Vibration Energy Harvesting System - Energy Harvesting Autonomous Sensor Systems - page 114

Knowing that the piezoelectric charge constant, d , [79] is given as

T
33

d 33 = o g 33 (4.5)

o is the permittivity of free space (8.85 x 10 − 12 ) and

T

where

33 is the per-
mittivity of the material at constant stress. It can be demonstrated that the
piezoelectric generator can be modelled as a capacitor of value [111],

T
33

C 3 =

o WL
t

(4.6)

Hence, the electrical power P 3 generated by the piezoelectric generator can
be calculated as the rate of the energy stored in the capacitor, which is given
by

1
2 C 3 V 3 f

1
2 g 33 d 33 F 3

t
A f

= =

P 3 (4.7)

where f is the frequency of the vibration. The derived relationship shows
that for a given piezoelectric material of fixed area A and thickness T the gen-
erated electrical power P under the force F is dependent on the piezoelectric
material charge constant d and voltage constant g .Inorder to obtain a high-
performance impact-based piezoelectric generator, the piezoelectric ceramic
element with high figures of merit ( d and g ) has to be selected. In addition,
the volume of the piezoelectric element and the amount of stress exerted on
the element are also the key factors to be considered in converting mechanical
input to electrical energy.
The next step is to determine the electrical characteristic of the piezoelectric
push-button igniter to facilitate the design of the PPU for powering the wire-
less transmitter load. The dimension of the piezoelectric push button used
in this research is 35 mm long and 5 mm in diameter and has a deflection
of 4.5 mm at a maximum force of 15 N. When an actuation force of 15 N
is applied onto the piezoelectric push button [108], the internal hammer is
released to strike the piezoelectric element as shown in Figure 4.5 . The ex-
citation force of the hammer generates a pressure wave on the piezoelectric
element to output a very high voltage of 6 kV. The high output voltage gen-
erated follows closely to an alternating current (AC) signal due to dynamic
polarization of the piezoelectric element. Each strike of the hammer creates a
mechanical resonance in the piezoelectric element as illustrated in the zoomed
version of Figure 4.5 whereby 10 small AC voltage pulses are observed. Sub-
sequently, about nine more iterations of the hammer striking the piezoelectric
element are observed in Figure 4.5 , and the harvested energy pulses from the
piezoelectric push-button generator occur for a short time span of around
1.5 ms.
Since each input actuation force provided by the human is not continuous
but rather behaves in a pulse-like manner, the output voltage will gradu-
ally attenuate following the attenuation of the mechanical vibrations in the