Biomedical Engineering Reference
In-Depth Information
Hence, the total current density (4.2.15) is expressed as
(
)
(
)
s
wee s wee
ss weee
+
j
+
j
100
V
d
1
0
1
2
0
2
0
i
=
(4.18)
(
)
++
j
+
1
2
0
1
2
This shows that the two-layer medium between the parallel plates is replaced
by a single dielectric medium with the following admittance between these
parallel electrode plates:
(
)
(
)
s
wee s wee
ss weee
+
j
+
j
1
0
1
2
0
2
Y
=
(4.19)
(
)
++
j
+
1
2
0
1
2
Two special cases are then obtained, when DC voltage (w =
0) and extremely
high frequency (w =•
) are applied, respectively:
ss
ss
12
Y
w
=
=
s
(4.20)
=
0
+
1
2
ee
ee
Yj
=•
=
we
12
=
j
we e
(4.21)
w
0
0
e
+
1
2
(
)
where
Using these expressions, the equivalent admittance
Y
in the middle fre-
quency region between DC and the extremely high frequency region is deter-
mined as follows by introducing a correction factor
Y
n
:
eeeee
e
=
+
2
.
12
1
ss
ss
ee
ee
12
12
Y
=
+
j
we
+
Y
0
n
+
+
1
2
1
2
=+
s
j
ee
+
Y
(4.22)
0
e
n
The correction factor is easily calculated using expressions (4.19) and (4.22):
2
(
)
1
es
-
es
ee
ee
12
21
12
Y
=
j
we
(4.23)
n
[
(
)
(
)
]
0
1
+
j
we
e
+
e
s
+
s
2
+
ee s
(
+
s
)
01 2
1
2
1
2
12
1
2
Introducing t =
(e
1
+ e
2
)e
0
/(s
1
+ s
2
) and
k
=
(e
1
s
2
- e
2
s
1
)
2
/[e
1
e
2
(s
1
+ s
2
)
2
], expres-
sion (4.23) becomes
jk
j
wee
wt
weet
wt
2
k
wee
wt
k
0
e
0
22
e
0
22
e
(4.24)
Y
=
=
+
n
1
+
1
+
1
+
From Eqns. (4.22) and (4.24), the following equivalent admittance
Y
expresses
the single-layer dielectric medium equivalent to the two-layer dielectric
medium:
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