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[Ray tracing] Resultant of electric field components

  1. Apr 2, 2009 #1
    Hi All,

    I am a beginner at Electromagnetics

    I'm implementing ray tracing SBR to predict propagation of waves. Each ray contribution will be in the form of:

    Ei = (some factors) e ^ (- j k r) u(theta, phi)

    where k = 2 pi / wavelength, r is the total unfolded path

    I'm not sure about the u(theta, phi) vector .. is right this way or no need for it?

    Now how can i add several Ei's? each one is multiplied by a complex and a vector .. i have no clue on how to proceed?

    Also does anybody know what is the field radiation pattern (f) of an isotropic antenna?

    thanks in advance
  2. jcsd
  3. Apr 3, 2009 #2


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    I really need to go to bed but I felt compelled to respond to this in order to provide further confusion.

    An isotropic antenna radiates equally in all directions, the radiation pattern is just a sphere.

    I'm not sure on how much of the SBR theory you know. You should be able to find papers on them, Andy Lee did a lot of work on it and he also developed Xpatch which uses SBR. I think his author name was S-W Lee. Anyways, knowing the theory behind it should answer a lot of your questions.

    It's been a while but... SBR works by representing the waves as a series of ray "tubes." The propagation of the wave is locally represented by a ray moving through space. The tube is the footprint of the EM wave associated with that ray. As the tube moves through space, it diverges, this is incorporated into the formula. The tube itself is a plane wave, and so it has an associated polarization. That is why you need a vector associated with each tube as that will contain the polarization of the plane wave in the tube. Since these are far-field ...um... fields they usually use the theta and phi unit vector conventions. Whenever the ray strikes a scatterer, physical optics is used to estimate the currents excited. The currents are painted over the footprint of the tube. These are the currents that are used in integral equations to calculate the scattered fields.

    So you send out a bunch of rays in accordance to your excitation, like the radiation pattern of an antenna. These rays represent far-field plane waves, so they have a theta and phi polarization. Whenever a ray strikes a surface, you calculate it's reflection and note any necessary attenuations or diffractions. After you have mapped the reflections of all the rays, you paint currents over the footprints of the rays on the scatterer(s). Then you use integral equations to calculate the scattered fields from the currents. There is some consideration on which bounces you will actually use to paint currents on. For example, a ray may have three bounces as it hits around on a surface (think like the inside of a cylinder with an opening in the side. One surface but the curvature may give multiple bounces of the ray on the same surface). Sometimes you might hear about the second bounce being ignored, only first and/or last bounces being used. I wouldn't worry too much about this, it makes an assumption that if you have multiple bounces on a scatterer that the currents usually cancel out and so only the first and last bounces make any considerable contribution.

    Classical EM follows linear superposition, so you combine rays that cause an overlapping footprint on a scatterer by just adding them together. Since these are vectors, you can simply use an array to hold the vector components.

    EDIT: I think this maybe one of Andy's early papers: http://intl.ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=702&arnumber=18706&count=21&index=8# Note though, a quick glance through it makes me think that he only paints the currents at the aperture. He was only interested in the fields leaving the cavity so he painted the currents across the aperture and then integrated them as opposed to the currents on the scatterer's surface.
    Last edited: Apr 3, 2009
  4. Apr 3, 2009 #3
    Thanks a lot for replying but I don't see what that has to do with my question :)

    I wanted equations.

    Also, I found this in a paper about ray tracing:
    "Each propagation mechanism is treated separately, and the total field is determined via coherent superposition of the individual contributions of each ray as weighted in time by a probing pulse identical to one commonly used in measurements to provide a wide band power delay profile representation of the propagation channel."

    What does it mean????? and how can I use it?

  5. Apr 4, 2009 #4


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    I don't know, it would make much more sense given its context in the paper. The equations and details can be found in the paper I linked and you should be able to find more papers written by S-W Lee on the subject. Additional topics related to SBR are physical optics, geometric optics, and the unified theory of diffraction which can all be found in Balanis' textbook on Electromagnetics (he even gives code for edge diffraction but that's probably more than you want).
  6. Apr 4, 2009 #5
    I will check these papers. I might need the diffraction part so that's great.

    Thanks a lot. :)
  7. Apr 4, 2009 #6


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    Normally you only really need to do the diffractions on edges. Balanis' code is in Fortran and I learned that he makes a few tricks with the Fortran. I think it was that certain range of variables are by default set to integers and so some of the equations will cast doubles as ints, so keep that in mind if you rewrite into a different language. That was the only problem I had with it.
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