Power harvesting describes the process of acquiring the ambient energy surrounding a system and converting it into usable electrical energy. Much of the work over the past two decades has focused on the conversion of ambient vibration energy sources using piezoelectric, electromagnetic and electrostatic transduction. Attempts were made to obtain a general model that could be applied to any transduction mechanism. Of the most interest is an electromagnetic generator model that was used by many researchers to model piezoelectric power harvesters. Two major results from the model are the power limit expression and the equal relationship between the electrically induced damping and the mechanical damping to reach the power limit. However, piezoelectric power harvesters cannot be accurately modeled by this electromagnetic model due to the essential difference in physics. There have also been attempts to obtain the power limit expression based on piezoelectric relationships, but they either neglect the piezoelectric backward coupling to the structure, or assume the power limit occurs at the resonance of the system. This paper obtains the power limit expression based on the piezoelectric coupled equations without those assumptions. In addition, the relationship between the electrically induced damping and mechanical damping at the power limit is studied. Furthermore, a closed-form criterion is derived and proposed to define strongly and weakly coupling power harvesters, whose differences in power characteristics are explained through analytical and numerical analysis. While most of the discussion is focused on linear power harvesters connected to a resistive circuit, the aim of this paper is to provide a comprehensive and deep understanding of this simple configuration, answers to important questions, and a starting point to develop a more general theory on power harvesters because similar system characteristics are observed in power harvesters with more complexities.
A piezoelectric based energy harvesting scheme is proposed here which places a capacitor before the load in the
conditioning circuit. It is well known that the impedance between the load and source contributes heavily to the
performance of the energy harvesting system. The additional capacitor provides flexibility in meeting the optimal
impedance value and can be used to expand the bandwidth of the system. A theoretical model of the system is derived
and the response of the system as a function of both resistance and capacitance is studied. The analysis shows that the
energy harvesting performance is dominated by a bifurcation occurring as the electromechanical coupling increases
above a certain value, below this point the addition of an additional capacitor does not increase the performance of the
systems and above the maximum power can be achieved at all point between these two bifurcation frequencies.
Additionally, it has been found that the optimal capacitance is independent of the optimal resistance. Therefore, the
necessary capacitance can be chosen and then the resistance determined to provide optimal energy harvesting at the
desired frequencies. For systems with low coupling the optimal added capacitance is negative (additional power to the
circuit) indicating that a second capacitor should not be used for. For systems with high coupling the optimal
capacitance becomes positive for a range of values inside the bifurcation frequencies and can be used to extend the
bandwidth of the harvesting system. The analysis also demonstrates that the same maximum energy can be harvested at
any frequency; however, outside the two bifurcation frequencies the capacitor must be negative.
The concept of power harvesting works towards developing self-powered devices that do not require replaceable power
supplies. One important parameter defining the performance of a piezoelectric power harvesting system is the
efficiency of the system. However, an accepted definition of the energy harvesting efficiency does not currently exist.
This article will develop a new definition for the efficiency of an energy harvesting system which rather than being
defined through energy conservation as the ratio of the energy fed into the system to maintain the steady state to the
output power, we consider the ratio of the strain energy over each cycle to the power output. This new definition is
analogous to the material loss factor. Simulations will be performed to demonstrate the validity of the efficiency and
will show that the maximum efficiency occurs at the matched impedance; however, for materials with high
electromechanical coupling the maximum power is generated at the near open and closed-circuit resonances with a lower