Two high-power and high-repetition-rate passively Q-switched Yb-doped double-clad fiber lasers have been demonstrated with small (5.4 Â¿m) and medium (10 Â¿m) core diameters using Cr4+ :YAG as an external saturable absorber. At a pump power of 13.8 W, 7.8 W single-mode outputs have been obtained with a pulse repetition rate of 120 kHz, pulse energy of 65 Â¿J , and pulse duration of 116 ns. A theoretical model is developed to predict the laser spectrum and numerically simulate the output characteristics versus pump power. The focused beam in Cr4+:YAG is assumed to have a Gaussian profile and is analyzed using traveling wave rate equations. The effect of amplified spontaneous emission is also investigated in the simulation, which shows reasonable agreement with experimental observations.