Measuring femto-level differntial capactiance changes

[charliehorse55]

My dad is a semi-retired physicist and he's interested in building a gravitational wave detector. The idea is to measure the differential change in capacitance of 2 capacitors oriented at 90 degrees. Gravity waves push the plates of the capacitor back and forth, causing the voltage on the capacitor to change:

The 0.1 ohm resistor is to filter the low frequency components (mainly drift due to internal leakage).

We're aware that we won't be able to observe anything with an experiment that fits into our cost/complexity budget, but the idea is to develop the technology to understand what would be required for a full-scale system. By creating smaller and smaller test inputs (for ex. mechanically vibrating the capacitor), we can validate how sensitive the instrument is, and how much it would have to improve in order to observe gravitational waves.

Ultimately, the signal will be buried in a lot of noise and require signal processing techniques to extract, so the amplifier needs enough gain to amplify the inherent noise to cover the entire range of the ADC (with room to prevent clipping). So, the lower the system noise, the higher the gain.

Frequency: 50-4kHz
Gain: noise floor (100nV?) -> 1V for a 3V ADC = ~10 million V/V = 140dB?

• Should we use discrete transistors for some sort of input stage, or directly go into a low noise op amp such as LT1128?
• Is there a practical limit to how much gain you can put onto a single op-amp stage? The LT1128 has >75MHz GBW, which would imply for 4kHz a single stage could already have a gain >10,000. Such high value resistors add noise of their own?
• How many stages of amplifier should we use?
• The source impedance here should be the ESR of the supercapacitor, which is extremely low. Could a small signal transformer be used? Do they have any non-linear effects that might destroy a femto-level signal?
• How to implement the 50Hz filter on the input? The required value of R for Fc=50Hz would be something in the ~10 uOhm range, which would get dwarfed by the internal resistance of the caps. A simple RC pole would introduce too much noise through the resistor, right?

I have little-to-no experience with analog design, so I'm kinda jumping into the deep end with this!

[jonpaul]

see the many articles and papers on capacitive sensors, and the basic equations for a 2 plate parallel capacitor.

The best G wave sensors today use special lasers and not Capacitive, and use masses of about 1000..10000 kG.

Jon

[iMo]

The first step would be to estimate a capacitance change when your capacitor's based system will be hit by a typical wave the LIGO/VIRGO/etc detect today.

[Kleinstein]

Capacitive sensor read out is a common thing. It is sensitive, but by far not good enough to detect gravitational waves.  It could still be something to experiment with and look at things like therma expansion, vibrations and seismic signals.

For best sensitivity discrete transistors (JFETs or maybe MOSFETs) have an advantage. The LT1128 and other BJT based parts are not really suitable because of there current noise, that is an issue, unless one operates at rather high frequencies.

[iMo]

The first step would be to estimate a capacitance change when your capacitor's based system will be hit by a typical wave the LIGO/VIRGO/etc detect today.

Wiki:

LIGO has a resolution of less than a ten-thousandth the charge diameter of a proton. 
Equivalently, this is a relative change in distance of approximately one part in 10^21.

PS: my estimation - a 10m*10m large plate capacitor, with 1mm plate distance, X7R dielectric, would change its aprox 3600uF capacitance by 0.0000000036fF..

[charliehorse55]

For best sensitivity discrete transistors (JFETs or maybe MOSFETs) have an advantage. The LT1128 and other BJT based parts are not really suitable because of there current noise, that is an issue, unless one operates at rather high frequencies.

I thought current noise won't be a problem because the source impedance is so low? A 3000F supercapacitor probably has a source impedance in the tens of milliohms, so the <1nA current noise becomes some pV of voltage noise, which would be orders of magnitude less than the 10-100nV voltage noise?

[charliehorse55]

The first step would be to estimate a capacitance change when your capacitor's based system will be hit by a typical wave the LIGO/VIRGO/etc detect today.

It's somewhere around 10^-20 to 10^-24. LIGO measures somewhere around 10^-22

[Dr. Frank]

I'm as well an experimental physicist, so I suggest to find other applications for measurement of small displacements, than Gravitational Waves.

Anyhow, you'd need extremely stable capacitors, so I guess the design of such a capacitor cell would be the most crucial problem in your experiment.
It would as well be necessary to design a capacitance bridge configuration.. very delicate.. somehow reinventing the wheel.


In the 1990ties, at Aachen University (RWTH), a colleague of mine made measurements on 'Magnetostriction and Thermal Expansion of High Temperature Superconductors', for his PhD thesis, using an absolute (direct) capacitive method to detect very small length changes. I don't remember the resolution any more, might have been on the order of nm.

We have used a GENRAD 1620 Bridge first, which allowed to measure 10^-5 pF or 10aF changes.

Later, we bought an automated and more stable electronic bridge, an Andeen-Hagerling AH 2500A, which allowed 0.5aF resolution, much faster and with comfortable GPIB readout. This brand is still available, I guess model 2700 is the most recent one. I propose to buy one of these, used. Maybe it's possible to measure capacitor differences as well.

