The soft-switched modulation techniques presented in recent literature for single-phase half-bridge matrix-based dual-active-bridge (MB-DAB) ac-dc converter either suffers from incomplete soft-switching or computationally and memory expensive numerical technique requirement. An analytical expression-based modulation scheme for half-bridge MB-DAB, which is directly implementable on a microprocessor, is presented in this article that is capable of achieving near full-cycle ZVS turn-on of all MOSFETs and unity power-factor (UPF) operation. The theoretical derivations, working principles, and loss modeling are presented through suitable formulations. A 2.2-kW(pk) hardware prototype is fabricated, for which a PSIM simulation model is also developed using the MOSFET manufacturer's SPICE models and other components' datasheet parameters. The experimental results demonstrate near full-cycle ZVS turn-on over a wide load range (12\%-100\%), UPF operation, and 96.6\% conversion efficiency at full-load in agreement with the simulation results, which validate the proposed modulation approach.