Simplified Small-Signal Discrete-Time Modeling Approach for Digital-Controlled PWM Converters

Based on well-known approaches to discrete-time modeling and the standard Z-transform, exact small-signal discrete-time model takes into account sampling, modulator effects and delays in the control loop. This model can be used for direct design of digital compensators for digitally controlled PWM DC-DC converters. However, the modeling process is complex and time-consuming for converters with non-unique state matrix. This paper proposed a simplified small-signal discrete-time model for digital-controlled PWM converters. The proposed modeling approach significantly reduced modeling complexity while maintain high accuracy, therefore, is more suitable for direct design of digital compensators. This paper presents general results valid for any converter with leading or trailing edge PWM under continuous conduction mode (CCM). Specific examples, including approximate closed-form expressions for control-to-output transfer functions, are given for Boost converter. The proposed model is verified by comparison with exact model and system identification results.