Inductive Post Arrays in Rectangular Waveguide

Waveguide band-pass structures employing cascades of inductive posts have been built for many years. They usually contain a symmetrical arrangement of posts in each cross-section, mostly one, two or three posts. The latter arrangement, for instance, is a favorite for X/4-coupled filters, since it s t r o n g l y r e d u c e s higher order mode interaction. This allows A/4 spacings to be used instead of the 3X/4 spacings required for single post filters, thus leading to shorter filters. In the past all of these structures had to be designed on the basis of measured data for the equivalent circuit of the cross-sectional post arrangement, because the available theoretical calculations1,2,8,9 are not sufficiently accurate. The obvious problem with measured data is, of course, that two errors are introduced, whose magnitudes are only poorly known: dimensional tolerances of the sample to be measured and errors in the measurement itself. Previous attempts to obtain theoretical data based on mode-matching techniques have consistently failed due to the convergence problem typically associated with taking a finite number of unknowns out of two sets of infinitely many unknowns. This paper presents a formulation which leads to only one set of infinitely many unknowns in the case of single or double posts. It may thus be expected that, when a finite number of these is taken, no convergence problem will be encountered. One may also speculate that this will continue to be true for arrays involving three or more posts, although in these cases more than one set of infinitely many unknowns is encountered again.