Abstract
This paper proposes a cyclostationary based approach to power analysis carried out for electric circuits under arbitrary periodic excitation. Instantaneous power is considered to be a particular case of the two-dimensional cross correlation function (CCF) of the voltage across, and current through, an element in the electric circuit. The cyclostationary notation is used for deriving the frequency domain counterpart of CCF—voltage–current cross spectrum correlation function (CSCF). Not only does the latter exhibit the complete representation of voltage–current interaction in the element, but it can be systematically exploited for evaluating all commonly used power measures, including instantaneous power, in the form of Fourier series expansion. Simulation examples, which are given for the parallel resonant circuit excited by the periodic currents expressed as a finite sum of sinusoids and periodic train of pulses with distorted edges, numerically illustrate the components of voltage–current CSCF and the characteristics derived from it. In addition, the generalization of Tellegen’s theorem, suggested in the paper, leads to the immediate formulation of the power conservation law for each CSCF component separately.
Highlights
Modern hardware systems performing digital signal processing can reach high complexity, since they typically consist of many specialized devices
This paper proposes a cyclostationary based approach to power analysis carried out for electric circuits under arbitrary periodic excitation
The approach proposed in this paper to power analysis in electric circuits under arbitrary periodic excitation suggests a systematic framework, which is mainly based on two ideas
Summary
Modern hardware systems performing digital signal processing can reach high complexity, since they typically consist of many specialized devices. A traditional and easy to understand model describing the property of components can be built as an electric circuit being assembled from lumped elements only or lumped elements properly combined with parts of transmission lines. The second point is determined by a certain relation between the spectrum width of the processed signals and the passband (or passbands) of the analyzed component. In the case of digital signal processing, where the spectrum is considered to be concentrated in a baseband with respect to the lowest resonant frequency range, the component’s electric property can often be modelled as a simplified RC circuits [2]. If the resonance behavior cannot be neglected, a more accurate model, exhibiting weak resonant properties, may well be introduced by means of a generalized resonant circuit, either of parallel or serial type, with relatively low Q factor, typically not exceeding the value of 2
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