Solution 3.8.5.2
For the opamp circuit of Figure 3.26 wehave
V
o
(s)
V
i
(s)
=
;(1=R
1
C
1
)s
s
2
+(1=R
2
C
1
+1=R
2
C
2
)s +1=R
1
C
1
R
2
C
2
Wewishtomake the denominator
(s +1;j2)(s+1+j2) = s
2
+2s +5
Letting
R
2
= aR
1
;; C
2
= bC
1
;; and =1=R
1
C
1
;;
weobtain
V
o
(s)
V
i
(s)
=
;s
s
2
+ (1=a +1=ab)s+
2
=ab
;;
with =1.
Then wehavethetwoequations
[(b+1)=ab] = 2
2
=ab = 5
Dividing the rst equation bythesecond yields
b+1
=0:4;;
or
b =0:4;1
Since =5then
b =1;;
and
a =
2
b1000
=
25
15
= 5:
Then wemust have
1
R
1
C
1
= =5;;
1
or
R
1
C
1
=0:2
Wechoose
R
1
=200k
and C
1
=1 f:
Then
R
2
=5R
1
=1:0M
and C
2
=1 f
2