# A 4 × 4 Active Antenna Array with Adjustable Beam Steering

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Complete Structure

#### 2.1. Power Divider

#### 2.2. Phase Shifter

#### 2.3. Antenna

## 3. Phase Shift Characterization

#### 3.1. Error Analysis

## 4. Far-Field Measurements

#### 4.1. Beamforming Strategy

#### 4.2. Measurement Setup

#### 4.3. Measurement Results

#### 4.4. Comparison with Simulation

## 5. Discussion

#### 5.1. Power Budget

#### 5.2. Comparison with Other Works

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Structure of the $4\times 4$ antenna array. The vertical dimensions are exaggerated for clarity.

**Figure 6.**Single phase shifter simulation results when the voltage is swept from 0 V to 12 V: (

**a**) ${S}_{11}$; and (

**b**) ${S}_{21}$.

**Figure 7.**Antenna with dual polarization control through two individually controlled PIN diodes: (

**a**) antenna; and (

**b**) equivalent circuit of PIN diode in ON and OFF state.

**Figure 8.**Simulation results of a single antenna at broadside: (

**a**) ${S}_{11}$ for both polarizations; and (

**b**) normalized gain at 3 GHz for both polarizations.

**Figure 9.**Fabricated a $4\times 4$ structure without an antenna for phase shift characterization: (

**a**) front side; and (

**b**) back side.

**Figure 11.**Measurement results of the $4\times 4$ structure without an antenna at 3 GHz when varactors are biased from 0 to 12 V: (

**a**) ${S}_{11}$ measurement; (

**b**) ${S}_{21}$ measurement; and (

**c**) unit cell mapping of the $4\times 4$ antenna array.

**Figure 13.**Fabricated $4\times 4$ structure: (

**a**) antenna side; (

**b**) phase shifter and power divider side.

Parameter | Value |
---|---|

${L}_{\mathrm{S}}$ | 1.23 nH |

${C}_{\mathrm{jo}}$ | 1.23 pF |

${V}_{\mathrm{j}}$ | 1.92 V |

m | 2.06 |

${C}_{\mathrm{P}}$ | 0.25 pF |

**Table 2.**Phase measurements to determine the amount of phase error in different unit cells for 10${}^{\circ}$ beam steering case.

Row 3 | Row 4 | ||||||||
---|---|---|---|---|---|---|---|---|---|

Unit Cell | Calculated | Measured | Voltage | Error | Unit Cell | Calculated | Measured | Voltage | Error |

B12 | 0.0${}^{\circ}$ | 0.0${}^{\circ}$ | 4.4 V | 0.0${}^{\circ}$ | B11 | 0.0${}^{\circ}$ | 0.0${}^{\circ}$ | 4.4 V | 0.0${}^{\circ}$ |

B22 | 25.0${}^{\circ}$ | 23.3${}^{\circ}$ | 5.3 V | 1.7${}^{\circ}$ | B21 | 25.0${}^{\circ}$ | 25.3${}^{\circ}$ | 5.3 V | −0.3${}^{\circ}$ |

B32 | 50.0${}^{\circ}$ | 49.2${}^{\circ}$ | 7.0 V | 0.8${}^{\circ}$ | B31 | 50.0${}^{\circ}$ | 50.3${}^{\circ}$ | 7.0 V | −0.3${}^{\circ}$ |

B42 | 75.0${}^{\circ}$ | 75.0${}^{\circ}$ | 12.0 V | 0.0${}^{\circ}$ | B42 | 75.0${}^{\circ}$ | 79.7${}^{\circ}$ | 12.0 V | −4.6${}^{\circ}$ |

**Table 3.**Phase measurements to determine the amount of phase error in different unit cells for 40${}^{\circ}$ beam steering case.

Row 3 | Row 4 | ||||||||
---|---|---|---|---|---|---|---|---|---|

Unit Cell | Calculated | Measured | Voltage | Error | Unit Cell | Calculated | Measured | Voltage | Error |

B12 | 0.0${}^{\circ}$ | 0.0${}^{\circ}$ | 1.9 V | 0.0${}^{\circ}$ | B11 | 0.0${}^{\circ}$ | 0.0${}^{\circ}$ | 1.9 V | 0.0${}^{\circ}$ |

B22 | 92.6${}^{\circ}$ | 97.7${}^{\circ}$ | 2.7 V | −5.2${}^{\circ}$ | B21 | 92.6${}^{\circ}$ | 94.5${}^{\circ}$ | 2.7 V | −1.9${}^{\circ}$ |

B32 | 185.1${}^{\circ}$ | 174.9${}^{\circ}$ | 4.0 V | 10.2${}^{\circ}$ | B31 | 185.1${}^{\circ}$ | 168.8${}^{\circ}$ | 4.0 V | 16.3${}^{\circ}$ |

B42 | 277.7${}^{\circ}$ | 270.5${}^{\circ}$ | 12.0 V | 7.2${}^{\circ}$ | B42 | 277.7${}^{\circ}$ | 269.0${}^{\circ}$ | 12.0 V | 8.7${}^{\circ}$ |

Target Angle | Measured Angle | Angle Error | Control Angle | Peak Gain | SLL |
---|---|---|---|---|---|

${0}^{\circ}$ | ${2}^{\circ}$ | $+{2}^{\circ}$ | ${0}^{\circ}$ | 4.4 dBi | −11.4 dB |

${5}^{\circ}$ | ${5}^{\circ}$ | ${0}^{\circ}$ | ${3}^{\circ}$ | 4.7 dBi | −12.0 dB |

${10}^{\circ}$ | ${11}^{\circ}$ | $+{1}^{\circ}$ | ${5}^{\circ}$ | 4.6 dBi | −11.4 dB |