Frank.

http://www.andeen-hagerling.com/ah2500a.htm

[nimish]

My dad is a semi-retired physicist and he's interested in building a gravitational wave detector. The idea is to measure the differential change in capacitance of 2 capacitors oriented at 90 degrees. Gravity waves push the plates of the capacitor back and forth, causing the voltage on the capacitor to change:
(Attachment Link)
The 0.1 ohm resistor is to filter the low frequency components (mainly drift due to internal leakage).

We're aware that we won't be able to observe anything with an experiment that fits into our cost/complexity budget, but the idea is to develop the technology to understand what would be required for a full-scale system. By creating smaller and smaller test inputs (for ex. mechanically vibrating the capacitor), we can validate how sensitive the instrument is, and how much it would have to improve in order to observe gravitational waves.

Ultimately, the signal will be buried in a lot of noise and require signal processing techniques to extract, so the amplifier needs enough gain to amplify the inherent noise to cover the entire range of the ADC (with room to prevent clipping). So, the lower the system noise, the higher the gain.

Frequency: 50-4kHz
Gain: noise floor (100nV?) -> 1V for a 3V ADC = ~10 million V/V = 140dB?

• Should we use discrete transistors for some sort of input stage, or directly go into a low noise op amp such as LT1128?
• Is there a practical limit to how much gain you can put onto a single op-amp stage? The LT1128 has >75MHz GBW, which would imply for 4kHz a single stage could already have a gain >10,000. Such high value resistors add noise of their own?
• How many stages of amplifier should we use?
• The source impedance here should be the ESR of the supercapacitor, which is extremely low. Could a small signal transformer be used? Do they have any non-linear effects that might destroy a femto-level signal?
• How to implement the 50Hz filter on the input? The required value of R for Fc=50Hz would be something in the ~10 uOhm range, which would get dwarfed by the internal resistance of the caps. A simple RC pole would introduce too much noise through the resistor, right?

I have little-to-no experience with analog design, so I'm kinda jumping into the deep end with this!

10 min on google scholar: https://arxiv.org/abs/2306.08124

money shot on page 12

[shabaz]

Hi,

I know nothing about the such a use-case, so I could be totally wrong, but perhaps it could be worth examining to rule in/out TI's FDC range (e.g. FDC2214), they can operate in a differential mode, and can sense tiny changes with 28 bit resolution, and very low noise, and supports measurements up to 4 ksps, although that rate is if only one channel is measured. There are low-cost evaluation boards for the FDC series.

I played with one for a bit, you can do neat things with it such as create dust sensors and so on, detected by the minute change in capacitance.

Technically it doesn't measure the capacitance directly, instead, it measures the frequency of oscillation of a tank circuit (LC circuit), to 28-bit granularity.

[Doctorandus_P]

Capacitive measurements are quite common. I have a kitchen scale that has a spring (in about the same shape as a load cell) but also two metal plates (approx 60x80mm) and measures the capacitance (and thus distance, and thus spring tension) between the plates. It's a pretty old scale.

Capacitive measurement is also common for calipers (especially the cheapest digital ones) and for rotary encoders. (Up to at least 20 bit)

But for a gravity wave detector? My first guess is that you are at least 5 orders of magnitude off with your estimated femto Farad resolution, and the rest will get swamped by vibration and other noise sources. Or, at least when we're talking about the same sort of thing:

https://en.wikipedia.org/wiki/Gravitational-wave_observatory

These things are between several hundred meters and multiple kilometers long, just to get enough signal to have any hope of being to measure something. Working on this in your backyard is just as bonkers as on "Free energy".

[Conrad Hoffman]

As Dr. Frank points out, the old GR transformer based capacitance bridges are the bomb for this. Download the manual for the 1615 and 1620 to see how they do it. If you have only a single value to measure/compare, you could wind your own transformer for the measurement, but used bridges are under $1k. I've never seen an affordable Andeen bridge for sale, unless $3k is in your budget. They studied the GR bridges for a long time before designing theirs.

[RoGeorge]

I'm curious about the 3000 Farad capacitance, that is a huge value.  How, or what of, are the capacitors made?

[tggzzz]

My dad is a semi-retired physicist and he's interested in building a gravitational wave detector. The idea is to measure the differential change in capacitance of 2 capacitors oriented at 90 degrees. Gravity waves push the plates of the capacitor back and forth, causing the voltage on the capacitor to change:

LIGO sensitivity: At its most sensitive state, LIGO will be able to detect a change in distance between its mirrors 1/10,000th the width of a proton! This is equivalent to measuring the distance to the nearest star (some 4.2 light years away) to an accuracy smaller than the width of a human hair. https://www.ligo.caltech.edu/page/facts

Compare and contrast that with the changes in capacitance you have mentioned.

Compare and contrast those capacitance changes with those due to Brownian motion and shock/vibration.

