Capacitive displacement measurement

Yes, I've thought about that. Then I also only need one amp at the measuring end, eliminating sources of error and drift. I hadn't thought of the transformer. Neat!

...or just put it down there in the sub-kelvin zone.

Heavens no, I don't! Thanks!

--Daniel

Use a bifilar winding to make your centre-tapped transformer, and you can get a 1:1 ratio that is accurate and stable to one part in a billion - see "Coaxial AC Bridges" referred to in my other post. The attainable accuracy drops off to the sub-parts per million that Win refers to when you want more than one tap - eleven are popular.

The transformers are surprisingly non-fancy for the performance that they offer.

That book seems to be pretty good; unfortunately my uni library doesn't have it.

--Daniel

I just looked up that thread and found that this was successfully used to measure the relative postion of two STM tips. Are there publications on results obtained with this instrument?

--Daniel

The circuit is actually rather simple when used for ordinary resolution applications. The circuit complexity arises as you add adjustable fixed offsets, e.g., switched transformer taps, allowing you to to reduce the analog-voltage range and add DC gain for sensitivity.

No, no, a ratio transformer has decades of switch settings, giving you 0.1 0.2 -- 0.9 1.0 for one decade, and 0.01 0.02 etc., for the next, 0.001 0.002 etc, and so on. This lets you digitally set the most significant part of the bridge balance, the coarse null in my circuit below. The analog servo voltage covers the fine 5% of the maximum range, strongly overlapping the switched settings for convenience.

For a slightly less-precise version one could use switched resistors for the offset voltages, or a multiplying DAC, etc.

. 5-20pF etc ............. . coax sensor-C coax : shielded box . ,---------x----o--||--o-----x------, : . | : | transresistance . | NULL : SJ- opamp --, . | coarse: ac summer : | : | . +--> ratio ----> G= -1.00 --x--||--' : | . | trans ,-> G= -0.05 : ref-C : 2 stages . | | servo range : 30pF : 10kHz amps . +--> AD734 --' :............ G = 500 . | MPY | . | | | error AD734 | sensitive . | | '-- GAIN -->> OUT . | +/-5V | x1 . '--+------>---- integrator ---->----' x10 . | -90 deg phase x100 . 10kHz, 10Vac

For 20x lower resolution you could further simplify,

. 5-20pF etc ............. . coax sensor-C coax : shielded box . ,----->----o--||--o-----x------, : . | : | transresistance . | : SJ- opamp --, . | null sig : | : | . +----> AD734 ---->------x--||--' : | . | MPY : ref-C : | . | | | : 20pF : 10kHz amp . | | | :............ G = 200 . | | | error AD734 | . | coarse '---+-- integrator DC GAIN -->> OUT . | | x1 500mV / pF . +------------->---- integrator -----' x10 5mV / fF . | -90 deg phase x100 50mV / fF . '-- right position for an STM's coarse approach motor. What did you

I didn't state the case well, it's the STM tip-assembly's position that we're measuring. And for that you do need high resolution, I'd say. One interesting thing, if you switch multiple sensors in both ends of the coax, and program the DACs to the correct offset for each one, you'll have a cool multichannel position readout! . . 5-20pF . coax sensors coax . o====o--||--o=====o . o====o--||--o=====o . o====o--||--o=====o . o====o--||--o=====o coax . ,-o-->o====o--||--o=====o ac DAC ---> G= -1.00 --x--||--' : | . | ,-> G= -0.05 : ref-C : 2 stages . | | servo range : 20pF : 10kHz amps . +--> AD734 --' :............ G = 500 . | MPY | . | | | error AD734 | . | | '-- GAIN -->> OUT . | | x1 10V / pF . +----------->---- integrator --->---' x10 100mV / fF . | -90 deg phase x100 1V / fF . '-- 10kHz, 10Vac

It's advisable to switch both ends of the coax, rather than leave a drive signal on the unused sensors, to avoid crosstalk.

Then get them to buy it ...

Oops, good point. What's the physics?

You could drive the ends of a diff capacitor from mdacs outputting programmable, opposite-phase sinewaves, and then the center-electrode signal would just have to null.

