CN112257334A - Reactance loading array construction method based on port characteristic model theory - Google Patents

Reactance loading array construction method based on port characteristic model theory Download PDF

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CN112257334A
CN112257334A CN202011046840.3A CN202011046840A CN112257334A CN 112257334 A CN112257334 A CN 112257334A CN 202011046840 A CN202011046840 A CN 202011046840A CN 112257334 A CN112257334 A CN 112257334A
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陶诗飞
孙通
叶晓东
王昊
许梦南
刘思行
陈玲
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Abstract

The invention discloses a reactive loading array construction method based on a port characteristic model theory. The method comprises the following steps: obtaining an array port impedance matrix of the antenna structure by utilizing full-wave simulation, establishing a characteristic value equation by the impedance matrix, and solving to obtain characteristic current and a characteristic value so as to obtain a characteristic electric field; the port current and the total electric field directional diagram are represented by linear superposition of characteristic current and characteristic electric field, and a plurality of objective functions are set for the port current and the total electric field directional diagram; the reactance values were optimized using a differential evolution algorithm: and each iteration adopts the reactance value to reversely deduce the weight coefficient required by the linear superposition of the characteristic current and the characteristic electric field, thereby judging whether the current reactance value meets the requirement of the objective function or not and obtaining the optimal reactance value for port loading after the termination condition is reached. The invention directly uses the reactance value as an optimization parameter, so that the optimization design of the reactance loading array is simpler and more convenient, the calculation resource and the time consumption are saved, and the objective function can adapt to diversified design requirements.

