Thursday, 28 July 2016

trigonometry - Complex argument and nyquist plot

I'm trying to sketch the nyquist plot of
jω1jω+1
but can't seem to calculate the argument correctly. I think it should be arctan(ω)arctan(ω)=2arctan(ω) but this doesn't give the correct nyquist plot behaviour for ω0 and ω - surely 2arctan(ω) implies that limx0=0 and \lim_{x\to \infty} = -180^\circ?



Wolfram Alpha disagrees but I can't see where I'm going wrong. Am I making a glaring error somewhere? Any help would be greatly appreciated.



Thanks very much

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