# The Optimization Design of a Novel Slotted Microstrip Patch Antenna with Multi-Bands Using Adaptive Network-Based Fuzzy Inference System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Resonant Frequency of Rectangular Microstrip Antenna with Slots Parallel to Resonance Edges

_{e}and W

_{e}are the effective dimensions. Reportedly, the width of the patch has direct effect on some important parameters of the antenna such as radiation pattern and the frequency in which the antenna probably resonates. The resonant frequency ${f}_{mn}$ of the antenna at its fundamental TM10 mode can be calculated from Equation (1):

_{e}= L + 2ΔL

_{e}is the effective length showing the field fringing at the end of the patch. They are indicating the effects of the non-uniform medium and the fringing fields at each end of the patch. Two formulas for Equations (2) and (3) presented by Schneider (1969) and Hammerstad (1975) can be used to calculate ${\epsilon}_{e}$ (W) and $\mathsf{\Delta}$L.

## 3. Adaptive Neuro-Fuzzy Inference System (ANFIS)

## 4. How to Take Advantage of the ANFIS in Calculating the Resonant Frequency of Rectangular Antennas Operating at Multi Bands

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Full ground plane microstrip antenna without slots on the left side and with two slots on the right side being parallel to resonance edges fabricated on FR-4 substrate with a thickness of 1.6 mm.

**Figure 5.**Finding the best coordination for Xslot on the patch with two slots being parallel to resonance edges.

**Figure 6.**The gain of the proposed slotted-patch antenna as the length and the width of the slots are changed.

**Figure 9.**Radiation patterns of the proposed microstrip antenna with slots parallel to resonance edges at (

**a**) 7.4 GHz (

**b**) 12.5 GHz (

**c**) 17.4 GHz (

**d**) 19.2 GHz.

**Figure 11.**S11 obtained from the whole possible cases simulated by High Frequency Electromagnetic Field Simulation software (HFSS).

**Figure 13.**Approximation of training data and fuzzy output (O and

*****are symbols representing the trained data and FIS output respectively).

Parameter | mm | Parameter | mm |
---|---|---|---|

L1 = L feed | 3 | LG | 15.528 |

L4 | 9 | WG | 18.44 |

L5 | 5 | W4 | 1 |

L6 | 5 | W1 | 3.2 |

L7 | 15.2 | - |

Microstrip Patch Antenna with Slots (L8 = 7.5 mm, W8 = 0.25 mm) | |||||
---|---|---|---|---|---|

Resonant Frequency (GHz) | 7.4 | 12.2 | 14.6 | 17.5 | 19.3 |

Bandwidth | 7–7.8 | 11.9–13.2 & 13.2–15.5 | 16.9–18 | 18–18.9 | 18.9–20 |

Return loss (dB) | −26 | −33 & −20 | −28 | −18 | −28 |

Gain (dB) | 4 | 2.8 & 5.3 | 5 | 7.75 | 10.8 |

Reference | Resonant Freq | Max Gain dBi | Size (mm^{3}) |
---|---|---|---|

[12] | 3.39/4.29/5.46/5.77 | 8 | 25 × 25 × 1.6 |

[13] | 2.6/5.45/0.08 | 5 | 29 × 16 × 1.6 |

[14] | 1.6/1.9/3.8 | 6.58 | 52 × 71 × 1.6 |

[15] | 3.35/3.70/5.20/5.80 | 9 | 50 × 50 × 5 |

The Proposed Antenna | 7.4/12.2/14.6/17.5/19.3 | 10.8 | 15.528 × 18.44 × 1.6 |

**Table 4.**Results of the adaptive network-based fuzzy inference system (ANFIS) tested with different membership functions.

MFs | |||||||||
---|---|---|---|---|---|---|---|---|---|

Stage | Trapmf | Trimf | Dsigmf | Psigmf | Pimf | Gbellmf | Gaussmf | Gauss2mf | |

training | MAE | 1.5722 | 1.536 | 1.5386 | 1.5385 | 1.5317 | 1.483 | 1.4653 | 1.5012 |

RMSE | 2.6385 | 2.6797 | 2.6823 | 2.616 | 2.6066 | 2.3713 | 2.515 | 2.341 | |

CC | 0.7982 | 0.8213 | 0.8511 | 0.8552 | 0.8695 | 0.8997 | 0.9187 | 0.9234 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Abbasi Layegh, M.; Ghobadi, C.; Nourinia, J. The Optimization Design of a Novel Slotted Microstrip Patch Antenna with Multi-Bands Using Adaptive Network-Based Fuzzy Inference System. *Technologies* **2017**, *5*, 75.
https://doi.org/10.3390/technologies5040075

**AMA Style**

Abbasi Layegh M, Ghobadi C, Nourinia J. The Optimization Design of a Novel Slotted Microstrip Patch Antenna with Multi-Bands Using Adaptive Network-Based Fuzzy Inference System. *Technologies*. 2017; 5(4):75.
https://doi.org/10.3390/technologies5040075

**Chicago/Turabian Style**

Abbasi Layegh, Mahmood, Changiz Ghobadi, and Javad Nourinia. 2017. "The Optimization Design of a Novel Slotted Microstrip Patch Antenna with Multi-Bands Using Adaptive Network-Based Fuzzy Inference System" *Technologies* 5, no. 4: 75.
https://doi.org/10.3390/technologies5040075