I. Introduction
Vibration measurement is an important topic in mechanical and electrical industries. The measurement of vibration frequency is widely used to monitor industrial machines. So far, vibration sensors with different principles have been developed for frequency measurement [1], [2]. Vibration sensors are usually designed to operate on a fixed energy source like a battery. But the battery has a limited lifetime, and importantly it is often impractical to take prompt actions to replace batteries in the wireless cable-free application [3]–[6]. In addition, the use of batteries has resulted in serious environmental problems [7]. Because the limited power supply is very crucial for vibration sensors [8], self-powered techniques become increasingly attractive and have been paid attention in the literature [9]–[12].