Analog Filter Prototypes

Contents

Butterworth
Chebyshev I with 0.5dB ripple in passband
Chebyshev II with 20dB ripple in stopband
Elliptic with 0.5dB ripple in passband 20dB in stopband

Butterworth

Design a normalized fourth-order Butterworth lowpass filter

% zb = zeros, pb = poles, kb = gain
% Butterworth analog prototype filter function
[zb pb kb] = buttap(4);

% zp2tf forms transfer function polynomials from the zeros, poles, and gains of a system in factored form.
[b a] = zp2tf(zb,pb,kb);

w = logspace(-1,1,201);
hh = freqs(b,a,w);
hb = abs(hh);
semilogx(w,hb,'LineWidth',2);
xlabel('frequency (rad/sec)');
ylabel('magnitude response');

Chebyshev I with 0.5dB ripple in passband

[zc1 pc1 kc1] = cheb1ap(4,0.5);

[b a] = zp2tf(zc1,pc1,kc1);

hh = freqs(b,a,w);
hc1 = abs(hh);
semilogx(w,hb,w,hc1,'LineWidth',2);
xlabel('frequency (rad/sec)');
ylabel('magnitude response');
legend('Butterworth','Chebyshev I');

Chebyshev II with 20dB ripple in stopband

[zc2 pc2 kc2] = cheb2ap(4,20);

[b a] = zp2tf(zc2,pc2,kc2);

hh = freqs(b,a,w);
hc2 = abs(hh);
semilogx(w,hc2,'LineWidth',2);
xlabel('frequency (rad/sec)');
ylabel('magnitude response');

Elliptic with 0.5dB ripple in passband 20dB in stopband

[ze pe ke] = ellipap(4,0.5,20);

[b a] = zp2tf(ze,pe,ke);

hh = freqs(b,a,w);
he = abs(hh);
semilogx(w,he,'LineWidth',2);
xlabel('frequency (rad/sec)');
ylabel('magnitude response');

semilogx(w,hb,w,hc1,w,hc2,w,he,'LineWidth',2);
xlabel('frequency (rad/sec)');
ylabel('magnitude response');
legend('Butterworth','Chebyshev I','Chebyshev II','Elliptic');