# Design and Optimization for 77 GHz Series-Fed Patch Array Antenna Based on Genetic Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Beam Synthesis Theory of the N-Element Linear Array Antenna

_{n}(n = 1, 2, 3 … N) represents the distance between the center of the element n and the reference origin O,. and N is the total number of similar elements in the array. Suppose that the radiation pattern of the element is F

_{0}(θ, ϕ), and the feeding current to the n-th element is

**I**

_{n}(n = 1, 2, 3… N). According to Figure 1, the radiation pattern of the linear array [25] is expressed as:

_{n}, and the element n has a progressive phase lead β

_{n}current excitation relative to the first element (O). Then, the array factor can be given by:

## 3. Design Method Description

#### 3.1. Description of the Genetic Algorithm Flow

#### 3.2. Design of the 77 GHz Series-Fed Patch Array Antenna

_{r}= 2.2, the thickness = 254 µm).

_{1}= 1260 µm, W

_{1}= 1540 µm, L

_{2}= 1260 µm, and W

_{2}= 320 µm. Then, the radiation pattern of the antenna element shown in Figure 4 was extracted from HFSS simulation, and we selected E-plane radiation intensity data from HFSS simulation and stored them in matrix F = [F

_{1}, F

_{2}, …, F

_{r},… F

_{360}], where F

_{r}(r = 1, 2, 3 …, 360) represented the intensity of the far-field electric field when theta was degree r.

_{ga}, from the Equation (2), we get AF

_{ga}as:

_{1}= 1, m

_{2}= 0, m

_{3}= 1, and m

_{4}= 1. The genetic algorithm randomly generates multiple array factors. Then, the array antenna radiation patterns with the same array elements and different array factors are calculated.

^{jx}=cos(x)+jsin(x), the array factor in Equation (3) can be expressed as:

_{ga}can be expressed as:

_{n+1}− d

_{n}= L

_{1}+ L

_{2}= 2520 µm (Figure 4). Assuming that d

_{0}= d

_{n+1}− d

_{n}= 2520 µm, from Equation (5), we get:

_{1}, m

_{2}, m

_{3}… m

_{N}] with the same number of elements as the expected antenna array. Multiple M matrices generated randomly were substituted into Equation (5) to obtain multiple genetic array factors (|AF

_{ga}|). In order to multiply with the element radiation pattern matrix F, we also put 360 theta values (θ ranges from 1° to 360°) into the Equation (5) and obtained multiple matrices such as F

_{ga}= [F

_{ga1}, F

_{ga2}

_{,}… F

_{gar},…, F

_{ga360}], where F

_{gar}(r = 1,2,3…360) represents the magnitude of |AF

_{ga}| in Equation (5) when theta is degree r. This meant that multiple AF

_{ga}matrices were also random because the M matrices representing the genes were random. Additionally, the number of random F

_{ga}matrices in each generation was equal to the number of the population set by the designer.

_{ga}matrices and obtained new matrices similar to F

_{al}= [F

_{al1}, …, F

_{alr}, …, F

_{al360}] = [F

_{1}F

_{ga1}, …, F

_{r}F

_{gar}, …, F

_{360}F

_{ga360}] (r = 1,2,3…360). In the genetic algorithm, the matrix F

_{al}represents the E-plane radiation diagram of the random patch antenna arrays.

_{al}matrices. The filter algorithm in this paper mainly considered the SLL. The filter function is as follows:

_{goal}= 8 in Inequality (7)), and the sidelobe suppression goal was set to 14 dB (SLL

_{goal}in Inequality (7)). The optimized value was obtained after generations of selection, crossover, and mutation through the loop calculation.

## 4. Electromagnetic Simulation and Measurement Verification

_{x}(dBm). Then, we replaced the transmitting antenna with a standard horn antenna whose gain value is known as G

_{s}(dBi) and adjusted this standard horn antenna angle; thus, the receiving maximum power level P

_{s}(dBm) was obtained. Assuming that the gain of the antenna under measurement was G

_{x}, we obtained the gain of the antenna to be measured as:

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 8.**(

**a**) Simulation and measurement results on E-plane of “1011111111” patch array antenna; (

**b**) simulation and measurement results on H-plane of “1011111111” patch array antenna.

**Figure 9.**(

**a**) Simulation and measurement results on E-plane of “1111111111” patch array antenna; (

**b**) simulation and measurement results on H-plane of “1111111111” patch array antenna.

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**MDPI and ACS Style**

Yang, S.; Zhang, L.; Fu, J.; Zheng, Z.; Zhang, X.; Liao, A.
Design and Optimization for 77 GHz Series-Fed Patch Array Antenna Based on Genetic Algorithm. *Sensors* **2020**, *20*, 3066.
https://doi.org/10.3390/s20113066

**AMA Style**

Yang S, Zhang L, Fu J, Zheng Z, Zhang X, Liao A.
Design and Optimization for 77 GHz Series-Fed Patch Array Antenna Based on Genetic Algorithm. *Sensors*. 2020; 20(11):3066.
https://doi.org/10.3390/s20113066

**Chicago/Turabian Style**

Yang, Shuo, Lijun Zhang, Jun Fu, Zhanqi Zheng, Xiaobin Zhang, and Anmou Liao.
2020. "Design and Optimization for 77 GHz Series-Fed Patch Array Antenna Based on Genetic Algorithm" *Sensors* 20, no. 11: 3066.
https://doi.org/10.3390/s20113066