This paper describes a detailed design procedure for passivity-based controllers developed using the Brayton-Moser (BM) framework. Several passivity-based feedback designs are presented for the voltage-source converter, specifically for the H-bridge converter, since nowadays it is one of the preferred solutions to connect direct current (dc) loads or distributed sources to the alternating current (ac) grid. Independent of the operating mode, namely, the rectifier and regenerative operating mode, the achieved control aims are: high power factor correction in the ac-side and optimal dc voltage regulation capability in the dc-side. The proposed controllers can use series or parallel damping-based solutions for the error dynamics, naturally providing the conditions for stability and tuning of control parameters. In addition, the BM structure facilitates the addition of virtual resistance-inductance-capacitance (RLC) filter circuits to the control design for the rejection of low frequency harmonics. The effectiveness of series/parallel damping is investigated in case of abrupt changes in the load, using conductance estimators. Simulation and experimental results validate the analysis.