# Optimization of split-ring resonator slots using levy-opposition-enhanced Newton Raphson method for high-gain UWB Vivaldi antenna design

## TL;DR

This paper introduces a new optimization algorithm to design a high-gain UWB Vivaldi antenna with improved performance and reduced size.

## Contribution

A novel hybrid metaheuristic algorithm, NRBO-LO, is proposed for optimizing UWB antenna design with enhanced convergence and performance.

## Key findings

- NRBO-LO outperforms existing algorithms in benchmark tests with better accuracy and stability.
- The optimized antenna achieves a 3.1–10.6 GHz bandwidth and 9.2 dB gain on a compact 40×40 mm² design.
- The antenna shows high radiation efficiency and minimal signal distortion across multiple orientations.

## Abstract

This paper presents a novel hybrid metaheuristic optimization algorithm, termed Lévy-opposition-enhanced Newton–Raphson-based optimization (NRBO-LO), and its application to the design of a high-gain ultra-wideband (UWB) antipodal Vivaldi antenna. The proposed algorithm enhances the conventional Newton–Raphson-based optimizer by integrating random opposition learning to improve population diversity and Lévy flight–based guided learning to strengthen exploitation, thereby mitigating premature convergence. The effectiveness of NRBO-LO is first rigorously evaluated using a comprehensive set of unimodal, multimodal, and composite benchmark functions, where it demonstrates superior convergence accuracy, robustness, and stability compared to several well-established metaheuristic algorithms. Following algorithmic validation, NRBO-LO is employed within a MATLAB–CST co-simulation framework to optimize the geometrical parameters of split-ring resonator (SRR) slots embedded on both the radiating surface and ground plane of a compact antipodal Vivaldi antenna fabricated on a low-cost FR-4 substrate. The optimized antenna occupies an area of 40 × 40 mm2 and achieves a continuous impedance bandwidth covering the entire 3.1–10.6 GHz UWB range by reducing the lower cutoff frequency from 4.8 GHz to approximately 3 GHz. A maximum realized gain of 9.2 dB is obtained, representing a significant improvement over the reference design. Comprehensive electromagnetic analyses are performed to assess antenna performance in both the frequency and time domains. The proposed design exhibits directive radiation characteristics, an average radiation efficiency of approximately 75% with a peak efficiency of 91%, stable group delay, and high fidelity factors across multiple antenna orientations, indicating minimal signal distortion. The results confirm that the combined use of the NRBO-LO algorithm and metamaterial-inspired SRR slots provides an effective and practical approach for the optimization of compact, high-performance UWB Vivaldi antennas suitable for radar, microwave imaging, and wireless communication applications.