Analog Signals and Systems - Digital Signal Processing: An Introduction with MATLAB and Applications - page 56

= log ð x LN Þ ¼½ 3 : 314 ¼ 4 ;

n 0 : 5 log A 2 1

where A ¼ A x L ð Þ¼ 10 A dB = 20

ð Þ . From Tables we get the normalized transfer

function as follows:

a o
1 þ 2 : 6131s N þ 3 : 4142s N þ 2 : 6131s N þ s N

Hs ðÞ¼

:

For B-LPF, G o = G m . Hence, G o ¼ 1 ¼ a o = 1 ! ) a o ¼ 1.
The true transfer function will be given by:

a o

H ð s Þ¼

s þ 3 : 4142 s 2 þ 2 : 6131 s 3 þ 2p s 4

2pM 2pM 2pM

1 þ 2 : 6131

s 4
s 4 þ 16 : 4Ms 3 þ 134 : 8M 2 s 2 þ 648 : 2M 3 s þ 1558 : 5M 4 :

¼

The resulting filter has four poles and four zeros.
Circuit Design:
Z = R L = 300 and FSF: W = x c = 2pM (see Fig. 1.37 ).

1.5.6 Chebychev-II Filters

The Chebychev-II Filter (a.k.a. the inverse Chebychev filter) has a maximally flat
pass band (no ripples) and an equiripple stopband. Its magnitude response is given
by:

R s =1 Ω 1.84H 0.76H

1 / 1.84 F 1 / 0.76 F

R s =1 Ω

LP HP

V s

0.76F 1.84F

V s

R L =1 Ω R L =100 Ω

1 / 0.76
H

1 / 1.84
H

288 pF 698 pF

300 Ω

V s

62.8 25.9

300 Ω

μ H μ H

Fig. 1.37 Design of a Butterworth HPF