Biomedical Engineering Reference
In-Depth Information
efficiency of the generation is only 5.5%. Yet, commercial thermoelec-
tric generators are able to produce 60
W/cm
2
for a temperature gradi-
ent of 5
C from body heat waste (Paradiso and Starner, 2005).
μ
The energy density for an electromagnetic generator (Maluf and
Williams, 2004) is defined as
u
em
5
1
2
B
2
=
μ
0
(1.5)
where B is the magnetic field and
μ
0
is the permeability of free space
π
3
0
2
7
H/m). Assuming a maximum value of 1 T for the mag-
netic flux B yields to a maximum theoretical of 400 mJ/cm
3
, as shown
in
Figure 1.4B
. A modest value of 0.1 T has an energy density of
4 mJ/cm
3
, which can be considered as a practical obtainable value.
(
μ
5
4
0
The maximum energy density for a piezoelectric material (Roundy
and Wright, 2004) is given as
2
y
k
2
u
pe
5
1
=
ð2YÞσ
(1.6)
where
y
is the yield strength of the material, k is the electromechani-
cal coupling coefficient, and Y is the modulus of elasticity. The previ-
ous expression can also be presented as
σ
2
y
d
2
u
pe
5
1
=
ð2εÞσ
(1.7)
ε
where d is the piezoelectric charge constant and
is the permittivity or
dielectric constant. Using the properties of a high performance piezo-
electric material, such as the single crystal PZN-8%PT (Pb(Zn
1/3
Nb
2/3
)
O
3
-PbTiO
3
, Ritter et al., 2000), the theoretical maximum value is
343 mJ/cm
3
. Employing the properties of a common piezoelectric
material, such as PZT-5H (Pb(Zr,Ti)O
3
, PZT-501 from Morgan
Electro Ceramics plc) with a safety factor of 2, an energy density of
19 mJ/cm
3
can be considered as a practical value. The trend for the
piezoelectric materials of
Table 1.2
is shown in
Figure 1.4C
.
The energy density for electrostatic generation (Maluf and
Williams, 2000), such as a capacitor, is defined as
u
es
5
1
2
εE
2
(1.8)
ε
where
is the dielectric constant and E is the electric field. Using the
permittivity of the free space (
8.85
3
10
2
12
A
2
s
4
/(kg m
3
)) and a
ε
0
