A general sampled-data representation of the dynamics of arbitrary power electronic circuits is proposed to unify existing approaches. It leads, via compact and powerful notation, to disciplined modeling and straightforward derivation of small-signal models that describe perturbations about a nominal cyclic steady state. Its usefulness is further illustrated by considering the representation and analysis of a class of symmetries in circuit operation. The results of the application of this methodology to modeling the small-signal dynamics of a series resonant converter are described. The results correlate well with simulation results obtained on the Massachusetts Institute of Technology's Parity Simulator. What is of greater significance is the fact that the small-signal model is obtained in a completely routine way, starting from a general formulation and working down to the actual circuit; this contrasts with the circuit-specific analyses that are more typical of the power electronics literature. The automatability of this procedure is also discussed, and it is pointed out that the key ingredients for automatic generation of dynamic models from a circuit specification are now available.

A General Approach to Sampled-Data Modeling for Power Electronic Circuits

The letter presents an exact small-signal discrete-time model for digitally controlled pulsewidth modulated (PWM) dc-dc converters operating in constant frequency continuous conduction mode (CCM) with a single effective A/D sampling instant per switching period. The model, which is based on well-known approaches to discrete-time modeling and the standard Z-transform, takes into account sampling, modulator effects and delays in the control loop, and is well suited for direct digital design of digital compensators. The letter presents general results valid for any CCM converter with leading or trailing edge PWM. Specific examples, including approximate closed-form expressions for control-to-output transfer functions are given for buck and boost converters. The model is verified in simulation using an independent system identification approach.

Small-Signal Discrete-Time Modeling of Digitally Controlled PWM Converters

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

State-space average-value modeling of pulsewidth modulation converters in continuous and discontinuous modes has received significant attention in the literature, and various models have been developed. This paper presents a new approach for generating the state-space average-value model. In the proposed methodology, the so-called duty-ratio constraint and the correction term are extracted numerically using the detailed simulation and are expressed as nonlinear functions of the duty cycle and average-value of the fast state variable. The parasitic effects of circuit elements are readily included. The resulting average-value model is compared to a hardware prototype, a detailed simulation, and several previously published models. The proposed model is shown to be very accurate in predicting the large-signal time-domain transients as well as the small-signal frequency-domain characteristics.

Numerical state-space average-value modeling of PWM DC-DC converters operating in DCM and CCM

Constant on-time current-mode control has been widely used to improve light-load efficiency, because it can reduce the switching frequency to save switching-related loss. Therefore, an accurate model for constant on-time control is indispensable to system design. However, available models for constant on-time control are unable to provide accurate physical insight or predict system response very well. This paper introduces a new modeling approach for constant on-time control. The inductor, the switches, and the pulsewidth-modulated modulator are treated as a single entity and modeled based on the describing function method. The fundamental difference between constant on-time control and constant-frequency peak-current-mode control is analyzed through the proposed model. This proposed modeling method can be easily extended to other current-mode controls, including V2 controls. A simple equivalent circuit representation is proposed for the sake of easy understanding and simulation of current-mode controls. Simulation and experimental results are used to verify the proposed model.

New Modeling Approach and Equivalent Circuit Representation for Current-Mode Control

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

A generalized discrete time domain modeling and andlysis technique is presented for all types of switching regulaors using any type of duty-cycle controller, and operat1nq 1n both continuous and discontinuous inductor current. 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.

Ralph P. Iwens

Papers

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

Generalized computer-aided discrete time domain modeling and analysis of DC-DC converters