Application of Representation Theory to Dual-Mode Microwave Bandpass Filters

This paper discusses the physics behind the operation of dual-mode bandpass filters from a field theoretical point of view. It is argued that the two degenerate modes of the empty dual-mode cavity, commonly taken as the vertical and horizontal polarizations, become nonphysical when coupling and tuning elements are inserted. Instead, the original degenerate modes are rotated, or modified in a complex way, to generate two new modes whose characteristics depend on the coupling and tuning elements. It is shown that the tuning elements, as placed in existing dual-mode filter designs, act as both tuning and coupling elements. A working dual-mode filter can be designed with only ldquotuningrdquo elements present. A physical representation of dual-mode filters in terms of the eigenresonances of the dual-mode cavities, with the tuning and coupling elements present, is introduced. Two fourth-order dual-mode rectangular cavity filters with the same response in the passband and its vicinity are also presented to demonstrate the similar role played by ldquotuningrdquo and coupling elements in dual-mode cavities. The first filter uses only ldquotuningrdquo elements, while the second is based only on ldquocouplingrdquo elements.