${15}^{\circ}$ | ${13}^{\circ}$ | $-{2}^{\circ}$ | ${10}^{\circ}$ | 4.6 dBi | −10.6 dB |

${20}^{\circ}$ | ${19}^{\circ}$ | $-{1}^{\circ}$ | ${20}^{\circ}$ | 3.8 dBi | −8.5 dB |

${25}^{\circ}$ | ${23}^{\circ}$ | $-{2}^{\circ}$ | ${30}^{\circ}$ | 3.4 dBi | −7.4 dB |

${30}^{\circ}$ | ${29}^{\circ}$ | $-{1}^{\circ}$ | ${35}^{\circ}$ | 3.4 dBi | −7.2 dB |

${35}^{\circ}$ | ${35}^{\circ}$ | ${0}^{\circ}$ | ${40}^{\circ}$ | 3.1 dBi | −7.6 dB |

${40}^{\circ}$ | ${39}^{\circ}$ | $-{1}^{\circ}$ | ${44}^{\circ}$ | 3.0 dBi | −7.4 dB |

${45}^{\circ}$ | ${43}^{\circ}$ | $-{2}^{\circ}$ | ${45}^{\circ}$ | 2.8 dBi | −7.8 dB |

Parameter | Value |
---|---|

Aperture size | 160 mm × 160 mm |

Ideal Directivity | 15.1 dBi |

Measured gain | 4.4 dBi |

Feed network loss | 0.8 dB |

Phase shifter loss | 0.8 dB |

PIN diode loss | 0.4 dB |

Fabrication tolerance losses | 0.8 dB |

ENIG and conductor loss | 5.8 dB |

Surface roughness | 2.1 dB |

Reference | Peak Gain | Steered Gain (Angle) | Scan Loss | Max Steering Error | Phase Profile | Characterization | Frequency | Array Size | Aperture Efficiency |
---|---|---|---|---|---|---|---|---|---|

[18] | 20.8 dBi | 18.3 dBi (-40${}^{\circ}$) | 2.5 dB | N/A | Discrete | Single, waveguide | 29 GHz | 20 × 20 | 9.5% |

[14] | 17.0 dBi | 14.9 dBi (40${}^{\circ}$) | 2.1 dB | N/A | Continuous | Datasheet ^{1} | 5.4 GHz | 8 × 8 | 28.5% |

[23] | 14.6 dBi | 12.9 dBi (45${}^{\circ}$) | 1.9 dB | N/A | Continuous & Discrete | Datasheet ^{1} | 4.8 GHz | 6 × 6 | 27.6% |

[15] | 15.0 dBi | 13.4 dBi (40${}^{\circ}$) | 1.6 dB | N/A | Continuous | Individual, method unclear | 5.0 GHz | 6 × 6 | 28.2% |

[24] | 13.8 dBi | N/A (60${}^{\circ}$) | 2.8 dB | 0.9${}^{\circ}$ | Discrete | Method unclear | 14.8 GHz | 24 × 2 | 6.3% |

[19] | 16.8 dBi | 14.5 dB (40${}^{\circ}$) | 2.3 dB | N/A | Discrete | Datasheet ^{1} | 5.0 GHz | 16 × 16 | 18.4% |

[16] | 15.6 dBi | 13.4 dB (45${}^{\circ}$) | 2.2 dB | 1.9${}^{\circ}$ | Continuous | Individual, near field probe | 4.8 GHz | 6 × 6 | 34.0% |

[17] | 19.9 dBi | N/A | N/A | 16${}^{\circ}$ | Continuous | Single unit cell | 5.2 GHz | 5 × 5 | N/A |

[25] | 23.7 dBi | 20.0 dBi (−45${}^{\circ}$) | 3.7 dB | N/A | Continuous and discrete | Datasheet ^{1} | 5.6 GHz | 16 × 16 | 33.5% |

[20] | 21.3 dBi | 15.4 dBi (60${}^{\circ}$) | 5.9 dB | N/A | Discrete | Datasheet ^{1} | 28 GHz | 20 × 20 | 12.5% |

[21] | 21.4 dBi | 19.9 dBi (40${}^{\circ}$) | 1.5 dB | N/A | Discrete | Datasheet ^{1} | 13.5 GHz | 16 × 16 | 14.8% |

[22] | 13.4 dBi | 10.7 dBi (45${}^{\circ}$) | 2.7 dB | 0.8${}^{\circ}$ | Discrete | Single, PIN & phase shifter measurement | 12 GHz | 16 × 2 | 24.5% |

This work | 4.7 dBi | 3.0 dBi (40${}^{\circ}$) | 1.7 dB | 2${}^{\circ}$ | Continuous | Measurement, average phase shift | 3 GHz | $4\times 4$ | 8.6% |

2.8 dBi (45${}^{\circ}$) | 1.9 dB |

^{1}Works that only present component values for PIN diodes and/or varactors are marked as datasheet.

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**MDPI and ACS Style**

Verho, S.; Nguyen, V.T.; Chung, J.-Y.
A 4 × 4 Active Antenna Array with Adjustable Beam Steering. *Sensors* **2023**, *23*, 1324.
https://doi.org/10.3390/s23031324

**AMA Style**

Verho S, Nguyen VT, Chung J-Y.
A 4 × 4 Active Antenna Array with Adjustable Beam Steering. *Sensors*. 2023; 23(3):1324.
https://doi.org/10.3390/s23031324

**Chicago/Turabian Style**

Verho, Sebastian, Van Thang Nguyen, and Jae-Young Chung.
2023. "A 4 × 4 Active Antenna Array with Adjustable Beam Steering" *Sensors* 23, no. 3: 1324.
https://doi.org/10.3390/s23031324