About the Maximum Transfer of Power in Time-Varying Linear Circuits

Abstract

This paper discusses the mathematical conditions of achievement of maximum power transfer from source to load in electric circuits where their basic elements (resistance, inductance and capacitance) are eventually linear and time-varying but not necessarily everywhere time-differentiable. This last concern is seen to be relevant for the inductive part of the circuit whose time- derivative, where it exists, plays the role of a resistor while it has an impulsive characterization at time instants where such a time-derivative does not exist. The power transfer degradation through time is also characterized related to the initial values of the circuitry provided that the source remains unaltered through time.