Radiation diagram

Question

I'd like to realize the radiation diagram of the dipole like you can see (both):

I 'd like add a caption. I've tried but I can't find the good program.

I'd like to add arrows to radiation diagram like you can see on the picture.

score 4 · Accepted Answer · 2019-01-01T17:30:56.617

Assuming you are talking about the standard dipoles, whose power goes like sin(theta)^1 (which, in the conventions of pgfplots becomes cos(theta)^2), you could use the 3d and polar plot facilities of pgfplots. For the subfigures I picked a random answer since it seems to be flexible enough to address alignment requirements.

\documentclass{article}
\usepackage{pgfplots} 
\pgfplotsset{width=8cm,compat=1.16}
\usepgfplotslibrary{polar} 
\usepackage{subcaption}
\usepackage{floatrow} % adapted from https://tex.stackexchange.com/a/389970/121799
\begin{document}

\begin{figure}[htb]
\floatsetup{valign=t, heightadjust=all}
\ffigbox{%
\begin{subfloatrow}
\ffigbox{\begin{tikzpicture}
\begin{axis}[view/h=45,axis lines = none,unit vector ratio=1 1 1]
        \addplot3[domain=0:360,domain y=0:360,surf,
    z buffer=sort]
       ({(sin(x+90)*sin(x+90))*cos(y)}, 
        {(sin(x+90)*sin(x+90))*sin(y)}, 
        {(sin(x+90)*sin(x+90))*sin(x)});
\end{axis}
\path(current bounding box.south west) rectangle (current bounding box.north
east);
\end{tikzpicture}}{\caption{3d plot.\label{fig:3dplot}}}
\ffigbox{\begin{tikzpicture}
\begin{polaraxis}[axis lines = none]
    \addplot[domain=0:360,samples=73,smooth] (x+90,{sin(x)*sin(x)});
\end{polaraxis}
\end{tikzpicture}}{\caption{Polar plot.\label{fig:polarplot}}}
\end{subfloatrow}}
{\caption{Dipole.}\label{fig:Dipole}}
\end{figure}
\end{document}

Here is a second option with instructions in case you want a single-color mesh instead for the 3d plot.

\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage{pgfplots} 
\pgfplotsset{width=8cm,compat=1.16}
\usepgfplotslibrary{polar} 
\usepackage{subcaption}
\usepackage{floatrow} % adapted from https://tex.stackexchange.com/a/389970/121799
\begin{document}

\begin{figure}[htb]
\floatsetup{valign=c, heightadjust=all}
\ffigbox{%
\begin{subfloatrow}
\ffigbox{\begin{tikzpicture}
\begin{axis}[view/h=45,axis lines = none,unit vector ratio=1 1 1]
        \addplot3[domain=0:360,domain y=0:360,samples=31,
        colormap/blackwhite,surf,%mesh,point meta=1, %<-if you want a mesh
    z buffer=sort]
       ({(sin(x+90)*sin(x+90))*cos(y)}, 
        {(sin(x+90)*sin(x+90))*sin(y)}, 
        {(sin(x+90)*sin(x+90))*sin(x)});
\end{axis}
\path(current bounding box.south west) rectangle (current bounding box.north
east);
\end{tikzpicture}}{\caption{3d plot.\label{fig:3dplot}}}
\ffigbox{\begin{tikzpicture}
\begin{polaraxis}[axis lines = none]
    \addplot[domain=0:360,samples=73,smooth] (x+90,{sin(x)*sin(x)});
\end{polaraxis}
\draw[-stealth] ([yshift=2cm]current axis.south) -- ([yshift=-2cm]current axis.north);
\draw[-stealth] (current axis.west) -- (current axis.east);
\end{tikzpicture}}{\caption{Polar plot.\label{fig:polarplot}}}
\end{subfloatrow}}
{\caption{Dipole.}\label{fig:Dipole}}
\end{figure}
\end{document}

\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage{pgfplots} 
\pgfplotsset{width=8cm,compat=1.16}
\usepgfplotslibrary{polar} 
\usepackage{subcaption}
\usepackage{floatrow} % adapted from https://tex.stackexchange.com/a/389970/121799
\begin{document}

\begin{figure}[htb]
\floatsetup{valign=c, heightadjust=all}
\ffigbox{%
\begin{subfloatrow}
\ffigbox{\begin{tikzpicture}
\begin{axis}[view/h=45,axis lines = none,unit vector ratio=1 1 1]
        \addplot3[domain=0:360,domain y=0:360,samples=31,
        mesh,point meta=1, %<-if you want a mesh
    z buffer=sort]
       ({(sin(x+90)*sin(x+90))*cos(y)}, 
        {(sin(x+90)*sin(x+90))*sin(y)}, 
        {(sin(x+90)*sin(x+90))*sin(x)});
\end{axis}
\path(current bounding box.south west) rectangle (current bounding box.north
east);
\end{tikzpicture}}{\caption{3d plot.\label{fig:3dplot}}}
\ffigbox{\begin{tikzpicture}
\begin{polaraxis}[axis lines = none]
    \addplot[domain=0:360,samples=73,smooth] (x+90,{sin(x)*sin(x)});
\end{polaraxis}
\draw[-stealth] ([yshift=2cm]current axis.south) -- ([yshift=-2cm]current axis.north);
\draw[-stealth] (current axis.west) -- (current axis.east);
\end{tikzpicture}}{\caption{Polar plot.\label{fig:polarplot}}}
\end{subfloatrow}}
{\caption{Dipole.}\label{fig:Dipole}}
\end{figure}
\end{document}

Another version. Setting point meta appropriately you can achieve practically any shading.

