Open-loop small-signal transfer functions of the quadratic buck PWM DC-DC converter in CCM

Abstract

The quadratic buck converter or the BUCK converter presents a non-linear dc-dc voltage conversion ratio. The large-signal model of the quadratic buck converter would possess greater number of higher order nonlinear ac terms compared to that of the conventional buck converter. One can gain better insight by considering the linear model to understand the dynamic characteristics of these converters. This paper presents the small-signal model of the open-loop lossy quadratic buck converter operating in continuous conduction mode (CCM). The dc, averaged, and the low-frequency linear equivalent models are developed using the circuit averaging technique. The small-signal transfer functions such as: control-to-output voltage transfer function (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> ), input-to-output voltage transfer function (M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> ), input impedance (Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ), and the output impedance (Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ) are derived. A quadratic buck converter with an input voltage of 24 V and an output voltage of 10 V at an output power of 10 W is considered and its equivalent circuit is simulated. The simulation results are provided in order to validate the presented small-signal model.