Analog and Digital Filters
645
The transfer function is given by
H(s) ϭ ϩ
ϩ ϩ
1
2
2
1
3
2
s
s
s
(6.4)
Equating the coeffi cients of Equation 6.3 with the coeffi cients of Equation 6.4 the following relations are obtained:
L 1 L 2 C = 1
L 1 C = 2
L 1 + L 2 = 2
Then solving for L 1 , L 2 , and C the following is obtained:
L 1 = 3/2 H, L 2 = 1/2 H, and C = 4/3 F
Then the normalized LPF at the component level is shown in Figure 6.70.
Frequency and magnitude scaling results in
new-R 0 = R * R 0 = 1 * 100 = 100 Ω
L
L R
01
1
0
4
4
2
10
3 100
2 10
3 10
2
15
ϭ
ϭ
ϭ
ϭ
Ϫ
*
*
*
*
mH
L
L R
02
2
0
4
4
2
10
100
2 10
0 5 10
5
ϭ
ϭ
ϭ
ϭ
Ϫ
*
*
*
.
m H
C
C
w R
c
0
0
4
2
6
4
3
1
10 10
4
3
10
1 33
ϭ
ϭ
ϭ
ϭ
Ϫ
*
*
*
*
.
F
FIGURE 6.69
Normalized fi lter’s plot of Example 6.17.
0
200
150
100
50
Ϫ50
Ϫ100
Ϫ150
Ϫ200
Ϫ4
Ϫ2
0
2
4
0
Ϫ5
Ϫ10
gain in db
Phase in degrees
w in rad/sec
w in rad/sec
Normalize filter/magnitude
Normalize filter/phase
Ϫ15
Ϫ20
Ϫ25
Ϫ30
Ϫ4
Ϫ2
2
4
0
CRC_47760_CH006.indd 645
CRC_47760_CH006.indd 645
7/23/2008 2:26:58 PM
7/23/2008 2:26:58 PM