Description

Reactance loading array construction method based on port characteristic model theory
Technical Field
The invention belongs to the technical field of antenna radiation performance optimization design, and particularly relates to a reactive loading array construction method based on a port characteristic model theory.
Background
Wireless communication technology is continuously developing, antennas are an essential part of communication systems, and since the increase of many antenna indexes complicates the design of antennas, it has been a challenging problem to optimally design antennas with satisfactory radiation performance. Antenna optimization often relies on scanning structural parameters, and antenna structures are complex and require a large amount of computing resources and time for optimization. Therefore, a reactive loading array based on port eigenmode theory is introduced.
The reactance loading control array means that only one array element in one array is connected with a feed port, other array elements or parasitic elements are connected with reactance loads as coupling units, and the reactance loading is generally realized by a variable capacitance diode. It has many unique advantages in wireless communications, including simple port feed structure, high reliability, low power consumption and low cost. The reactance control array can save the calculation resource of antenna optimization and realize the functions of multi-frequency, wave beam control, bandwidth enhancement, directional diagram reconstruction and the like.
The current reactance loading control array mainly uses a weight coefficient as an optimization variable and can only be optimized aiming at a single frequency point. The optimized weight coefficient is convenient for calculation of the objective function, but the reactance value actually used for loading is deduced from the weight coefficient, so that the time and calculation resource requirements of the algorithm are high, and the performance requirement of the algorithm is high.
Disclosure of Invention
The invention aims to provide a reactive loading array construction method based on a port characteristic model theory, which is simple and convenient in design and capable of reducing the consumption of memory and time resources, and is suitable for the optimal design of various antenna arrays.
The technical solution for realizing the purpose of the invention is as follows: a reactive loading array construction method based on a port characteristic model theory comprises the following steps:
step 1, obtaining an array port impedance matrix of an antenna structure by utilizing full-wave simulation, establishing a characteristic value equation by the impedance matrix, and solving to obtain characteristic current and a characteristic value so as to obtain a characteristic electric field;
step 2, the port current and the total electric field directional diagram are represented by linear superposition of characteristic current and characteristic electric field, and a plurality of objective functions are set for the port current and the total electric field directional diagram;
step 3, optimizing the reactance value by using a differential evolution algorithm: and each iteration adopts the reactance value to reversely deduce the weight coefficient required by the linear superposition of the characteristic current and the characteristic electric field, thereby judging whether the current reactance value meets the requirement of the objective function or not and obtaining the optimal reactance value for port loading after the termination condition is reached.
Compared with the prior art, the invention has the following remarkable advantages: (1) the optimization design of the reactance loading antenna is simpler and more convenient, and the consumption of a large amount of computing resources and time caused by the original antenna optimization is saved; (2) the reactance value is used as an optimization variable, so that the optimization efficiency is greatly improved; (3) more complex and diversified target functions are designed aiming at the single frequency point to adapt to more design requirements, array parameter optimization of a broadband is supported, and the method has great application value.
Drawings
Fig. 1 is a general flowchart of a method for constructing a reactive loading array based on a port eigenmode theory according to the present invention.
Fig. 2 is the radiation pattern of the ten-element yagi antenna with the optimized reactance value loaded according to the present invention.
Detailed Description
With reference to fig. 1, the invention provides a reactance loading array construction method based on a port characteristic model theory, which includes the following steps:
