This paper presents a comprehensive time-domain analysis of the dual-input LLC converter. By utilizing PSM and FSM, the converter power stage interfaces two photovoltaic (PV) panels to achieve maximum power point tracking (MPPT). The detailed mode-by-mode operation and steady-state analysis are derived using three parameters: the switching frequency, phase shift, and load weight. Furthermore, the DC gain equations of each PV panel and their characteristic curves are derived. In addition, the waveform boundaries and ZVS analysis are discussed as well. Moreover, an extended perturbation & observation (P&O) algorithm that guarantees achieving MPPT for each panel is proposed. Finally, the theoretical analysis has been tested and verified by a 450-W prototype of dual-input LLC converter.