Significant advances are needed to optimize the charging speed, reliability, safety, and cost of today's conservatively designed electric vehicle (EV) charging systems. The design and optimization of these novel engineering systems require concurrent consideration of thermal and electrical phenomena, as well as component and system level dynamics and control to guarantee reliable continuous operation, scalability, and minimum footprint. This work addresses the concurrent thermal and electrical design constraints in a high-density, on-board, bidirectional charger with vehicle-to-grid (V2G), grid-to-vehicle (G2V), vehicle-to-house (V2H), and vehicle-to-vehicle (V2V) power transfer capabilities. The electrical design of this charger consists of DC–DC and DC–AC power stages connected in series. The power-stage circuits are implemented on a printed circuit board (PCB) with 16 surface-mount silicon carbide MOSFETs, three inductors, and one transformer. The main goal of this work is to investigate the interplay between the cooling architecture and the PCB layout, and the corresponding impact on the heat dissipation and parasitic inductance. This work compares the performance of three generations of this multifunctional charger that employ different design methodologies and proposes high-level design guidelines derived from multiphysics simulations and experimental tests.