Quarter Wave Coupled Wave-Guide Filters

Abstract

This paper considers the theory of band-pass wave-guide filters formed by cascading rectangular cavities separated by quarter guide wave-lengths. Formulas for resonant frequency, loaded Q, and insertion loss in the pass band are derived for a single stage using matrix theory and are in a form suitable for design purposes. The general theory of ``n'' stages is worked out using matrix algebra, and it is shown that the insertion loss and phase shift of ``n'' stages are given by: Ln=1+x2Un2(x) φ=tan−1[Tn(x)/Un(x)],where Tn(x) and Un(x) are the first and rationalized second kind Tschebyscheff polynomials. The specific design procedure is outlined including the design of a finite thickness inductive aperture.