# Evolutionary Optimization of Asymmetrical Pixelated Antennas Employing Shifted Cross Shaped Elements for UHF RFID

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## Abstract

**:**

## 1. Introduction

## 2. Employed Optimization Technique

## 3. Results and Discussion

#### 3.1. Impedance Measurement

#### 3.2. Antenna Gain Pattern Measurement

#### 3.3. Design Considerations

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Possible connections between copper elements of different shape: (

**a**) rectangles, (

**b**) hexagons, (

**c**) crosses. The red elements show vertical and diagonal neighbours. In (

**a**) it is shown that vertically spaced elements result in an adequate connection, whereas diagonal elements result in singularities, due to a (theoretically) infinitesimally small connection. In (

**b**) and (

**c**) no singularities can occur, regardless of how neighbouring elements are connected to each other. In (

**c**) the cross size (${S}_{\mathrm{cross}}$) is defined and its seperation into different Sonnet Software cells with size ${S}_{\mathrm{cell}}$ is shown.

**Figure 2.**Flowchart of the proposed optimization technique. (

**a**) First a predifined area is pixelated. (

**b**) After pixelation an initial population is created with Matlab and fed into Sonnet where the antenna is simulated. The results are then handed back to Matlab and the fitness function is computed from the optimized parameters. The population is rated and if it does not meet the termination criteria, a new one is created based on the first optimization.

**Figure 3.**Different exemplary antennas generated with the proposed method. (

**a**) 6 × 6 cm and 4 mm cross size, (

**b**) 4 × 4 cm and 2 mm cross size, (

**c**) 3 × 3 cm and 2 mm cross size. The red structure in the center of the respective antennas mark the ports.

**Figure 4.**Reflection coefficient plots of the manufactured antennas from the simulations shown in Figure 3. (

**a**) 6 × 6 cm, (

**b**) 4 × 4 cm, (

**c**) 3 × 3 cm.

**Figure 5.**Simulated 3D antenna gain pattern (

**1**) and the simulated and measured azimuth (

**2**) and elevation antenna gain patterns (

**3**) for the antennas A (

**a**), B (

**b**) and C (

**c**) depicted in Figure 3a–c.

Antenna | ${\mathbf{f}}_{\mathbf{sim}}$ [MHz] | ${\mathbf{S}}_{11,\mathbf{sim}}$ [dB] | ${\mathbf{f}}_{\mathbf{meas}}$ [MHz] | ${\mathbf{S}}_{11,\mathbf{meas}}$ [dB] | ffl [%] | $\Delta $ [%] |
---|---|---|---|---|---|---|

Antenna A | 861.5 | −16.06 | 874.9 | −17.21 | 0.79 | 0.75 |

Antenna B | 863 | −15.87 | 875.1 | −38.08 | 0.81 | 0.58 |

Antenna C | 873.5 | −15.99 | 878.8 | −8.32 | 1.15 | 0.63 |

Antenna | ${\mathbf{G}}_{\mathbf{sim}}$ [dBi] | ${\mathbf{G}}_{\mathbf{meas}}$ [dBi] | MAE${}_{\mathbf{azi}}$ [dB] | MAE${}_{\mathbf{ele}0}$ [dB] | MAE${}_{\mathbf{ele}90}$ [dB] |
---|---|---|---|---|---|

Antenna A | 1.3 | 1.49 | 1.32 | 0.92 | 1.03 |

Antenna B | −1.37 | −0.11 | 0.96 | 0.59 | 0.91 |

Antenna C | −3.9 | −2.02 | 0.87 | 1.35 | 1.3 |

**Table 3.**Comparison of different published antennas. Publications marked with an asterisk (*) did not directly measure the antenna gain and publications marked with a cross (x) only included simulations of the gain.

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**MDPI and ACS Style**

Mair, D.; Renzler, M.; Pfeifhofer, A.; Ußmüller, T.
Evolutionary Optimization of Asymmetrical Pixelated Antennas Employing Shifted Cross Shaped Elements for UHF RFID. *Electronics* **2020**, *9*, 1856.
https://doi.org/10.3390/electronics9111856

**AMA Style**

Mair D, Renzler M, Pfeifhofer A, Ußmüller T.
Evolutionary Optimization of Asymmetrical Pixelated Antennas Employing Shifted Cross Shaped Elements for UHF RFID. *Electronics*. 2020; 9(11):1856.
https://doi.org/10.3390/electronics9111856

**Chicago/Turabian Style**

Mair, Dominik, Michael Renzler, Alexander Pfeifhofer, and Thomas Ußmüller.
2020. "Evolutionary Optimization of Asymmetrical Pixelated Antennas Employing Shifted Cross Shaped Elements for UHF RFID" *Electronics* 9, no. 11: 1856.
https://doi.org/10.3390/electronics9111856