Hi Martin,

The phase starting point in Bode plots depends solely on the term (s^n) in the transfer function, e.g, say that you have the following open loop transfer function

G(s) = (s+1)/s(s^2+1).

this transfer function in the Bode form becomes

G(jw) = (jw+1)/ (jw) ((jw)^2+1)

by looking at the free term (jw) in the denominator, you will realize that it has a power of 1, then in this case, the phase plot will start from -90 degrees, i.e. 90 because the power of the free term (jw) is (1), and the phase is negative because the free term (jw) is in the denominator.

So, in your case when the phase starts from -270, this means that in your open loop transfer function, you have (s^3) in the denominator, i.e. (3*90 = 270) and because it is negative, this free term is in the denominator.

P.S. I mean by free term here where you have only (s) not added or subtracted from any term in the numerator or the denominator..

Regards

Thank you for great explanation. And how is the phase defined? I am working with software called MathCAD and when I am trying to plot phase, its starting point is not in -270 nevertheless I have (s^3) in denominator. I think it is caused by the function arg() I am using. This function gives the range between -pi and pi. My current definition of phase looks like this: arg(W(jw))*180/pi .Can you suggest how to change this expression? Thank you one more time.

My answer in short:

In the BODE diagram the starting phase depends on the particular system and its frequency properties only.

It would be helpful if you could give one or more examples which systems you are interested in. Please, be aware that -270deg is identical to +90deg. This is the starting phase for an idealized inverting intergator. In real practice such an integrator will have a phase of -180deg at DC.

In general: Each stable feedback system must have a starting phase (0 Hz) of -180deg.

Hi Martin,

Beside Lutz answer, you can numerically evaluate the phase for the term (jw)^n by using the atan2() matlab function... by the way, the term (jw)^2 corresponds to the low frequencies region in the Bode plot ... To evaluate the angle of this term you basically use:

atan2((jw)^n) = n* atan2(jw)

and

atan2(jw) = atan2 (imaginary/real) = atan2(w/0) = atan2(inf) = 90 degrees

then,

atan2((jw)^n) = n* atan2(jw) |_{n=-3} = -3 * 90 = -270 degrees.

I don't have in fact experience with MathCAD, but the above shows how the angle can be calculated. Just make sure that you know how the function arg() exactly works.

Regards,