Bode different phase issue

Hello,

I have a homework. I have a transfer function which is related to butterworth low pass filter. Teacher asks me phase and amplitude response, and bode diagram separately. I use freqs(num,den) for the phase and amplitude response. I use bode(sys) for the bode diagram. When I compare the outputs, amplitude responses are quite similar. But phase responses are quite different. You can see the outputs and my codes.

Here is my code:

>> wp = 1;
>> ws = 1.2;
>> Rp = 0.2;
>> Rs = 25;
>> [n, Wn] = buttord(wp,ws,Rp,Rs,'s');
>> [num, den] = butter(n, Wn, 's');
>> sys = tf(num, den);
                                                                             
 
Continuous-time transfer function.

>> bode(sys)
>> freqs(num, den)

bode(sys) output:

freqs(num, den) output:

Is it necessary to see them similar or same? Could you please explain me?

Thanks in advance.

Answer 1

[Star Strider]

In the freqs call, the phase is wrapped. Unwrap it and freqs matches bode —

wp = 1;
ws = 1.2;
Rp = 0.2;
Rs = 25;
[n, Wn] = buttord(wp,ws,Rp,Rs,'s');
[num, den] = butter(n, Wn, 's');
sys = tf(num, den);
sys

sys =
 
                                                                                        
                                                                                   5.373
                                                                                        
  -----------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                         
  s^25 + 17.03 s^24 + 145.1 s^23 + 821.6 s^22 + 3471 s^21 + 1.164e04 s^20 + 3.215e04 s^19 + 7.51e04 s^18 + 1.509e05 s^17 + 2.639e05 s^16 + 4.054e05 s^15 + 5.504e05 s^14 
                                                                                                                                                                         
          + 6.626e05 s^13 + 7.087e05 s^12 + 6.734e05 s^11 + 5.675e05 s^10 + 4.225e05 s^9 + 2.763e05 s^8 + 1.574e05 s^7 + 7.708e04 s^6 + 3.191e04 s^5 + 1.089e04 s^4      
                                                                                                                                                                         
                                                                                                                                    + 2949 s^3 + 595.6 s^2 + 80 s + 5.373
                                                                                                                                                                         
 
Continuous-time transfer function.

figure
bode(sys)

figure
freqs(num,den, 1E+2)
Ax2 = get(subplot(2,1,2));
Line = Ax2.Children;
Ax2.Children.YData = rad2deg(unwrap(deg2rad(Line.YData)));

Helpful functions for this are unwrap, deg2rad and rad2deg.

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