Is my bode plot inaccurate?

Given the following transfer function

s = tf('s');
P = 125/(s*(s+1)*(s+5));
bode(P);

Why at 5 rad/s is magnitude -3.19 dB?

Should it not be -7.6 dB?

I get -7.6 dB if I compute the magnitude at 5 rad/s:

>> 20*log10(125/(5*(5+1)*(5+5)))

ans =

     -7.6042

Answer 1

[Mischa Kim]

Quid, the Bode plot is correct. To compute the magnitude of the P you need to replace (substitute) the complex frequency s by iw = i5.

 syms s
 Ps  = 125/(s*(s+1)*(s+5));
 Pw  = subs(Ps,s,i*5);
 aPw = double(20*log10(abs(Pw)))
 aPw =
  -3.180633349627616
 pPw = (180/pi)*double(angle(Pw))
 pPw =
   1.463099324740202e+02

[Quid]

Mischa thanks, and sorry for my mistake.

One last thing, I'm also trying to understand how MATLAB computes phase, my question is: do MATLAB computes phase for each pole and zero and total up or there is a simpler formula as for magnitude: 20*log10(abs(Pw)) ?

[Mischa Kim]

Misread. If you want to do it yourself (with correct sign!) you could do a partial fraction decomposition and then add phase components. I would suspect that that's also the way MATLAB does it internally. To get a definite answer you could go into the code itself.

[Quid]

Mischa, there must be a mistake in your example... phase at 5 rad/s is -214 deg not 146 deg, how is it possible? Look at the diagram that I posted.

[Quid]

Ok thanks, but I don't see how to use the angle function to compute the correct phase at a given frequency, because the angle function always returns angles between [-pi, pi]. I think that there is no simple formula in this case, am I right?