Minimal realizations of three-port resistive networks

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The classical n-port resistive synthesis problem

INTRODUCTION: An n-port resistive network is an n-port circuit consisting of only passive resistors, which is an important class of passive networks. An n-port resistive network is usually characterized by its impedance or admittance matrix. Since there are no reactive elements, passivity and reciprocity imply that the impedance and admittance matrices of n-port resistive networks must be nonnegative definite if they exist [21]. Since no transformers are present, there are further constraints. The realizability problem of n-port resistive networks was an active topic and was widely investigated from the 1950s to the 1970s. Recently, the invention ...postprin

Realization of three-port spring networks with inerter for effective mechanical control

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Realizability of n-port resistive networks with 2n terminals

In this paper, we consider the realizability problem of n-port resistive networks containing 2n terminals. A necessary and sufficient condition for any real symmetric matrix to be realizable as the admittance of an n-port resistive network containing 2n terminals is obtained. The condition is based on the existence of a parameter matrix. We then focus on a three-port resistive network containing six terminals. A necessary and sufficient condition is derived for any real symmetric matrix to be realizable as the admittance of a three-port resistive network containing six terminals and at most five positive elements, whose topological structure is properly restricted. © 2013 IEEE.published_or_final_versio

Network synthesis

A discussion, with numerous examples, on the application of state variable methods to network analysis and synthesis is reported. The state variable point of view is useful in the design of control circuits for regulators because, unlike frequency domain methods, it is applicable to linear and nonlinear problems. The reported are intended as an introduction to this theory

Synthesis of biquadratic impedances with at most four passive elements

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