The impact of different carbon concentrations in the Al 0.06 Ga 0.94 N graded back-barrier and GaN buffer of high electron mobility transistors (HEMTs) is investigated. Four epi-wafers with different carbon concentrations, ranging from 1 x 10(17) to 5 x 10(17) cm( -3) , were grown by metal organic chemical vapor deposition (MOCVD). HEMTs with 100 and 200 nm gate lengths were fabricated and characterized with dc, Pulsed-IV, drain current transient spectroscopy (DCTS), and large-signal measurements at 30 GHz. It is shown that the back-barrier effectively prevents buffer-related electron trapping. The highest C-doping provides the best 2DEG confinement, while lower carbon doping levels are beneficial for a high output power and efficiency. A C-doping of 1 x 10(17)cm( -3) offers the highest output power at maximum power added efficiency (PAE) (1.8 W/mm), whereas 3 x 10(17) cm( -3) doping provides the highest PAE ( > 40%). The C-profiles acquired by using secondary ion mass spectroscopy (SIMS), in combination with DCTS, is used to explain the electron trapping effects. Traps associated with the C-doping in the back-barrier are identified and the bias ranges for the trap activation are discussed. The study shows the importance of considering the C-doping level in the back-barrier of microwave GaN HEMTs for power amplification and generation.