EXPERIMENT - 4

AIM

To design a high pass Chebyshev - II Filter based on Frequency Response.

THEORY

The Chebyshev filter provides a steeper roll-off than the more commonly use Butterworth filter.

However the additional roll-off of the Chebyshev filter comes at the expense of ripple, and this makes it unsuitable for a number of applications.

The type 2 Chebyshev filter may also be known as the inverse Chebyshev. It is less commonly used than the Type 1 filter because it does not roll off as fast, and also requires more components. However, its big advantage is that it has no ripple in the pass-band, but does have what is termed equi-ripple in the stopband.

MATLAB COMMANDS USED

* [N,Wn]=cheb2ord(Wp,Ws,Rp,Rs);
* [b a]=cheby2(N,stopband_ripple,Wn,'filter type');
* [H,w]=freqz(b,a);

MATLAB CODE

%Chebyshev 2 high pass
clear all;
[N,Wn]=cheb2ord(0.5,0.4,0.5,60);
[b,a] = cheby2(N ,60,Wn,'high');
[h w]=freqz(b,a,256);
H=abs(h);
HdB=20*log10(H);
figure (1);
plot(w/pi,H,'black','linesmoothing','on');
grid on;
title('Magnitude Repsonse of a Chebyshev I 
High pass filter with Wp=0.4 and Ws=0.5 
and attenuation at 60dB in stopband');
xlabel('Normailized Frequency ( rad/sec )');
ylabel('Gain');
axis([0 1 0 1.1]);
print('cheb2_high','-dpng');


figure (2);
plot(w/pi,HdB,'black','linesmoothing','on');
grid on;
title('Magnitude Repsonse of a Chebyshev I 
High pass filter with Wp=0.4 and Ws=0.5 
and ripple at 60dB in stopband');
xlabel('Normailized Frequency ( rad/sec )');
ylabel('Gain in dBs');
axis([0 1 -120 2]);

print('cheb2_high_dB','-dpng');

RESULT

The Chebyshev II filter have been designed and response plotted. It has steeper roll-off but the there is equi-ripple in stop band.