode weighting coefficient and the characteristic model; and calculating radiation and scattering related parameters according to the solved electromagnetic flow coefficient. The invention realizes the combination of characteristic mode analysis and antenna radiation and scattering characteristic analysis, and can accelerate the solving speed; the method realizes the characteristic mode expansion method of antenna radiation and scattering under the excitation of the port, can improve guidance for subsequent antenna design and quickens the design process.

Description

Antenna radiation and scattering characteristic analysis method based on characteristic mode theory
Technical Field
The invention belongs to the technical field of antennas, and relates to an analysis method for antenna radiation characteristics and scattering characteristics, in particular to a method for analyzing antenna radiation and scattering performance by using a characteristic mode based on a characteristic mode theory. The method can be used for quickly analyzing the radiation and scattering characteristics of the antenna, designing the antenna with specific performance and accelerating the design process of the antenna.
Background
Modern antenna design relies on electromagnetic field numerical calculation methods including Finite Element Method (FEM), Finite Difference Time Domain (FDTD) and moment of mass (MOM) to analyze the performance of the antenna, and these methods can rapidly and accurately analyze and obtain the radiation and scattering performance of the antenna, and have a wide application range. Although these methods can obtain accurate solutions to the corresponding electromagnetic problems, they cannot physically explain the intrinsic mechanism of antenna performance, and it is difficult to design antennas with specific performance.
Harrington et al put forward a characteristic model theory to analyze the radiation and scattering fields of pure metals and pure dielectric bodies on the basis of a moment method, and the theory can not only give out the physical essence of the actual electromagnetic problem and explain the internal mechanism of the radiation and scattering characteristics of an object, but also accurately obtain the radiation and scattering performance of the object. The theory is already used in the design of antennas such as base station antennas, mobile phone antennas and the like, and can be used for guiding the design of antennas with characteristic performance and accelerating the design process of the antennas. Therefore, the antenna is guided and designed by using the characteristic model theory, and the method has high value in practical engineering application.
Most of existing analysis methods based on the eigenmode theory use the theory as a design reference, when antenna performance is analyzed, calculation still needs to be performed by means of full-wave simulation, the two processes are performed separately, and therefore the total calculation time is increased.
Disclosure of Invention
In view of the above technical background, the present invention provides an antenna radiation and scattering characteristic analysis method based on a characteristic mode theory, which is based on the characteristic mode theory, and on the basis of solving characteristic modes, directly utilizes the characteristic modes to analyze the radiation and scattering performance of an antenna, gives consideration to the capability of the characteristic modes to guide the antenna design, and can accelerate the speed of solving an impedance matrix equation in a moment method.
In order to achieve the purpose, the technical scheme comprises the following steps:
step 1: for the antenna to be analyzed for radiation and scattering characteristics, a surface area equation representing the relation between an antenna source and a field is established, RWG triangular basis functions are used for discretizing the surface current and the magnetic current of the antenna, and an impedance matrix [ Z ] is obtained based on a moment methodmn]N×NN denotes the number of unknowns of the discretized surface integral equation, the element Z in the matrixmnRepresenting the sampling of the electric or magnetic field generated at the mth basis function for the nth basis function;
step 2: according to the eigenmode theory, from an impedance matrix [ Z ]mn]N×NEstablishing generalized eigenvalue equation of corresponding eigenmode of the antenna to obtain corresponding eigenvalue lambdanAnd a feature vector vnCharacteristic value lambdanArranging the characteristic modules according to the amplitude from small to large, wherein n represents the serial number of the characteristic module;
and step 3: question classes according to concrete analysisType, calculating an excitation vector [ V ] of the antennan]NN represents the number of unknowns of the discretized surface integral equation, and for the radiation problem, the element V in the excitation vectornIndicating the sampling of the electric or magnetic field generated by the antenna excitation source at the antenna surface, V for the scattering problemnRepresenting a sampling of an electric or magnetic field of an incident field on the antenna surface, the impedance matrix and the excitation vector satisfy the relation:
[Zmn]N×N[In]N＝[Vn]N
wherein [ I ]n]NElectromagnetic flow coefficient vector, I, representing RWG basis function to be solvednRepresenting the current coefficient or magnetic current coefficient of RWG basis function corresponding to the nth unknown quantity;
and 4, step 4: and (3) using the characteristic model as a new basis function, expanding the magnetic current on the surface of the antenna, and establishing a new matrix equation:
Figure BDA0002234554170000021
wherein M is the number of the set characteristic modes to be solved, and a matrix
Figure BDA0002234554170000022
Is an impedance matrix using the eigenmodes as new basis functions, αnA mode weighting coefficient representing an nth characteristic mode,
Figure BDA0002234554170000023
is an excitation vector using the eigenmode as a new basis function;
step 5. weighting factor by mode [ α ]n]MAnd the eigenvectors v of the eigenmodesnDetermining coefficient vector J of magnetic current on antenna surfaceM，JMThe calculation formula is as follows:
Figure BDA0002234554170000024
wherein, αiIndicates the ith modeV.of the mode weighting coefficient ofiThe characteristic vector representing the i-th mode is composed of the surface magnetic current coefficient vector JMFurther obtain the electromagnetic flow coefficient vector [ In]N；
Step 6: from the electromagnetic current coefficient vector [ I ]n]NAnd integrating to solve the electric field Es and the magnetic field Hs, and solving relevant parameters in the radiation problem and the scattering problem by the obtained electric field Es and the magnetic field Hs to obtain the radiation and scattering characteristics of the antenna.
