A unified equivalent circuit and impedance analysis method for galloping piezoelectric energy harvesters

In the past decade, galloping-based energy harvesters (GPEH) connected with various interface circuits have been developed and analytical models have been built. However, the power performances of these advanced structures and circuits are always treated separately, and a general model is missing to gain insights at a system level. To tackle this issue, this paper proposes a unified analysis framework for GPEHs. Its results are consistent with validated (but disconnected) results in the literature. The method provides an integrated view of the physics of linear GPEHs in multiple domains at the system level, and elucidates the similarities and differences among power behaviors of GPEHs connected with various interface circuits. The framework is based on two major elements: an equivalent circuit that represents the entire system, and an equivalent impedance that represents the interface circuit. Firstly, the electromechanical system is linearized and modeled in the electrical domain by an equivalent self-excited circuit with a negative resistive element representing the external aerodynamic excitation, and a general load impedance representing the interface circuit. Then, a closed-form, analytical expression of the harvested power is obtained based on the Kirchhoff's Voltage Law, from which the optimal load, maximum power, power limit, and critical electromechanical coupling (minimum coupling to reach the power limit) are determined. In this unified analysis, the exact type of energy harvesting interface circuit is not assumed. After that, the power characteristics of a GPEH connected with five representative interface circuits are analytically derived and discussed, by using the particular equivalent impedance of the interface circuit of interest. It is shown that they are subjected to the same power limit. However, the critical electromechanical coupling depends on the type of circuit. Throughout the discussions, impedance plots are used to illustrate the relationship between the internal system characteristics and external load impedance, facilitating the understanding of system power behavior.