This paper presents a method to analyze the dynamic physical limits of a phase-shifted full bridge (PSFB) circuit used for the power supply of Magnetic Resonance Imaging (MRI) gradient amplifiers. Based on the time-optimal control theory, the detailed optimal transient response process under a sudden load current change is analyzed considering the sample time delay, the minimum voltage undershoot and the minimum recovery time are calculated. The analytic results are validated by simulations and experiments on a 120 V/30 A PSFB converter.