- #1
Neofit
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Homework Statement
I need to be able to sketch Nyquist diagrams for transfer functions. I spent a lot of time but I cannot wrap my head around the idea of mapping the GH(jw) in the complex plane. Let's consider the following example for this question:
[tex]GH(s) = \frac{4} {s(s+2)^2}[/tex]
2. The attempt at a solution
The transfer function is factored as [tex] \frac{4}{jw}\times\frac{1}{jw+2}\times\frac{1}{jw+2} [/tex]
[tex] MAG \frac{4}{jw}=\frac{4}{w}; ARG=\frac{-pi}{2} [/tex]
[tex] MAG \frac{1}{jw+2}=\frac{1}{ \sqrt{w^2\times2^2} }; ARG=-tan^-1{w} [/tex]
Then I make a table for all three elements of the transfer function and calculate their magnitude and angle for some values of frequency, including zero and infinity. After that, I convert the resultant polar coordinates to rectangular and plot them. This is what I understand I need to do, and it is not working.
I have had only one lecture on this topic and did not had a chance to ask the professor anything. Please offer some help - I really need it! An example on how to sketch the above TF's Nyquist diagram will be very appreciated. Also, how can I decide what frequency values to use in the calculation?
Thanks