in this paper, the steady-state and dynamic analyses of the continuous and the discontinuous conduction mode of the uk converter with nonzero mutual inductance by the state-space averaging method are described. For the analysis of the discontinuous conduction mode of the uk converter, the critical duty ratio is used. The analysis of the dynamic responses is presented for both the open- and closed-loop cases. The obtained results are useful for the optimum design of the uk converters.