Small-Signal Discrete-Time Modeling of Digitally Controlled PWM Converters

The letter presents an exact small-signal discrete-time model for digitally controlled pulsewidth modulated (PWM) dc-dc converters operating in constant frequency continuous conduction mode (CCM) with a single effective A/D sampling instant per switching period. The model, which is based on well-known approaches to discrete-time modeling and the standard Z-transform, takes into account sampling, modulator effects and delays in the control loop, and is well suited for direct digital design of digital compensators. The letter presents general results valid for any CCM converter with leading or trailing edge PWM. Specific examples, including approximate closed-form expressions for control-to-output transfer functions are given for buck and boost converters. The model is verified in simulation using an independent system identification approach.