Energy in lossless and low-loss networks, and Foster's reactance theorem

Abstract

Energy stored in a lossless network driven by a voltage (current) source is related to a frequency derivative of the network susceptance (reactance). This relation is proven to be valid also for low-loss networks at frequencies far from the network resonance frequencies. Close to the resonance frequency, the stored energy is expressed in terms of the network susceptance (reactance) and the bandwidth of the resonance. A proof of Foster's reactance theorem follows from this consideration. It is also proven that Foster's theorem is a direct consequence of causality. >