The isolated bidirectional dc transformer(DCX) based on CLLC resonant converter has been extensively investigated for solid-state transformer application due to its open-loop constant voltage gain at resonant frequency and zero-voltage switching(ZVS) characteristics. However, owing to the complex multi-resonance mechanism of the fourth-order CLLC resonant tank, traditional first harmonic approximation(FHA) cannot accurately describe the time domain response of the resonant tank, which may lead to the inability of CLLC-DCX to achieve ZVS and obtain the unity voltage gain under light load conditions. This paper adopts the time domain model(TDM) to characterize the CLLC resonant tank for DCX application. Accordingly, the accurate time domain responses of the resonant tank, the related ZVS constraint and the boundary load condition for CLLC-DCX application are derived. Finally, an RMS current oriented optimal design method is proposed to minimize the conduction loss of CLLC-DCX during bidirectional operations. The simulation results verified that the sum of the squared RMS currents is optimized to the minimum with the obtained optimal design under different load conditions.