The method has the advantages that: (1) the impedance matrix calculation is the same as the traditional moment method, the calculation can be carried out by the traditional moment method, the calculation can be realized in a modularization mode, and the calculation amount is the same as that of the original method; (2) the radiation and scattering problem is solved by using the characteristic mode, LU decomposition or iterative solution is not needed, calculation can be accelerated, the newly constructed matrix equation is usually small in dimension (less than 100), the required calculated amount is small, and the precision is high; (3) the method simultaneously comprises the analysis capability of characteristic mode analysis and the analysis capability of radiation and scattering characteristics of the traditional moment method, and provides additional characteristic mode information while meeting the requirement of obtaining the radiation and scattering performance of the traditional antenna, thereby providing guidance for the actual engineering design. (4) The moment method wave port theory and the characteristic mode theory are combined to realize the characteristic mode analysis containing the excitation port which can not be realized by the prior art, so that the method can analyze the influence of the actual excitation structure on the modes and the contribution of the port excitation to each mode.
Drawings
Fig. 1 is a flow chart of the antenna radiation and scattering characteristic analysis method based on the characteristic mode theory;
FIG. 2 is a top view of a model of an embodiment antenna;
FIG. 3 is a bottom view of a model of an exemplary antenna;
FIG. 4 is a cross-sectional view of a model of an embodiment antenna;
FIG. 5 is a graph of the reflection coefficient of an antenna port according to an embodiment;
FIG. 6 is a diagram of parameters of an antenna port S according to an exemplary embodiment;
FIG. 7 is an XOY areal gain pattern for an exemplary embodiment antenna at a frequency of 3GHz radiation;
FIG. 8 is a XOZ gain pattern for an exemplary embodiment antenna at a frequency of 3GHz radiation;
FIG. 9 is a YOZ plane gain pattern for an exemplary antenna at 3GHz radiation;
FIG. 10 shows the mode weighting coefficients of 60 characteristic modes of the antenna according to the embodiment under the radiation condition of 3GHz frequency;
FIG. 11 is a schematic diagram of the mode current distribution of the characteristic mode 1 of the antenna of the exemplary embodiment at a frequency of 3 GHz;
FIG. 12 is a pattern far field pattern for characteristic mode 1 at a frequency of 3GHz for an exemplary antenna;
FIG. 13 is a schematic diagram of the mode current distribution of the characteristic mode 4 of the antenna of the exemplary embodiment at a frequency of 3 GHz;
FIG. 14 is a pattern far field pattern of characteristic mode 4 at a frequency of 3GHz for an exemplary antenna;
FIG. 15 is a schematic diagram of the mode current distribution of characteristic mode 5 at a frequency of 3GHz for an antenna according to an embodiment;
FIG. 16 is a pattern far field pattern of characteristic mode 5 at a frequency of 3GHz for an exemplary antenna;
FIG. 17 is a schematic diagram of the mode current distribution of the characteristic mode 10 of the antenna of the exemplary embodiment at a frequency of 3 GHz;
FIG. 18 is a pattern far field pattern of a characteristic mode 10 of an exemplary antenna at a frequency of 3 GHz;
FIG. 19 is a diagram showing the mode current distribution of the characteristic mode 14 of the antenna of the embodiment at a frequency of 3 GHz;
FIG. 20 is a pattern far field pattern of a characteristic mode 14 of an exemplary antenna at a frequency of 3 GHz;
FIG. 21 is a current distribution obtained by direct solution of the antenna of the embodiment by MOM method in a radiation state with a frequency of 3 GHz;
FIG. 22 is a far field pattern directly solved by MOM method for an antenna of an embodiment at a frequency of 3GHz radiation;
FIG. 23 is a current distribution obtained by direct solution of the antenna of the embodiment by MOM method in a scattering state at a frequency of 3 GHz;
