Analog Signals and Systems - Digital Signal Processing: An Introduction with MATLAB and Applications - page 53

Now a Chebychev filter will be tried. The specifications state the ripple must be
less than or equal to 1 dB. Potential designs for both 0.5 and 1 dB ripple will be
considered. Checking the C-LPF gain plot for r = 0.5 dB in Fig. 1.34 (right), it is
found that n = 4 is the minimum order which is adequate to meet specifications.
Checking the C-LPF gain plot for r = 1 dB shows that the minimum order
required is also n = 4. The r = 0.5 dB alternative is chosen as it corresponds to
the minimum ripple(hence, from Tables, e 2 ¼ 0 : 122). The normalized transfer
function is obtained from Tables as follows:

a o
0 : 3791 þ 1 : 0255s N þ 1 : 7169s N þ 1 : 1974s N þ s N

H ð s N Þ¼ :

Since n = 4 is even:

p

1 þ e 2 ¼ 1 =

p

G o ¼ G m = 1 : 122 ¼ 0 : 9441 ¼ H ð s N ¼ 0 Þ¼ a o = 0 : 3791 ! a o

¼ 0 : 3579 :

The denormalized frequency response is given by:

a o

H ð s Þ¼

100p 2 þ 1 : 1974 100p 3 þ s 100p 4

s s s

0 : 3791 þ 1 : 0255

100p þ 1 : 7169

1.5.4.2 Circuit Design

From Tables one arrives at the circuit in Fig. 1.35 (left). It uses impedance and
frequency denormalization given by ISF: Z = R L = 100 and FSF:

W = x c = 100p.

1.5.5 Design of Butterworth and Chebychev-I High-Pass, Band-
Pass, and Band-Stop Filters

Standard Tables are also only available for LPF design, but can be adapted via
standard transformations to designing high-pass filters (HPFs), band-pass filters
(BPFs) and band-stop filters (BSFs),

Denormalize:
Z =100
W =100

R s =1.98 Ω 2.58H 1.82H R s =198 Ω 0.82H 0.4H

π

→

V s V s

R L =100 Ω

0.92F 1.3F 29 μ F 41 μ F

Fig. 1.35 Circuit Design of a 4th-order C-LPF