The state-space averaging method, associated with power converters, is discussed, Emphasis is on the motivation and objectives of modeling by equivalent circuits based on physical interpretation of state-space averaging. The discussion is limited to pulse-width-modulated DC-to-DC converters. >

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Small-signal modeling of pulse-width modulated switched-mode power converters

A generalized discrete time-domain modeling and analysis technique is presented for all types of switching regulators using any type of duty-cycle controller and operating in both continuous and discontinuous inductor currents. State-space techniques are employed to derive an equivalent nonlinear discrete time model that describes the converter exactly. The system is linearized about its equilibrium state to obtain a linear discrete time model for small signal performance evaluations, such as stability, audiosusceptibility, and transient response. The analysis makes extensive use of the digital computer as an analytical tool. It is universal, exact, and easy to use.

Generalized Computer-Aided Discrete Time-Domain Modeling and Analysis of DC-DC Converters

The nonlinear modeling and analysis of dc-dc converters has been done by averaging and discrete-sampling techniques. The averaging technique is simple, but inaccurate, as the modulation frequencies approach the theoretical limit of one-half the switching frequency. The discrete technique is accurate even at high frequencies, but is very complex and cumbersome. An improved model is developed by combining the aforementioned techniques. This new model is easy to implement in circuit and state variable forms and is accurate to the theoretical limit.

Improved Switching Converter Model Using Discrete and Averaging Techniques

State-space techniques are employed to derive an equivalent nonlinear recurrent time-domain model that describes the switched dc-dc converter behavior exactly. This model is employed effectively to analyze both large signal behavior by propagating the recurrence equation and matching boundary conditions through digital computation and small signal behavior by linearizing it about the equilibrium state.

Computer-Aided Analysis and Simulation of Switched DC-DC Converters

The known analysis of dc-dc converters in discontinuous operation mode and with voltage commutation based on a piecewise-linear description is extended to the analysis of line-commutated converters. With the latter as system-dependent pulsewidths the overlap angles appear, which can be computed in a manner analogous to the current-flow duration and the reloading time, respectively. This leads to a unified state-space modeling of dc-dc and ac-dc converters by which the steady-state and the dynamic small-signal behavior can be evaluated directly. If the piecewise-defined system equations are integrated numerically, a rather generalized analysis of power converters is found if the structure of switched systems is taken into account. As an illustrative example, a voltage-commutated dc-dc converter with a nonlinear dc inductance is studied.

Unified Modeling of Rectifier-Controlled DC-Power Supplies

Using discrete time state variable representation, a generalized computer-aided modelling and analysis of DC-DC converters is presented. The methodology provides exact modelling and is applicable to all types of power stages and duty-cycle control, including continuous and discontinuous inductor current operation. Converter stability, transient behavior and audio susceptibility can be analytically evaluated and predicted. The generalized theory of the proposed approach to converter modelling and analysis is presented first, followed by a demonstrative example applying the theory to a constant frequency buck converter operating in continuous and discontinuous inductor current mode. Excellent agreement with laboratory test data has been observed.

J.E. Triner

Papers

Discrete time domain modelling and analysis of dc-dc converters with continuous and discontinuous inductor current

Discrete Time Domain Modelling and Analysis of DC-DC Converters with Continuous and Discontinuous Inductor Current