In this paper, a new gate-recessed AlGaN/GaN-based high electron mobility transistor (HEMT) on SiC substrate is proposed and its DC as well as microwave characteristics are discussed for Si₃N₄ and SiO₂ passivation layers using technology computer aided design (TCAD). THe two-dimensional electron gas (2DEG) transport properties are discussed by solving Schödinger and Poison equations self-consistently resulting in various subbands having electron eigenvalues. From DC characteristics, the saturation drain currents are measured to be 600 mA/mm and 550 mA/mm for Si₃N₄ and SiO₂ passivation layers respectively. Apart from DC, small-signal AC analysis has been done using two-port network for various microwwave parameters. The extrinsic transconductance parameters are measured to be 131.7 mS/mm at a gate voltage of $V_{gs} = -0.35$ V and 114.6 mS/mm at a gate voltage of $V_{gs} = -0.4$ V for Si₃N₄ and SiO₂ passivation layers respectively. The current gain cut-off frequencies $(f_{t})$ are measured t be 27.1 GHz and 23.97 GHz in unit-gain-point method at a gate voltage of -0.4 V for Si₃N₄ and SiO₂ passivation layers respectively. Similarly, the power gain cut-off frequencied $(f_{max})$ are measured to be 41 GHz and 38.5 GHz in unit-gain-point method at a gate voltage of -0.1 V for Si₃N₄ and SiO₂ passivation layers respectively. Furthermore, the maximum frequency of oscillation or unit power gain (MUG = 1) cut-off frequencies for Si₃N₄ and SiO₂ passivation layers are measured to be 32 GHz and 28 GHz respectively from MUG curves and the unit current gain, $|h_{21}| = 1$ cut-off frequencies are measured to be 140 GHz and 75 GHz for Si₃N₄ and SiO₂ passivation layers respectively from the $abs |h_{21}|$ curves. HEMT with Si₃N₄ passivation layer giver better results than HEMT with SiO₂ passivation layer.