# Design and Application of a Metamaterial Superstrate on a Bio-Inspired Antenna for Partial Discharge Detection through Dielectric Windows

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Printed Monopole Antenna (PMA)

_{0}and L

_{0}are the antenna length and width, respectively, L and W are the length and width of the patch, respectively, L

_{g}and W

_{g}are the length and width of the truncated ground plane, respectively, W

_{f}is the width of the transmission line, g is the distance between the patch and the ground plane, and h is the substrate thickness.

_{re f}is the relative permittivity of the dielectric, approximated as [21]:

## 3. Metamaterials: Concept and Design

_{1}and r

_{2}represent the external and internal mean radius length, respectively, and S

_{circ}is the existing gap in each ring with external and internal resonance frequencies defined by f

_{C1}and f

_{C2}, respectively. Similarly, for the rectangular SRR [53]:

_{1}and l

_{2}represent the external and internal side length, respectively, and W

_{m}is the width of each resonance ring with external and internal resonance frequencies defined by f

_{R}

_{1}and f

_{R}

_{2}, respectively.

_{11}) and transmission (S

_{21}) of the designed set, as presented in Equations (9) and (10), respectively [54].

_{11}and S

_{21}values are represented by its respective magnitude and phase components, Re[] and Im[] represent the real and imaginary components, respectively, k represents the wave number, l the longest metamaterial unit cell length, and e

^{inkl}is defined as [54]:

## 4. Material and Methods

_{r}= 4.4, h = 1.6 mm and loss tangent (δ) equal to 0.02. Moreover, the simulations were performed for the frequency of 200 MHz up to 1600 MHz with a discrete sweep type with 201 points. The solution frequency was centered in 1 GHz (central frequency for the designed antenna) with a maximum number of passes and Delta S equals to 6 and 0.02, respectively.

#### 4.1. Bio-Inspired PMA Design

#### 4.2. Metamaterial Unit Cell Simulations

_{11}and S

_{21}values used for the calculation of ε and µ, as presented in Equations (5)–(9). From the ε and µ values, it was possible to classify the unit cells as metamaterials (ε < 0 and µ < 0).

#### 4.3. Metamaterial Superstrate Simulations

#### 4.4. Reflection Coefficient and Gain Measurements

_{R}= 4.5 dBi), the designed bio-inspired PMA gain (G

_{D}) was calculated according to the adapted Friis equation [20]:

_{21aut}and S

_{21ref}represent the transmission coefficient of the antenna under test and reference antenna, respectively, and S

_{11aut}and S

_{11ref}represent the reflection coefficient of the antenna under test and reference antenna, respectively.

_{21ref}). The second measurement was performed with the PMA positioned at the AUT distance, allowing the obtaining of the S

_{21aut}. A photograph of the schematic shown in Figure 11 is presented in Figure 12.

#### 4.5. PD Detection Sensitivity Tests

#### 4.6. PD Detection in a 230 kV Current Transformer

## 5. Results

#### 5.1. Simulation Results

#### 5.2. Laboratory Experimental Results

#### 5.3. PD Detection in a 230 kV Substation

## 6. Discussion

## 7. Conclusions

- (1)
- Both the SRR-CLS designed unit cells presented the double negative behavior (µ < 0, ε < 0) for almost all the main frequency range of PD activity (300–1500 MHz). Therefore, both the SRR unit cells were classified as metamaterials applicable as superstrate for the designed bio-inspired PMA;
- (2)
- The application of a metamaterial superstrate resulted in displacements in the bio-inspired PMA operating frequency range, resulting in a 3.9% and 1.8% bandwidth reduction for the circular and rectangular SRRs, respectively;
- (3)
- Although there was a bandwidth reduction regarding the bio-inspired PMA, the application of the both metamaterial superstrates resulted in higher reflection coefficient values for the frequency range of 1100–1500 MHz, in which some reflection coefficient values were lower than the threshold of −10 dB, improving the antenna power transmission/reception capacity for this frequency range;
- (4)
- Radiation patterns distortions were observed at the upper bio-inspired PMA operating frequencies for both metamaterial superstrates, in which the rectangular SRR presented lower radiation patterns distortions than the circular one for the upper frequencies, mainly at the back lobe direction;
- (5)
- The application of both designed superstrates resulted in maximum gain values almost increased in double regarding the reference bio-inspired PMA for the frequency range of 500–1000 MHz, resulting in a mean gain improvement higher than 1 dBi;
- (6)
- The practical application of the rectangular SRR superstrate resulted in a UHF sensor with an operating bandwidth (540–1500 MHz) that covers 80% of the main frequency range of PD activity (300–1500 MHz);
- (7)
- The measured mean gain for the bio-inspired PMA-metamaterial set was equal to 3.61 dBi, resulting in an enhancement of 0.7 dBi regarding the bio-inspired PMA (2.92 dBi) and representing a good detection sensitivity for PD application;
- (8)
- In PD laboratory tests, the bio-inspired PMA-metamaterial set was able to detect apparent charges above 15 pC, generated in a point-to-plane electrode configuration in an oil cell;
- (9)
- The bio-inspired PMA presented measured voltage values with half of the magnitude obtained from the IEC 60270 standard method, resulting in a high PD detection sensitivity for a radiometric based method;
- (10)
- Lastly, the bio-inspired PMA-metamaterial set presented itself as effective in the practical PD detection application, since it was possible to detect a significant level of PD activity in a 230 kV substation CT.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Material classification based on electrical permittivity and magnetic permeability values.

