Abstract
Thevenin'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 Thevenin'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 shortcircuit) 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 Thevenin's and Norton's representations. Results are validated via case studies treated analytically and via computer simulations.
Highlights
Circuit analysis is a topic of central importance in modern engineering
This work takes its moves from a recent publication on the subject of power equivalence [5], in which it is shown that the power dissipated by a linear dc network composed by resistors and independent voltage generators consists of a constant term, equal to the dissipated power in open-circuit conditions, plus a load-dependent contribution numerically equal to the power dissipated by the network’s Thévenin’s resistance when traversed by the same load current as in the original network
The sought network S should have the following properties: P1 The dissipated power of S should be calculated consistently with the definition given in Section II, i.e. it should coincide with the total power dissipated by the resistors of S; P2 Independent voltage sources contained in S should, when acting alone and with S in open-circuit condition, reproduce the corresponding power dissipation Ph,OC-E of the original network; FIGURE 3
Summary
Circuit analysis is a topic of central importance in modern engineering. Theory of linear networks, in particular, is a cornerstone for the understanding of electrical circuits, its principles and methodologies being introduced in any undergraduate curriculum in electrical engineering. One of the key concepts in circuit analysis is the idea of equivalent circuit, i.e. a network of reduced complexity capable of exactly reproducing the voltage-current electrical relationship at the terminals of a more complex network For linear circuits, this idea is formalized by the well known Thévenin’s and Norton’s theorems [1]–[4]. This work takes its moves from a recent publication on the subject of power equivalence [5], in which it is shown that the power dissipated by a linear dc network composed by resistors and independent voltage generators consists of a constant term, equal to the dissipated power in open-circuit conditions, plus a load-dependent contribution numerically equal to the power dissipated by the network’s Thévenin’s resistance when traversed by the same load current as in the original network.
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