An analytical model of the Buck converter is proposed based on the per-unit method. For the principle of power conservation, the critical inductance between the continuous conduction and discontinuous conduction modes are determined, and also the critical average current are deduced. Taken the critical inductance, the critical average current and the rated load as basis variables, the per-unit equation set of the Buck converter are deduced from the basic current and power equations. By analyzing the per-unit equation set with different relative inductance, the mathematical current formulas of the inductor, the switch device and diode are deduced. Also the analytical continuous and discontinuous duty ratios of the inductor current are deduced. Finally, simulation and experimental results are presented to verify those formulas.