4170 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 12, DECEMBER 2010 Power Processing Circuits for Piezoelectric Vibration-Based Energy Harvesters Reinhilde D’hulst, Tom Sterken, Member, IEEE, Robert Puers, Senior Member, IEEE, Geert Deconinck, Senior Member, IEEE, and Johan Driesen, Member, IEEE Abstract—The behavior of a piezoelectric vibration-driven en- ergy harvester with different power processing circuits is evalu- ated. Two load types are considered: a resistive load and an ac–dc rectifier load. An optimal resistive and optimal dc-voltage load for the harvester is analytically calculated. The difference between the optimal output power flow from the harvester to both load circuits depends on the coupling coefficient of the harvester. Two power processing circuits are designed and built, the first emulating a resistive input impedance and the second with a constant input voltage. It is shown that, in order to design an optimal harvesting system, the combination of both the ability of the circuit to harvest the optimal harvester power and the processing circuit efficiency needs to be considered and optimized. Simulations and exper- imental validation using a custom-made piezoelectric harvester show that the efficiency of the overall system is 64% with a buck converter as a power processing circuit, whereas an efficiency of only 40% is reached using a resistor-emulating approach. Index Terms—Energy efficiency, energy harvester, piezoelectric devices, power conditioning. I. I NTRODUCTION T HE current advances in performance and functionality of micro- and nanosystems have stimulated the development of intelligent networks of autonomous systems. The demand for a small, mobile, and reliable energy supply for each au- tonomous network node has led to the development of a new type of generators, as the use of conventional electrochemical batteries is not always an option because of the need for replacement and the volume dependence on the amount of stored energy. Motion energy or vibrations are an attractive source for powering miniature energy-harvesting generators [1]. Vibration energy can be converted into electrical energy through piezoelectric [2], electromagnetic [3], and electrostatic [4] devices. This paper focuses on piezoelectric devices. The output power of such devices, made using micromachining techniques, is limited, ranging from milliwatts down to only a few microwatts. Manuscript received May 8, 2009; revised July 29, 2009; accepted November 8, 2009. Date of publication March 1, 2010; date of current version November 10, 2010. R. D’hulst was with the Department of Electrical Engineering, Katholieke Universiteit Leuven, 3000 Leuven, Belgium. She is now with VITO. T. Sterken was with the Interuniversitary Center for Microelectronics, 3001 Leuven, Belgium. He is now with the University of Ghent, 9000 Ghent, Belgium. R. Puers, G. Deconinck, and J. Driesen are with the Department of Electrical Engineering, Katholieke Universiteit Leuven, 3000 Leuven, Belgium (e-mail: johan.driesen@esat.kuleuven.be). Digital Object Identifier 10.1109/TIE.2010.2044126 The output voltage of an energy harvester, generally, is not directly compatible with what is needed to power the load elec- tronics; moreover, the power transfer from an energy harvester, generally, can be maximized by optimizing the load impedance connected to the harvester. Thus, a power processing circuit needs to be connected between harvester and load. To date in literature, the work on power processing circuits for vibration- based energy harvesters can be roughly classified into two different approaches. In a first approach, the efficiency of the power processing circuit itself is the major point of attention, including the design of efficient control circuitry for the inter- face circuit (see, among others, [5]–[7]). In a second approach, maximizing the output power transfer from the energy harvester is the main focus (see, among others, [8]–[10]). In this paper, it will be shown that, in order to design an optimal harvesting system, the combination of both the efficiency and the ability of the processing circuit to harvest the maximum available output power needs to be optimal. This optimal combination depends on the harvester design. Two different load types are considered in this paper: a resistive load and an ac–dc rectifier load. In literature, much work has been done concerning the optimal power flow of the harvester in case the load is a linear resistor (see, among others, [11]). Since the vibration-based harvester provides a varying ac power and because electronic loads typically need a stable dc power supply, it is useful to analyze the harvester behavior when connected to an ac–dc rectifier. Other load types, as described in [6], [12], and [13], are not considered in this paper. The remainder of this paper is organized as follows. Section II discusses the modeling of piezoelectric energy har- vesters. Section III describes the behavior of the model with the two different load types. In Section IV, the design and, in particular, the efficiency of the power processing circuits are discussed. In Section V, all findings are illustrated by simulations and measurements on a custom-made piezoelectric harvester. II. HARVESTER MODEL Energy harvesters of the inertial type are considered, i.e., the motion of the vibration source is coupled to the generator by means of the inertia of a seismic mass. This mass m is modeled as being suspended by a spring with spring constant k, while its motion is damped by a parasitic damping d due to friction and air. The mass is also damped by the generator, the piezoelectric transducer, exerting a force F g . The displacement of the mass 0278-0046/$26.00 © 2010 IEEE