Quarter Wave Coupled Wave-Guide Filters

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: $$L_n{\text{=1+x}}^2{\mathrm{Un}}^2\mathrm{(x)\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\phi =}{\tan }^{\text{−1}}\mathrm{[Tn(x)/Un(x)]}$$ , 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.