Transitioning from Analytical to Numerical Methods for Synthesizing Microwave Bandpass Filters

Microwave filters, integral to modern wireless communication systems, have been refined to possess more compact structures and sharper rejection capabilities. The introduction of the theory for exhaustive topology search has led to the development of irregular filter topologies, which couldn’t be synthesized using traditional rotation methods. These novel coupling topologies, such as “trapezoid” and “grid” configurations, are designed to achieve more transmission zeros (TZs) and compact structures. The exhaustive solution search, proposed to identify all possible real-valued solutions for any given topology based on filtering functions, is discussed in detail in this paper. The potency of the mapping between the original coupling matrix and its corresponding folded matrix is demonstrated, with comparisons offered to underline the advantages of the proposed mapping over others. Furthermore, synthesis examples for irregular topologies, including trapezoid and grid topologies, are provided. This method paves the way for the purely analytical synthesis for microwave filters.