# Derivation of a Universally Valid Array Factor of a Conformal Arrays Based on Phase Compensation and Genetic Learning Particle Swarm Optimization

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## Abstract

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## 1. Introduction

## 2. Derivation of 3D Array Factor

#### 2.1. Improvement of Pattern Degradation of Conformal Arrays through Phase Compensation

#### 2.2. Results of Array Factor Calculation through Simulations

#### 2.3. Amplitude Tapering Method of Array Factor (Bernstein Polynomial Using GLPSO)

## 3. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Single element information used for conformal-array characteristic analysis: (

**a**) element type, (

**b**) S-parameters information.

**Figure 2.**Description of array type and related variables: (

**a**) 12$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$24 planar array, (

**b**) 12$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$24 conformal array, (

**c**) description of variable r.

**Figure 3.**Comparison of 2D radiation patterns of 12$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$24 planar and conformal arrays: (

**a**) $\varphi $ = 0${}^{\circ}$ plane and (

**b**) $\varphi $ = 90${}^{\circ}$ plane.

**Figure 4.**Arrangement shape on the XZ plane: (

**a**) linear array (planar array) shape and (

**b**) curved array (conformal array) shape.

**Figure 6.**Cavity-backed patch antenna: (

**a**) element shape, (

**b**) S-parameters, (

**c**) $\varphi $ = 0${}^{\circ}$ radiation pattern and (

**d**) $\varphi $ = 90${}^{\circ}$ radiation pattern.

**Figure 7.**8$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$8 random grid array shape: (

**a**) 3D view and (

**b**) XY plane view.

**Figure 8.**Comparison of 8$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$8 random grid array uniform feeding 2D radiation patterns: (

**a**) array factor of conformal array calculated using MATLAB and (

**b**) radiation pattern from EM simulation.

**Figure 9.**Array factors (−25 dB) of conformal array optimized based on GLPSO: (

**a**) conformal array type 1; (

**b**) conformal array type 2; comparison of radiation patterns of (

**c**) 1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$16 conformal array type 1 and 1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$16 planar array, (

**d**) 1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$16 conformal array type 2 and 1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$16 planar array, (

**e**) 1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$24 conformal array type 1 and 1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$24 planar array, (

**f**) 1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$24 conformal array type 2 and 1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$24 planar array, (

**g**) 1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$30 conformal array type 1 and 1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$30 planar array, and (

**h**) 1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$32 conformal array type 2 and 1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$32 planar array.

**Figure 12.**Application of the calculated amplitude based on the optimization trend: (

**a**) conformal array shape with amplitude applied and (

**b**) 1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$16 conformal array radiation pattern vs. linear array radiation pattern.

**Figure 14.**Comparison of 8$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$8 random-grid amplitude-tapering 2D radiation patterns: (

**a**) array factor of conformal array calculated with MATLAB, (

**b**) comparison of simulated radiation patterns for uniform and amplitude tapering feeding.

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**MDPI and ACS Style**

Park, J.; Lim, H.J.; Trinh-Van, S.; Park, D.; Jung, Y.K.; Lim, D.; Hwang, K.C.
Derivation of a Universally Valid Array Factor of a Conformal Arrays Based on Phase Compensation and Genetic Learning Particle Swarm Optimization. *Appl. Sci.* **2022**, *12*, 6501.
https://doi.org/10.3390/app12136501

**AMA Style**

Park J, Lim HJ, Trinh-Van S, Park D, Jung YK, Lim D, Hwang KC.
Derivation of a Universally Valid Array Factor of a Conformal Arrays Based on Phase Compensation and Genetic Learning Particle Swarm Optimization. *Applied Sciences*. 2022; 12(13):6501.
https://doi.org/10.3390/app12136501

**Chicago/Turabian Style**

Park, Jinsu, Hong Jun Lim, Son Trinh-Van, Daesung Park, Youn Kwon Jung, Dongju Lim, and Keum Cheol Hwang.
2022. "Derivation of a Universally Valid Array Factor of a Conformal Arrays Based on Phase Compensation and Genetic Learning Particle Swarm Optimization" *Applied Sciences* 12, no. 13: 6501.
https://doi.org/10.3390/app12136501