Antenna Q-Factor Topology Optimization with Auxiliary Edge Resistivities

TL;DR

This paper introduces a bi-level topology optimization method for antennas that uses auxiliary edge resistivities and combines automatic differentiation with Bayesian optimization to efficiently minimize the Q-factor.

Contribution

It proposes a novel optimization strategy leveraging auxiliary edge resistivities and Bayesian optimization, outperforming existing methods in convergence and solving binarization issues.

Findings

Outperforms state-of-the-art topology optimization methods in convergence speed.

Successfully minimizes Q-factor for electrically small antennas.

Achieves self-resonance and approaches the Q-factor lower bound in design.

Abstract

This paper presents a novel bi-level topology optimization strategy within the method-of-moments paradigm. The proposed approach utilizes an auxiliary variables called edge resistivities related to the Rao-Wilton-Glisson method-of-moments basis functions, for a definition of a fast local optimization algorithm. The local algorithm combines automatic differentiation with adaptive gradient descent. A Bayesian optimization scheme is applied on top of the local algorithm to search for an optimum position of the delta-gap feeding and optimizer hyperparameters. The strength of the algorithm is demonstrated on Q-factor minimization for electrically small antennas. Auxiliary edge resistivity topology optimization outperforms current state-of-the-art topology optimization methods, including material density-based approaches and memetic schemes, in terms of convergence. However, due to the nature of gradient descent, careful tuning of the optimizer hyperparameters is required. Furthermore, the proposed method solves the known binarization issue. Two designs that achieved self-resonance and approached the Q-factor lower bound were further assessed in CST Microwave Studio.