The design and fabrication technology of high-power Schottky-barrier microwave mesa photodiodes from 10 to 40 μm in diameter back-illuminated through the substrate are described. The diodes were made on MBE-grown InAlAs/InGaAs/InP heterostructures. The operating frequency of photodiodes 10 μm in diameter has been found to be 40 GHz, and the maximal microwave output at 20 GHz for photodiodes 15 μm in diameter have been found to reach 58 mW. The coefficient of amplitude-to-phase conversion has been determined to be 1.5 rad/W. This value outperforms the available literature data and makes the given design of photodiodes promising for systems of analog microwave signal generation and transmission, which are very sensitive to phase noise.