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In a recent paper, it was shown that (i) any reciprocal system with a propertransfer function possesses a signature-symmetric realization in which eachstate has either even or odd parity; and (ii) any reciprocal and passivebehavior can be realized as the driving-point behavior of an electric networkcomprising resistors, inductors, capacitors and transformers. These resultsextended classical results to include uncontrollable systems. In this paper, weestablish new lower bounds on the number of states with even parity(capacitors) and odd parity (inductors) for reciprocal systems that need not becontrollable.

On the internal signature and minimal electric network realizations of reciprocal behaviors