**Figure 6.**Bio-inspired PMA: (

**a**) Jatropha mollissima (Pohl) Baill leaf; (

**b**) details of the final designed model (all the dimensions are in centimeters) [26].

**Figure 7.**SRR models for each metamaterial unit cell (the green strips are the CLS structures): (

**a**) rectangular; (

**b**) circular.

**Figure 9.**Metamaterial superstrates positioned over the bio-inspired PMA: (

**a**) rectangular; (

**b**) circular.

**Figure 18.**Reflection coefficient phases for the metamaterial unit cells: (

**a**) circular; (

**b**) rectangular.

**Figure 19.**Transmission coefficient phases for the metamaterial unit cells: (

**a**) circular; (

**b**) rectangular.

**Figure 22.**E-plane co-polarization (red) and cross-polarization (purple) radiation patterns for 487 MHz: (

**a**) reference bio-inspired PMA; (

**b**) FR4 Superstrate; (

**c**) rectangular SRR; (

**d**) circular SRR.

**Figure 23.**E-plane co-polarization (red) and cross-polarization (purple) radiation patterns for 992 MHz: (

**a**) reference bio-inspired PMA; (

**b**) FR4 Superstrate; (

**c**) rectangular SRR; (

**d**) circular SRR.

**Figure 24.**E-plane co-polarization (red) and cross-polarization (purple) radiation patterns for 1497 MHz: (

**a**) reference bio-inspired PMA; (

**b**) FR4 Superstrate; (

**c**) rectangular SRR; (

**d**) circular SRR.

**Figure 25.**Rectangular plots of the E-plane radiation patterns for the frequencies of (

**a**) 500 MHz; (

**b**) 900 MHz; (

**c**) 1500 MHz.

**Figure 27.**Manufactured bio-inspired PMA: (

**a**) without metamaterial superstrate [26]; (

**b**) with metamaterial superstrate.

**Figure 28.**Measured and simulated reflection coefficients for the bio-inspired PMA with and without metamaterial superstrate.

**Figure 29.**Measured and simulated gain for the bio-inspired PMA with and without metamaterial superstrate.

**Figure 30.**PD pulses sample detected by the bio-inspired PMA-metamaterial set and IEC 60270 standard method, respectively, for the application of 13.4 kV on the oil cell.

**Figure 31.**Spectrogram of the PD pulses sample detected by the bio-inspired PMA-metamaterial set presented in Figure 30.

**Figure 32.**Comparison between the 230 kV Current Transformer (CT) PD pulses detected by the bio-inspired PMA with and without the metamaterial superstrate, respectively.

Apparent Charge (pC) | Voltage (mV) |
---|---|

20 | 25.6 |

100 | 121 |

500 | 584 |

Model | Maximum Mean Gain (dBi) |
---|---|

Bio-inspired PMA | 2.81 |

FR4 Superstrate | 2.83 |

Rectangular SRR | 3.96 |

Circular SRR | 4.07 |

Antenna | Bandwidth (GHz) | Gain (dBi) | Size (mm) |
---|---|---|---|

Proposed PMA-Metamaterial Set | 0.5–1.5 | 3.61 (mean) | 200 × 200 × 135 (depth) |

[74] (Hornet Antenna) | 0.5–8 | 3–17 | 418 × 318 × 645 (length) |

[75] (Hornet Antenna) | 0.5–3 | 4–11 | 440 × 290 × 350 (length) |

[76] (Vivaldi Antenna) | 0.5–6 | 3.07–7.7 | 120 (width) × 225 (length) |

[77] (Vivaldi Antenna) | 0.5–4 | 2–11 | 173 (width) × 299 (length) |

[78] (Reference Antenna–Hyperlog 30100X) | 0.4–10 | 4.5 (mean) | 360 (width) × 640 (length) |

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Xavier, G.V.R.; Serres, A.J.R.; da Costa, E.G.; de Oliveira, A.C.; Nobrega, L.A.M.M.; de Souza, V.C.
Design and Application of a Metamaterial Superstrate on a Bio-Inspired Antenna for Partial Discharge Detection through Dielectric Windows. *Sensors* **2019**, *19*, 4255.
https://doi.org/10.3390/s19194255

**AMA Style**

Xavier GVR, Serres AJR, da Costa EG, de Oliveira AC, Nobrega LAMM, de Souza VC.
Design and Application of a Metamaterial Superstrate on a Bio-Inspired Antenna for Partial Discharge Detection through Dielectric Windows. *Sensors*. 2019; 19(19):4255.
https://doi.org/10.3390/s19194255

**Chicago/Turabian Style**

Xavier, George Victor Rocha, Alexandre Jean René Serres, Edson Guedes da Costa, Adriano Costa de Oliveira, Luiz Augusto Medeiros Martins Nobrega, and Vladimir Cesarino de Souza.
2019. "Design and Application of a Metamaterial Superstrate on a Bio-Inspired Antenna for Partial Discharge Detection through Dielectric Windows" *Sensors* 19, no. 19: 4255.
https://doi.org/10.3390/s19194255