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 of a new mechanical element named inerter [25] has revived research into passive network synthesis. Investigation on n-port resistive network synthesis can be a critical step towards solving transformerless realizations of multi-port passive networks, and its results can be directly applied to minimal realizations of one-port mechanical and electrical networks based on element extraction [11,12]. Therefore, the significance of this topic has become apparent again.