The Singlet: Direct Synthesis of Pseudo-Elliptic Inline Filters With Frequency Variant Couplings

A general and direct synthesis of
$N_{p}$
poles pseudo-elliptic inline filters having
$N_{p}$
purely real and/or imaginary frequency transmission zeros is presented. Using an appropriate model of the resonators (bandpass distributed or lumped element) and shifting the reference planes at the input and output of the filter network, a novel direct synthesis and realization of filters based on frequency variant coupling (inductive or capacitive) in the distributed domain is demonstrated for accurate modeling of narrow and broadband filters. First, a complete general synthesis procedure is described that allows for flexible or mixed topologies realizing transmission zeros anywhere on the frequency plane (including complex and infinite frequencies). Furthermore, by exploiting the power of modular design, a synthesis procedure that enables simultaneous extraction of reflection zero (a pole) and a transmission zero in the form of a symmetrical and physically realizable singlet as an elementary unit is showcased. The physical dimensions of the extracted singlets are independently determined in any chosen technology, and the overall filter is obtained by directly cascading the physical singlets. To validate this novel synthesis technique, three design examples are shown: a narrowband four-pole, four transmission zeros (fully canonical) filter from literature is synthesized and physically dimensioned, a wideband three-pole, three transmission zero (fully canonical) filter, and a broadband three-pole, one transmission zero, filter. In the first two examples, each of the singlet blocks was implemented in an overmoded rectangular waveguide cavity operating at the TE201 mode coupled at the input and output to the fundamental nonresonating TE10 mode. The third example was implemented in a re- entrant coaxial resonator operating at the fundamental mode. The simulation of the electromagnetic (EM) [high-frequency structure simulator (HFSS)] models of the overall example filters was in excellent agreement with the synthesized models, thereby validating the effectiveness of the proposed synthesis technique. Furthermore, the measured results of the fabricated wide bandpass filter showed close agreement with synthesis and EM model.