FIG. 24 is a far field pattern of the exemplary antenna solved by eigenmode method at a frequency of 3GHz scattering;
FIG. 25 is a diagram of an XOY-plane dual-station RCS with a scattering frequency of 3GHz for an antenna according to an exemplary embodiment;
FIG. 26 is a diagram of an XOZ-plane dual-station RCS with a scattering state at a frequency of 3GHz for an antenna according to an embodiment;
FIG. 27 is a diagram of a YOZ-plane dual-station RCS for an exemplary antenna operating at a frequency of 3GHz scattering;
FIG. 28 is a graph showing the mode weight coefficients of 60 characteristic modes of the exemplary antenna in a scattering state at a frequency of 3 GHz;
FIG. 29 is a mode current distribution of characteristic mode 2 at a frequency of 3GHz for an embodiment antenna;
FIG. 30 is a pattern far field pattern for characteristic mode 2 at a frequency of 3GHz for an exemplary embodiment antenna;
FIG. 31 is a schematic diagram of the mode current distribution of the characteristic mode 12 of the antenna of the exemplary embodiment at a frequency of 3 GHz;
FIG. 32 is a pattern far field pattern of a characteristic mode 12 at a frequency of 3GHz for an exemplary embodiment antenna;
FIG. 33 is a diagram showing the mode current distribution of the characteristic mode 21 of the antenna of the embodiment at a frequency of 3 GHz;
FIG. 34 is a pattern far field pattern of a characteristic mode pattern 21 at a frequency of 3GHz for an exemplary embodiment antenna;
FIG. 35 is a schematic current distribution of a characteristic mode 28 at a frequency of 3GHz for an exemplary antenna;
FIG. 36 is a pattern far field pattern of a characteristic mode pattern 28 at a frequency of 3GHz for an exemplary embodiment antenna;
Detailed Description
Embodiments of the present application will be described in detail with reference to the drawings and examples, so that how to implement technical means to solve technical problems and achieve technical effects of the present application can be fully understood and implemented.
As shown in fig. 1, the detailed steps of the analysis of the antenna radiation and scattering properties based on the eigenmode theory are as follows:
step 1: for the antenna to be analyzed for radiation and scattering characteristics, a surface area equation representing the relation between an antenna source and a field is established, RWG triangular basis functions are used for discretizing the surface current and the magnetic current of the antenna, and an impedance matrix [ Z ] is obtained based on a moment methodmn]N×NN denotes the number of unknowns of the discretized surface integral equation, the element Z in the matrixmnIndicating that the sample of the electric or magnetic field generated at the mth basis function is taken for the nth basis function.
Step 2: for impedance matrix [ Zmn]N×NPartitioning:
Figure BDA0002234554170000031
wherein A is11Representing the sampling of the electric field generated by the current on the surface of the metal and medium of the antenna, A12Representing the sampling of the magnetic current on the surface of an antenna medium to generate an electric field on the surface of the metal and the medium, A13Representing the sampling of the electromagnetic current applied to the antenna port to generate an electric field on the surface of metals and media, A21Representing the sampling of the magnetic field generated on the surface of the medium by the current on the surface of the metal and medium of the antenna, A22Representing the sampling of the magnetic field generated by the magnetic current on the surface of the antenna medium, A23Representing the sampling of the magnetic field generated on the surface of a medium by the electromagnetic current supplied to the antenna port, A31Representing the sampling of the electromagnetic field generated by the current on the surface of the metal and medium of the antenna at the antenna port, A32Representing the sampling of the magnetic flux on the surface of the antenna medium to generate an electromagnetic field at the antenna port, A33Representing a sampling of an electromagnetic field at the antenna port that is energized by the electromagnetic current at the antenna port to produce an electromagnetic field at the antenna port.
