Small-Signal Frequency Response Theory for piecewise-constant two-switched-network dc-to-dc converter systems

Small-Signal Frequency Response Theory is a theory for calculating the output spectrum of ideal dc-to-dc converter systems, i.e. systems with system coefficients piecewise constant in time, for a given spectrum of the signal injected into the control-input, in the small-signal limit. This theory, unlike other methods, can be applied to both resonant and PWM converters, and gives analytic results in closed form for ideal converters. This paper discusses the special case of ideal two-switched-network converter systems in PWM, programmed, and bang-bang operation. For the examples under study, theoretical prediction and experimental results are found to differ by at most 2dB in amplitude and 10 degrees in phase at most frequencies up to three times the switching frequency. Examples are given in this paper for which the theory gives the correct prediction, while other methods fail.