The isolated two-stage ac-dc-dc converter containing an isolated dual-active-bridge (DAB) dc-dc converter and an ac-dc rectifier has been widely used for connecting the dc sources to the ac utility grid. However, the impedance interaction between the DAB converter and the ac-dc rectifier may cause the instability problem. To address this issue, this paper proposes two control methods to reshape the impedances of the isolated two-stage ac-dc-dc converter by building a virtual impedance connected in parallel or series with the input impedance of the DAB converter. The magnitude of the input impedance of the DAB converter is increased to satisfy the Middlebrook criterion without changing its negative resistance characteristics by the proposed control methods. Furthermore, the design requirements for the proposed controllers are also given to ensure the stable operation of the two-stage converter. The comparison of these two proposed methods is also discussed in terms of stabilizing ability, dynamic performance, and cost. The comprehensive experimental results are provided to validate the proposed methods. INDEX TERMS Impedance shaping, modeling, stability criterion, two-stage converter.