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Two measurement schemes, namely, the modulation signal perturbation scheme and the pulse perturbation scheme, have been used for evaluating the loop gain of dc–dc converters. However, the two measured loop gains do not give consistent results due to the use of different forms of the injected small perturbation signal, and the difference in the two schemes cannot be distinguished by the usual averaged model. In this paper, the two loop gain measurement schemes are analyzed based on an extended-frequency-range small-signal model. Expressions of the loop gain are derived and their use in stability assessment and derivation of closed loop transfer functions is demonstrated. A sample-and-hold scheme is proposed as a simple alternative implementation of the pulse perturbation scheme. Finally, experimental prototypes of buck, boost, and buck–boost converters are tested for verification of the analytical results and the effectiveness of the sample-and-hold scheme. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Application of pulse width modulation (PWM) is known to produce sideband effects. The accuracy of the models of dc–dc converters can be improved if essential information of the sideband effects of PWM can be incorporated. In this paper, the aliasing effect of the sideband components on the closed-loop control is analyzed, and an effective representation of the transfer function of the pulse-width modulator is derived. Applying this transfer function to the dc–dc converter, an extended-frequency-range small-signal model is obtained, which can be conveniently used for deriving the loop gain of a PWM-controlled dc–dc converter. Furthermore, for wideband control applications, the large switching ripple in the modulation signal necessitates adjustment of the representation of the gain of the pulse-width modulator, which is dependent on the controller. Despite being highly accurate for stability assessment, the extended-frequency-range model is relatively complex after incorporating the effects of the sideband components and the large switching ripple. An approximate approach is introduced to simplify the loop gain expression and to provide physical insights into the effects of the sideband components and large modulation ripple amplitude. Experimental verification of the extended-frequency-range model is provided for a buck converter and a boost converter. [ABSTRACT FROM AUTHOR]

For dc–dc converters with pulsating output current, such as boost and buck–boost converters, the use of leading-edge or trailing-edge pulse width modulation (PWM) can result in distinctly different behavior. This phenomenon is not readily captured by the usual averaged model but can be predicted with a discrete-time model. However, the discrete-time model, which tracks the dynamics of state variables over a switching period, is usually more complex and less convenient to apply for the design of the feedback control. Based on the low-pass characteristics of dc–dc converters, an approximate discrete-time model is proposed in this paper, and upon transforming to the s-domain, the model results in transfer functions that can be conveniently used for deriving practical closed-loop parameters. With the proposed model, the loop gain, the input and output impedances are derived and analyzed. The effects of applying different types of PWM on the stability of a single dc–dc converter and a system of cascaded dc–dc converters are discussed. Finally, prototypes of a buck converter, a boost converter, and a cascaded system of buck and boost converters are constructed to verify the effectiveness of the approximate discrete-time model. [ABSTRACT FROM AUTHOR]