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Waveguide 2
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I'm puzzled about the low resistance coating for this application. I thought the skin effect was only a problem on wires. Cavities do not suffer from the skin effect, if anything the current would be pushed to the outside of the cavity conductor.
Is this right, or am I missing something?
Mart
Is this right, or am I missing something?
Mart
Extassi,
sorry for the delay in answering. I missed your question.
The book referred to was "Microwave Circuit Analysis and Amplifier Design" by Samuel Liao (1987).
GraviMan,
cavities do suffer from the skin effect. The waves are inside the cavity/guide and are constrained by the guide walls. Currents flow in the guide walls and therefore dissipate heat. I seem to recall cavities being plated with silver to increase the conductivity in the inner surface layer, increasing the Q of the cavity. Note it is the inner surface which is in contact with the wave. The skin depth is so small that the wave does not penetrate the conductor and get to the outer surface.
sorry for the delay in answering. I missed your question.
The book referred to was "Microwave Circuit Analysis and Amplifier Design" by Samuel Liao (1987).
GraviMan,
cavities do suffer from the skin effect. The waves are inside the cavity/guide and are constrained by the guide walls. Currents flow in the guide walls and therefore dissipate heat. I seem to recall cavities being plated with silver to increase the conductivity in the inner surface layer, increasing the Q of the cavity. Note it is the inner surface which is in contact with the wave. The skin depth is so small that the wave does not penetrate the conductor and get to the outer surface.
"cavities do suffer from the skin effect. The waves are inside the cavity/guide and are constrained by the guide walls...The skin depth is so small that the wave does not penetrate the conductor and get to the outer surface."
Thanks for helping my mechano brain, Logbook! If there was an identical wave approaching, say a flat sheet of copper from the other side, would the skin effect still apply? Basically the em field would no longer have a gradient across the sheet.
For the cavity I was thinking about it being circular cross section. I take it that if it was actually carrying voltage a signal, that current would be forced to the outside? Is there a case for a weak signal in the waveguide, matching at 180', the em field being carried? This would also avoid any radiation, as well as expensive metals!
Mart
Thanks for helping my mechano brain, Logbook! If there was an identical wave approaching, say a flat sheet of copper from the other side, would the skin effect still apply? Basically the em field would no longer have a gradient across the sheet.
For the cavity I was thinking about it being circular cross section. I take it that if it was actually carrying voltage a signal, that current would be forced to the outside? Is there a case for a weak signal in the waveguide, matching at 180', the em field being carried? This would also avoid any radiation, as well as expensive metals!
Mart
The best coating for waveguides is silver plate, with a rhodium flash on top (to keep the underlying silver from oxidizing). The silver should be thick (200 microinches or more), and the rhodium should be thin (this is from memory, but 10-30 microinches maybe).
"The silver should be thick (200 microinches or more)..."
That's about 5um in metrispeak. What's the best way to get this done? Any idea how much this would cost, say per cm^2 (or inch^2)? What sort of field strength can this handle (V/m or teslas)?
Mart
That's about 5um in metrispeak. What's the best way to get this done? Any idea how much this would cost, say per cm^2 (or inch^2)? What sort of field strength can this handle (V/m or teslas)?
Mart
I would imagine the coating is good for a couple tens of killowatts cw in a standard waveguide. What you have to address is that, in a resonator, there can be very large standing waves. Wherever the voltage standing wave is a minimum, the current will be at a maximum. You can figure out how much resistance is in the surface layer, and how much heat that will produce, and decide if that is acceptable.
The depth of penetration into the silver coating will be:
D [meters] = 0.0642 / (f)^1/2 = 1.3 micron or 51 microinches, hence the 200 microinch recommendation.
Conductivity of silver is 6.17X10^7 mho/meter.
"Resistance of a conductor with exponential decrease in current density is exactly the same as though current were uniformly distributed over a depth D"
If it is helpful, the surface resistivity in ohms per square is Rs = 2.52 X 10^-7 * (f)^1/2
OF COURSE, if there are any discontinuities in your resonator, like where a lid meets the cavity body, you had better be exciting a resonator mode that does not put a current maximum there.
