Problem with atan with pgfplots

Question

I'm trying to plot simple Bode plots using pgfplots. After much research, I discarded the package Bodegraph due to its bad documentation and a lot of troubles with the gnuplot. So, I'm using an axis environment with the logarithmic x-axis activated. The next code is sample example of a tikzpicture that shows the problem.

\begin{tikzpicture}
\begin{axis}[
    width=0.8\linewidth,
    height = 3cm,
    xmode = log,   
    axis x line*=box,
    axis y line*=box,
    xmin=1e-2, xmax=1e2,% range for the x axis
    ymin=-100, ymax = 100,
    scale only axis ,
    ytick distance=40,
    xmajorgrids = true,
    ymajorgrids = true,
    title = Fase,
    ylabel = $\phi$,
    xlabel = $\omega$
]
    \addplot[smooth, 
             blue,
             ultra thick,
             mark=none,
             domain=1e-2:1e2,
             samples=400,
             trig format plots = deg]
    {atan((2*0.1*(x/2))/(1-(x/2)^2))};   
\end{axis}
\end{tikzpicture}

The problem is that I get the following wrong plot:

What I'm expecting to get is something like:

Please, notice that I'm using the trig format plots=true to set degrees for the trigonometric functions. Can anybody help me out? This is just the phase angle plot of a second order system.

Thanks in advance

Answer 1

The plot you show is correct I think, in the sense that it correctly displays the formula you entered. As mentioned in a comment, you divide by 1-x/2 in the argument to atan, and the limit of atan(x) as x approaches infinity is 90 degrees.

percusse mentions in a another comment that you want to use atan2 instead. atan2 takes two values, atan2(y,x). I have no idea exactly what kind of expression you're supposed to use, but as an example (atan2(1,x)-45)*2 gives you something similar to what you expect, though with a less steep curve in the middle part. I'm not familiar with these things though, so I cannot help you find a more appropriate formula.

\documentclass{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
    width=0.8\linewidth,
    height = 3cm,
    xmode = log,   
    axis x line*=box,
    axis y line*=box,
    xmin=1e-2, xmax=1e2,% range for the x axis
    ymin=-100, ymax = 100,
    scale only axis ,
    ytick distance=40,
    xmajorgrids = true,
    ymajorgrids = true,
    title = Fase,
    ylabel = $\phi$,
    xlabel = $\omega$
]
    \addplot[smooth, 
             blue,
             ultra thick,
             mark=none,
             domain=1e-2:1e2,
             samples=400,
             trig format plots = deg]
    {(atan2(1,x)-45)*2};   
\end{axis}
\end{tikzpicture}
\end{document}