Biomedical Engineering Reference
In-Depth Information
which can be re-written in a convenient form:
1
/R
e
1
(
1
+
L
e
1
s/R
e
1
)
Y
N
(s)
=
(5.30)
G
e
1
/G
e
1
C
e
1
s
(
1
+
1
/G
e
1
C
e
1
s)R
e
1
(
1
+
L
e
1
s/R
e
1
)
1
+
G
e
1
/G
e
1
C
e
1
s
(
1
+
1
/G
e
1
C
e
1
s)R
e
2
(
1
+
L
e
2
s/R
e
2
)
1
+
G
e
2
/G
e
2
C
e
2
s
(
1
+
1
/G
e
2
C
e
2
s)R
e
2
(
1
+
L
e
2
s/R
e
2
)
1
+
G
e
2
/G
e
2
C
e
2
s
(
1
+
1
/G
e
2
C
e
2
s)R
e
3
(
1
+
L
e
3
s/R
e
3
)
...
1
+
...
G
e(N
−
1
)
/G
e(N
−
1
)
C
e(N
−
1
)
s
(
1
+
1
/G
e(N
−
1
)
C
e(N
−
1
)
s)R
eN
(
1
+
L
eN
s/R
eN
)
1
+
G
eN
/G
eN
C
eN
s
1
+
(
1
+
1
/G
eN
C
eN
s)R
eN
(
1
+
L
eN
s/R
eN
)
We introduce the notation
W
d
(s)
=
1
R
e
1
C
e
1
s
,
1
G
e
1
C
e
1
s
L
e
1
s
R
e
1
0
(s)
=
and
W
1
(s)
=
(5.31)
and replace the ratios in (
5.30
) and we obtain
1
/R
e
1
(
1
+
W
1
(s))
Y
N
(s)
=
(5.32)
W
d
(s)/(W
0
(s)
+
1
)
(
1
+
W
1
(s))
1
+
W
d
(s)/λ(W
0
(s)
+
1
)
(
1
+
W
1
(s)/αλ)
1
+
W
d
(s)/λχ(oW
0
(s)/χ
+
1
)
(
1
+
W
1
(s)/αλ)
1
+
W
d
(s)/λ
2
χ(oW
0
(s)/χ
+
1
)
+
W
1
(s)/α
2
λ
2
)
(
1
1
+
...
...
W
d
(s)/λ
N
−
1
χ
N
−
2
(o
N
−
2
W
0
(s)/χ
N
−
2
+
1
)
W
1
(s)/α
N
−
1
λ
N
−
1
)
(
1
+
1
+
W
d
(s)/λ
N
−
1
χ
N
−
1
(o
N
−
1
W
0
(s)/χ
N
−
1
+
1
)
1
+
W
1
(s)/α
N
−
1
λ
N
−
1
)
(
1
+
For the set of conditions from (
5.18
) and for
α
·
χ>
1
,α
·
λ>
1
,λ>
1 and
χ
≥
o, o >
1
,
(5.33)
o
N
−
1
we find that the term
(G
e
1
C
e
1
s)χ
N
−
1
from (
5.32
) goes to zero as frequency increases.
In this case, the limit
N
→∞
does not play any role, since
χ
=
o
; however, if
1
/(G
e
1
C
e
1
s)
1 then we can then re-write (
5.32
)as
Y
N
(s)
=
1
/R
e
1
(
1
+
W
1
(s))
(5.34)
W
d
1
+
W
d
/λ
1
+
W
d
/χλ
1
+
W
d
/χλ
2
1
+
...
...
W
d
/χ
N
−
2
λ
N
−
1
1
+
1
+
W
d
/χ
N
−
1
λ
N
−
1
which is similar in form to (
5.22
)
Y
N
(s)
1
/R
e
1
(
1
+
W
1
(s)))
≈
(5.35)
1
+
g(W
d
(s), λ, χ)
in which
g
W
d
(s), λ, χ
=
W
d
(s)
(5.36)
W
d
(s)/λ
1
+
W
d
(s)/λχ
1
+
W
d
(s)λ
2
χ
···
1
+