\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage{pgfplots} 
\pgfplotsset{width=8cm,compat=1.16}
\usepgfplotslibrary{polar} 
\usepackage{subcaption}
\usepackage{floatrow} % adapted from https://tex.stackexchange.com/a/389970/121799
\begin{document}

\begin{figure}[htb]
\floatsetup{valign=c, heightadjust=all}
\ffigbox{%
\begin{subfloatrow}
\ffigbox{\begin{tikzpicture}
\begin{axis}[view/h=45,axis lines = none,unit vector ratio=1 1 1]
        \addplot3[domain=0:360,domain y=0:360,samples=31,
        point meta=sqrt(x^2+y^2),
        colormap/blackwhite,surf,%mesh,point meta=1, %<-if you want a mesh
    z buffer=sort]
       ({(sin(x+90)*sin(x+90))*cos(y)}, 
        {(sin(x+90)*sin(x+90))*sin(y)}, 
        {(sin(x+90)*sin(x+90))*sin(x)});
\end{axis}
\path(current bounding box.south west) rectangle (current bounding box.north
east);
\end{tikzpicture}}{\caption{3d plot.\label{fig:3dplot}}}
\ffigbox{\begin{tikzpicture}
\begin{polaraxis}[axis lines = none]
    \addplot[domain=0:360,samples=73,smooth] (x+90,{sin(x)*sin(x)});
\end{polaraxis}
\draw[-stealth] ([yshift=2cm]current axis.south) -- ([yshift=-2cm]current axis.north);
\draw[-stealth] (current axis.west) -- (current axis.east);
\end{tikzpicture}}{\caption{Polar plot.\label{fig:polarplot}}}
\end{subfloatrow}}
{\caption{Dipole.}\label{fig:Dipole}}
\end{figure}
\end{document}

\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage{pgfplots} 
\pgfplotsset{width=8cm,compat=1.16}
\usepgfplotslibrary{polar} 
\usepackage{subcaption}
\usepackage{floatrow} % adapted from https://tex.stackexchange.com/a/389970/121799
\begin{document}

\begin{figure}[htb]
\floatsetup{valign=c, heightadjust=all}
\ffigbox{%
\begin{subfloatrow}
\ffigbox{\begin{tikzpicture}
\begin{axis}[view/h=70,axis lines = none,unit vector ratio=1 1 1]
\addplot3[domain=0:360,domain y=0:360,samples=31,
        point meta=sqrt(x^2+y^2),
        colormap/blackwhite,surf,%mesh,point meta=1, %<-if you want a mesh
    z buffer=sort]
       ({(sin(x+90)*sin(x+90))*cos(y)}, 
        {(sin(x+90)*sin(x+90))*sin(y)}, 
        {(sin(x+90)*sin(x+90))*sin(x)});
\pgfplotsinvokeforeach{0,1,...,7}{
\draw[-latex] ({2*cos(#1*45)},{2*sin(#1*45)},0)
-- ({4*cos(#1*45)},{4*sin(#1*45)},0);
\addplot3[samples=81,samples y=1,domain=0:1260,color=blue,thin]
({(x/720+2)*cos(#1*45)},{(x/720+2)*sin(#1*45)},{0.25*sin(x)});
\addplot3[samples=81,samples y=1,domain=0:1260,color=red,thin]
({(x/720+2)*cos(#1*45)-0.25*sin(#1*45)*sin(x)},{(x/720+2)*sin(#1*45)+0.25*cos(#1*45)*sin(x)},{0});
}       
\end{axis}
\path(current bounding box.south west) rectangle (current bounding box.north
east);
\end{tikzpicture}}{\caption{3d plot.\label{fig:3dplot}}}
\ffigbox{\begin{tikzpicture}
\begin{polaraxis}[axis lines = none]
    \addplot[domain=0:360,samples=73,smooth] (x+90,{sin(x)*sin(x)});
\end{polaraxis}
\draw[-stealth] ([yshift=2cm]current axis.south) -- ([yshift=-2cm]current axis.north);
\draw[-stealth] (current axis.west) -- (current axis.east);
\end{tikzpicture}}{\caption{Polar plot.\label{fig:polarplot}}}
\end{subfloatrow}}
{\caption{Dipole.}\label{fig:Dipole}}
\end{figure}
\end{document}

If you have additional requests, may I kindly ask you to ask a new question for that? Asking questions is free, after all.

