A Dual Band MMIC Low frequency 180° Hybrid

Abstract
F In this paper design formulas, for the development of an unusual 180° hybrid working in two distinct frequency bands, are provided. In particular the design formulas of a lumped-element rat race, starting from a conventional transmission-line rat-race, are found out. In order to generalize the matching problem the input and output port impedances are considered to be different .I. I NTRODUCTION Hybrid couplers are key components in the design of microwave circuits such as mixers and modulators [1]. Moreover, they can be used as power dividers and combiners in array antennas. The rat-race, one of the simplest 180° hybrid to be designed, is normally realized, also in the MMIC version, using microstrip lines, at least at frequencies over 20 GHz. In the lower microwave frequency range the conventional transmission-line rat-race has too large dimensions to be effectively integrated in a MMIC, so that the most suitable realization becomes the lumped element one. As it is known, in order to realize a rat race using lumped elements (L.E.), the transmission-line segments are replaced, in the design procedure, by equivalent pi and tee networks, by equating the ABCD transmission matrices of the line segments to the corresponding ABCD matrices of the L.E. pi and tee networks [2]. This design approach normally results in a very effective realization both in terms of isolation and transmission performances among the relevant ports, but normally in a narrow frequency bandwidth, so limiting a widespread utilization of the L.E. solution [3]. On the other hand, there are many important applications where it is necessary to implement a 180° hybrid that has to work in two frequency ranges, very apart from each other, as in the case, for instance, of mixers working with RF (or LO) frequency much greater than LO (or RF) frequency. This problem is usually approached by carrying out a broadband hybrid solution, trying to overcome the rat-race frequency limitations which normally does not exceed two octaves in bandwidth. However a completely different approach can be followed designing a Dual Band Rat-Race, i.e. a hybrid having the requested performances