A computationally efficient small-signal modeling technique for switch mode power converters

Techniques used to model the nonlinear characteristics of a switch mode power converter can generally be categorized as either a state averaging approach or as a discrete modeling approach. The averaging technique uses numerous matrix manipulations or equivalent circuit manipulations to obtain the final small-signal model, but this model becomes inaccurate as the modulation frequency approaches one-half the switching frequency. On the other hand, the discrete modeling technique provides accurate information even at high frequencies, but the modeling process is very complicated. A computationally efficient method for obtaining the small-signal model of a switch mode power converter operating in the continuous conduction mode is presented. To apply this proposed technique, the only analytical work involved is the derivation of the two switched circuits of a given switch mode power converter in state-space representation form, and the developed computer simulation program provides a good approximated small-signal model in the form of open-loop Bode plots. Programming algorithms of finding the steady-state operating point are discussed. An important difference between this method and existing techniques is that a small-signal perturbation is applied to the control signal not to the duty-ratio signal. Therefore, the derived model reflects better to the actual hardware behavior. The proposed modeling technique is applied to the boost-derived power factor correction circuit as well as buck converter. The derived models are compared with the small-signal model obtained using the state-space averaging technique. To further verify the validity of the proposed modeling technique, a 24W buck converter is experimentally implemented. To measure the open-loop characteristics of the buck converter, a computer-based gain and phase meter is also developed using a PC, plug-in data acquisition board, and instrumentation software.; The interface circuits are designed and programed to measure the ac amplitudes and ac component time delay of the control signal (perturbed control signal) and controlled signal (output voltage). The experimental results indicate that the proposed modeling technique is a valid technique for describing the dynamic behavior of a switch mode power converter operating in the continuous conduction mode at a given operating point.