Biomedical Engineering Reference
In-Depth Information
such the simulated capacitance value obtained in each Cole-Cole plot plays a crucial role in
assigning the origin of each semicircle response. Therefore, understanding and calculating
the dielectric parameters especially the capacitance value become essential. This section
describes the formulae for the capacitance in both one-layer and two-layer dielectrics.
One-Layer Model
When a voltage is applied to a parallel-plate capacitor in vacuum, the capacitor will store
charge. In the presence of a dielectric, an additional phenomenon happens within the
dielectric, which allows the capacitor to store more charge.
For an empty plate capacitor, the capacitance in the electrostatic system is given by:
=
area
π
C
(4.33)
0
4
d
where
d
is the distance between plates.
C
= 4
πε
0
C
0
(4.34)
Note that these formulae neglect the fringing of the field at the edges of the capacitor
plates. When a capacitor is filled with a dielectric, its static capacitance is given by:
C
= 4
πε
0
ε
s
C
0
(4.35)
Here again, fringe fields have been neglected.
The capacitance under dynamic conditions may be expressed in terms of
ε
*(
ω
).
The complex capacitance thus becomes:
C
*(
ω
) = 4
πε
0
C
0
ε
*(
ω
)
(4.36)
Alternating current measurements give the impedance
Z
*(
ω
) of the capacitor containing
the dielectric, which is related to the complex capacitance by
1
*
(
Z
)
=
(4.37)
ω
*
(
i C
)
ω
ω
The impedance can be represented by an equivalent circuit. For a given frequency
ω
, an
impedance can be represented by a large number of possible equivalent circuits, the sim-
plest of which are the parallel and the series circuit.
Table 4.2 compares the characteristics of these circuits for a given
ω
. If the same dielectric
is represented in one case by the parallel circuit and in the other case by the series circuit,
then:
1
C R
tan
δ
=
=
(4.38)
ω
C R
s
s
ω
p p
