Generation of wave digital structures for networks containing multiport elements

Most standard wave digital filters are derived from passive reference circuits, where only parallel and serial connections between one-port elements occur. In this paper, a framework for the automated generation of the wave digital structures is presented, where the reference circuit is assumed to comprise arbitrary connection types. It is shown how the representation of the underlying graph by its so-called SPQR-tree is related to a suitable adaptor structure and how this concept can be generalized to also cope with networks containing certain multiport elements. We propose two different novel approaches to finding a valid tree representation from a given reference circuit. The first approach relies on the usage of apt replacement graphs for the multiport elements. The second one is based on searches for circles on suitably constructed graph representations and generates wave digital structures with minimum implementation effort even in presence of nonreciprocal elements. In both approaches, standard separation algorithms with known efficient implementations can be applied.