Aluminum Nitride (AlN) Piezoelectric Micromachined Ultrasonic Transducers (PMUTs) are gaining interest for biomedical implant power due to biocompatibility and lowtemperature processing. However, due to the low piezoelectric coefficient of AlN PMUTs, storage capacitors are often used to accumulate ultrasonic power transferred over an extended time. The accumulated energy is then used to power a DC load, which leads to a long start-up time, and insufficient duty cycle for some applications. We present an ultrasonically powered system for biomedical implants capable of delivering mW-range instantaneous power to DC loads, without pre-storing it. The system features a 25 mm2 AlN PMUT, an inductive matching network, and an application-specific power management integrated circuit(ASIC). For an acoustic intensity of 360 mW/cm2 at the surface of the PMUT, an open-circuit voltage of 1.11 V and an aperture efficiency of 30.5 % are measured. Furthermore, by connecting a series-matching inductor to the PMUT, the highest-reported power delivered to the load (PDL) of 6.4 mW is measured over an optimal load of 7.6 Ω. Finally, together with the ASIC and at the intensity of 108 mW/cm2, our system delivers 1.04 mW DC power to a 3.3 kΩ load, which is over two orders of magnitude higher than the previously reported average DC power for AlN PMUTs.