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, G_vd (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 G_vd in the frequency domain are derived, which are simple and accurate up to half the switching frequency. Using the approximate G_vd , 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.