Elliptic function band multiplexers

Frequency-periodic multiplexers can be built by inserting allpasses in the links between series connected hybrids, provided the phase difference between these allpasses behaves like a staircase function with increasing frequency. Such allpasses can be made by loading two arms of a hybrid with cascades of commensurate transmission lines that are terminated by a short or open circuit. The whole filter bridge, consisting of four hybrids and line cascades, is analysed, and, after application of Richards transform, the filter discrimination function can be used for approximation. The approximation leads to the class of odd-order Cauer-Chebyshev filters of which the pure Cauer-parameter (Zolotarev) type has been studied more closely. Maximally flat response is included as a special case. Design formulas and curves for the transmission line admittances are given up to the 7th order. Measurements on a five pole filter built from quasioptical waveguides containing high permittivity dielectrics are reported for the range 28 to 84 GHz. Some suggestions are made on how to apply this type of filter in stripline technology and how to replace the hybrids by power dividers or circulators. The most simple multiplexer configuration consists of one circulator, one hybrid and two transmission-line cascades.