step 1, obtaining an array port impedance matrix of an antenna structure by utilizing full-wave simulation, establishing a characteristic value equation by the impedance matrix, and solving to obtain characteristic current and a characteristic value so as to obtain a characteristic electric field;
step 2, the port current and the total electric field directional diagram are represented by linear superposition of characteristic current and characteristic electric field, and a plurality of objective functions are set for the port current and the total electric field directional diagram;
step 3, optimizing the reactance value by using a differential evolution algorithm: and each iteration adopts the reactance value to reversely deduce the weight coefficient required by the linear superposition of the characteristic current and the characteristic electric field, thereby judging whether the current reactance value meets the requirement of the objective function or not and obtaining the optimal reactance value for port loading after the termination condition is reached.
Further, in step 1, a specific process of solving the characteristic electric field by the characteristic current is as follows: [ Z ]]N×NSolving a characteristic current matrix [ J ] for an array port impedance matrix of the antenna structureN]Substitution matrix equation [ Z]N×N[JN]N×N＝[VN]N×NObtaining a mode voltage matrix [ V ] corresponding to each modeN]N×NAnd setting voltage source parameters of each port of the original antenna array according to the voltage matrix to obtain N characteristic electric fields EiI is 1,2, …, and N is the number of modes and also the number of ports.
Further, the objective function in step 2 is set according to the radiation direction of the total electric field, the maximum radiation direction gain, the side lobe level, the half-power lobe width, and the reflection coefficient, and the specific form is as follows:
F＝w1f1+w2f2+w3f3+w4f4+w5f5 (1)
Figure BDA0002708263470000021
f2＝-max(Gain) (3)
Figure BDA0002708263470000022
Figure BDA0002708263470000031
Figure BDA0002708263470000032
wherein F is the total objective function value, w1～w5Is a target weight coefficient, f1～f5Is an objective function; objective function f1In (1),
Figure BDA0002708263470000033
in order to be the direction of maximum radiation,
Figure BDA0002708263470000034
is a target angle; objective function f2In the middle, max represents the maximum value, and Gain is the antenna Gain; objective function f3SLL is the maximum sidelobe level, SLLdIs a target level; objective function f4Medium, half power lobe width, HPBWdFor lobe width, objective function f5In, S11Is the reflection coefficient.
Further, in step 3, the reactance value is used to reversely estimate the weight coefficient required by the linear superposition of the characteristic current and the characteristic electric field, and the specific steps are as follows:
(3.1) establishing a relation between a new impedance matrix of the antenna after the load is added and a port current matrix according to the Thevenin equivalent circuit, and obtaining the port current matrix according to the loaded reactance value;
and (3.2) obtaining a weight coefficient by the port current matrix.
Further, in the step (3.1), the relationship between the new impedance matrix of the antenna after the load is added and the port current matrix is as follows:
[ZA+ZL]N×N[Jport]N×1＝[Vport]N×1 (7)
wherein N is the total number of ports, ZAIs an impedance matrix, VportIs the voltage at the port, and is,
Figure BDA0002708263470000035
reactance value for port loading, JportIs the port current.
Further, in the step (3.2), the weight coefficient is obtained from the port current matrix, and the specific form is as follows:
[Jport]N×1＝[JN]N×N[α]N×1 (8)
wherein J is the characteristic current obtained by solving, and alpha is the weight coefficient to be solved.
Further, in step 3, the reactance value inversely deduces a weight coefficient required by the linear superposition of the characteristic current and the characteristic electric field, and the specific formula is as follows:
Figure BDA0002708263470000036
further, in step 3, the reactance value is optimized by using a differential evolution algorithm, and a specific flow of each iteration is as follows:
first generating a random population N of reactance valuesPOP (k)Setting an initial iteration algebra k to be 0, and setting [ Z ] for each individual of the population for each iterationL](k)All give corresponding individual fitness F(k)Selecting the individual with the most suitable fitness function value
Figure BDA0002708263470000041
Then for each individual [ ZL](k)All undergo mutation and cross operation to obtain new variant cross individuals
Figure BDA0002708263470000042
