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The LLC resonant converter can be used as a dc-dc transformer (DCX) to provide isolation and fixed voltage transfer ratio. For applications requiring bidirectional power transmission, this paper proposes a PWM modulation and control strategy to achieve naturally bidirectional power flow for LLC-DCX, even in the case when the resonant parameters vary. Without the loss of generality, the proposed modulation can achieve ZVS of one side switches and ZCS of other side switches. Meanwhile, the additional benefits are that the PWM logic exchanging of the primary full bridge and the secondary full bridge is avoided and the auxiliary SR circuit is not needed. This simplifies the control and makes the converter to achieve naturally bidirectional power flow. Meanwhile, according to the analysis, it can also provide a fixed voltage conversion ratio independent of switching frequency if properly designed. Furthermore, to …