Chebyshev Low-Pass Filters with 0.1-dB Ripple calculating s value issue

I have a project to design low-pass filter via Chebyshev. I use 0.1-dB Ripple (ε = 0.15262) value but I don't know how to calculate s value. I use n= 6; (s2 + 0.22939s + 1.12939) (s2 + 0.62670s + 0.69637) (s2 + 0.85608s + 0.26336).

Here my code is below.

clear all;
w=0;
H=0;
wn=0;
wi=0;
  for j=1:2000
  wi(j)=j;
  wn=w;
       % calculate s value........

        a1=1.12939/(s^2+0.22939*s+1.12939);
        a2=0.69637/(s^2+0.62670*s+0.69637);
        a3=0.26336/(s^2+0.85608*s+0.26336);
        H(j)=abs( a1*a2*a3 );
        plot(wi,H);
    end

Answer 1

[Grégory SEABRA]

Are you trying to draw a bode plot?

If so, "s" is an imaginary number which is equal to "w*i" (i being the imaginary unit)

You can thus establish, in your script, that s=wi*1i

[Sercan Noyan Germiyanoglu]

Yes , I am trying to show low filter graph via plot.

So, The code is shown as

clear all;
w=0;
H=0;
wn=0;
wi=0;
  for j=1:2000
  wi(j)=j;
  wn=w;
       s=wi*i;
        a1=1.12939/(s^2+0.22939*s+1.12939);
        a2=0.69637/(s^2+0.62670*s+0.69637);
        a3=0.26336/(s^2+0.85608*s+0.26336);
        H(j)=abs( a1*a2*a3 );
        plot(wi,H);
    end

Is it right ?

Answer 2

[Star Strider]

Your design does not produce what I would expect from a Chebyshev Type I filter.

You need to make a few changes to your loop to make it work correctly. I will leave it to you to troubleshoot the filter design:

w=0;
H=0;
wn=0;
wi=0;
for j=1:2000
    wi(j)=j;
    wn=w;
    s=wi(j)*1i;                                         % <— Subscript ‘wi’ Here
    s2 = s*conj(s);                                     % <— ‘s’ Is Complex, So Multiply By The Complex Conjugate To Square It
%     a1=1.12939/(s^2+0.22939*s+1.12939);
%     a2=0.69637/(s^2+0.62670*s+0.69637);
%     a3=0.26336/(s^2+0.85608*s+0.26336);
    a1=1.12939/(s2+0.22939*s+1.12939);
    a2=0.69637/(s2+0.62670*s+0.69637);
    a3=0.26336/(s2+0.85608*s+0.26336);
    H(j)=abs( a1*a2*a3 );
%     plot(wi,H);
end

figure(1)
semilogy(wi,H);                                         % <— Put The Plot Outside The Loop
grid

[Sercan Noyan Germiyanoglu]

Can you say me where I troubleshoot the code to get right Chebyshev Type I filter. Its formula is ok and its equation is solved and I get the right result but I want to get it without solving the algoritm.

Here the code is after solution and I changed the loop's number as 1000 .

wn=0;
w=0;
wi=0;
H=0;
Ha=0;
for w=1:1000
wi(w)=w;
wn=w;
H(w)=(112939)*(696370)*(263360)/((-wn*wn + 229.39*i*wn + 112939)*(-wn*wn + 626.70*i*wn + 696370)*(-wn*wn + 856.08*i*wn + 263360));
Ha(w)=abs(H(w));
plot(wi,Ha);
end

How I do that.