Modeling of Average Current in Non-Ideal Buck and Synchronous Buck Converters for Low Power Application

Abstract

In this paper, a comparative analysis of the average switch/inductor current between ideal and non-ideal buck and synchronous buck converters is performed and verified against a standard LTspice model. The mathematical modeling of the converters was performed using volt-sec and amp-sec balance equations and analyzed using MATLAB/Simulink. The transients in the output voltage and the inductor current were observed. The transfer function of the switch current to the duty cycle (Gid) in open loop configuration for low-power converters operating in continuous conduction mode (CCM) was modeled using thestate space averaging (SSA) technique and analyzed using MATLAB/Simulink. Initially, using the volt-sec and amp-sec, balance equations for the converters were modeled. The switch current to duty ratio (Gid) was derived using the SSA technique and verified using standard average models available in LTspice software. Though the Gid was derived using various methods in earlier works, the analyses of parameters such as low frequency gain, stability, resonant frequency and the location of poles and zeros were not presented. It was observed that the converters were stable, and the non-ideal converter showed smaller resonant frequency than the ideal converter due to the equivalent series resistances (ESR) of the inductor and the capacitor. The non-ideal converters showed higher stability than the ideal converters due to the placement of the poles closer to the s-plane. However, the Gid of the non-ideal converters remained the same in the open loop configuration.