Solution 3.8.5.3
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)(s +100)
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
:
Then wehavethetwo equations
[(b+1)=ab] = 101
2
=ab = 100
Dividing the rst equation bythesecond yields
b +1
=1:01;;
or
b =1:01;1
If =10then
b =9:1;;
and
a =
2
b100
=
100
9:1100
= 0:1099
Then wemust have
1
R
1
C
1
= =10;;
or
R
1
C
1
=0:1
1
Wechoose
R
1
=100k
and C
1
=1 f:
Then
R
2
= 0:1099R
1
= 0:1099100 k
= 10:99 k
! 1110:99 k
:
Also
C
2
= 9:1C
1
= 9:11 f
= 9:1 f:
The closest value in Table 3.1 is 10 f. If wechoose this value then we
obtain the denominator
(s +0:9175)(s+99:1):
If this is not close enough then wecancombine some of the capacitors in
Table 3.1 to obtain a value closer to 9:1 f, for instance, 10 finseries
with 100 ffor an equivlentcapacitance of 9:09 f.
2