An analysis of a novel, monolithic integrated master oscillator power amplifier (M-MOPA) is presented. The M-MOPA consists of a DBR master oscillator which injects power into a linear chain of amplifiers and detuned second-order grating output couplers. The analysis self-consistently includes amplified spontaneous emission buildup and residual reflections throughout the amplifier stages. It predicts that output powers in excess of 1 W can be expected from a single-lateral-mode waveguide multistage amplifier less than 1 cm in length, injected with less than 15 mW of input power. In addition to the signal gain of >25 dB, the signal-to-noise ratio at 1-W output exceeds 15 dB. Because of the small reflections associated with the grating output couplers, and gain saturation by the injected signal, the amplifier self-oscillation threshold is suppressed to current densities above 15 kA/cm2.