Abstract
In this chapter, we treat power calculations for a linear circuit in sinusoidal steady state, where the input and every other current and voltage in the circuit are sinusoidal and have the same frequency. We show how to perform and interpret power calculations in terms of phasors and impedances (or admittances), without having to refer to functions of time and without making explicit use of time averages. Important applications include power-factor correction and impedance matching for maximum or efficient power transfer. We begin by defining complex power and obtaining related expressions for average power dissipated at a terminal pair of a sinusoidally excited linear circuit or device.
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Notes
- 1.
Equation (13.22) is a degenerate case of Tellegen's theorem, which is a remarkable property of any pair of circuits having the same topology. See Artice M. Davis, Linear Circuit Analysis, PWS Pub. Co., (1998), pp 1052ff.
- 2.
The proof can be skipped without ill effect.
- 3.
It is possible for the real part of the impedance of a load containing one or more dependent sources to be negative. The terminology introduced here is used only in references to source-free loads.
- 4.
Again, these remarks pertain to source-free loads. A load containing dependent sources, capacitors, and resistors (no inductors) can be made to appear inductive, as shown in a subsequent chapter.
- 5.
Line voltage varies somewhat with load because of losses in transmission, but not nearly to the degree that line current varies with load.
- 6.
Superposition of real power is treated in Chapter 5.
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© 2011 Springer Science+Business Media B.V.
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Glisson, T.H. (2011). Complex Power. In: Introduction to Circuit Analysis and Design. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9443-8_13
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DOI: https://doi.org/10.1007/978-90-481-9443-8_13
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Publisher Name: Springer, Dordrecht
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