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Unfolder-based quasi-single-stage ac-dc power converter has been widely used for high-power electric vehicle (EV) charging systems for its high efficiency and power density. However, the resonance between the grid inductance (impedance) and the capacitors on the soft-dc-link of the converter impacts the system stability and significantly limits the system control bandwidth and dynamic response performance. A quasi-single-stage ac-dc converter with unfolder plus T-bridge series resonant converter (T-SRC) is studied in this work. The small-signal modeling and plant transfer function derivation of the T-SRC is presented in this paper. A damping filter design using the extra element theorem (EET) is then proposed to achieve high- bandwidth and stable operation of the quasi-single-stage ac-dc converter. Simulation and hardware results from an 18 kW module for high-power EV charging are provided to validate the proposed modeling and damping filter design.