0
\$\begingroup\$

This is what I've done The magnitude at w=0 comes out to be 0 (=1/infinity) , which is different from previous problems (they didn't have any zero) I've calculated, is this right? I guess it should be right (because G(s)should be zero at w=0, that's what comes to my mind if u ask me meaning of having zero at s = 0) but I'm not sure how to do Polar plot if this is right.. pls help me

PS: Did I calculate magnitude for w = 0 right?

\$\endgroup\$
5
  • \$\begingroup\$ Magnitude will be zero and phase will have a limiting value of 90deg at \$\omega = 0\$ \$\endgroup\$
    – sarthak
    Nov 1, 2017 at 16:06
  • \$\begingroup\$ @sarthak, for w = infinity, what will be magnitude & phase? \$\endgroup\$
    – Deep
    Nov 1, 2017 at 16:42
  • 1
    \$\begingroup\$ When \$w=\infty\$, magnitude is \$\frac{1}{T}\$ and phase is \$0 {}^{\circ}\$. \$\endgroup\$ Nov 1, 2017 at 17:13
  • \$\begingroup\$ @SubaThomas can you please draw rough sketch, I have absolutely no idea how am I gonna plot that \$\endgroup\$
    – Deep
    Nov 1, 2017 at 17:21
  • \$\begingroup\$ I will show a plot in the answer for various \$T\$ values. \$\endgroup\$ Nov 1, 2017 at 17:26

2 Answers 2

2
\$\begingroup\$

As requested in the comments, here is the polar plot for various \$T\$ values as \$\omega\$ goes from \$0\$ to \$\infty\$.

enter image description here

\$\endgroup\$
0
\$\begingroup\$

A Zero at s=0 is sometimes called a "free differentiator", meaning that the physical interpretation of the system's behavior is that its output will behave according to the derivative of its input. In the case of a zero frequency, the input is constant. The derivative of a constant is zero, so it is correct to say that the output magnitude ratio is zero in that case. At higher frequencies, the pole will begin to "cancel" this effect, for lack of a better word.

I'm not especially familiar with polar plots, I tend to use nichols/nyquist/bode plots for my analysis, but the idea seems to be the same between all of them. If you intend to construct a parametric plot with R=magnitude and theta=phase, you simply need to solve for magnitude and phase as a function of frequency, then use algebra to combine the two functions in such a way as to cancel the frequency term out. It will be messy, but you should be able to solve it

If you don't want to go that route, you can try evaluating a couple of points on your polar plot. The phase shift is going to take place over about two decades (using a log scale) centered on the frequency of your pole, so I would probably find the magnitude and phase at zero (0, 90 degrees), then at infinity, then two or three places around your pole frequency, and sketch up the plot based on those numbers.

\$\endgroup\$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.