0.1pF three-terminal capacitor

Hello Terry,

I'd go for a screwdriver. It contains oranges (West) and Vodka (East).

That's why I'd simply measure it with a resonant circuit, checking the oscillator frequency with and without the little cap. Of course, in academic circles that might be considered cheating ;-)

Regards, Joerg

Hello Terry,

Maybe to torment his students a little? We were bombarded with Maxwell for two semesters until it came out of our ears.

That's for sure. Normally you'd have to have a long beard for that though and IIRC he had shaved that off.

Regards, Joerg

Not a pcb in my case, but yes that's a good plan B. If necessary I could project the 0.1pF electrode plug into my chamber, closer to the pickup electrode:

. insulating signal . ring | outside world . 0V __________ \\_ _|_ _ __________ _ . XXXXXX || || || || 0V shield, . XXX_________||_|| ||_||_________ _ 0.125 thick . |___| . __________________________________ _ 0.125 space . XXXXXX . XXXX______________________________ _ 0.125 ring . / | . / |___Connection to SJ(at 0v) . pickup electrode

Apparently at these scales fringing-fields have a *huge* effect. Sloggett, et.al., J Physics A, 19, p2725 (1986), has an accurate formula with fringing-field correction terms (see a.b.s.e.). **

Using the terms in their equation 36, the correction factor is a huge 3.466 times! for disks spaced with a separation of half the disc diameter (considered a fairly-distant separation, enhancing the fringing-field effects). Wow! Actually, I suspect a typo in the equation; so perhaps the correct ratio is 2.447 times. Hmm.

At any rate these big numbers raise my eyebrows, and I'll try to check them out with some bench measurements later today, and Mike here at the Institute will probably look at them with his FEA. Bartlett & Corle, J Physics A, 18, p1337 (1985) and another fellow, J Cooke (1958) have the brute-force numerical calculations that the Sloggett team used to evaluate the various formulas in their paper.

BTW, the 0.1pF capacitor at issue is the feedback element for a sensitive five-axis capacitive position-measuring system.

Good guess, but for those one needs 25kV of insulation. I use old color-TV rectifier tubes, 1B3, etc., IIRC, for capacitance dividers to measuring and servo-control the high rf voltage.

As Win says, the hole will be about 0.7" diameter, a bit under 3x the platc thickness.

To simplify the math enough to even consider an analytic solution, I'd consider "large" to be 100:1 maybe. 3-4 isn't "large" in this context.

John

I beg to differ; the hole will be at least 2 times the thicknes; i am guessing ruoghly 3-4 times the thickness.

That is not too different than my wild guess given earlier.

Do an n-tuple (I just love that word :) of different geometry runs with FEA, and curve-fit :)

I think Joerg underestimates the required caffeine dosage for an analytic solution :)

Can you use, by analogy, Snellings formula for fringing flux? (wild-assed guess)

Cheers Terry

Plan B is to see if you can move the mechanical design to the classic guarded ring construction, which is calculable.

___________|__________ |______________________| __________ _ ___ _ __________ 0v|__________||_||_|_||_||__________|0v / | / |___Connection to SJ(at 0v) / Insulating ring

Might even be a pcb layout......

So: Whiskey in honour of Maxwell, or Vodka for Schelkunoff?

I suspect stabbing oneself with a pencil will be far more fun than this analysis.

Cheers Terry

Does your FEA plot show the electric flux lines emanating from the top plate above the hole passing through the hole, and then splitting, with some ending on the bottom of the middle plate and others, closer to hole centerline, terminating on the bottom plate? This will be the only type of field that would yield zero work for a vertical path integration of the E field from bottom plate to middle plate, and if that is the case, then the equivalent "electrostatic hole" should be smaller than the physical hole in so far as using a simple parallel plate capacitance formulation. I'll look for an analytical solution but it will most likely have to be an infinite series of hyperbolic sines and cosines...I don't see why the bottom plate cannot be reduced to a sheet charge density so that the coupling capacitance between it and the top plate can be defined as the ratio of the integral of bottom plate total sheet charge to V.

My guess would by HV voltage-current converter at frequency....

A synergistic harmony. May lead to dancing badly though.

I'd go for a 100:1 scale model using tinfoil, cardboard and glue. Bugger all use analytically though.

Seriously, I'd do a bunch of parametric sweeps with FEA, and curve-fit. If a curve-fit is good enough for Grover, its good enough for me :)

I am curious why Win needs an analytic approach though - I'm sure its not just masochism. I guess he needs to build a variety of different ones. Still, if anyone here is up to the task, its Win.

Cheers Terry

ditto. I especially liked analysing the 2nd order butterworth filter using maxwells equations. Talk about cracking a nut with a nuke. But afterwards it proved a great example of just why we simplify whenever possible. Yay for electrically small circuits.

That guy would happily chalk up 5-deep nested integrals, from memory. Amazingly smart, yet paid surprisingly little.

LOL :)

Cheers Terry

Hello John

If I understood correctly Win needs to determine the capacitance between drive electrode and opamp input, through the hole. So, why not rig up an oscillator where a small part of the LC capacitance is just that capacitance? Measure the frequency with and without the capacitance connected. The oscillator would need to be a diff version or at least the LC needs to be symmetrical to ground to accommodate the third terminal (GND). Amidon #12 iron powder might be suitable to transfer the LC from symmetrical to non symmetrical.

Or simply feed a signal from a known impedance into the drive electrode, terminate the other side and see what comes through. I think an oscillator would be more accurate.

Regards, Joerg

Maybe plug some dielectric material (Al203 or something) into the intermediate plate hole.

Testing the posting just now - it downloads and displays fine. But it's a two-part post, because of the binary file's length. Perhaps your viewing program didn't successfully download the second part to complete the file? Would you like me to repost it to see if that fixes the problem?

I'm think you'd be interested in the article.

Doesn't that frost you? Adobe is getting as bad as M$oft for generating version incompatibilities :-(

...Jim Thompson

I read it on my computer with Adobe 6.0, so that's not the problem.