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I need to plot a rectangular waveform with Latex. The main problem is how to make the height of the pulse "variable" not a "number" as you can see in the figure below. "x" here is some variable that will be found by calculations.

A PSTricks solution just for comparison purpose.

documentclass[pstricks,border=12pt,12pt]{standalone}

usepackage{pst-plot}

begin{document}

begin{pspicture}(-1,-1)(11.5,5.5)

    psaxes[ticks=x,labels=x]{->}(0,0)(-1,-1)(11,5)[$t$,0][$A(t)$,90]

    multips(0,0)(2,0){5}{psline[linecolor=blue,linewidth=2pt](0,0)(0,4)(1,4)(1,0)(2,0)}

    uput{5pt}[180](0,4){$sqrt{R_s}$}

end{pspicture}

end{document}

Since this question is tagged tikz-pgf, I thought you may also be interested in a TikZ code. (One of its advantageous is that this works with pretty much any compiler.)

documentclass[tikz,border=3.14mm]{standalone}

begin{document}

begin{tikzpicture}

pgfmathsetmacro{h}{2}

pgfmathsetmacro{L}{4}

draw[thick,-latex] (0,-0.5) -- (0,h+2) node[above] {$A(t)$};

draw[thick,-latex] (-0.5,0) -- (2*L+1,0) node[right] {$t$};

foreach X [evaluate=X as Z using {int(2*X-1)},] in {1,...,L}

{draw[very thick,blue] (2*X-2,0) |- (2*X-1,h) |- (2*X,0);

draw (Z,0.1) -- (Z,-0.1) node[below]{$Z$};}

end{tikzpicture}

end{document}

A simple approach using TikZ.

documentclass[border=3.14mm]{standalone}

usepackage{tikz}

begin{document}

  begin{tikzpicture}

    defx{1} % replace 1 with desired value here

    draw[-latex] (0,0) -- ++(4,0)  node[right]{$t$};

    draw[-latex] (0,0) -- ++(0,2.0x)node[left]{$A(t)$};

    draw[thick] (0,x)node[left]{$sqrt{x}$} -- ++(1,0) -- ++(0,-x)node[below]{1} -- ++(1,0) -- ++(0,x) -- ++(1,0) -- ++(0,-x)node[below]{3} -- ++(0.5,0);

  end{tikzpicture}

end{document}