Generation of wave digital structures for connection networks containing ideal transformers

Most standard wave digital filters are derived from passive reference circuits where only parallel and series connections between two-terminal elements occur. In this paper, a framework for the automated generation of 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 SPQR-tree is related to a suitable adaptor structure and how this concept can be generalized to also cope with additional ideal transformers. To this end, suitable replacement graphs are derived such that networks with multi-terminal elements can also be treated with standard separation algorithms.