# Searching for Multimode Resonator Topologies with Adaptive Differential Evolution

## TL;DR

This paper introduces a new method to automatically design microwave resonators with specific frequency properties using an optimization algorithm.

## Contribution

The novel contribution is an automated approach using L-SRTDE to explore and optimize new resonator topologies that were previously undiscovered.

## Key findings

- The proposed method successfully discovers novel resonator topologies with high-quality frequency-selective properties.
- Automated tuning using the L-SRTDE algorithm outperforms traditional manual design methods in exploring new configurations.
- Some discovered topologies differ from existing ones but maintain high performance.

## Abstract

Microwave devices based on microstrip resonators are widely used today in communication, radar, and navigation systems. The requirements to these devices may include specific frequency-selective properties, as well as size and production costs. The design of resonators and filters are mostly performed manually, as the process requires expert knowledge and computationally expensive modeling, so practitioners are usually limited to tuning a chosen example from a set of known, typical topologies. However, the set of possible topologies remains unexplored and may contain specific constructions, which have not been discovered yet. In this study we propose an approach to automatically search the space multimode resonator topologies using a zero-order optimization algorithm and numerous computational experiments. In particular, a family of symmetrical resonators constructed out of four rectangles is considered, and the parameters are tuned by the recently proposed L-SRTDE algorithm. We state the problem of building the topology of a microwave device conductor with specified frequency-selective characteristics as an optimization problem, and the minimized function (target function) in this problem is based on the evaluation of the deviation between the specified frequency-selective characteristics and their values obtained via electrodynamic modeling. The experiments with two target function formulations have shown that the proposed approach allows finding novel topologies and automatically tune them according to the required frequency-selective properties. It is shown that some of the topologies are different from the known ones but still demonstrate high-quality properties.