On the modeling of PWM converters for large signal analysis in discontinuous conduction mode

Several methods have been developed until today for the analysis of PWM converters operating in Discontinuous Conduction Mode (DCM) and many endeavours have been done in order to solve two well known problems: the nontrivial calculation of the internally controlled instant at which the current flowing into the diode falls to zero and the subsequent order reduction of the state-space model of the circuit due to the disappearance of one state variable. In this work a new approach to the modeling of PWM converters for the large signal analysis in DCM operation is presented. It is based on a closed-form discrete-time state-space model obtained by introducing a time-adaptive function for the calculation of the instant at which the diode current falls to zero, and an equivalent fictitious configuration of the circuit during the idle phase, in order to prevent the unconditioned order reduction of the state-space model. A four-terminal device is also introduced which allows a unified representation of the PWM buck, boost, buck-boost, and Cuk converters in DCM operation using the fictitious configuration. The model proposed can be used for circuit oriented simulations both in open and closed loop operation and for an accurate ripple inspection, automatically accounting for DCM to CCM transitions and vice versa.