Non-uniform Dielectric Capacitance

Yes. The interposition of a conducting sheet between the layers does not change any current nor disturb any electric field lines, unless the geometry has a LOT of 'fringe field' outside the dielectrics.

That assumes your conductors are evenly spaced (like capacitor normal construction) and the dielectric layers are uniform in thickness.

To first order yes if you ignore any fringe fields.

In a real capacitor the fringe fields may not be negligible and the first configuration sees more electric field leakage through air.

Adding a sheet of aluminium foil to the (almost equipotential) boundary of the dielectric would be the closest approximation to delivering configuration 2 whilst minimising the difference in capacitance.

Try it and see if you can measure the difference on the bench.

ISTR some liquid sensors use a variant of this trick. With a thin layer of inert dielectric applied to the surface to protect the conductors.

I'm looking at an adjustable capacitor made of parallel plates with an adjustable space between them. By adding a dielectric to reduce the size while maintaining the working voltage it makes the adjustment at high capacitance values difficult.

Say e1 is 4 and e2 is air at 1. When the spacing of e2 is just 1/4 that of e1 the capacitance will have been cut in half from the spacing of e2 being zero. I'm looking at the thickness of e1 being 1 mm. That will be difficult to accurately control. Keeping it all air gap will require at least 8 mm of gap and allow much better control over the capacitance, but will need 4 times more plate area.

I suppose that is why they normally use plates that slide between each other.

Sounds tricky, how much capacitance variation do you need? You could fix the plates and slide the dielectric between them to change the C.

George H.

You've received an answer to your question, but just for fun, the calculation of the self capacitance of a flat conducting disk is a challenging exercise...

Yeah, thought of that. Need at least 10x and would like to get 15x. I think the mechanism that drives the separation will need to use a cam to provide small adjustment when the gap is small and more rapid adjustment with a wide gap. So I think the dielectric can still be used.

I didn't know. I thought it was just the parallel plate capacitor formula which I assume ignores the edge effects. Or are you talking about something else like the capacitance of one plate to the rest of the universe? What is the sound of one hand clapping?

Yep, that's self-capacitance. Even the earth has a self capacitance, iirc it's not very much, on the order of a few hundred uF.

Basically the other "plate" is considered to be an imaginary sphere located at infinity...weeeeeoooooh

Interesting - I hadn't seen anybody actually bend the loop like that. I wonder how many cycles it can go through, before metal fatigue causes the loop to fail?

A fourth method I've seen used in quite a few home-built "small transmitting loop" antennas is a trombone capacitor, made with sections of copper tubing that slide in and out of one another, with a sheet of dielectric (e.g. Kapton or Teflon) wound around the inner tube to provide the necessary high-voltage insulation.

Most commonly, there are two outer tubes (bonded to the two ends of the loop segment), and the inner element is a U-shaped piece (sometimes two pieces of tubing soldered/welded to a flat bar, sometimes a single seamless piece of tubing). A motor-driven screw raises and lowers the U-shaped inner element to tune the loop.

Ask Aloha Airlines.

Yep.

Some complain that the standard trombone adds to the loop losses. So I'm thinking of a configuration that is parallel to the loop or even part of the loop rather than the standard trombone configuration. Fused silica can be found in tube form at a good price if copper or aluminum tubes can be found with the right ID and OD.

I was just looking at vacuum variable caps (VVCs) and discovered they work not just like the trombone type, but nested trombones. Because of the very low pressure the spacing between the cylinders is very small and they use multiple concentric cylinders to get high capacitance values.

I had forgotten about Paschen's Law. Low pressure is no different from small spacing. The product of the two determines the breakdown voltage. What is important is that as the product is reduced the breakdown voltage drops until a minimum beyond where it increases dramatically. I expect VVCs work at the low end of the curve where the breakdown voltage goes way up.

Don't bank on the low end of the curve. Breakdown can be induced by things like photo-emission from stray oxides and small particles of miscellaneous gnnnnr. In a hard vacuum with very clean surfaces breakdown can still happen but usually heals - a vacuum cap may arc a few times but will settle down and go on happily thereafter.

If you have an organic dielectric (PTFE) any arc will generate a carbon track - never heals. Some materials (delrin) vaporize, generally don't end up with a carbon track, and seem to heal but delrin is lossy. Ceramics are generally good but an arc in an inert gas or vacuum will deposit metal on your insulator. Then it's not an insulator.

Gasses and a hard vacuum heal.

If they aren't using the low end of Paschen's Law, how do they get such small spacing and high voltages? In the linear region of the curve it is a positive slope, more gas pressure = higher breakdown voltage. You have to get to the very low end of the curve where it goes to a steep negative slope for the vacuum to work for you. Otherwise it is working

Lots of people use the low end of the curve. Just don't expect sunshine and angels and birds chirping all the time. For instance, If your PA can't handle a few milliseconds of high VSWR at exactly the wrong phase while the cap clears itself after a month nap, you might have to adjust your thinking.

The Paschen curve doesn't always follow the 'law':

He's not saying they're not using the low end. He's saying that real materials won't achieve theoretical limits, for various materials-sciencey and atomic-physicsy reasons.

An ordinary 6L6GC vacuum tube will stand off a bit over 1kV, before it arcs over at the base or socket. It doesn't help that the plate (+Vpk) and screen (+400V at most) are right next to each other.

If the plate is moved away through a whole lot of glass, you get a 6BG6. Now the tube can withstand peaks of some 6kV! But only while in cutoff (Ip

It looks to me like there might be a hinge in the base

I saw that too, but I assure you there is no hinge. That would create much too large a resistance to the RF current and spoil the high Q of the antenna. That is why they use tubing. With the skin depth a solid conductor is of no value. A tubular conductor of large diameter is used to provide as low a resistance to the RF signal as possible. Many don't even use soldered joints because of the added resistance might impact the q of the loop and capacitor.