I have a friend asking for waveguide information, in reference to the proposed PCB layout on this url:
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He asks the following; ....................................................................................... What I need is the time-delay between spark generation and sympathetic spark occurrence, which will depend on spacing D and relative dielectric constant of the board material. Another way to ask is "what is the propagation velocity within such a waveguide?", or "what is the wavelength of the EM energy within such a waveguide?".
There will be a LOWER "cutoff frequency" for such propagation, too. So the sparks will have to be fast. ..................................................................................... I think he's looking for the math to lead him in the right direction. Thanks, Mike
I really don't know what he's trying to do here, (Switching delay for TEA laser discharge perhaps?) but what he has is an open traveling wave structure as it isn't closed like a waveguide. In some circumstances the traveling waves can be confined under the ground planes so that the edges do not enter in significantly, but I'm not sure it's the case in his device.
Generally speaking when you need a 'waveguide' on a PCB tri-plate line is a geometry of choice. There are lots of data and formulas available for such structures and even if he doesn't use one, it still should give him some hints as to propagation velocities and the like. And yes, waveguides have a low frequency cut off (waves switch from propagating to evanescent).
The propagation velocity is determined by "epsilon r" (c0/sqrt(er)). It is in fact a parallel plate transmission line (with oval shape and some shorts). For TEM propagation, there is no cut off frequency (even DC power can be transported with a parallel plate transmission line).
In you situation only the shorts (reflectors?) will impede low frequency energy transport.
I occasionally add an SMA footprint to a multilayer pcb layout, so I can TDR the power planes. I've never observed edge-of-board reflections, presumably because the FR4/copper structure is pretty lossy at the sorts of frequencies involved.
On the board we just finished, I have a 2.5 volt power plane, about
5x7 inches, 12 mils from ground. One test SMA is in the center, one sort of near a corner. So I can TDR and TDT the combo, and see how things propagate and/or reflect inside the planes. I'll do that in a week or so and post if anything interesting shows up.
I agree that the proposed board will have no useful focussing effect.
At wavelengths short enough for there to be optical focussing, the different path lengths will smear the pulse that arrives at the focus, so peak voltage will be down. And for the focus to be localized, the whole structure will have to be many, many wavelengths in size.
Are you really sure about the non-coherence. I was expecting that the path length via one reflection at the ellipse is always the same irrespective of the reflection point on the ellipse. The same principle is/was used in the medical scene to treat kidney stones (acoustical waves in water).
To me this looks better. Now you don't have dielectric loss and dispersion and because of the metallic walls, you don't have any radiation loss. John has doubts about the coherence of the reflection, so probably you should figure this out first.
In fact, the height (B) can be rather large (so above 0.25lambda). The walls perfectly reflect TEM waves. When you have B>0.5lambda, it depends on the coupling from the spark gap to the waveguide and construction of receiving spark gap whether it will work. The transmitting gap must generate TEM waves and the receiving gap must be able to "guide" all the TEM energy into the gap. When B is around
0.25lambda or less, it easier to generate mostly TEM waves and to receive the TEM waves (by the receiving spark gap).
When your complete sphere is many wavelengths large (for example B =
5mm, width 300mm) and the distance between the transmitting and receiving gap is also large, you may remove the "reflecting" shorts. As the received E field via the direct path will be negligible with respect to the E field received by all the single reflection paths.
When the coherence question is demystified, the next point will be the construction of the transmitting spark gap and receiving spark gap.
How you are going to check whether you get a spark at the receiver? What is your actual application for this experiment?
Yes, reflecting (pun!) in the string-loop construction of the ellipse, all reflected paths have the same length; and only the direct path is unsynchronized. But it's still going to be dicey to get a sharp focus of electric field in real life at practical wavelengths. Again, why?
If you're willing to add a distinct receiver to concentrate the field at the second focus - say, two cones that almost touch in the middle, making a small spark gap - then it's a spin on Hertz's experiments. Yes, one should be able to observe a small spark at the receive node, given enough input power at the transmit focus. Given enough power, an arc could be achieved without a concentrator. Waveguides do arc over at kilowatt to megawatt power levels.
A properly constructed spark gap can deliver fast megawatt pulses.
Thank you for your feedback with regards to the application.
I'm not familiar with the details of the pulse required for such laser devices (I am in electronics and antennas). When your goal is to get a high voltage wave front at the edge of the half ellipsoid, the ellipsoid is not the preferred shape. In addition, because the wave fronts do not concentrate as in the full ellipse example, now the direct path may lead to premature discharge initiation.
Because of the Marx generator, I expect that you will use really high voltage.
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