Strongly coupled piezoelectric cantilevers for broadband vibration energy harvesting

Vibration energy harvesters based on piezoelectric resonators are promising for powering Wireless Sensors Nodes (WSNs). Yet, any mismatch between the resonant frequency of traditional harvesters and the vibration frequency can drastically decrease the scavenged power and make them ineffective. Electrical techniques able to tune the resonant frequency of piezoelectric harvesters has been proposed as a solution and opens up new perspectives. To be fully competitive, this approach requires energy harvesters with very strong global electromechanical coupling coefficients k2 (>10%), whose design remains a challenge today. This work reports on a method to design strongly coupled piezoelectric cantilevers thanks to an analytical approach based on the Rayleigh-Ritz method and a two degrees-of-freedom model, which considers the proof mass inertia effects. Through an expression of the coupling coefficient, we provide design guidelines, which are experimentally validated. We show that a long proof mass is a very effective configuration to maximize the global electromechanical coupling coefficient and consequently the frequency bandwidth of the system. Three proposed prototypes exhibit some of the strongest squared global electromechanical coupling coefficients k2 of the state-of-the-art of piezoelectric harvesters (16.6% for the PMN-PT cantilever, 11.3% and 16.4% for the narrow and wide PZT-5A cantilevers respectively) and demonstrate a wide bandwidth behavior (10.1%, 7.8% and 11.3% of the central frequency respectively). Using a strongly coupled prototype based on PZT-5A leveraged by a dedicated integrated circuit, we experimentally show that it can harvest enough power (more than 100 µW) to supply a WSN over a frequency bandwidth as large as 21%.