This work presents a comprehensive modeling strategy for advanced large-size AlGaN/GaN HEMTs. A 22-element equivalent circuit with 12 extrinsic elements, including 6 capacitances, serves as small-signal model and as basis for a large-signal model. Analysis of such capacitances leads to original equations, employed to form capacitance ratios. Basic assumptions of existing parameter extractions for 22-element equivalent circuits are perfected: A) Required capacitance ratios are evaluated with device's top-view images. B) Influences of field plates and source air-bridges on these ratios are considered. The large-signal model contains a gate charge's non-quasi-static model and a dispersive-IDS model. The extrinsic-to-intrinsic voltage transformation needed to calculate non-quasi-static parameters from small-signal parameters is improved with a new description for the measurement's boundary bias points. All IDS-model parameters, including time constants of charge-trapping and self-heating, are extracted using pulsed-DC IV and IDS-transient measurements, highlighting the modeling strategy's empirical character.