Biomedical Engineering Reference
In-Depth Information
TABLE 4.2
Characteristics of
R
-
C
Circuits in Series and in Parallel at a Given Frequency,
Respectively
Circuit
R
s
and
C
s
inSeries
R
p
and
C
p
inParallel
Z
*(
ω
)
i
C
R
i C R
p
R
−
ω
s
1
+
ω
s
p
p
→
Z
(
ω
)
→
1
R
p
1
2
2
2
+
ω
C R
s
s
ω
C
2
2
2
1
+
ω
C R
s
p p
i
R
1
C
i C R
C
−
ω
*
(
s
C
)
=
ω
p
1
+
ω
*
(
p
i Z
)
ω
ω
s
s
tan
δ
ω
C
s
R
s
1
ω
C R
p
p
τ
C
s
R
s
1
ω
C R
p
p
whereas the values of the equivalent series and parallel components are related by
C
C
1
p
(4.39)
=
1
tan
δ
2
+
s
and
R
R
2
1
+
tan
tan
δ
p
(4.40)
=
2
δ
s
In the parallel representation, it is convenient to work with the resistivity of a material,
which is measured as the resistance between electrodes applied to opposite faces of a cube
of unit edge. A capacitor of these dimensions has, in the electrostatic system, a capacitance
C
0
= 1/4
π
cm, so that Equation 4.37 gives
=
1
0
*
(
*
(
)
)
(4.41)
ε ω
C
ω
ε
or, in the parallel representation,
1
i
1
i
*
(
)
C
(
)
C
(
)
(
)
ε
ω
=
ω
−
=
ω
−
ω
γ ω
(4.42)
p
p
R
(
)
ε
ω
ω
ε
0
p
0
where
γ
(
ω
) is the conductivity,
C
p
is the capacitance, and
ε
*(
ω
) is expressed in e.s.u.
Frequency dependence of permittivity (
ε
), conductivity (
γ
), resistivity (
ρ
), and dielectric
loss (tan
δ
) in the one-layer dielectrics model is shown in Figure 4.6. From the position