According to the eigenmode theory, the matrix for eigenmode analysis is:
Figure BDA0002234554170000041
wherein N is2Expressing the number of unknown quantities of the magnetic current coefficient after discretization of the surface of the antenna medium, and establishing a generalized characteristic value equation:
XCMνn＝λnRCMνn
wherein R isCMIs a matrix ZCMReal part of, XCMIs a matrix ZCMImaginary part of, λnCharacteristic value, v, representing the nth characteristic modenA feature vector representing the nth eigenmode.
And step 3: according to the problem type of specific analysis, calculating excitation vector V of the antennan]NN represents the number of unknowns of the discretized surface integral equation, and for the radiation problem, the element V in the excitation vectornIndicating the sampling of the electric or magnetic field generated by the antenna excitation source at the antenna surface, V for the scattering problemnRepresenting a sampling of an electric or magnetic field of an incident field on the antenna surface, the impedance matrix and the excitation vector satisfy the relation:
[Zmn]N×N[In]N＝[Vn]N
wherein [ I ]n]NElectromagnetic flow coefficient vector, I, representing RWG basis function to be solvednIndicating the current coefficient or magnetic current coefficient of the nth unknown corresponding to the RWG basis function.
And 4, step 4: simplified impedance matrix [ Z ]mn]N×NAnd an excitation vector [ V ]n]NThe relationship is as follows:
[ZM]·[JM]＝[VM]
wherein the content of the first and second substances,
Figure BDA0002234554170000042
Figure BDA0002234554170000043
V1、V2and V3The excitation vector in step 3 is segmented, and the relationship is:
Figure BDA0002234554170000044
assuming that the magnetic current on the surface of the antenna medium can be unfolded by using a characteristic mode as follows:
Figure BDA0002234554170000051
substituting the expression into a simplified equation to establish a weighting factor [ α ] for the characteristic moden]MThe relation of (1):
Figure BDA0002234554170000052
wherein M is the number of the set characteristic modes to be solved, and a matrix
Figure BDA0002234554170000053
Is an impedance matrix using the eigenmodes as new basis functions, αnA mode weighting coefficient representing an nth characteristic mode,
Figure BDA0002234554170000054
is an excitation vector, matrix, using eigenmodes as new basis functions
Figure BDA0002234554170000055
Sum vector
Figure BDA0002234554170000056
The calculation formula of the elements in (1) is:
Figure BDA0002234554170000057
Figure BDA0002234554170000058
wherein the content of the first and second substances,<vm,ZMvn>representing the multiplication of the m-th eigenmode by the n-th eigenmode by an impedance matrix ZMThe inner product of (a) is,<vn,VM>represents the nth eigenmode and the excitation vector VMThe inner product of (d).
And 5: magneto-rheological coefficient J of antenna medium surfaceMThe calculation formula is as follows:
Figure BDA0002234554170000059
according to the obtained magnetic current coefficient JMCalculating the surface current coefficient J of the antenna metal medium and the current coefficient J on the portPThe calculation formula is:
Figure BDA00022345541700000510
Figure BDA00022345541700000511
wherein, J, JMAnd JPIs a vector of electromagnetic flow coefficients [ I ]n]NThe relationship is as follows:
Figure BDA00022345541700000512
step 6: from the electromagnetic current coefficient vector [ I ]n]NIntegral solution electric field EsAnd a magnetic field HsFrom the obtained electric field EsAnd a magnetic field HsThe relevant parameters in the radiation problem and the scattering problem can be solved, and the radiation and scattering characteristics of the antenna can be obtained.
In one embodiment of the present invention, the antenna is a rectangular microstrip antenna, and is fed by using a coaxial line with a characteristic impedance of 50 Ω, the excitation mode is probe excitation, and the model is shown in fig. 2-4, where the antenna size and the dielectric material parameters are labeled. Firstly, port parameters of an antenna in a radial state are analyzed, the resonant frequency of the antenna is about 3GHz, a frequency range is 2.4GHz-3.6GHz, a comparison graph of port reflection coefficients obtained by direct solution through a moment method and solution through a characteristic model is given in fig. 5, results are basically identical, a comparison graph of port S parameters obtained by two methods is given in fig. 6, the difference between the resonant frequency obtained by solution through the characteristic model and the result obtained by direct solution through the moment method is 0.06GHz, the relative error is 2%, and the precision can meet the general solution requirements.
