Marquette Seminar Presentation :: Nov. 14th 2008
Below is my presentation for today.
I’ve come down to the end and all I have left to do is write. This presentation gives a good summary of why I am doing it, what I have done, and where I have to stop. The conclusion: non-trivial problems are too complex for analytical solutions, full geometry 3d numerical modeling is needed. If each slot was individually excited this problem would have been finished, but since they are all excited by one source that gives rise to eddy currents to drive the slots they become mutually coupled in a non trivial way.
Either case great learning experience on the Equivalence principle, limits of Born’s first approximation and dyadic Green’s functions. All and all, I’m proud of my work.
All done in Latex with the beamer class.
Sidabras, J.W., “Coupling into Waveguide Evanescent Modes with Applications in Electron Paramagnetic Resonance”, Marquette Microwave Seminar, November 18, 2008.
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November 19th, 2008 at 10:29 pm
I would be careful about making statements that exciting all slots individually would reduce the mutual coupling problem…even if all slots are indivisually excited, it is very difficult to acurately model the coupling. I may be mising a key point baout the fact that the waves are evanescent?
The presentation looks great, I am interested in reading it — but it seems to download as a very small pdf size? Do I need to do something special here?
And beamer class…i recently got to know beamer very well.
Now you just need to write down what’s in this presentation and get your masters already!
November 20th, 2008 at 9:48 am
2.4 MB file size looks right.
So two things are happening. I agree that the mutual coupling problem wouldn’t be reduced but simple first order method of moments or your typical mutual coupling problem would occur. When all the slots are excited by individual sources you can think of the reciprocity theorem and that a current on one excites a voltage on another. Then superposition holds.
When they are all excited from an external source, or excited from eddy-currents arising from an external source’s interaction with the outside of the waveguide it become non-trivial and superposition does not hold exactly true.
Instead the sources are determined _outside_ the problem and are a combination of voltage on one gives rise to current on the other (classic mutual coupling) and that when the two slots are close together the eddy current pattern changes to change the voltages. Now imagine adding two different slot depths and their eddy-current interactions.
At the end of the day, you need a 3d model of your problem.
November 20th, 2008 at 9:50 am
Also I said “mutually coupled in a non-trivial way”. My statement still stands. Individual sources would be a “trivial” mutually coupled problem from you standard antenna books.
November 22nd, 2008 at 7:06 pm
I see what you are saying about the external source, but there isn’t a whole lot of difference between the two cases. I am coming from a traveling wave, antenna array perspective, so I am curious if there is a difference between this and a quasi-static, or low frequency (are you quasi-static in thsi problem?), and the fact that the slots and the waveguide are well below what you’d consider “cutoff”.
For arrays, you can find the full impedance matrix of all of the elements, including self and mutual impedances, by posing the problem as an incident plane wave on an array - as you said, reciprocity holds - but moving your source from the array to an external wave doesn’t change the problem. Even if one slot is excited and the others are all parasitic, your problem is just as complex as if they all were excited. Superposition does hold when finding the impedances, but that’s exactly the point — the problem with all slots excited can be found from a superposition over all of the individual slots excited, including the coupling coefficients, of course.
How is the interaction of two slots close together different from ordinary mutual coupling? If regular mutual coupling assumed regular element currents and voltages (of an isolated element) then the array of elements would be trivial to solve. This is practically never the case. Even a simple array of dipoles, you can do some analytic approximations to estimate array performance, but you cannot just take the isolated dipole performance and assume that performance will hold in an array environment.
Of course, I agree that there really is no way of characterizing the full mutual coupling without full 3D wave solutions, using computational methods.
November 22nd, 2008 at 7:40 pm
Classic Mutual Coupling:
Apply a voltage on one antenna and measure the current on the other. This is done with a source that is not affected by the placement of the second antenna.
Non-trivial Mutual Coupling:
The same voltage on one antenna and measure the current on the other is still valid. Except that now the voltage source on the first is dependent on position. This dependence is not easily characterized except by just doing a full 3d simulation. I did some work with using Faraday’s law but I couldn’t get the boundary right and I think it is going to be beyond the scope of this thesis but I am going to try and continue work post graduation with my adviser.
EDIT: It is important to note that in the classic mutual coupling problem you aren’t changing the source to change your fields but you are changing the current pattern. In this case both the current pattern and the source are changing with position.
These are great questions because it helps me get my thoughts together for writing! Thanks!