Solution 3.8.3.6
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
3
=
R
2
R
2
C
2
s +1
+ R
3
=
R
2
+ R
2
R
3
C
2
s + R
3
R
2
C
2
s +1
=
R
2
R
3
C
2
s +(R
2
+ R
3
)
R
2
C
2
s +1
:
Then
Z
2
Z
1
=
R
2
R
3
C
2
s +(R
2
+ R
3
)
R
2
C
2
s +1
R
1
C
1
s +1
C
1
s
(C
1
s)(R
2
R
3
C
2
s +(R
2
+ R
3
))
(R
1
C
1
s +1)(R
2
C
2
s +1)
=
(R
3
=R
1
)s(s +
R
2
+R
3
R
2
R
3
C
2
(s +
1
R
1
C
1
)(s +
1
R
2
C
2
)
:
We next havetochoose some values. We rst let
R
2
=10
6
;; C
1
=10
;6
f;;
so that
1
R
2
C
2
=
1
10`10
;6
= 1:
Wenextnote that
R
2
+ R
3
R
2
R
3
C
2
=5;;
or
5R
2
R
3
C
2
= R
2
+ R
3
;;
1
or
R
3
(5R
2
C
2
;1) = R
2
;;
or nally
R
3
=
R
2
5R
2
C
2
;1
:
Since R
2
C
2
=1,wehave
R
3
=
R
2
4
=25010
3
:
A nearbyvalue is 24010
3
. Then since the gain is R
3
=R
1
wemust have
R
2
=2410
3
:
Finally,wemust have
1
R
1
C
1
=50;;
or
C
1
=
1
50R
1
=
1
502410
3
=0:83310
;;6
:
A nearbyvalue in the table is 0:82 f. Thus, the values weneedare
R
1
=24k
C
1
=0:82 f
R
2
=1M
C
2
=1 f
R
1
=240k
2