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.

中文翻译：

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基于神经网络模型的微波和毫米波滤波器同伦优化

高性能微波和毫米波滤波器的设计是一项具有挑战性的任务，因为滤波器特性对几何尺寸和电气尺寸的变化相当敏感。滤波器设计中的常见做法是从一组初始值开始优化设计变量。但是，如果初始值与最优解不够接近，则优化通常无法提供任何令人满意的结果。针对这一问题，本文首次将同伦方法引入微波和毫米波滤波器的优化问题中。同伦方法制定了一系列中间优化问题，可以指导优化器为目标滤波器设计逼近最优解。在本文中，采用人工神经网络 (ANN) 作为耗时电磁模型的替代模型，以加快同伦滤波器优化过程。给出了两个设计示例来演示基于 ANN 模型的同伦优化技术，包括全极点滤波器和具有频率相关耦合的广义 Chebyshev 滤波器。对具有优化几何尺寸的两个滤波器进行仿真，并制造和测量全极点滤波器。仿真和测量结果验证了ANN模型的准确性，验证了同伦优化方法。包括一个全极点滤波器和一个具有频率相关耦合的广义 Chebyshev 滤波器。对具有优化几何尺寸的两个滤波器进行了仿真，并制造和测量了全极点滤波器。仿真和测量结果验证了ANN模型的准确性，验证了同伦优化方法。包括一个全极点滤波器和一个具有频率相关耦合的广义 Chebyshev 滤波器。对具有优化几何尺寸的两个滤波器进行了仿真，并制造和测量了全极点滤波器。仿真和测量结果验证了人工神经网络模型的准确性，验证了同伦优化方法。