# Solution of ECE 316 Test #7 S03 3/5/03 ( )

```Solution of ECE 316 Test #7 S03 3/5/03
1.
What numerical value of K in this system will make it marginally stable?
X(s)
1
s
1
s
Y(s)
K
10
−K &plusmn; K 2 − 40
1
The transfer function is H( s) = 2
. The poles are at s =
. For a system to
2
s + Ks + 10
be marginally stable the poles must lie on the ω axis which means the real parts must be zero. That
happens when K = 0 .
200 s
is realized in the parallel
s + 9 s + 18
configuration below. What are the numerical values of K1 , K 2 and K 3 ?
2.
A system whose transfer function is H( s) =
2
1
s
K1
3
X(s)
1
s
K3
Y(s)
K2
.
The transfer function can be expanded in partial fractions as H( s) =
200 s
200
400
=−
+
.
s+3 s+6
(s + 3)(s + 6)
Therefore K1 = −200 , K 2 = 6 and K 3 = 400 .
3.
A normalized lowpass Butterworth filter has a pole at s = e
the transfer function of this filter?
j
3π
5
. How many poles are there in
For a Butterworth lowpass filter the poles lie at angles which are integer multiples of
the number of poles. Since this pole lies at an angle of
3π
, n must be 5.
5
π
where n is
n
```