A method for designing multistage broad-band amplifiers based upon well-known filter synthesis techniques is presented. Common all-pole low-pass approximations are used to synthesize prototype amplifier circuits that may be scaled in frequency and impedance. All-pass filters introduced at the first stage are shown to improve input match while maintaining circuit performance less 6 dB gain. A theoretical comparison is made with the distributed amplifier and the cascaded single-stage distributed amplifier. Theoretically, a larger gain-bandwidth product is achieved using the synthesis technique. A proof-of-concept Butterworth low-pass two-stage amplifier was designed, simulated, and measured and achieved a flat gain performance of 1-4 GHz with a power gain of 14.5±1 dB close to the predicted 1-4.2 GHz, 15±1 dB.