And obtaining a new population N through selection operationPOP (k+1)To obtain the optimal individual in the new population
Figure BDA0002708263470000043
And corresponding adaptation function values
Figure BDA0002708263470000044
If the objective function is set, the objective function f2Corresponding weight coefficient w 20, according to whether the convergence condition is satisfied
Figure BDA0002708263470000045
And whether the iteration algebra k reaches the set maximum iteration algebra kmaxTo decide whether to continue the iteration; if w2If not, then k is determined according to the maximum iteration algebramaxTo decide whether to continue the iteration;
and outputting the optimal individual, namely the finally optimized reactance value after the iteration is finished.
The invention is described in further detail below with reference to the figures and specific embodiments.
Examples
The method for constructing the reactance loading array based on the port characteristic mode theory specifically comprises the following steps:
firstly, carrying out characteristic analysis on the array antenna by using a port characteristic model theory, and comprising the following steps:
(1) reading geometric information and control parameters such as frequency, port number and the like;
(2) extracting a port impedance matrix;
(3) establishing a generalized eigenvalue equation by the impedance matrix, and solving the generalized eigenvalue equation;
(4) calculating a characteristic current and a characteristic field;
thirdly, in order to constrain the radiation performance of the antenna array in a certain direction, the objective function may be set as follows:
F＝w1f1+w2f2+w3f3+w4f4+w5f5 (1)
Figure BDA0002708263470000046
f2＝-max(Gain) (3)
Figure BDA0002708263470000047
Figure BDA0002708263470000048
Figure BDA0002708263470000049
wherein F is the total objective function value, w1～w5Is a target weight coefficient, f1～f5Is an objective function. Objective function f1In (1),
Figure BDA00027082634700000410
in order to be the direction of maximum radiation,
Figure BDA00027082634700000411
for the target angle, the objective function f2In the equation, max represents the maximum value, Gain is the antenna Gain, and the objective function f3SLL is the maximum sidelobe level, SLLdFor the target level, the objective function f4Medium, half power lobe width, HPBWdFor lobe width, objective function f5In, S11Is the reflection coefficient.
And fourthly, optimizing the optimal reactance value by using a differential evolution algorithm (DE) algorithm. Each iteration reversely deduces a weight coefficient required by the linear superposition of the characteristic current and the characteristic electric field by using the reactance value, thereby judging whether the current reactance value meets the requirement of the objective function. According to the multi-port Thevenin equivalent circuit, a new impedance matrix after the antenna is externally connected with a load meets the following requirements:
[ZA+ZL]N×N[Iport]N×1＝[Vport]N×1 (7)
wherein N is the total number of ports, ZAIs an impedance matrix, VportIs the voltage at the port, and is,
Figure BDA0002708263470000051
reactance value for port loading, JportPort current obtained by linear superposition of characteristic currents:
[Jport]N×1＝[J]N×N[α]N×1 (8)
wherein J is the characteristic current obtained by solving, and alpha is a weight coefficient.
Substituting equation (8) into equation (7) yields:
Figure BDA0002708263470000052
and obtaining the weight coefficient, and obtaining the port current and the total electric field through linear superposition so as to obtain an individual adaptive function value F corresponding to the current reactance value. And obtaining a new population through variation crossing and selection, judging whether to continue iteration according to the adaptive function value of the optimal individual in the new population, and stopping iteration to output the optimal reactance value after multiple iterations finally meet the termination condition or reach the maximum iteration step number.
And fifthly, substituting the optimal reactance value optimized by a Differential Evolution (DE) algorithm into a loading port of the full-wave simulation platform for simulation to obtain a reflection coefficient and a gain directional diagram.
To verify the feasibility of the method, an example of a design method for a reactive loading array based on port eigenmode theory is given below, and the feasibility of the method can be seen in the general flow chart of fig. 1. The ten-element yagi antenna loading reactance simulation result in fig. 2: the gain is 13.83dBi and the side lobe level is-15.40 dB. According to the result, the radiation pattern calculated by the method meets the target design requirement, and the correctness of the method is verified.

