Stochastic analysis of a bistable piezoelectric energy harvester with a matched electrical load

We present the analysis of a bistable piezoelectric energy harvester with matched electrical load, subject to random mechanical vibrations. The matching network optimizes the average energy transfer to the electrical load. The system is described by a set of nonlinear stochastic differential equations. A perturbation method is used to find an approximate solution of the stochastic system in the weak noise limit, and this solution is used to optimize the circuit parameters of the matching network. In the strong noise limit, the state equations are integrated numerically to determine the average power absorbed by the load and the power efficiency. Our analysis shows that the application of a properly designed matching network improves the performances by a significant amount, as the power delivered to the load improves of a factor about 17 with respect to a direct connection.