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There are many steps in the design of a microwave filter: mathematically describing the filter characteristics, representing the circuit as a network of lumped elements or as a coupling matrix, implementing the distributed elements, finding the initial dimensions of the physical structure, and carrying out numerical tuning using electromagnetic (EM) simulators. The whole process is painstaking and time-consuming, and it requires a great deal of engineering expertise. Microwave filters are extremely complex geometric structures, and their simple circuits are often quite hard to represent. Moreover, manufacturing them is costly: to be sure that the hardware resulting from the design will meet the performance goals, rigorous computer tools are used to determine the physical dimensions and evaluate all of the adjustments at the final stage. This last stage is particularly challenging, and advanced computational techniques are required.
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Balewski et al. (2020) studied this question.
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