Nonlinear Stochastic Dynamics of an Energy Harvester with Matched Load

Nonlinear energy harvesting is a promising technology to supply power or recharge batteries, to micro-electromechanical-systems requiring small amount of energy for their operation. Nonlinear response and multi-stability, can be exploited to increase the energy scavenged and the power efficiency of energy harvesting systems. In this work, we analyze the dynamics of a nonlinear, bi-stable energy harvester subject to random mechanical vibrations. As a solution to further increase the harvested power, we propose the application of an impedance matching network. The role of the matching network is to optimize the energy transfer from an oscillating mechanism, designed to capture vibration kinetic energy, to the electrical load. The systems is described by a set of nonlinear stochastic differential equation. We use a power series expansion method to find an approximate solution of the stochastic differential equations, in the weak noise limit. The approximate solution is the used to optimize the circuit parameters of the impedance matching network. In the strong noise limit, the state equations are integrated numerically to determine average power absorbed by the load and power efficiency. Our analysis shows that the application of the optimized matching network improves the performances by a significant amount with respect to a direct connection of the load.