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Electric vehicles (EVs) and plug-in hybrid electric vehicles (PHEVs) are gaining popularity because they are more environmentally friendly, less noisy and more efficient. These vehicles have batteries can be charged by on-board battery chargers that can be conductive or inductive. In conductive chargers, the charger is physically connected to the grid by a connector. With the inductive chargers, energy can be transferred wirelessly over a large air-gap through inductive coupling, eliminating the physical connection between the charger and the grid. A typical on-board battery charger consists of a boost power factor correction (PFC) converter followed by a dc-dc converter. This dissertation focuses on the design, modeling and control of a bidirectional dc-dc converter for conductive battery charging application. In this dissertation, a detailed design procedure is presented for a bidirectional CLLLC-type resonant converter for a battery charging application. This converter is similar to an LLC-type resonant converter with an extra inductor and capacitor in the secondary side. Soft-switching can be ensured in all switches without additional snubber or clamp circuitry. Because of soft-switching in all switches, very high-frequency operation is possible, thus the size of the magnetics and the filter capacitors can be made small. To further reduce the size and cost of the converter, a CLLC-type resonant network with fewer magnetics is derived from the original CLLLC-type resonant network. First, an equivalent model for the bidirectional converter is derived for the steady-state analysis. Then, the design methodology is presented for the CLLLC-type resonant converter. Design of this converter includes determining the transformer turns ratio, design of the magnetizing inductance based on ZVS condition, design of the resonant inductances and capacitances. Then, the CLLC-type resonant network is derived from the CLLLC-type resonant network. To validate the proposed design procedure, a 3.5 kW converter was designed following the guidelines in the proposed methodology. A prototype was built and tested in the lab. Experimental results verified the design procedure presented. The dynamics analysis of any converter is necessary to design the control loop. The bandwidth, phase margin and gain margin of the control loops should be properly designed to guarantee a robust system. The dynamic analysis of the resonant converters have not been extensively studied, with the previous work mainly concentrated on the steady-state models. In this dissertation, the continuous-time large-signal model, the steady-state operating point, and the small-signal model are derived in an analytical closed-form. This model includes both the frequency and the phase-shift control. Simulation and experimental verification of the derived models are presented to validate the presented analysis. A detailed controller design methodology is proposed in this dissertation for the bidirectional CLLLC-type resonant converter for battery charging application. The dynamic characteristics of this converter change significantly as the battery charges or discharges. And, at some operating points, there is a high-Q resonant peaking in the open-loop bode-plot for any transfer functions in this converter. So, if the controller is not properly designed, the closed-loop system might become unstable at some operating points. In this paper, a controller design methodology is proposed that will guarantee a stable operation during the entire operating frequency range in both battery charging mode (BCM) and regeneration mode (RM). To validate the proposed controller design methodology, the output current and voltage loop controllers are designed for a 3.5 kW converter. The step response showed a stable system with good transient performance thus validating the proposed controller design methodology.