Biomedical Engineering Reference
In-Depth Information
of the applied forces. A common arrangement for piezoelectric genera-
tors is the cantilever beam architecture. The cantilever beam is either
subject to mechanical deformation or subject to an external vibration.
The cantilever beam is typically designed with the objective to match its
natural resonant frequency to that of the external vibration.
Energy generation from electrostatic transduction is based on the
charging of capacitor plates. The separation of charged capacitor
plates is varied by environmental motion or vibration and changing
the capacitance of the capacitor structure. The change in capacitance
changes the voltage across the capacitor according to the fundamental
capacitor relationship:
Q
5
CV
(1.2)
where the charge on the capacitor Q is equal to the capacitance C
times the voltage V. When the capacitance is decreased (by an increas-
ing separation of the capacitor plates), the voltage through the capaci-
tor increases (because there is a charge on the capacitor). Therefore,
the mechanical energy due to vibrations or motion that increases the
plate separation is converted into electrical energy.
1.3 ENERGY LIMITS
Transduction generation limits are defined as energy per volume, or
energy density, and expressed with the lower case letter u. Maluf and
Williams (2004) offered one of the first descriptions for the transduc-
tion limits for thermal, electromagnetic, piezoelectric, and electrostatic
generation. The thermal approach is based on the thermal expansion
u
te
(for one dimension) defined as
u
te
5
1
2
2
YðαΔTÞ
(1.3)
where Y is the Young
'
s modulus,
is the coefficient of thermal expan-
sion (the volumetric thermal expansion is approximately 3
α
T
is the temperature difference. Different materials will have different
energy densities based on their properties, this is shown in
Figure 1.4A
. This energy density can reach values near 400 mJ/cm
3
depending on the material considered for a temperature difference of
25
C. A temperature difference between 37
C from the human body
and 22
C environment leads to 15
C gradient. This gradient still
α
), and
Δ
