Approximate Discrete-Time Small-Signal Models of DC–DC Converters With Consideration of Practical Pulsewidth Modulation and Stability Improvement Methods

It is generally known that averaged models are inadequate in describing the effects of leading-edge and trailing-edge pulsewidth modulation (PWM) on the stability of dc-dc converters. In this paper, using discrete-time models of the buck, boost, and buck-boost converters and considering the effects of leading-edge and trailing-edge PWM, the general expressions of the duty-cycle-to-output-voltage transfer function, Gvd(z), in the discrete-time domain are derived. Based on the low-pass characteristics of the dc-dc converters and related properties of the matrix functions, approximate expressions of Gvd in the frequency domain are derived, which are simple and accurate up to half the switching frequency. Using the approximate Gvd, the stability of the three basic dc-dc converters under leading-edge and trailing-edge PWM is analyzed. It is shown that the stability of the buck converter is unaffected by the type of PWM, while the leading-edge modulated boost and buck-boost converters have better stability than the trailing-edge modulated ones. Since the trailing-edge modulation is commonly available in PWM controller integrated circuits, the modulation signal zero-order holding (ZOH) method and the inductor current feedback control method are proposed for use in the trailing-edge modulated boost and buck-boost converters to achieve the same effect of leading-edge modulated converters. Experimental buck and boost converters were constructed for verification of the accuracy of the proposed model and the validity of the proposed control schemes.