Questions on Bode Plot and Nyquist Plot

[promach]

Bode Plot


1) Why the gain plot |G(jw)| drops and then increases for conjugate zeroes ?

2) Why the gain plot |G(jw)| increases and then drops for conjugate poles ?





Nyqust Plot

3) For Figure 9-18(B), could anyone explain in a bit more details than the book as on how to obtain the Nyquist plot pattern ?

 

[Akanimo]

Hi,

Bode Plot


1) Why the gain plot |G(jw)| drops and then increases for conjugate zeroes ?

2) Why the gain plot |G(jw)| increases and then drops for conjugate poles ?

The actual point of consideration is at 'wd'. We are having two poles or two zeroes at wd.

For two poles at wd, you lose 40dB/dec (20dB/Dec *2) starting from wd.

For two zeroes at wd, you gain 40dB/Dec starting from wd.

 

[FvM]

As for the complex pole/zero transfer function, it seems to me that you are acting stupid on purpose, asking things that you know since long.

The complex pole pair transfer function describes a second order low pass. Did you never hear or even observe that the low pass filter has a magnitude overshoot depending on the pole pair Q? E.g. if you compare a Bessel or Butterworth with a Chebyshev filter? The behavior can be visualized by a mechanical oscillator with varying damping. Review your high school physics text book. Of course the magnitude response can be calculated by basic complex math.

The complex zero question is more or less the same thing.

Regarding Nyquist, I'm not sure what the exact question is. You obtain the Nyquist plot by drawing the complex magnitude response Im(A) over Re(A). A circuit simulator like Ltspice does this easily. Or do you ask why the pattern looks like it is? In this case, you'll define the transfer function of interest (e.g. 3 zeros/three poles in the example) and plot it.

 

[promach]

I have understood the nyquist plot for figure 9-18(b)

Why the gain expression for the case of conjugate zeros does not imply a trough at wd ?

 

[Akanimo]

...
Why the gain expression for the case of conjugate zeros does not imply a trough at wd ?
...

Please explain what you mean by "does not imply a trough at wd"

 

[promach]

The trough should be at wn instead of wd, I presume.