R. D. Middlebrook

A general unified approach to modelling switching-converter power stages

A method for modelling switching-converter power stages is developed, whose starting-point is the unified state-space representation of the switched notworks and whose end result is either a complete state-space description or its equivalent small-signal low-frequency linear circuit model. A new canonical circuit model is proposed, whose fixed topology contains all the essential input-output and control properties of any d.c.-to-d.c. switching converter, regardless of its detailed configuration, and by which different converters can be characterized in the form of a table conveniently stored in a computer data bank to provide a useful tool for computer-aided design and optimization. The new canonical circuit model predicts that, in general, switching action introduces both zeros and poles into the duty ratio to output transfer function in addition to those from the effective filter network.

A general unified approach to modelling switching DC-tO-DC converters in discontinuous conduction mode

A method for modelling switching converters in the discontinuous conucction mode is developed, whose starting point is the unified state-space representation, and whose end results is a complete linear circuit model which correctly represents all essential features, namly, the input, output, and transfer properties (static dc as well as dynamic ac small signal). While the method is generally applicable to any switching converter operating in the discontinuous conduction mode, it is extensively illustrated for the three common power stages (buck, boost, and buck-boost). The results for these converters are then easily tabulated owing to the fixed equivalent circuit topology of their canonical circuit model. The outlined method lends itself easily to investigation of the discontinuous conduction mode in more complex structures (cascade connection of buck and boost converters, for example), in which more thean one inductor current may become discontinuous. As opposed to other modelling techniques, the new method considers the discontinuous conduction mode as a special case of the continuous conduction mode.

Transformerless DC-to-DC converters with large conversion ratios

A novel switching DC-to-DC converter is introduced in which large voltage step-down ratios can be achieved without a very small duty ratio and without a transformer. The circuit is an extension of the Cuk converter to incorporate a multistage capacitor divider. A particularly suitable application would be a 50 V to 5 V converter in which DC isolation is not required. The absence of a transformer and a larger duty ratio permits operation at a high switching frequency and makes the circuit amenable to partial integration and hybrid construction techniques. An experimental 50 W three-stage voltage divider Cuk converter converts 50 V to 5 V at 500 kHz, with an efficiency higher than that for a basic Cuk converter operated at the same conditions. A corresponding voltage-multiplier Cuk converter is described, as well as dual buck-boost-derived step-down and step-up converters. >

Sampled-data modeling of switching regulators

The high-frequency capabilities of two switching regulator modeling techniques, state-space averaging and discrete modeling, are compared. A new linear, small-signal modeling technique, which combines the continuous form of state-space averaging with the accuracy of discrete modeling, is then developed. This new method, called sampled-data modeling, succeeds, where state-space averaging fails, in predicting the subharmonic instability in current-programmed regulators, and is shown to be of significant usefulness in the design of high-performance switching regulators.

Large-signal modelling and analysis of switching regulators

A large-signal switching regulator model is derived, and prominent features of the transient response are determined. In particular, analytical expressions are found for the equilibrium points of the system which yield insight into the large-signal response, and computer-generated transient waveforms are obtained. As an example, a boost regulator is investigated, and is found to be stable for small signals but unstable for large transients.

Topics in multiple-loop regulators and current-mode programming

Some general considerations about multiple-loop feedback are discussed, and it is concluded that incorporation of a current-programmed power stage into a “new” power stage model is both justified and useful. A new circuit-oriented model of the current feedback path is derived which augments the well-known power stage canonical circuit model.

A unified analysis of converters with resonant switches

Quasi-resonant converters are a recently introduced family of single-switch resonant converters featuring zero-current or zero-voltage switching. Recognition of the topological structure uniting these converters — and the PWM converters on which they are based — leads to general models of their dc and low-frequency ac behavior. An expression is derived that yields the dc conversion ratio of a quasi-resonant converter in terms of the well-known conversion ratio of the underlying PWM topology. A small-signal, low-frequency dynamic model is developed whose parameters also incorporate the PWM conversion ratio. The dc and ac models reveal that any quasi-resonant converter with a full-wave resonant switch has dc and low-frequency behavior identical to that of its PWM parent, with switching frequency control replacing duty ratio control. Converters with half-wave resonant switches act more like PWM converters under current programming or discontinuous conduction mode, exhibiting lossless damping in the small-signal model and output resistance at dc.

Advances in Switched-Mode Power Conversion Part I

A number of important practical extensions to the basic ¿uk converter are presented. They include dc isolation, multiple-output power sources, and a physical realization of the sought for hypothetical dc-to-dc transformer, a device which converts from pure dc (no voltage or current ripple) at one terminal, to pure dc (at a different voltage) at the other terminal. The application of the circuit in a highly efficient amplifier for the servo control of a dc motor or other loads is also presented.

A continuous model for the tapped-inductor boost converter

A continuous, low-frequency, small-signal averaged model for the tapped-inductor boost converter with input filter is developed and experimentally verified, from which the dc transfer function and the small-signal line input and duty ratio input describing functions can easily be derived. A new effect due to storage-time modulation in the transistor switch is shown to explain observed excess filter damping resistance without associated loss in conversion efficiency. The presence of an input filter can cause a severe disturbance, even a null, in the control duty ratio describing function, with consequent potential performance difficulties in a converter regulator.

Modelling and analysis of switching DC-to-DC converters in constant-frequency current-programmed mode

An analysis of dc-to-dc switching converters in constant-frequency current-programmed continous conduction mode is performed, and leads to two significant resuslts. The first is that a ramp function, used to eliminate a potential instability, can be chosen uniquely to assure both stability and the fastest possible transient response of the programmed current. The second is the development of an extension of the state-space averaging technique by means of which both the input and output small-signal properties of any such converter may be accurately represented by a linear small-signal equivalent-circuit model. The model is presented and experimentally verified for the cuk converter and for the conventional buck, boost, and buck-boost converters. All models exhibit basically a one-pole control-to-output transfer fuction response.