# Re: Nyquist by hand

Jerry Avins wrote:
Jerry Avins wrote:
parrishc@xxxxxxxxx wrote:
Can someone PLEASE direct me to a resource which explains the
construction of Nyquist plots by hand? The threads I looked at in
this forum do not concern this specifically. I have been in the dark
on this matter for longer than I care to discuss. Gratefully yours.

Chris Parrish

Check out http://tinyurl.com/4vxxvz

A Nyquist plot is a polar plot of frequency and phase response.
Magnitude -- linear, not dB --is the radius and phase is the angle.

What I meant: A Nyquist plot is a polar plot of amplitude vs. phase
response with frequency as a parameter. Magnitude -- linear, not dB --
is the radius and phase is the angle.

For a chosen frequency, place a dot in the right place on polar paper.
(I write the frequency as a label.) Plot enough dots to see the
curvature -- more where the curve bends more sharply, then connect the
dots.

Jerry
--
Engineering is the art of making what you want from things you can get.
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Jerry, I believe that is so called Nichols plot. Nichols plot gives
amplitude vs phase chart. That is different from Nyquist plot.
For example if feedback transfer functions is T = G/(1+GH), usually in
order to determine stability of a system, its Nyquist plot is drawn
for GH and observed if it encircles point (-1,0) and how many times.
Nyquist plot represents simple graphical form of GH(s) mapping. Since
s = a+jw, GH(s) maps that complex domain into new complex variable
domain u+jv. Nyquist plot represents Im{GH(s)} vs Re{GH(s)} plot or
"v" vs "u" plot.
Procedure to draw it by hand can be very tedious and with many
software pacjkages available today, I'm surprised that someone ask
this question.
However there are some formal rules that can be used when drawing
Nyquist plot for simple systems.
Usually you devide GH(s) into portions for s = jw. Then you observed
how portion from w = 0+ to w = +inf is mapped. Then you try and see
how portion from w = +inf to w = -inf is mapped.
You do this by findind limit values (lim).
Nyquist plot is always symmetrical around x (Real) axis.
Like I said, constructing Nyquist plot by hand is very complex and
difficult for most but few simple examples. I usually use tables with
graphical plots or some powerful software tools such Matlab or Scilab.
I would recommend Scilab, because it is very powerful and entirely
free alternative to expensive Matlab.

Best regards,
Asim Vodencarevic
.