Nyquist (Polar) plots in circuits, phase question

  • #1

Homework Statement

Okay, this is probably a really simple thing but I'm just not able to wrap my head around it for whatever reason.
I've got a second order system with feedback, where I've found the transfer function (and the real and imaginary parts of the transfer function), given by -AB = K/((1+jwt)^2).
So I work through it, get to tan(theta) = Im/Re.
To draw the Nyquist plot, I know I need to analyse what happens to theta as frequency (w) approaches zero and infinity.

Homework Equations

I end up with tan(theta) = [2wtK] / [(-K)(1-(wt)^2)]
where w = omega = angular frequency
K = gain factor, a constant
t = tau = time constant = RC (R = resistance, C = capacitance)

The Attempt at a Solution

I can manage finding what theta approaches as w tends to zero. In this case it also goes to zero.
But I just can't wrap my head around why, when w tends to infinity, theta tends to -180 degrees.
Could someone please explain this? I know it's simple, but it's just not clicking for me.

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  • #2
Look at the transfer function as a complex number (not just the imaginary/real ratio), and as [tex]\omega\to\infty[/tex], you'll see that it approaches the negative real axis.

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