The depth of penetration into the silver coating will be:
D [meters] = 0.0642 / (f)^1/2 = 1.3 micron or 51 microinches, hence the 200 microinch recommendation.
Conductivity of silver is 6.17X10^7 mho/meter.
"Resistance of a conductor with exponential decrease in current density is exactly the same as though current were uniformly distributed over a depth D"
If it is helpful, the surface resistivity in ohms per square is Rs = 2.52 X 10^-7 * (f)^1/2
OF COURSE, if there are any discontinuities in your resonator, like where a lid meets the cavity body, you had better be exciting a resonator mode that does not put a current maximum there.
The best way to get it done is the standard way: take your machined resonator to a good plating house. I think you can directly plate silver over copper, but ask them. Also, becarefull of plating berrilium or other alloys of copper as sometimes the cleaning solvents will attack the copper after plating. Cost is pretty reasonable, as I recall. The cost of the silver is negligible.
Beware if the plating wants to first plate with some lossy metal, like nickel!
Beware if the plating wants to first plate with some lossy metal, like nickel!
How does this change if the field is coming from both sides at the same time (ie constant electric field strength)? If a circular waveguide had a voltage directly injected into it would this help with the skin effect?
The concept is that the voltage would induce a current in the outside circumference, while the em wave induced the current in the inside. By chosing the signal voltage the wave would still be totally reflected along the wave (ie no leakage), but the entire thickness of (say) copper would pass the induced current. This would minimise resistance losses...
Mart
The concept is that the voltage would induce a current in the outside circumference, while the em wave induced the current in the inside. By chosing the signal voltage the wave would still be totally reflected along the wave (ie no leakage), but the entire thickness of (say) copper would pass the induced current. This would minimise resistance losses...
Mart
I am having a hard time picturing what you mean. If by circular waveguide you mean a long "pipe", and you want energy on the inside of the pipe, and energy on the outside of the pipe, THEN if the pipe walls are more than around 8+ skin depths thick there will be NO interaction of the fields whatsoever. So energy added on the outside of the pipe will not supplant energy lost on the inside of the pipe.
There are "active resonators" being studied for improved Q. They involve an active semiconductor device making up for resonator losses. I am not sure how practical they are, but there are some papers around. There is a term "vacuum port" used sometimes in RF space communication where you can use reactive energy to improve a receiver's noise figure over what should normally be considered to be the theoretical limit.
Give me a better idea what you are interested in doing, maybe I can help.
There are "active resonators" being studied for improved Q. They involve an active semiconductor device making up for resonator losses. I am not sure how practical they are, but there are some papers around. There is a term "vacuum port" used sometimes in RF space communication where you can use reactive energy to improve a receiver's noise figure over what should normally be considered to be the theoretical limit.
Give me a better idea what you are interested in doing, maybe I can help.
Yeah, wacky stuff like this:
"The main goal of our research is the achievement of substantial squeezing of the vacuum fluctuations associated with a soliton. If the soliton is injected into the probe port of a Mach-Zehnder interferometer and the squeezed vacuum is injected into the vacuum port, sub-shot noise measurements of the phase difference between the two arms of the interferometer can be performed."
So if you want to squeeze some solitons, don't squeeze too hard? This stuff makes my brain ache. Solitons, BTW, are waves that never decay because they keep reforming themselves. Sounds a little like what you are trying to do? Solitons were discovered in nature, from satellite pictures of the oceans. People realized that every once in a while, a wave forms that goes most of the way around the world. Cool huh? You can make a broadband microwave frequency multiplier with solitons, but that is a different story.
"The main goal of our research is the achievement of substantial squeezing of the vacuum fluctuations associated with a soliton. If the soliton is injected into the probe port of a Mach-Zehnder interferometer and the squeezed vacuum is injected into the vacuum port, sub-shot noise measurements of the phase difference between the two arms of the interferometer can be performed."
So if you want to squeeze some solitons, don't squeeze too hard? This stuff makes my brain ache. Solitons, BTW, are waves that never decay because they keep reforming themselves. Sounds a little like what you are trying to do? Solitons were discovered in nature, from satellite pictures of the oceans. People realized that every once in a while, a wave forms that goes most of the way around the world. Cool huh? You can make a broadband microwave frequency multiplier with solitons, but that is a different story.
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