Transient analysis of DC to DC converters in discontinuous operation mode by using alternator equations

The time-varying part of a power electronic circuit formed by two switching elements is extracted in a two-port called an alternor. The V-I constitutive equations of the alternor are defined and depend on two time-varying parameters, α and β. The remaining part of the network is linear time-invariant. The modified nodal equations of the cyclically switching circuit are formulated by including the alternor equations. The s-domain solution holds for all transients of the circuit. Its inverse Laplace transform represents the global time-domain response, which, particularized for the corresponding values of α and β in each switched interval, gives the partial analytic solutions of the converter for each switched configuration. By using these expressions cyclically, together with boundary and threshold conditions, a computer program can give the transient and steady-state response