I. Introduction
Vibration energy harvesters [1], [2] are widely used to feed wireless sensor networks [3], [4] because they offer an alternative to batteries or at least they allow the increase of their life-time, avoiding their frequent replacement [5], [6]. This paper is focused on resonant electromagnetic vibration energy harvesters (REVEHs) [7], [8], which are typically made of a permanent magnet with a mass m linked to a spring with a stiffness ks and of a coil fixed to the REVEH housing [9], [10]. When the REVEH is subject to a vibration, the magnet moves out of phase with respect to the housing and therefore a relative displacement x(t) occurs between magnet and coil. Such a relative displacement leads to the conversion of mechanical energy into electric energy, inducing an electromotive force ε(t) in the coil and a current iAC(t) flowing into the load [11], [12]. In Fig. 1, the typical equivalent electric circuit of a REVEH [9], [10] is shown. The nomenclature of parameters shown in Fig. 1 is reported in Table I.
Equivalent electric circuit of a REVEH.
Nomenclature of the Main ParametersSymbol | Description | Expression |
---|---|---|
m | Mass of the permanent magnet | |
ks | Spring stiffness | |
θ | Electromechanical coupling coefficient | |
c | Viscous damping coefficient | |
Rm | Equivalent parallel resistance | θ2/c |
Lm | Equivalent parallel inductance | θ2/ks |
Cm | Equivalent parallel capacitance | m/θ2 |
Rc | Coil resistance | |
Lc | Coil inductance | |
fresonance | Harvester resonance frequency | |
a(t) | Housing vibration acceleration | |
ω | Vibration pulse | |
f | Vibration frequency | ω/2π |
AMAX | Vibration amplitude | |
x(t) | Magnet-coil relative displacement | |
ε(t) | Coil induced electromotive force | |
iAC(t) | AC load current | |
vAC(t) | AC load voltage |