Electrical Network Synthesis: A Survey of Recent Work
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Abstract
The field of electrical network synthesis has a number of long-standing unanswered questions. The most perplexing concern minimality in the context of resistor, inductor and capacitor (RLC) network synthesis. In particular, the famous Bott–Duffin networks appear highly non-minimal from a system theoretic perspective. We survey some recent developments on this topic. These include results establishing the minimality of the Bott–Duffin networks and their simplifications for realising certain impedances; enumerative approaches to the analysis of RLC networks within given classes of restricted complexity; and new necessary and sufficient conditions for a (not necessarily controllable) system to be passive. Finally, some remaining open questions are discussed.