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A typical two-level pulsewidth modulation scheme for a dc-dc converter generates a signal that has two values: 0 and 1. For a random aperiodic scheme, the switching period can be modulated in a random fashion with a known probability density function (pdf). In this paper, analytical expressions for both discrete and continuous spectra are provided for the case where different pdfs are used to modulate the switching signal of a dc-dc converter. Experimental results for a random aperiodic scheme that is used to optimize the output ripple of a buck dc-dc converter are provided to support the theoretical claims.
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Shrivastava et al. (2009) studied this question.
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