Design Synthesis of Electromagnetic Vibration-Driven Energy Generators Using a Variational Formulation

This paper reports upon the design of electromagnetic vibration-driven energy generators using a variational formulation to derive the equation of motion of such generators, thereby gaining insight into the device physics. Using this approach, the characteristics of the generator are analytically studied, a newly developed optimization theory of the generator is derived, and a guide for the sizing process is described. A fabricated prototype of an electromagnetic vibration harvester is presented. For the fabrication of the prototype, printed circuit board materials and PMMA have been used to lower the cost and to achieve lightweight device. Analytical and experimental results are presented and compared. The fabricated harvester weighs 7 g, delivers 315 μW at optimum excitation parameters at room temperature, and has a mechanical damping ratio of 0.0186. Experimental and analytical results show good agreement with the newly developed optimization theory. An analytical expression of the optimum load resistance is also developed and validated with experimental results, which show the frequency dependence of the optimum load resistance. It is also demonstrated that the optimization process needs two iterations if the mechanical damping ratio is unknown at the start of development and that the coil parameters represent the degree of freedom of the designer.