# Design Procedure of a Frequency Reconfigurable Metasurface Antenna at mmWave Band

^{*}

## Abstract

**:**

## 1. Introduction

#### Metamaterials and Metasurface Structures

## 2. Related Works

#### Contribution

- Firstly, a demonstration of a step-by-step procedure on how to achieve SRR geometrical parameters at dual frequency of operation is provided;
- Secondly, the proposed unit cell was used to design a 16 element frequency RMS;
- Finally, the characteristics of the proposed frequency RMS were analyzed and compared with previous works.

## 3. Design Procedure

## 4. Simulation Processes

## 5. Results and Analysis

#### 5.1. Reflection Coefficient

#### 5.2. Reflection Phase

#### 5.3. Gain and Directivity

#### 5.4. Effective Permittivity, and Permeability

#### 5.5. Comparison with Previous Work

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 7.**Return loss simulation results of 16 element metasurface array with and without PIN diodes.

**Figure 9.**Simulation results of a 16 element metasurface array with and without PIN diodes indicating (

**a**) Directivity (

**b**) Gain.

**Figure 10.**Retrieved effective constitutive parameters of the simulated results (

**a**) Effective permeability (

**b**) Effective permittivity.

Step | Equation | Purpose |
---|---|---|

1 | Equation (6) | Calculate the width of a characteristic impedance ${Z}_{o}$ |

2 | Equations (5) and (14) | Calculate the dielectric constant and use it to find the internal and external average lengths ${L}_{T1}$ & ${L}_{T2}$ for each frequency |

3 | Equation (9) | Calculate the internal and external side lengths of each outer ring using the calculated average lengths in Step 2 |

Dimensions | Before Optimization (mm) | After Optimization (mm) |
---|---|---|

h | 0.5 | 0.56 |

W | 1.54 | 1.54 |

${l}_{1}$ | 3.51 | 3.47 |

${l}_{2}$ | 4.68 | 4.4 |

Capacitance (pF) | Resonating Frequency (GHz) | Bandwidth (GHz) |
---|---|---|

Without diodes | 26.90–31.39, 32.26, and 40.20 | 4.46, 0.66, and 1.36 |

0.03 | 26.61–31.49, 32.49, and 40.28 | 4.88, 0.42, and 1.41 |

0.035 | 23.60, 26.72–31.47, 32.48, and 40.28 | 1.17, 4.73, 0.43, and 1.41 |

0.04 | 23.08, 26.79–31.46, 32.48, and 40.24 | 1.17, 4.68, 0.44, and 1.39 |

0.045 | 22.72, 26.81–31.44, 32.48, and 40.24 | 1.05, 4.63, 0.45, and 1.38 |

0.05 | 22.48, 26.89–31.43, 32.44, and 40.24 | 0.98, 4.58, 0.46, and 1.38 |

Capacitance | Angular | Gain | Directivity | Radiation |
---|---|---|---|---|

(pF) | Beamwidth (°) | (dBi) | (dBi) | Efficiency (%) |

Without diodes | 16.5 | 15 | 17.2 | 87.2 |

0.03 | 15.3 | 27.23 | 43.37 | 62.79 |

0.035 | 15.0 | 27.50 | 43.06 | 63.86 |

0.04 | 14.5 | 27.93 | 44.28 | 63.08 |

0.045 | 14.31 | 28.42 | 44.93 | 63.25 |

0.05 | 13.9 | 28.8 | 45.6 | 63.31 |

Ref | Size | Reconfiguration | Actuators | Frequency | Detailed Design |
---|---|---|---|---|---|

(mm${}^{2}$) | Band | Procedure | |||

[68] | 2 × 4 | Frequency | GaAs air-bridged Schottky diode | mmWave | Not specified |

[42] | 80 × 80 | Pattern | 12 PIN diodes | Sub-mmWave | Not specified |

[43] | 180 × 180 | Frequency | Liquid metal | Sub-mmWave | Not specified |

[44] | 117 × 117 | Frequency and Pattern | 16 PIN diodes | mmWave | Not specified |

This work | 17.6 × 17.6 | Frequency | 16 PIN diodes | mmWave | Specified |

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**MDPI and ACS Style**

Ledimo, B.K.; Moaro, P.; Ramogomana, R.; Mosalaosi, M.; Basutli, B.
Design Procedure of a Frequency Reconfigurable Metasurface Antenna at mmWave Band. *Telecom* **2022**, *3*, 379-395.
https://doi.org/10.3390/telecom3020020

**AMA Style**

Ledimo BK, Moaro P, Ramogomana R, Mosalaosi M, Basutli B.
Design Procedure of a Frequency Reconfigurable Metasurface Antenna at mmWave Band. *Telecom*. 2022; 3(2):379-395.
https://doi.org/10.3390/telecom3020020

**Chicago/Turabian Style**

Ledimo, Bokamoso Kebatho, Pako Moaro, Reuben Ramogomana, Modisa Mosalaosi, and Bokamoso Basutli.
2022. "Design Procedure of a Frequency Reconfigurable Metasurface Antenna at mmWave Band" *Telecom* 3, no. 2: 379-395.
https://doi.org/10.3390/telecom3020020