# How does phase affect the Nyquist Diagram - imaginary axis, how should it look?

1. Apr 18, 2012

### thomas49th

http://gyazo.com/e5c5b4f7808a63e7e664440259ac3058

I agree with all notes made on that slide, but I don't actually get how they constructed the diagram from that? I understand that they line represents frequency so going to 0 to infinity means the line would travel from -0.5 to 0, but HOW DO THEY KNOW what the size values the curve peak at on the imaginary axis???

Further, it says phase decreases from -180 to -270, I agree from the transfer function, but how does this look on the Nyquist diagram? How does phase affect the Nyquist diagram?

Thanks

EDIT: Apologies if this may seem like a double post

2. Apr 19, 2012

### Staff: Mentor

Perhaps you should consider reducing the given transfer function into real and imaginary components. So then:
$$\frac{1}{(jω + 1)(jω + 2)(jω - 1)} = \frac{-2}{(1 + ω^2)(4 + ω^2)} + j\frac{ω}{(1 + ω^2)(4 + ω^2)}$$
This should help pick out any particular relationships or extrema of the real and imaginary components, as well as phase relationships since $\phi = tan^{-1}(Im/Re)$.