[iMo]

All that written above make me quite curious how the people at LIGI/VIRGO/etc. provide the measurements actually.
I somehow doubt they just do measure a single pass through the tube with messing with X/Y interference afterwards, perhaps they do a "multiplication" of the path the photons travel through the pipes - like somehow none-planar mirrors where the photons pass the tube length many times actually (ie 1 billion times)..
PS: Well, 1 billion times multiplied by 4km would be too far , so - say 10000x.. 
PS1: the large supercapacitors have to be cooled down to near zero, imho, otherwise the chemical reactions and thermal vibration will mask any measurements. Perhaps SpaceX will be ready to provide a fleet of Starships soon, such you may create a 1000km x 1000km large plate capacitors with 0.1mm plate distance which might indicate ~100fF differences.. 

[RoGeorge]

Don't know the details, but the path is under vacuum, mirrors are cooled and sited on very elaborated active vibration cancelling platforms, plus a lot of measurements averaging and a lot of DSP postprocessing.  It is so elaborated that the first time they detected something, everybody assumed the signal might have been a processing artifact, or maybe an inside joke from other coworkers. 

[rteodor]

Mandatory Veritasium video on the subject:

[The Absurdity of Detecting Gravitational Waves]
https://youtube.com/watch?v=iphcyNWFD10

I just can not see how this can be done even with supercooled capacitors. It is a nice thought experiment thou.

[dietert1]

Don't know much details either but i assume there is huge disturbance from the rotation of our planet in the gravitational field of the sun. Probably they need to suppress this by high pass filtering and only detect gravitational waves at time scales much below an hour or so.
Another problem is that those neutron star/black hole events that generate strong enough gravitational waves are rare and the longer you wait, the more noise events.
So if you detect "once per hour" and you have to wait 5 years, you need about 9 sigma discrimination, in other words a sensitivity much below the expected effect. It's difficult to understand how they excluded some kind of planetary recoil event. A space based confirmation would be interesting.

Regards, Dieter

[RoGeorge]

The detected oscillations at LIGO are in the audio range.

[iMo]

..I somehow doubt they just do measure a single pass through the tube with messing with X/Y interference afterwards, perhaps they do a "multiplication" of the path the photons travel through the pipes - like somehow none-planar mirrors where the photons pass the tube length many times actually (ie 1 billion times)..
PS: Well, 1 billion times multiplied by 4km would be too far , so - say 10000x..  ..

The guy in the Veritasium video above said the laser pulse is at MWatt level. That may indicate they let the pulse bounce many times between the mirrors, thus doing the multiplication effect.. For a single pass they would not need MW pulses..

PS: thus for example with 10000x bounces the pulses travel 80000km in X and Y, the X-Y difference could be roughly 80 fm, compared to the 1 um laser wavelength, for example.

[rteodor]

..I somehow doubt they just do measure a single pass through the tube with messing with X/Y interference afterwards, perhaps they do a "multiplication" of the path the photons travel through the pipes - like somehow none-planar mirrors where the photons pass the tube length many times actually (ie 1 billion times)..
PS: Well, 1 billion times multiplied by 4km would be too far , so - say 10000x..  ..

The guy in the Veritasium video above said the laser pulse is at MWatt level. That may indicate they let the pulse bounce many times between the mirrors, thus doing the multiplication effect.. For a single pass they would not need MW pulses..

PS: thus for example with 10000x bounces the pulses travel 80000km in X and Y, the X-Y difference could be roughly 80 fm, compared to the 1 um laser wavelength, for example.

"The more photons you use the smaller the uncertainty gets, as a fraction of the total."

The way I understood it is that interference is the key. Big power is required because a lot of photons are needed to detect a minuscule interference (a trillionth of a laser wavelength). Put it another way: the amplitude of the signal resulted from the interference detector is very very tiny so the laser amplitude is boosted up to make that minuscule signal larger.

It is an interesting question if multiple passes are used but I have a hunch that they are not. And that is because of the complications in the optics.
Also another question is if there is a detection if the GW comes at 45 degree angle in the plane of the detectors. Would that be a "blind spot" ?

[iMo]

I've just asked ChatGPT4 what would be the maximum number of bounces between two mirrors and I've got, for example - see below. There will be a latency as you have to wait till the pulse arrives after the N-bounces, but you may timestamp them thus the latency cannot be a problem.

PS:
N.of Bounces = ln(SensThr/InitInt)/ln(MirrRefl)

[iMo]

But let us continue with the "thought experiment" - for example what is "almost practically doable within next 50 years" - an 1m x 1m x 1m large multilayer ceramic capacitor, eps_r=500 dielectric, 50nm dielectric and 50nm metal, 10 million layers, all around zero temperature, will give you aprox 1MegaFarad. That may generate 1femtoF X-Y difference (when the stack of layers changes by 1e-21)..

PS: that will not probably work as the relative permittivity of most dielectrics drops with lower temperatures, almost to 1.

[dietert1]

The detected oscillations at LIGO are in the audio range.

On their web page they write: "Consequently, the time they spend orbiting and emitting gravitational waves in LIGO’s detectable range is typically very brief, ranging from a fraction of a second to tens of seconds."
I'd guess they can use signal processing to have something audible for the general public. They describe that procedure, too. Apparently the time between events is also shorter than 5 years, as they observed a dozen events since 2017.

Regards, Dieter

[iMo]

The duration of the "orbiting" takes fraction of seconds to several seconds, but the "frequency of their orbiting" could be hundreds of Hertz easily, imho..