Claims (8)

1. A reactive loading array construction method based on a port characteristic mode theory is characterized by comprising the following steps:
step 1, obtaining an array port impedance matrix of an antenna structure by utilizing full-wave simulation, establishing a characteristic value equation by the impedance matrix, and solving to obtain characteristic current and a characteristic value so as to obtain a characteristic electric field;
step 2, the port current and the total electric field directional diagram are represented by linear superposition of characteristic current and characteristic electric field, and a plurality of objective functions are set for the port current and the total electric field directional diagram;
step 3, optimizing the reactance value by using a differential evolution algorithm: and each iteration adopts the reactance value to reversely deduce the weight coefficient required by the linear superposition of the characteristic current and the characteristic electric field, thereby judging whether the current reactance value meets the requirement of the objective function or not and obtaining the optimal reactance value for port loading after the termination condition is reached.
2. The method for constructing the reactance loading array based on the port eigenmode theory as claimed in claim 1, wherein the specific process of solving the eigenelectric field by the eigencurrent in step 1 is as follows: [ Z ]]N×NSolving a characteristic current matrix [ J ] for an array port impedance matrix of the antenna structureN]Substitution matrix equation [ Z]N×N[JN]N×N＝[VN]N×NObtaining a mode voltage matrix [ V ] corresponding to each modeN]N×NAnd setting voltage source parameters of each port of the original antenna array according to the voltage matrix to obtain N characteristic electric fields EiI is 1,2, …, and N is the number of modes and also the number of ports.
3. The method for constructing a reactance loading array based on port eigenmode theory as claimed in claim 1, wherein the objective function in step 2 is set according to the radiation direction of the total electric field, the maximum radiation direction gain, the side lobe level, the half power lobe width and the reflection coefficient, and the specific form is as follows:
F＝w1f1+w2f2+w3f3+w4f4+w5f5 (1)
Figure FDA0002708263460000011
f2＝-max(Gain) (3)
Figure FDA0002708263460000012
Figure FDA0002708263460000013
Figure FDA0002708263460000014
wherein F is the total objective function value, w1～w5Is a target weight coefficient, f1～f5Is an objective function; objective function f1In (1),
Figure FDA0002708263460000015
in order to be the direction of maximum radiation,
Figure FDA0002708263460000016
is a target angle; objective function f2In the middle, max represents the maximum value, and Gain is the antenna Gain; objective function f3SLL is the maximum sidelobe level, SLLdIs a target level; objective function f4Medium, half power lobe width, HPBWdFor lobe width, objective function f5In, S11Is the reflection coefficient.
4. The method for constructing the reactance loading array based on the port characteristic mode theory as claimed in claim 1, wherein the step 3 of using the reactance value to reversely deduce the weight coefficient required by the linear superposition of the characteristic current and the characteristic electric field comprises the following specific steps:
(3.1) establishing a relation between a new impedance matrix of the antenna after the load is added and a port current matrix according to the Thevenin equivalent circuit, and obtaining the port current matrix according to the loaded reactance value;
and (3.2) obtaining a weight coefficient by the port current matrix.
5. The method for constructing the reactance loading array based on the port eigenmode theory as claimed in claim 4, wherein the relationship between the new impedance matrix of the antenna after the load is added and the port current matrix in step (3.1) is as follows:
[ZA+ZL]N×N[Jport]N×1＝[Vport]N×1 (7)
wherein N is the total number of ports, ZAIs an impedance matrix, VportIs the voltage at the port, and is,
Figure FDA0002708263460000021
reactance value for port loading, JportIs the port current.
6. The method for constructing the reactance loading array based on the port eigenmode theory as claimed in claim 5, wherein the weight coefficient is obtained from the port current matrix in step (3.2), and the specific form is as follows:
[Jport]N×1＝[JN]N×N[α]N×1 (8)
wherein J is the characteristic current obtained by solving, and alpha is the weight coefficient to be solved.
7. The method for constructing the reactance loading array based on the port characteristic mode theory as claimed in claim 6, wherein the reactance value in step 3 inversely deduces the weight coefficient required by the linear superposition of the characteristic current and the characteristic electric field, and the specific formula is as follows:
Figure FDA0002708263460000022
8. the method for constructing the reactance loading array based on the port eigenmode theory as claimed in claim 7, wherein the reactance value is optimized by using the differential evolution algorithm in step 3, and the specific flow of each iteration is as follows:
first generating a random population N of reactance valuesPOP (k)Setting an initial iteration algebra k to be 0, and setting [ Z ] for each individual of the population for each iterationL](k)All give corresponding individual fitness F(k)Selecting the individual with the most suitable fitness function value
Figure FDA0002708263460000031
Then for each individual [ ZL](k)All undergo mutation and cross operation to obtain new variant cross individuals
Figure FDA0002708263460000032
And obtaining a new population N through selection operationPOP (k+1)To obtain the optimal individual in the new population
Figure FDA0002708263460000033
And corresponding adaptation function values
Figure FDA0002708263460000034
If the objective function is set, the objective function f2Corresponding weight coefficient w20, according to whether the convergence condition is satisfied
Figure FDA0002708263460000035
And whether the iteration algebra k reaches the set maximum iteration algebra kmaxTo decide whether to continue the iteration; if w2If not, then k is determined according to the maximum iteration algebramaxTo decide whether to continue the iteration;
and outputting the optimal individual, namely the finally optimized reactance value after the iteration is finished.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113517570A (en) * 2021-06-04 2021-10-19 南京理工大学 Special-shaped yagi antenna and wave beam control method thereof
CN116956539A (en) * 2023-05-06 2023-10-27 中国科学院国家天文台 Feed source antenna design method for conducting impedance self-adaption on ultra-wideband

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
梁志鹏: "基于特征模理论的天线及阵列优化设计研究", 《中国优秀博硕士学位论文全文数据库（博士） 信息科技辑》 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113517570A (en) * 2021-06-04 2021-10-19 南京理工大学 Special-shaped yagi antenna and wave beam control method thereof
CN113517570B (en) * 2021-06-04 2024-09-13 南京理工大学 Special-shaped yagi antenna and beam control method thereof
CN116956539A (en) * 2023-05-06 2023-10-27 中国科学院国家天文台 Feed source antenna design method for conducting impedance self-adaption on ultra-wideband
CN116956539B (en) * 2023-05-06 2024-04-09 中国科学院国家天文台 Feed source antenna design method for conducting impedance self-adaption on ultra-wideband

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