We present the detailed dc and radio-frequency characteristics of an Al_0.3Ga_0.7N/GaN/In_0.1Ga_0.9 N/GaN double-heterojunction HEMT (DH-HEMT) structure. This structure incorporates a thin (3 nm) In_0.1Ga_0.9N notch layer inserted at a location that is 6-nm away from the AlGaN/GaN heterointerface. The In_0.1Ga_0.9N layer provides a unique piezoelectric polarization field which results in a higher potential barrier at the backside of the two-dimensional electron gas channel, effectively improving the carrier confinement and then reducing the buffer leakage. Both depletion-mode (D-mode) and enhancement-mode (E-mode) devices were fabricated on this new structure. Compared with the baseline AlGaN/GaN HEMTs, the DH-HEMT shows lower drain leakage current. The gate leakage current is also found to be reduced, owing to an improved surface morphology in InGaN-incorporated epitaxial structures. DC and small- and large-signal microwave characteristics, together with the linearity performances, have been investigated. The channel transit delay time analysis also revealed that there was a minor channel in the InGaN layer in which the electrons exhibited a mobility slightly lower than the GaN channel. The E-mode DH-HEMTs were also fabricated using our recently developed CF₄-based plasma treatment technique. The large-signal operation of the E-mode GaN-based HEMTs was reported for the first time. At 2 GHz, a 1times100 mum E-mode device demonstrated a maximum output power of 3.12 W/mm and a power-added efficiency of 49% with single-polarity biases (a gate bias of +0.5 V and a drain bias of 35 V). An output third-order interception point of 34.7 dBm was obtained in the E-mode HEMTs