Thanks! and is it possible to add the axes on the polar plot ? and to remove colors on the 3d plot? — Aurélien, Dec 31 '18 at 02:52
I've got a problem, when I use your code, latex display "the package subcaption can't be use in cooperation with the subfigure package", I can't find a solution .... How can I change the code ? pls — Aurélien, Dec 31 '18 at 05:13
@Aurélien My code does not lead to the error message because it does not load subfigure. If you embed it into a code that does, then you need either to remove subfigure there or to use subfigure instead of subcaption. — , Dec 31 '18 at 06:53
Ok thanks and I've got one more request...About the colors for the 3d plot, all around the outside should be white, not black and more you are going inside the middle section it should be black. Does this make sense? — Aurélien, Dec 31 '18 at 09:33
Is it possible to have the little arrows to the top and down ?pls — Aurélien, Jan 01 '19 at 22:09

score 1 · Answer 2 · edited Mar 28 '21 at 22:36

Like you I was very intrested in drawing the radiation plot of the radiation diagram of an Hertzian dipole, and I've tested the solution provided by user121799, but it didn't worked very well for me: it was a little buggy and it took a lot of time to compile.
Then i decided to modify the solution of user121799 with the tikz-3dplot package. This first snippet is about the power radiation diagram which polar equation is sin(θ)^2

\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage{pgfplots} 
\pgfplotsset{width=8cm,compat=1.16}
\usepgfplotslibrary{polar} 
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{70}{135}
\begin{figure}[]
\begin{center}
    \begin{tikzpicture}[scale=2,line join=bevel,tdplot_main_coords, fill opacity=.7]
        \pgfsetlinewidth{.4pt}
        \tdplotsphericalsurfaceplot{72}{24}%
        {sin(\tdplottheta)^2}{black}{blue}%
        {\draw[color=black,thick,->] (0,0,0) -- (2,0,0) node[anchor=north east]{$x$};}%
        {\draw[color=black,thick,->] (0,0,0) -- (0,2,0) node[anchor=north west]{$y$};}%
        {\draw[color=black,thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};}
    \end{tikzpicture}
    \caption{Power radiation Hertzian dipole 3d}\label{fig:3dplot_radiation_dipole}
\end{center}
\end{figure}
\begin{figure}[]
\begin{center}
        \begin{tikzpicture}
            \begin{polaraxis}[axis lines = none]
                \addplot[domain=0:360,samples=73,smooth] (x+90,{sin(x)^2});
            \end{polaraxis}
            \draw[-stealth] ([yshift=1.5cm]current axis.south) -- ([yshift=-1.5cm]current axis.north) node[anchor=north,yshift=1cm]{$z$};
            \draw[-stealth] (current axis.west) -- (current axis.east) node[anchor=west]{$x$};
        \end{tikzpicture}
        \caption{Power radiation Hertzian dipole in x-z plane}
\end{center}
\end{figure}
\end{document}

OUTPUT:

If you are intrested about the radiation pattern (and not the power), in many notes ( like this in italian) you can find that its equation is |sin(θ)|, then the code becomes:

\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage{pgfplots} 
\pgfplotsset{width=8cm,compat=1.16}
\usepgfplotslibrary{polar} 
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{70}{135}
\begin{figure}[]
\begin{center}
    \begin{tikzpicture}[scale=2,line join=bevel,tdplot_main_coords, fill opacity=.7]
        \pgfsetlinewidth{.4pt}
        \tdplotsphericalsurfaceplot[parametricfill]{72}{24}%
        {abs(sin(\tdplottheta))}{black}{\tdplotphi}%
        {\draw[color=black,thick,->] (0,0,0) -- (2,0,0) node[anchor=north east]{$x$};}%
        {\draw[color=black,thick,->] (0,0,0) -- (0,2,0) node[anchor=north west]{$y$};}%
        {\draw[color=black,thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};}
    \end{tikzpicture}\caption{radiation pattern Hertzian dipole 3d}
\end{center}
\end{figure}
\begin{figure}[]
\begin{center}
        \begin{tikzpicture}
            \begin{polaraxis}[axis lines = none]
                \addplot[domain=0:360,samples=73,smooth] (x+90,{abs(sin(x))});
            \end{polaraxis}
            \draw[-stealth] ([yshift=1.5cm]current axis.south) -- ([yshift=-1.5cm]current axis.north) node[anchor=north,yshift=1cm]{$z$};
            \draw[-stealth] (current axis.west) -- (current axis.east) node[anchor=west]{$x$};
        \end{tikzpicture}
        \caption{radiation pattern Hertzian dipole in x-z plane}
\end{center}
\end{figure}
\end{document}

OUTPUT:

This last 3d plot is coloured because i liked that, you can find more in the tikz-3dplot documentation.
I hope i could be helpful to someone facing the problem like me

Radiation diagram

2 Answers2

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