Characterization of the Response Maps of Alternating-Current Networks

Abstract

In an alternating-current network, each edge has a complex conductance with positive real part. The response map is the linear map from the vector of voltages at a subset of boundary nodes to the vector of currents flowing into the network through these nodes. In this paper, it is proved that the known necessary conditions for a linear map to be a response map are sufficient, and we show how to construct an appropriate network for a given response map.