Solution 3.8.2.1
Let
Z
1
= R
1
+
1
C
1
s
=
R
1
C
1
s +1
C
1
s
;;
and
Z
2
=
R
2
C
2
s
R
2
+
1
C
2
s
=
R
2
R
2
C
2
s +1
:
Then
V
o
(s)=
Z
2
Z
1
+ Z
2
V
i
;;
Thus
V
o
(s)
V
i
(s)
=
R
1
C
1
s+1
C
1
s
R
1
C
1
s+1
C
1
s
+
R
2
R
2
C
2
s+1
(C
1
s)(R
2
C
2
s +1)
(C
1
s)(R
2
C
2
s +1)
=
(R
1
C
1
s +1)(R
2
C
2
s +1)
(R
1
C
1
s +1)(R
2
C
2
s +1)+R
2
C
1
s
=
R
1
R
2
C
1
C
2
s
2
+(R
1
C
1
+ R
2
C
2
)s +1
R
1
R
2
C
1
C
2
s
2
+(R
1
C
1
+ R
2
C
2
+ R
2
C
1
)s +1
=
s
2
+
R
1
C
1
+R
2
C
2
R
1
R
2
C
1
C
2
s +
1
R
1
R
2
C
1
C
2
s
2
+
R
1
C
1
+R
2
C
2
+R
2
C
1
R
1
R
2
C
1
C
2
s +
1
R
1
R
2
C
1
C
2
:
1