Extended describing function (EDF) and reduced-order models are widely employed to derive small-signal TF for PID controller design of digitally controlled LLC converters under pulse-frequency modulation (PFM). However, achieving well-damped, high bandwidth (BW) transients with linear control remains challenging, as higher-order TFs are highly sensitive to parameter variations and load or input changes. In contrast, discrete-time (DT) models accurately capture small-signal behavior and enable high BW operation with enhanced dynamic performance. This digest presents a generalized DT modeling framework of the full-bridge LLC converter by characterizing dynamic behavior across operating modes and defining boundary conditions between adjacent modes. Using this model, a digital PID controller is designed to achieve well-damped, load-invariant transients at high BW. Thereafter, a hybrid digital nonlinear frequency adaptation technique is developed using a commercial microcontroller (MCU) to enhance transient performance and closed-loop output impedance using only voltage sensing. The effectiveness of this technique and nonlinear analysis is validated through a hardware prototype.
