Diffraction by a perfectly conducting cylinder using UTD?

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Diffraction by a perfectly conducting cylinder using UTD???!

Hi all,

Does anybody know the equations needed to predict the diffraction of electromagnetic waves by a perfectly conducting cylinder using UTD?
I want to use these equations in ray tracing.
I tried to read some papers and a book "Introduction to the Uniform Geometrical Theory of Diffraction" .. They were so complicated and I didn't understand anything actually (I'm a computer science student :) ).

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I think you have to consider two extremes: When the wavelength is much less than the diameter of the cylinder, and when the wavelengths is much more. In one case the reflection is specular, and in the other, it is re radiated. But both will produce interference effects at large distances.

I'm not sure I totally understand you.

When the wavelength is bigger than the dimensions of an object, the waves suffer scattering and when the wavelength is small compared to the dimensions of an object, the waves suffer reflection. right?

What does this has to do with diffraction? and what equations can I use to model diffraction? (Equations or reference would be fine)

Born2bwire
Gold Member

UTD is only valid in cases where the wavelengths are much smaller than the feature size of the scatterer. The highest frequency estimation is geometric optics which is just straight ray optics. UTD is a better approximation as it adds in the diffraction of the waves. I can't remember how to do diffraction from cylinders. If you are still doing SBR solver then you can just mesh the cylinder and ignore the diffraction effects. Most of the more important diffraction effects come from edges. I can't remember what we did for cylinders or cylindrical trenches. When I needed to model the diffraction I just used a full wave solution provided by Balanis but that's a rather impractical solution for a general solver.

The problem is I want to model human shadowing effects and as I read a human is approximated by a perfectly conducting cylinder.

I guess the key to this is to learn how to model the diffraction by a perfectly conducting cylinder. I have no knowledge of anything regarding GTD or UTD.

Born2bwire
Gold Member

If you want to see the scattering of an infinitely long PEC cylinder, then you should find an exact solution in Balanis I think. The problem is that the solution is the summation over an infinite series and you may have to run the sums to a very large number for the solution to converge if you are doing a high frequency scattering.

I don't know how to do it using UTD, I've only done code for the scattering by a wedge. When I did cylinders, my cylinders were on the order of the wavelength of the incident field so I used a full-wave solution.

Hi all,

After I posted my question here, I read this book "Introduction to Uniform Geometrical Theory" of Diffraction" by McNamara, Pistorius and Malherbe, specifically chapter 8.

I noticed that in all the equations and derivations of the diffraction by a cylinder, the authors assumed an observation point in the shadow region and continued accordingly.

I'm using Ray Tracing to predict EM propagation. So basically there isn't a single observation point. I'm dealing only with rays and then sum the contribution of all rays at different points.

How can I determine the length of the creeping part of the ray without the need of specifying an observation point? In other words how can I know where to emerge the ray from the surface of a cylinder?

Born2bwire
Gold Member

In the end you do have an observation point. The SBR is meant as a means to calculate the currents excited on your scatterers. Unless you are interested in the currents excited on a receiving antenna, you will generally use these currents to solve for the scattered electric field and find a measurement of interest, like the RCS, at specific point. The UTD will not give you the excited currents, so it is more or less useless for getting information for the intermediary step of getting the excited currents. So the only other pieces of information, the fields, always have an associated observation point for you to solve for.

In the end, the easiest thing to do is to assume only line of sight diffraction. Wherever you wish to place your observation points will be the point to which you will want to solve the UTD equations. If the line of sight from the diffracting surface and the observation point is blocked by another scatterer, then the first order approximation would be to ignore this diffraction. Otherwise, you will need to find all the diffracted rays that strike the scatterer and then proceed with your SBR, finding the excited currents and reflections off the scatterer from the diffracted rays. This will be much more complicated since you will have to search out for all possibe reflections.

So basically, because you cannot get directly get the excited currents that create the diffracted field, it is not a first-order contributor. You can only get currents from any reflections. So restrict yourself to only calculating the diffracted fields at the points of observation that the user will specify that they wish to know the calculated fields, RCS, etc. If you want to go further, you will have to think of a way to treat the diffracting surface as another ray source. You will have to send out rays to the observation point and to any other scattering surfaes to find the reflections and second-order excited currents. One exception may be if the user is interested in the signal received by an antenna. Then, what you could do is have the user note that you want to measure the diffracted fields at that antenna and then you could calculate the excited currents from the diffracted fields on the antenna only.

This is really all a matter of how far you want to take this I believe.