John

Or how about optical? A linear-scale quadrature encoder fed by fiberoptic cables would be nice... a few 125u glass fibers won't conduct much heat. It would be fun to design the interpolating electronics, but I'm pretty sure you can just buy everything you'd need.

John

It might have been mentioned in the fine print.

So the fact that there were publications might have been mentioned in the fine print of -- what?

--Daniel

Couldn't that one be replaced by a synchronous rectifier using CMOS switches? And besides, assuming any reasonable hourly wage for an engineer or scientist, winding that multi-tapped transformer is more painful than $50 worth of multipliers.

I think I'm going to look at a solution as suggested by Fred Bloggs, maybe with a switchable tap at the transformer. I've got a differential cap, so things are a bit nicer. Is there anything I have to look out for when doing the transformer, or will any little ol' pot core do? Absolute precision isn't important.

--Daniel

I don't even want to start listing the reasons why I'm utterly appalled at the mere idea of doing that.

--Daniel

Sounds reasonable to me. Four fibers, a pair of Moiré gratings, a little electronics, tons of signal.

John

How about this: drive the differential capacitor ends with programmable-amplitude, opposite-phase sinewaves, such as to null the signal induced into the center plate. So the gain of the sense path doesn't matter much any more.

Make the pair of sinewave drives from a single 16-bit current-steering dac with dual outputs, with a sinewave reference input. Just walk the dac codes up and down to get phase detector null. No ADC, no nasty multipliers, very low sensitivity to strays, near absolute longterm stability.

John

Wow, what the hell are the first 30 pages about?

John

Yeah, but then you've got a digital soul underneath that macho analogue exterior. ;)

This is sort of an inside-out version of the voltage-sensing method, but its balance is only as good as the DACs, whereas the transformer method is as good as the transformer. For a bifilar winding, that's probably 4 orders of magnitude better, as long as the transformer is down in the cryostat. Your version would have the advantage of providing digitization along with the nulling, but will need an auxiliary null detector.(*) You still need some phase sensitive detection function in there somewhere. I assume you're thinking of using a couple of comparators and an XOR to get the up/down decision.

I think this measurement could be done amazingly accurately, e.g. with one of the slightly-heated-JFET type buffers we were discussing a few weeks back. You could use a second transformer in the Dewar to do the subtraction, then run a cable out to something like an LT1028. The balanced AC bridge subtracts off the background, ideally leaving only small residual scale errors and not offsets. Putting the second transformer in pretty well eliminates problems with crosstalk between phases, which will otherwise cause a null shift.

The multipliers would work on the background-subtracted signal. They don't have to be linear--analog switches would work fine, so you don't have to put up with the linearity errors of your average multiplier chip.

Getting good position accuracy would require high amplitude stability in the oscillator, which your nulling method doesn't require (which is nice). Moving the null position electrically doesn't preserve the mechanical symmetry, though, so it won't by itself give you the sort of stability you expect in a normal nulling measurement.

You could use the AC nulling digitizer idea instead of the multiplier/filter/digitizer sequence. That combination would get us both the high stability and the amplitude insensitivity. (Sounds like it would be a nice measurement by the time we were done.)

It was mainly the proposal to use a TIA that I was ki-yiyying about. The main thing is to use a differential mechanical setup with high symmetry, and not to draw any current from the capacitive tap.

Cheers,

Phil Hobbs

(*) I built something vaguely like that for my thesis project back in the bronze age--it was a phase digitizer using a varactor/diff amp phase shifter plus a successive approximation register with an extra flipflop for positive vs negative half-cycle. The calibrator was about 10x more complicated than the digitizer--it was two synthesizers with divide-by-360 counters, one of which was a pulse swallower so I could walk their relative phases around in 1-degree steps. Getting those steps accurate took a lot of isolation amplifiers and metal shields to keep the two phases from talking to each other.

You forgot that his experiment is in an 8-T field. Unless you're suggesting a second cryostat?

John Perry

I'm electronically promiscuous; I'll design anything.

John

Flux capacit.......?

martin