Solution 3.8.3.1
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
Z
2
Z
1
=
R
2
R
2
C
2
s+1
R
1
C
1
s+1
C
1
s
(C
1
s)(R
2
C
2
s+1)
(C
1
s)(R
2
C
2
s+1)
=
R
2
C
1
s
(R
1
C
1
s +1)(R
2
C
2
s+1)
=
(1=R
1
C
2
)s
(s+1=R
1
C
1
)(s+1=R
2
C
2
)
:
We next havetochoose some values. Welet
R
1
=10
6
;; C
1
=10
;5
f;; ;; R
2
=5110
3
and C
2
=10
;6
f:
Then
G(s)=
s
(s+10)(s+19:6)
:
Given that wenormally use 5% components, this compensator is very close
to the desired one.
1