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In this study the power flow in a coupled mechanical and electromagneticharvesting system in presence of both positional and electrical fluctuations isanalyzed. Explicit expressions for the power into and out of the mechanical andelectrical parts of the system are found in the case of weak coupling, and itis shown how the power flows between the domains consistent with energyconservation. The case of thermal fluctuations is considered in particular, anduse of the fluctuation-dissipation theorem explicitly demonstrates that thepower delivered to the mechanical system from the electrical system is the sameas the power delivered to the electrical system from the mechanical system. Onthe other hand, the power dissipated in the electrical circuit is not the sameas the power transferred from the mechanical domain if the electrical circuitcontains its own current fluctuations. The electrical noise power dissipated ina load resistor is calculated, and found to consist of a component due toelectromagnetic coupling in addition to the well-known Nyquist component. Thecomponent due to electromagnetic coupling scales with size, and becomes moreimportant than the Nyquist component only for sufficiently small systems.

Power flow in a small electromagnetic energy harvesting system excited by mechanical motion