Fig. 7-9 show the gain pattern comparison of three surfaces (XOY surface, XOZ surface, and YOZ surface) in the rectangular coordinate system under the radiation state, and it can be seen that the result obtained by the eigen mode solution matches the result obtained by the direct solution, and the error is small. Fig. 10 shows mode excitation coefficient diagrams of different modes in a radiation state, and it can be seen that modes with large radiation contribution include mode 1, mode 4, mode 5, mode 10 and mode 14, fig. 11-20 show mode current distributions and mode fields of these modes, fig. 21 and fig. 22 show current distributions and electric field patterns obtained by direct solution, and it can be found by comparison that the mode current distribution and mode field of mode 10 with the largest contribution are similar to the result obtained by direct solution, and due to the limitation of an actual feeding structure, it is usually difficult to excite a single mode, and this feeding also excites other modes, and the combination of these modes finally obtains an electric field pattern obtained by direct solution.
In the scattering state, considering that a plane wave is incident from the positive Z direction, the electric field polarization direction is the positive Y direction, fig. 23 and 24 show the current distribution solved by direct solution and the eigen mode of 60 modes, and mark the incident field direction and the electric field polarization direction, and it can be seen from comparing the two figures that the current distribution solved by the two is the same. Fig. 25-27 show the comparison graphs of the two-station RCS of three planes (XOY plane, XOZ plane, and YOZ plane) in the rectangular coordinate system under the scattering state, and it can be seen that the results of the eigen-mode solution and the direct solution are also consistent. Similarly, fig. 28 shows the mode excitation coefficient diagrams of different modes in the scattering state, and it can be understood from the diagrams that mode 2, mode 12, mode 21 and mode 28 have their main effects on scattering, and the mode currents and mode fields of these several modes are shown in fig. 29-fig. 36.
In summary, the method of the present invention can solve parameters of the antenna in the radial state and the scattering state based on the eigen-mode analysis, and has high precision, and parameters such as pattern current distribution, pattern field, pattern weighting coefficient, etc. obtained by the eigen-mode analysis can be used as technical guidance for subsequent design.

Claims (1)

1. An antenna radiation and scattering characteristic analysis method based on a characteristic mode theory is characterized by comprising the following steps:
step 1: for the antenna to be analyzed for radiation and scattering characteristics, a surface area equation representing the relation between an antenna source and a field is established, RWG triangular basis functions are used for discretizing the surface current and the magnetic current of the antenna, and an impedance matrix [ Z ] is obtained based on a moment methodmn]N×NN denotes the number of unknowns of the discretized surface integral equation, the element Z in the matrixmnRepresenting the impedance matrix [ Z ] for the sampling of the n-th basis function to produce an electric or magnetic field at the m-th basis functionmn]N×NIt can be further decomposed into a 3 × 3 block matrix form:
Figure FDA0002518611280000011
wherein A is11Representing the sampling of the electric field generated by the current on the surface of the metal and medium of the antenna, A12Representing the sampling of the magnetic current on the surface of an antenna medium to generate an electric field on the surface of the metal and the medium, A13Representing the sampling of the electric field generated by the electromagnetic current on the antenna excitation port on the surfaces of metals and media, A21Representing the sampling of the magnetic field generated on the surface of the medium by the current on the surface of the metal and medium of the antenna, A22Representing the sampling of the magnetic field generated by the magnetic current on the surface of the antenna medium, A23Representing the sampling of the magnetic field generated on the surface of a medium by the electromagnetic current supplied to the excitation port of an antenna, A31Representing the sampling of the electromagnetic field generated by the current on the surface of the metal and medium of the antenna on the excitation port of the antenna, A32Indicating that magnetic current on the surface of antenna medium generates electromagnetic field on antenna excitation portSampling of (A)33The method comprises the steps of representing sampling of electromagnetic fields on an antenna excitation port to generate electromagnetic fields on the antenna excitation port;
