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This paper describes an approach to harvesting electrical energy from a mechanically excited piezoelectric element. A vibrating piezoelectric device differs from a typical electrical power source in that it has a capacitive rather than inductive source impedance, and may be driven by mechanical vibrations of varying amplitude. An analytical expression for the optimal power flow from a rectified piezoelectric device is derived, and an "energy harvesting" circuit is proposed which can achieve this optimal power flow. The harvesting circuit consists of an AC-DC rectifier with an output capacitor, an electrochemical battery, and a switch-mode DC-DC converter that controls the energy flow into the battery. An adaptive control technique for the DC-DC converter is used to continuously implement the optimal power transfer theory and maximize the power stored by the battery. Experimental results reveal that use of the adaptive DC-DC converter increases power transfer by over 400% as compared to when the DC-DC converter is not used.