Synthesis of PWM-based power gyrators

A systematic procedure to synthesize power gyrators operating at constant switching frequency is presented. Based on the gyrator equations, topological constraints on the power stage are first established and two types of gyrators, i.e., G and R, are defined. Subsequently, the equivalence between ideal sliding-dynamics and PWM zero-dynamics is used to derive the control law of the duty cycle. As a result, new gyrator structures are eventually disclosed. Namely, the buck converter with input filter and the Cuk converter are shown to have stable characteristic of a G-gyrator if damping networks are inserted and certain parametric conditions are satisfied. Similarly, a boost converter with output filter is also shown to behave as a power R-gyrator with stable dynamics.