A better SPQR‐tree decomposition of electrical circuits containing multiports and its application to wave digital emulation

Abstract

SummaryWe report on a systematic method for the port‐wise decomposition of electrical networks. Our method exploits the SPQR‐tree decomposition as an algorithmic way for decomposing a given circuit into a maximal set of one‐port and multiports. We provide a solution for representing multiports by suitable replacement graphs, such that they are encapsulated not decomposed or processed by the SPQR‐algorithm. Contrary to current methods, our replacement graphs are not sophisticated but rather simple, which, in general, enhances the performance of the algorithm, when it comes to decomposing large electrical networks containing multiports. Some electrical devices, such as transistors or op‐amps, are commonly described in terms of their terminals rather than their ports. Thus, we cover the application of the template‐based approach to three‐terminal devices. Lastly, we make use of the new decomposition method for the emulation of a wave digital filter.