General Power-Equivalent Synthesis of Resistive DC Networks

Abstract

Thévenin's and Norton's theorems are cornerstones of linear circuit analysis as they enable the terminal representation of any single-port linear network as the series of an ideal voltage generator and a linear impedance, or as the parallel between an ideal current generator and a linear admittance. While Thévenin's and Norton's representations are, by construction, electrically equivalent to the original network, they do not preserve power equivalence, in that they do not reproduce the power dissipated by the original network, nor they are power-equivalent to each other. This work discloses a general expression of the internal power $P_{h}$ dissipated by a linear dc network composed by resistors and a mixture of independent voltage and current generators. The expression reveals a theoretical link between $P_{h}$ and key open-circuit (or short-circuit) parameters of the network itself, and provides renewed insights on the relationship between power dissipation, load and network's efficiency. Furthermore, the result leads to the formulation of a class of circuits which are both electrically and power-equivalent to the original network, and that can be regarded as power-equivalent generalizations of Thévenin's and Norton's representations. Results are validated via case studies treated analytically and via computer simulations.