# Characteristic Polynomial and Angle (Negative Feedback)

1. Mar 16, 2014

### Vaedoris

I hope this is the right place to ask...

For a close-loop system with negative feedback, the transfer function is

G(s) / (1 + G(s)H(s))

where, s is in frequency domain, G(s) is the function of the forward loop, and H(s) is the function of the negative feedback.

So the characteristic polynomial is

1 + G(s)H(s) = 0

Therefore, in polar form, G(s)H(s) has magnitude 1 with argument -180 degrees.

So why is the standard -180 degrees instead of positive 180 degrees?

If the net angle of the zeros and poles of GH is positive 180, doesn't it also satisfy the characteristic polynomial?

Last edited: Mar 16, 2014