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Start a BodePlot at -180 degree phase?

Why when I plot diagram of Bode G(s)=4 (s-20)/(s (s+0.8)), it does not recognize that the constant gain is negative and should be started from -180 degree phase, while Methematica starts to + 0 Degree ? There is a problem in PhasePlot. Anyone can verify,please? :-)enter image description here

POSTED BY: Giovanni Ferdina
2 Replies
Posted 8 years ago

At low frequencies the phase is Arg[-20]/Degree-90 = 90 which is what is seen on the BodePlot.

You may desire that the phase of -20 be considered as -180 degrees instead. In that case just tweak the PhaseRange .

BodePlot[(4 (s - 20))/(s (s + 0.8)), PlotLayout -> "Phase", PhaseRange -> {-((3 [Pi])/2) - 2 [Pi], -((3 [Pi])/2)}]

enter image description here

POSTED BY: Suba Thomas
Posted 8 years ago

I can verify that BodePlot gives the correct answer. You can plot the function yourself with LogLogPlot, and LogLinearPlot as follows: f[x_]:=Abs[4(s-20)/(s (s+0.8))/.s->I x] g[x_]:=Arg[4(s-20)/(s (s+0.8))/.s->I x] LogLogPlot[f[x],{x,0.001,10000}] LogLinearPlot[180/[Pi] g[x],{x,0.1,10000}]

If you have an electrical engineering background, I recommend you reorder the terms as zeros, and poles form. You expression becomes -100 1/s (1-s/20)/(1 + s/0.8)

Let's look at the magnitude of the frequency response first. 1/s gives 20db/dec drop. then you hit a pole at 0.8. now you have 40db/dec drop. then you hit a right-half plane zero. so it bends backwards, returning to 20db/dec drop again.

You can see two knee points at 0.8 and 20.

Now about the phase. a normal 1/s will give you -90 constant phase. but the term is -1/s. so it flips. to become a +90 phase lead. then around the pole (+0.8), you drop 90 degree at -45deg/dec. so you reach 0 degree. then you hit a right-plane zero, which drops you another 90 degree to -90 degree.

So the BodePlot is correct.

POSTED BY: Zhe Hu
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