Modeling of multisampled pulse width modulators for digitally controlled DC-DC converters

This paper presents steady-state and small-signal models for digital pulsewidth modulators (DPWM) employed in multiple sampling digital control schemes for dc-dc switched mode power supplies (SMPS), and identifies the triangular modulation as intrinsically superior to other modulation schemes in multisampling applications. In conventional digital control of dc-dc converters, closed-loop bandwidth limitations are mainly set by analog-to-digital conversion times, computational delays and DPWM delays originated by the sampled nature of the PWM. While the use of hardwired logic and fast A/D converters minimizes computational and A/D delays, the DPWM small-signal phase lag strictly depends on the adopted sampling strategy. Multiple sampling techniques recently proposed in literature can achieve a strong reduction of the DPWM delay by operating the control and modulation steps at a sampling frequency strictly higher than the converter switching frequency. On the other hand, multisampled pulse width modulators (MSPWMs) exhibit nonlinear behaviors which do not have analog counterparts nor are encountered in conventional digital control, the most relevant effect being the onset of sampling induced dead bands, i.e., regions of zero modulation gain in the modulator transcharacteristic which may compromise proper closed-loop operation of the converter. The models proposed in this paper fully characterize the steady-state and small-signal behavior of DPWMs operated in multiple-sampling fashion. Multisampled triangular modulators are proven to be intrinsically superior to trailing edge or leading edge modulators in terms of linearity. Simulation and experimental results validate the proposed models and confirm the properties of triangular modulations.