Matrix Synthesis for Filters With Internal Dual Extracted-Pole Sections

This article introduces a matrix synthesis approach for filters with internal dual extracted-pole (DEP) sections. Each DEP section can contribute one reflection zero (RZ) and two transmission zeros (TZs) to the overall filter network. In the synthesis procedure of a DEP section, first, the leading resonant node in a classical quartet coupling configuration is split into two resonant nodes sandwiching a singular nonresonant node (NRN). Then, the quartet is transformed into a DEP section through a sequence of node scaling, row/column addition, and matrix rotation operations. The proposed procedure is general as it applies to high-order filters with symmetric or asymmetric filter responses. Two synthesis examples are presented to demonstrate the application of the novel matrix transformation procedure, including a 5-2 and a 6-4 generalized Chebyshev filter. The 5-2 filter with a DEP section is realized by an in-line waveguide structure. The simulated and measurement results of the designed filter agree very well with theoretical characteristics. Furthermore, this study observes that synthesized DEP filters have a distinguished property in which the degree of realized filtering function is less than the number of resonant nodes in the coupling diagram. Such phenomenon is named degree deficiency and is discussed in this article.