Block coupling transformations in multiband filters

This work extends an already known method for the design of multiband filters based on frequency transformations. A set of resonators is coupled to each resonator of a conventional single-band filter, constituting a block with as many resonators as pass bands. The star topology of the couplings makes this block impossible to implement except for the simplest cases. The solution consists of modifying the coupling topology of the block through similarity transformations, without affecting the rest of the network. Algorithms to obtain basic star and simple path topologies from generic coupling structures are presented, as well as an algorithm for arbitrary trees that is based on the simpler ones. The described theory is illustrated by means of two three-band microstrip filters, with star and simple path topology resonator blocks.