Maximum power, optimal load, and impedance analysis of piezoelectric vibration energy harvesters

Abstract

This paper performs an analysis of maximum power output of piezoelectric energy harvesters. It has been observed that there exists an overall power limit that can be obtained by tuning energy harvesting circuits, including both linear and nonlinear. The significance of the power limit is that it represents the maximum possible power output or capacity of an energy harvester. In other words, the harvested power is always capped by this limit regardless of the type and tuning of the energy harvesting circuit interface. The power limit and the optimal generalized electrical load or impedance to reach this power limit are first obtained directly by using the electromechanically coupled equations of the system, and then obtained by using the equivalent circuit analysis and impedance matching approach. Both are commonly used methods in energy harvesting research. This paper presents an effort to unify them but also offer insights on the power limit from two different perspectives. In the second part of this paper, the power limit and impedance matching results are applied to a linear energy harvesting circuit interface, i.e., resistive energy harvesting (REH) circuit, and a nonlinear circuit interface, i.e., standard AC–DC energy harvesting (SEH) circuit, to study their physical constraints on the impedance matching and clearly explain their power behaviors such as the maximum power and the effect of electromechanical coupling on the power. In addition, closed-form expressions, a relationship between the mechanical damping and the effective electromechanical coupling coefficient, to define the three types of coupling, i.e., weak, critical, strong, are obtained. It is found that the SEH harvesters require about 1.5 times of minimum electromechanical coupling of that of REH harvesters to reach the power limit, and the frequency bandwidth between the two power limit frequencies of a SEH harvester is narrower than that of a REH harvester given the same level of strong electromechanical coupling.