Sampled-data Modeling of a Single-Ended Primary Inductor Converter in Discontinuous Conduction Mode

Abstract

This paper presents the small-signal modeling of a Single-Ended Primary Inductor
Converter power stage operating in discontinuous conduction mode using the sampled-data
modeling technique. In addition, two algebraic manipulating features are revealed; the simpler
periodic solution determination by the concept of Volt-Second and Capacitor-Charge balance,
and the replacement of the expression involving the singular matrix by the equivalent function
with the s  domain matrix. Four pulse transfer functions are derived from the model: the smallsignal
input-to-output voltage pulse transfer function, the small-signal duty duration-to-output
voltage pulse transfer function, the input-to-output voltage pulse transfer function, and the duty
duration-to-output voltage pulse transfer function. The model verification is analyzed by the
simulation results. The response sequences from the pulse transfer functions oscillate by the same
phase and frequency to the one from the simulation with slightly peak amplitude differences,
confirming the validity of the acquired pulse transfer functions.