Nonlinear modelling of switching DC-DC converters operating in discontinuous conduction mode

Analytical large-signal frequency-domain modelling of switching DC-DC converters, operating in the discontinuous conduction mode, is presented. The modelling approach is to derive analytical expressions of the converter output response using the extended Volterra functional series. Nonlinear frequency responses, including additional DC offset as well as significant subharmonic and higher harmonic components, due to large-signal perturbations of both the duty ratio and source voltage, are investigated. Their vulnerability to switching frequencies are also described. This modelling approach has been applied to various PWM DC-DC converters, including boost, buck and buck-boost types, operating in the discontinuous conduction mode, and the results are verified. Since the approach is so general, it can readily be extended to other switching power converters.