step 2: according to the eigenmode theory, from an impedance matrix [ Z ]mn]N×NEstablishing generalized eigenvalue equation of corresponding eigenmode of the antenna to obtain corresponding eigenvalue lambdanAnd a feature vector vnCharacteristic value lambdanArranging the amplitudes from small to large, wherein n represents the serial number of the characteristic module, and the calculation formula of the characteristic module is as follows:
XCMνn＝λnRCMνn
wherein R isCMIs a matrix ZCMReal part of, XCMIs a matrix ZCMImaginary part of, λnCharacteristic value, v, representing the nth characteristic modenEigenvectors representing the nth eigenmode, matrix ZCMThe calculation formula of (2) is as follows:
Figure FDA0002518611280000012
wherein N is2Representing the number of unknown magnetic current coefficients after discretization of the surface of the antenna medium;
and step 3: according to the problem type of specific analysis, calculating excitation vector V of the antennan]NN represents the number of unknowns of the discretized surface integral equation, and for the radiation problem, the element V in the excitation vectornIndicating the sampling of the electric or magnetic field generated by the antenna excitation source at the antenna surface, V for the scattering problemnRepresenting a sampling of an electric or magnetic field of an incident field on the antenna surface, the impedance matrix and the excitation vector satisfy the relation:
[Zmn]N×N[In]N＝[Vn]N
wherein [ I ]n]NElectromagnetic flow coefficient vector, I, representing RWG basis function to be solvednRepresenting the current coefficient or magnetic current coefficient of RWG basis function corresponding to the nth unknown quantity;
and 4, step 4: and (3) using the characteristic model as a new basis function, expanding the magnetic current on the surface of the antenna, and establishing a new matrix equation:
Figure FDA0002518611280000021
wherein M is the number of the set characteristic modes to be solved, and a matrix
Figure FDA0002518611280000022
Is an impedance matrix using the eigenmodes as new basis functions, αnA mode weighting coefficient representing an nth characteristic mode,
Figure FDA0002518611280000023
is an excitation vector, matrix, using eigenmodes as new basis functions
Figure FDA0002518611280000024
Sum vector
Figure FDA0002518611280000025
The specific calculation method comprises the following steps:
a. calculating a simplified impedance matrix [ Z ]mn]N×NAnd an excitation vector [ V ]n]NThe calculation formula is as follows:
Figure FDA0002518611280000026
Figure FDA0002518611280000027
wherein, V1、V2And V3The excitation vector in the step 3 is obtained by blocking, and satisfies the relation
Figure FDA0002518611280000028
Simplified impedance matrix [ Z ]mn]N×NAnd an excitation vector [ V ]n]NSatisfies the relation [ ZM]·[JM]＝[VM]；
b. Expanding coefficient vector J of magnetic current on surface of antenna medium by the characteristic model obtained in the step 2MAnd calculate a matrix
Figure FDA0002518611280000029
Sum vector
Figure FDA00025186112800000210
The specific calculation formula is as follows:
Figure FDA00025186112800000211
Figure FDA00025186112800000212
Figure FDA00025186112800000213
wherein, < v >m,ZMvnThe mth eigenmode and the nth eigenmode are multiplied by an impedance matrix ZMInner product of (v)n,VMIs the nth eigenmode and the excitation vector VMM denotes the vector J for the expansion coefficientMNumber of characteristic modes, matrix
Figure FDA00025186112800000214
Sum vector
Figure FDA00025186112800000215
Satisfy the relationship
Figure FDA00025186112800000216
Solving the equation yields a pattern weighting coefficient vector αn]M；
Step 5. weighting factor by mode [ α ]n]MAnd the eigenvectors v of the eigenmodesnDetermining coefficient vector J of magnetic current on surface of antenna mediumM，JMThe calculation formula is as follows:
Figure FDA0002518611280000031
wherein, αiMode weighting factor, v, representing the ith modeiThe characteristic vector representing the i-th mode is composed of the surface magnetic current coefficient vector JMFurther obtain the electromagnetic flow coefficient vector [ In]NThe specific calculation formula is as follows:
Figure FDA0002518611280000032
Figure FDA0002518611280000033
wherein J is the current coefficient of the surface of the antenna metal and the medium, JPCurrent flow coefficient for antenna excitation port, J, JMAnd JPIs a vector of electromagnetic flow coefficients [ I ]n]NElement of (1), satisfies the relationship
Figure FDA0002518611280000034
Step 6: from the electromagnetic current coefficient vector [ I ]n]NIntegral solution electric field EsAnd a magnetic field HsFrom the obtained electric field EsAnd a magnetic field HsThe relevant parameters in the radiation problem and the scattering problem can be solved, and the radiation and scattering characteristics of the antenna can be obtained.
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