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Rectangular waveguide with continuous source
Parallel-plate waveguide with pulse source


red bullet What is this? If you're reading this, you're probably in my Microwave and RF engineering class. Hi, I'm Laurie. :) Below are some images and animations of fields in rectangular and parallel-plate waveguides. If you have any comments or if there's something you'd like to see, please email me.

red bullet How to use this page: Each simulation has a movie (mpeg) and an image (gif) associated with it, and each movie and image comes in two sizes (other than the tiny image shown). Your browser is probably set up to view them automatically by clicking on the links. If not there's some suggestions on the ToyFaq. The movies are all 500 frames long, so if they appear shorter than that or jerky, you'll need to set your movie player's "play-all-frames" option. If you're still stuck, find your nearest computer wizard and beg for help. :-)
           What the colors mean: In each movie/image below the entire simulation region is highlighted with a box. Red/Yellow indicates positive values, with yellow representing the greatest intensities and red representing values near zero. Blue/Green indicates negative, green the greatest intensities and blue values near zero. In some simulations, the most negative value is mapped to yellow, so a yellow spot in the middle of green represents the most negative point. 
          Two kinds of color scaling are used. Autoscaling every timestep scales the field intensities in that timestep to the full range of color values. This means that dim timesteps will look as bright as intense ones, but the structure of the fields in the dim timesteps will show well. Autoscaling is used unless global scaling is specified. Global scaling over all timesteps scales the entire simulation as a whole. Dim timesteps will barely show anything visible, but you get a good idea of intensity variation over time.

red bullet Rectangular waveguide: The following animations show a rectangular waveguide sourced with a plane wave and terminated in a PEC (Perfect Electric Conductor) boundary. The code simulates an idealized rectangular waveguide by treating the interior of the mesh as free space/air and enforcing PEC conditions on the faces of the mesh. The problem is taken from Field and Wave Electromagnetics, 2nd ed., by David K. Cheng, pages 554-555. It is a WG-16 waveguide useful for X-band applications, with interior width = 2.29cm and interior height = 1.02cm. 

Image of rectangular guide with continuous source  Movies:
  green dot 256x256 mpeg, 500 frames [1.4Mb]
  green dot 512x512 mpeg, 500 frames [4.0Mb]		    Images:
   red dot 256x256 gif [76Kb]
   red dot 512x512 gif [0.3Mb] 
WG-16 waveguide at 10 GHz. The frequency is chosen to be in the middle of the frequency range for TE10 operation for this waveguide.

Image of rectangular guide with cw source  Movies:
  green dot 256x256 mpeg, 500 frames [1.4Mb]
  green dot 512x512 mpeg, 500 frames [4.0Mb]		    Images:
   red dot 256x256 gif [76Kb]
   red dot 512x512 gif [0.3Mb] 
WG-16 waveguide at 12.5 GHz, which is nearing the cutoff frequency for the next higher-order mode, TE20. The wavelengths looked squished in comparison to the previous simulation; they are still the width of the guide, but the wavelength is shorter.

Image of rectangular guide with cw source  Movies:
  green dot 256x256 mpeg, 500 frames [1.4Mb]
  green dot 512x512 mpeg, 500 frames [4.0Mb]		    Images:
   red dot 256x256 gif [76Kb]
   red dot 512x512 gif [0.3Mb] 
WG-16 waveguide at 15 GHz, which is well beyond the cutoff frequency for TE20, yet the wave continues to propagate as TE10 due to the way the source is applied. Energy from the source could propagate as TE20 at this frequency, but there's nothing to make it want to, nothing to trip it over into a higher-order mode.

Image of rectangular guide with pulse source  Movies:
  green dot 256x256 mpeg, 500 frames [.8Mb]
  green dot 512x512 mpeg, 500 frames [3.4Mb]		    Images:
   red dot 256x256 gif [76Kb]
   red dot 512x512 gif [0.3Mb] 
Rectangular waveguide with pulse source at 10.0 GHz. Note the smearing of the pulse by the guide: The transfer characteristic of the waveguide does not include all of the frequency content of the pulse. The continuous source in the above simulations contains a single frequency, but here the truncation of the pulse causes a spread of frequencies traveling at different rates. The range of colors is autoscaled every timestep to the range of field values in that timestep, so that the structure of the fields in later timesteps can be seen..

Image of rectangular guide with pulse source  Movies:
  green dot 256x256 mpeg, 500 frames [.56Mb]
  green dot 512x512 mpeg, 500 frames [2.2Mb]		    Images:
   red dot 256x256 gif [76Kb]
   red dot 512x512 gif [0.3Mb] 
Rectangular waveguide with pulse source at 10.0 GHz, as in previous simulation. The range of colors is scaled globally for all timesteps for contrast with the previous animation, so the initial pulse appears bright, and the colors grow fainter as the energy spreads through the guide.



red bullet Parallel-plate waveguide: The following animations show a parallel-plate waveguide sourced with a sinusoidal pulse and terminated in a PEC (Perfect Electric Conductor) boundary. The code simulates an idealized parallel-plate waveguide of infinite width by treating the interior of the mesh as free space/air while applying PMC (Perfect Magnetic Conductor) symmetry on two faces of the mesh and PEC conditions on the remaining faces. All are shown at 10 GHz, which is the middle of the range for TE10 operation for the rectangular guide above.
Image of parallel-plate guide with pulse source  Movies:
  green dot 256x256 mpeg, 500 frames [.96Mb]
  green dot 512x512 mpeg, 500 frames [2.1Mb]		    Images:
   red dot 256x256 gif [76Kb]
   red dot 512x512 gif [0.3Mb] 
Parallel-plate waveguide with pulse source at 10.0 GHz. The initial pulse is positive as shown in the gif above, but when the pulse strikes the PEC termination the reflection is negative, shown in the animation in blues and greens The source face becomes a PEC termination after the emission of the pulse, and the pulse bounces back and forth forever, though it grows steadily more ragged over many repetitions.

Image of parallel-plate guide with continuous source  Movies:
  green dot 256x256 mpeg, 500 frames [1.2Mb]
  green dot 512x512 mpeg, 500 frames [4.8Mb]		    Images:
   red dot 256x256 gif [76Kb]
   red dot 512x512 gif [0.3Mb] 
Parallel-plate waveguide with continuous plane wave source at 10.0 GHz. Note the standing wave that quickly develops.

Image of parallel-plate guide with continuous source  Movies:
  green dot 256x256 mpeg, 500 frames [1.2Mb]
  green dot 512x512 mpeg, 500 frames [4.8Mb]		    Images:
   red dot 256x256 gif [76Kb]
   red dot 512x512 gif [0.3Mb] 
Parallel-plate waveguide with continuous plane wave source at 10.0 GHz. The range of colors is scaled globally for all timesteps for contrast with the previous animation. As a result, only colors representing lower intensities are present early in the simulation. As the simulation progresses, more and more energy is pumped into the system, giving greater intensities. Because of the PEC termination, no energy can leave the system.


red bullet Image montages giving close-up views of some parallel plate waveguide simulations:
Montage of pulse striking absorbing boundary    red dot PulseGeneration gif[40Kb]
   red dot PECReflection gif[32Kb] 

      Montage page		    red dot PeriodicBoundary gif[14Kb]
   red dot AbsorbingBoundary gif[31Kb]

 



red bullet Contact the perpetrators:
lemiller@borg.umn.edu


red bullet Waves of the future: If you'd like the source code that performed the computation for these simulations, it's available free at (click on the pretty logo to get there):
Link to ToyFDTD main page

 
  Colorbar made from a ToyFDTD simulation