Pure mathematics

Mathematics

Algorithm

Filter (signal processing)

Engineering

Mathematical analysis

Optimization problem

Homotopy analysis method

Artificial intelligence

m-derived filter

Chebyshev filter

Filter design

Control (management)

Electronic engineering

Microwave

Computer science

Computer vision

Control theory (sociology)

Artificial neural network

Homotopy

Telecommunications

IEEE Transactions on Microwave Theory and Techniques

High-performance microwave and millimeter-wave filters' design is a challenging task because the filter characteristic is rather sensitive to the variation of geometric dimensions and electrical sizes. A common practice in filter design is to optimize the design variables starting from a set of initial values. However, if the initial values are not sufficiently close to the optimal solution, the optimization often fails to provide any satisfactory result. To deal with this problem, for the first time, the homotopy method is introduced to microwave and millimeter-wave filters' optimization problems in this article. The homotopy method formulates a series of intermediate optimization problems, which can guide the optimizer to approach the optimal solution for the target filter design. In this article, the artificial neural network (ANN) is adopted as the surrogate model to the time-consuming electromagnetic model to speed up the homotopy filter optimization process. Two design examples are given to demonstrate the homotopy optimization technique based on the ANN model, including an all-pole filter and a generalized Chebyshev filter with a frequency-dependent coupling. Both filters with optimized geometric dimensions are simulated, and the all-pole filter is fabricated and measured. The simulation and measurement results verify the accuracy of the ANN model and validate the homotopy optimization method.

Homotopy Optimization of Microwave and Millimeter-Wave Filters Based on Neural Network Model