Efficient Approach to Determine the Steady-State Energy in Networks with Periodic Discontinuous Excitations

Abstract

A new method for the solution of non-sinusoidal periodic states in linear networks is presented. It avoids the Fourier series calculations of the input and output network quantities. In the proposed method, the steady-state network response is formulated directly in the time domain as a superposition of the zero-input and forced responses for each continuous piecewise segments of the input quantity, separately. The whole periodic response is reached by taking into account the continuity and periodicity conditions at instants of discontinuities of the input quantity and then using the concatenation procedure for all segments. The method can be applied efficiently to continuous and discontinuous input quantities equally well. When we divide the network into two parts, i.e. a supplying two-terminal source and a two-terminal load, this method can be applied more efficiently to determine one-period energy for each of these particular subnetworks. Solutions are exact and there is no need to apply any of the widely up-to-date used frequency approaches. The Fourier series is completely cut out of the network analysis.