3
$\begingroup$

I'm trying to do a Bode plot in 3D for the function below, but there is no built-in function for that.

How can I do that? It would also be nice if you could use a mesh to make it easier to see.

tf = s^2/(s^2 + 2 s + 5)

The shape of the plot may not be same as in the image, but it is a 3D object like that.

In a 2D Bode plot, s is replaced with i*w and then the magnitude/modulus of the function with frequency w is plotted. However, in a 3D plot you replace s with σ + i*w and plot the magnitude of the function with a different σ and w.

tf = s^2/(s^2 + 2 s + 5);
mag = Abs[ComplexExpand[tf /. s -> \[Sigma] + I*w]];
Plot3D[mag, {\[Sigma], -1000, 1000}, {w, -100, 100}, 
 ScalingFunctions -> {None, None, "Log"}]

Enter image description here

Improve this question
$\endgroup$
4
  • 1
    $\begingroup$ what is a Bode plot, mathematically? the wikipedia article is a bit hard to parse for someone without the EE background. (hopefully someone who already knows comes along, but in the event they don't...) $\endgroup$
    – thorimur
    Jun 2, 2021 at 23:00
  • $\begingroup$ In 2D bode plot, they replace s with i*w and then plot the magnitude/modulus of the function with frequency w. However, in 3D plot you should replace s with σ + i*w and plot the maginitude of the function with different σ and w. $\endgroup$
    – emnha
    Jun 2, 2021 at 23:04
  • $\begingroup$ Like this?: ComplexPlot3D[tf, {s, -2 - 3 I, 0 + 3 I}, AxesLabel -> {\[Sigma], I*\[Omega]}, BoxRatios -> {2, 3, 1}] $\endgroup$
    – Michael E2
    Jun 2, 2021 at 23:18
  • $\begingroup$ @MichaelE2 that is nice. Adding mesh may be easier to see though. How can I make a bold red curve in the intersection of the graph and the plane forming by σ = 0 and w? $\endgroup$
    – emnha
    Jun 2, 2021 at 23:22

2 Answers 2

Reset to default
6
$\begingroup$

May be like this.

tf = s^2/(s^2 + 2 s + 5);
mag = Abs[ComplexExpand[tf /. s -> σ + I*w]];
SetOptions[Plot3D, BoundaryStyle -> None, PlotRange -> {0, 8}, 
  ViewPoint -> {2.54, 1.27, 1.8}, BoxRatios -> {1, 1, 1}, 
  ClippingStyle -> Yellow];
fig1 = Plot3D[mag, {σ, -2, 0}, {w, -3, 3}, 
   MeshFunctions -> {#3 &}, 
   MeshShading -> {Yellow, Pink, Brown, Gray, Blue, Orange, Purple, 
     Cyan}, Mesh -> {20, 20, 8}];
fig2 = Plot3D[mag, {σ, -2, 1}, {w, -3, 3}, 
   MeshFunctions -> {#1 &, #2 &}, MeshShading -> None, 
   PlotStyle -> None, Mesh -> {20, 20}];
fig3 = Plot3D[mag, {σ, -2, 1}, {w, -3, 3}, 
   MeshFunctions -> {#1 &}, Mesh -> {{0}}, PlotStyle -> None, 
   MeshStyle -> {Thick, Red}];
Show[fig1, fig2, fig3]

enter image description here

Improve this answer
$\endgroup$
1
  • $\begingroup$ the plot is very nice $\endgroup$
    – emnha
    Jun 3, 2021 at 3:50
6
$\begingroup$ 
Clear["Global`*"]

tf = s^2/(s^2 + 2 s + 5);

Manipulate[
 Show[
  ComplexPlot3D[tf,
   {s, -2 - 3 I, 1/4 + 3 I},
   MeshFunctions -> mf,
   MeshStyle -> {Black, Darker[Green]},
   Mesh -> 9,
   PlotPoints -> 50,
   MaxRecursion -> 5,
   PlotLegends -> BarLegend[Automatic,
     LegendLabel -> HoldForm[Arg[tf]]],
   PlotRange -> {0, 10}],
  ComplexPlot3D[tf,
   {s, -2 - 3 I, 1 + 3 I},
   PlotStyle -> Opacity[0],
   MeshFunctions -> {Re[#1] &},
   Mesh -> {{0.}},
   MeshStyle -> {{Red, Thick}}],
  AxesLabel ->
   (Style[#, 14, Bold] & /@ {σ, ω, 
      "|tf|"}),
  BoxRatios -> {2, 3, 1},
  SphericalRegion -> True,
  ImagePadding -> 30],
 {{mf, {Abs[#2] & , Arg[#2 ] & }, "MeshFunctions"},
  {{Abs[#2] & , Arg[#2 ] & } -> {"|tf|", "arg(tf)"},
   {Re[#2] &, Im[#2] &} -> {"Re(tf)", "Im(tf)"},
   {Re[#1] &, Im[#1] &} -> {"Re(s)", "Im(s)"}}, 
  ControlType -> PopupMenu}]

enter image description here

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.