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.

Small-Signal Models With Extended Frequency Range for DC–DC Converters With Large Modulation Ripple Amplitude

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.

Reconsideration of Loop Gain and Its Measurement in DC–DC Converters

For the digitally controlled buck converters, the nonlinearity and time periodicity, caused by the pulsewidth modulator (PWM) and sample and hold, make the accurate frequency-domain analysis intractable. In this article, based on the harmonic transfer function (HTF) approach, a precise small-signal continuous-time modeling for the digitally controlled Buck converter operating in continuous-conduction mode (CCM) under constant-frequency voltage-mode control is presented. The sideband components on the closed-loop control are embedded in the model. Thus, this model is accurate within the full frequency domain region, which breaks the limit of Nyquist frequency. Furthermore, by overcoming the barrier of infinite series introduced by the sideband effects, the analytical loop gain expression is derived, which contributes to accurate stability assessment and reduction of computation burden. In addition, the proposed exact small-signal model has explained the reasons why different information injection points lead to different measured loop gains. Simulations and experimental results are conducted to verify the effectiveness of the proposed method.

Accurate Loop Gain Modeling of Digitally Controlled Buck Converters

The circuit averaging technique has long been used as the basis for modeling the behavioral effects of switched-mode pulsewidth-modulated (PWM) dc–dc power converter circuits due to its simplicity and efficiency in simulation. However, circuit-averaged models struggle to capture the effects of higher order harmonics on the output waveforms. Alternatively, multiharmonic models that capture high-frequency characteristics of output waveforms are typically very complex and computationally expensive. A general, efficient, and accurate multiharmonic modeling and simulation technique for low-power on-chip PWM dc–dc converters is presented in this article. The technique is based on the large-signal averaged model of the PWM switch cell and on the Fourier series expansion of the typical converter waveforms. Its applicability range includes current-mode-controlled dc–dc converters. The method is exemplified on a buck and on a boost converter and achieves a speedup of one order of magnitude with an accuracy loss below 3% over the transistor-level simulation. The method accounts for nonideal circuitry and supports any number of harmonics.

Fast SPICE-Compatible Simulation of Low-Power On-Chip PWM DC–DC Converters With Improved Ripple Accuracy

With the growing demand for electrical DC storage and sources, DC-AC conversion has become an indispensable component for not only high and medium, but also low-power applications. This paper introduces an efficient and accurate multi-harmonic circuit-averaged modeling technique for nonideal pulse-width modulated DC-AC inverters for low-power applications. The proposed model significantly reduces simulation times by using circuit-averaging and accurately anticipates the AC signal response by modeling the circuit behavior at different harmonics. The proposed model deploys the inductor current in the filter at the inverter output as a state variable, and accurately records circuit dynamics while accounting for switching losses associated with non-ideal devices. We show that the developed index-0 and index-1 circuits compare well with transistor-level simulations under a variety of operating conditions.

Circuit-Averaged Modeling of Non-Ideal Low-Power DC-AC Inverters

Small-signal models of pulse-width modulation (PWM) converters are widely used for analyzing stability and play an important role in converter design and control. However, existing small-signal models either are based on averaged DC behaviors, and hence are unable to capture frequency responses that are faster than the switching frequency, or greatly approximate these high-frequency responses. We address the severe limitations of the existing models by proposing a multiharmonic model that provides a complete small-signal characterization of both DC averages and high-order harmonic responses. The proposed model captures important high-frequency overshoots and undershoots of the converter response, which are otherwise unaccounted for by the existing techniques. In two converter examples, the proposed model corrects the misleading results of the existing models by providing truthful characterization of the overall converter AC response and offers important guidance for converter design and closed-loop control.

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Multiharmonic Small-Signal Modeling of Low-Power PWM DC-DC Converters

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Multiharmonic Small-Signal Modeling of Low-Power PWM DC-DC Converters