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Design, Visualize and Explore Inverse Chebyshev Filter - II

This example shows how to design a fourth-order inverse Chebyshev low-pass filter with stopband frequency of 10000 rad/sec, and epsilon of 0.01 (please see the reference section) using rffilter. This rffilter could be used in a circuit or in a rfbudget object.

The rffilter object is used to design a RF filter. A filter requires a minimum set for parameters to completely define it.

The parameters to design an inverse Chebyshev filter can be one of the following:

  • Filter order, Passband frequency, Passband and Stopband Attenuation

  • Passband and Stopband frequencies, Passband and Stopband Attenuation

  • Filter order, Stopband frequency, Stopband Attenuation

Design Filter

N           = 4;                                    % Filter order
Fs          = 1000/(2*pi);                          % Stopband frequency
epsilon     = 0.01;             
Rs          = 10*log10((1+epsilon^2)/epsilon^2);    % Stopband attenuation

Use the first set of parameters to define the filter.

r = rffilter('FilterType','InverseChebyshev','ResponseType','Lowpass',  ...
    'Implementation','Transfer function','FilterOrder',N,               ...
    'PassbandFrequency',Fs,'PassbandAttenuation',Rs,                    ...

Note: Alternative, you can also use the third set of parameters to design the same filter:

r = rffilter('FilterType','InverseChebyshev','ResponseType','Lowpass',  ...
'Implementation','Transfer function','FilterOrder',N,                   ...

The limitation of this parameter set is that it assumes the passband attenuation to be fixed at 10*log10(2) dB.

Visualize magnitude response, phase response, and phase delay of filter

frequencies = linspace(0,2*Fs,1001);
rfplot(r, frequencies);

Figure S-Parameters 21 contains an axes object and another object of type uitoolbar. The axes object with title s21 vs. Frequency contains an object of type line.

Optionally, you can also use Signal Processing Toolbox to visualize the analog filter using:


Find zeros, poles, and gain

[z,p,k] = zpk(r);

You can obtain zeros, poles, and gain of Transfer function (S21) by:

format long g
zeros_21 = z{2,1}
zeros_21 = 4×1 complex

   0.0000 + 1.0824i
   0.0000 - 1.0824i
   0.0000 + 2.6131i
   0.0000 - 2.6131i

poles_21 = p                % Same denominator for S11, S12, S21 and S22
poles_21 = 4×1 complex

  -1.7116 + 4.7610i
  -1.7116 - 4.7610i
  -5.0453 + 2.4079i
  -5.0453 - 2.4079i

k_21     = k{2,1}
k_21 = 

View transfer function in factorized form

View these factor forms directly from the filter r.

disp('Numerator of Transfer function as factors:');
Numerator of Transfer function as factors:
ans = 2×3

    0.0000         0    1.1716
    0.0000         0    0.0683

disp('Denominator of Transfer function as factors:');
Denominator of Transfer function as factors:
ans = 2×3

    0.0000    0.0034    2.5596
    0.0000    0.0101    3.1253

Alternatively, use |zpk| from Control System Toolbox to view the transfer function in factorized form.

G_s = zpk(zeros_21,poles_21,k_21)
G_s =
     0.0099995 (s^2 + 1.172e06) (s^2 + 6.828e06)
  (s^2 + 1009s + 3.125e05) (s^2 + 342.3s + 2.56e05)
Continuous-time zero/pole/gain model.


[1] Paarmann, L. D. Design and Analysis of Analog Filters: A Signal Processing Perspective. SECS 617. Boston: Kluwer Academic Publishers, 2001.

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