Steady state analysis of periodically time-varying networks by new developments in the spectral domain
✍ Scribed by Tohumoğlu, Gülay; Köksal, Muhammet
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 574 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0098-9886
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✦ Synopsis
The analysis of networks with time-varying elements is more complicated than the analysis of networks with constant elements. Frequency domain analysis methods are well established for the analysis of timeinvariant networks. Since the complete solution can be computed for only a very narrow class of periodically time-varying linear systems, ' general methods such as the piecewise constant approximation method (PWCAM)' and spectral analysis334 are of interest in many cases. Although differential equations can be bypassed by the latter method, operations on matrices of infinite order are involved. K ~r t h ' . ~ and Gense17,* have applied it to frequency modulator circuits which are a cascade of several two-ports, namely filter and modulator, with switching time variations. Later, it was shown that the method is appropriate for the computer-aided design of linear ladder and cascade connected networks.'-" In fact, other literature on this subject can hardly be found and this paper is intended to be a complete and extended theoretical and computer-aided analysis treatment of the subject with the following contributions.
- The use of spectral analysis is not limited to ladder or cascade networks and/or switching-type modulator circuits only. Spectral analysis of any type of periodically time-varying system is now as straightforward as the well-known classical computation of the steady state sinusoidal response of a linear time-invariant circuit. This is made possible by the improved spectral theory. 2. The known frequency domain formulation techniques developed for time-invariant linear circuits are also suitable for the analysis of periodically time-varying linear circuits by the introduction of new spectral matrices such as didem, indem, dimodem, inmodem, demodem and others and by the validity of Kirchhoffs laws in the spectral domain. 3. Concerning the comparison with other methods, spectral analysis has advantages when the time variations of system parameters are smooth. On the other hand, the PWCAM" gives more satisfactory results in the neighbourhoods of times where discontinuities occur.
It is observed that spectral analysis, like the staircase approximation scheme, is a first-order process with respect to the number of harmonics considered in the computations (see Figure 3).
Briefly, the scope of this work compensates for the present theoretical and computational deficiency in the literature about spectral analysis of periodically time-varying networks; furthermore, a general and unified mathematical basis for it is set up. Some new concepts are defined and a comparison of spectral analysis with other methods is presented.