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Just a simple question on Transfer Functions.

If I was give a open loop TF, G, and a feedback loop H, then the closed loop TF is G'=[itex]\frac{G}{1+GH}[/itex].

So my first attempt was to simplify the G' by hand and then plot it in excel which produced a crescent shaped moon.

By simplification, I mean this:

Let G=1/s and H=1/(s+1)

G'=[itex]\frac{G}{1+GH}=\frac{1/s}{1+\frac{1}{s}+\frac{1}{s+1}}[/itex]=[itex]\frac{s+1}{s(s+1)+1}[/itex]

But, then I go to mathematica and enter the G' without simplification (just [itex]\frac{G}{1+GH}[/itex])and it gave me a totally different graph.

Even though the the G' is the same (mathematically) in both cases, why does the Nyquist (and thus Bode) plots are different?

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# Homework Help: Question on Transfer Functions

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