Solution 3.8.3.3
Let
Z
1
= R
1
k C
1
+ R3
=
R
1
C
1
s
R
1
+
1
C
1
s
+ R
3
=
R
1
R
3
C
1
s +(R
1
+ R
3
)
R
1
C
1
s +1
;;
and
Z
2
=
R
2
C
2
s
R
2
+
1
C
2
s
=
R
2
R
2
C
2
s +1
:
Then
Z
2
Z
1
=
R
2
R
2
C
2
s+1
R
1
R
3
C
1
s+(R
1
+R
3
)
R
1
C
1
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
(R
1
C
1
s +1)
[R
1
R
3
C
1
s +(R
1
+ R
3
)](R
2
C
2
s +1)
=
(1=R
3
C
2
)[s +(1=R
1
C
1
)]
[s +(R
2
+ R
3
)=(R
1
R
3
C
1
)][s+(1=R
2
C
2
)]
:
We next havetochoose some values. We knowthat
1
R
3
C
2
= 10
R
2
+ R
3
R
1
R
3
C
1
= 1
1
R
1
C
1
= 0:1
1
R
2
C
2
= 10
Let
R
2
=10
4
and C
2
=10
;5
f:
1
Then
R
3
=
1
10C
2
=10
4
:
Looking at the second equation wenowhave
R
2
+ R
3
R
1
R
3
C
1
=1;;
or
R
2
= R
1
C
1
R
3
;R
c
=10R
c
;R
c
=9R
c
Thus
R
2
=90k
:
A convenientvalue from the Table is 91 k
. The last step is to nd C
2
.
Since
R
2
C
2
=0:1;;
C
2
=
0:1
R
2
=1;;1 f:
If wechoose 1 f, then the pole will be at
s = ;
1000
91
= ;11;;
whichisclose enough.
2