Modeling and control of switching converters : I. Unified modeling and measurement of current-programmed converters. II. A generic averaged model for switches in dc-to-dc converters

Citation

Tan, Fang Dong (1994) Modeling and control of switching converters : I. Unified modeling and measurement of current-programmed converters. II. A generic averaged model for switches in dc-to-dc converters. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/TGBG-N220. https://resolver.caltech.edu/CaltechETD:etd-12072007-113216

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Part I A unified model is established for a current-programmed converter, which unifies and extends previous models. A low-frequency modification leads to a unified duty-ratio control law for the buck, the boost, and the buck/boost converters, which results in improved predictions for several essential quantities of the current-loop gain. Inclusion of the sampling effect allows the presence of an additional pole [...] in the current-loop gain to be derived. The resulting final double-slope asymptote is fixed in position, and the crossover frequency cannot exceed half the switching frequency. Two parameters are found to be central quantities of interest. A parameter [...] represents the minimum value of D', the complementary duty ratio, to maintain stability of the current loop, and shows explicitly the stabilizing effect of a compensating ramp. A "stability parameter" [...] determines the additional pole [...] and describes the degree of peaking in the closed-loop transfer functions. Experimental verification employs an analog signal injection technique, which is easier to use, and contains more information about high-frequency dynamics than a conventional digital signal injection technique. Part II A generic averaged model for switches in dc-to-dc converters is established for the first time by using, in addition to averaging, volt-second and amp-second balance equations. The generic model inherits advantages of previous models and extend then to a new height: switches in dc-to-dc converters can now be handled as linear-time-invariant two-terminal circuit elements for their low-frequency characterizations. It is shown that the generic model is equivalent to the canonical circuit model from state-space averaging when it is substituted into a particular converter. It is also shown that the model for PWM switches is a special case of the generic model. A theoretical discussion about the equivalent duty ratio [...] reveals that averaging can retain low-frequency information contained in the original quantity regardless of its ripple content. The conditions are that the dc value of the original quantity is not vanishingly small, and the perturbation frequency is limited to half the switching frequency for amplitude perturbation or to a quarter of the switching frequency for frequency perturbation. Extensions of the generic model to converters with isolations, in discontinuous conduction mode, in current programming, and in other modes of operation are obtained. The concept of equivalent duty ratio is found useful. One salient feature of the extended generic model, which distinguishes it from similar previous models, is that different versions of the model have exactly the same form. The invariance of the form of the model is extremely useful for computer simulations of the averaged large- and small-signal dynamics in dc-to-dc converters under various modes of operation. One important feature of the approach, which separates it from all previous modeling approaches, is that its application is not limited by the number of switches in a converter. A three-switch converter is analyzed to show key steps in the derivation of a generic model for converters with multiple switches. Experimental results support the predictions from the generic model for the three-switch converter.

Thesis Files