Resonance and impedance matching in a bistable energy harvester with L-matching network under Gaussian white noise

The energy management circuit plays an important role in the performance of vibrational energy harvesters (VEHs). The paper investigates the resonance characteristics and impedance matching of a nonlinear bistable electromagnetic VEH equipped with an L-matching network under Gaussian white noise. For the complex circuit equations containing a rectifier, an improved stochastic averaging method is proposed to solve the system's probability density function, yielding analytical expressions for the output DC voltage and power. It is found that adjusting the parameters of the L-matching network enables resonance between the mechanical and electrical subsystems, with an optimal ratio of electrical to mechanical natural frequencies, where the output DC power is maximized. Furthermore, specific values of coil resistance and load resistance optimize both output power and rectification efficiency. Experimental validation demonstrates that the optimized L-matching network increases the rectified voltage by approximately 1.86 times and the output power by about 3.45 times compared to the case without the network, while maintaining robust performance. The obtained results provide theoretical guidance and experimental support for the co-design of electromechanical coupling and circuit impedance matching in nonlinear VEHs under ambient random excitations.