Measuring femto-level differntial capactiance changes

[dietert1]

They write: "LIGO can convert its space-time distortion signals into an audible sound called a chirp so we can all  “hear” the final moments of the lives of two black holes and two neutron stars. While it’s likely that these objects had been orbiting each other for billions of years, LIGO captured the last fraction of a second or tens of seconds of those lifetimes together."
Read here: https://www.ligo.caltech.edu/page/gw-sources

Regards, Dieter

[coppercone2]

3.6 yoctofarad

[KT88]

…and how would we get such a large capacitance in resonance at a high enough frequency?

[iMo]

They write: "LIGO can convert its space-time distortion signals into an audible sound called a chirp so we can all  “hear” the final moments of the lives of two black holes and two neutron stars. While it’s likely that these objects had been orbiting each other for billions of years, LIGO captured the last fraction of a second or tens of seconds of those lifetimes together."
Read here: https://www.ligo.caltech.edu/page/gw-sources

Regards, Dieter

It is my understanding the two objects are orbiting each other slowly, and their angular velocity is low. Then, when they are much closer together, their angular velocity (of the orbiting around a central point of gravity) starts to increase dramatically, with maximum at the moment they join together. In this very moment, lasting that fraction of a second or tens of seconds, their angular velocity is at max (and could be quite high, ie. we have the milliseconds magnetars and quasars), and at this time they generate the max peak of space time distortion, imho. What LIGO can only detect is that very moment. Before that very moment of the joining (the moment==fraction of a second or tens of seconds) and afterwards the LIGO detects nothing..

[dietert1]

On the page i linked they explicitly demonstrate how they use time-lapse to convert the detected signal into audible sound. But yes, there may be events where the last second or fraction of a second is audible without time-lapse.
They use the chirp as a signature, but i didn't find their detection bandwidth. As far as i remember, a table tennis ball coming to rest on the table can also produce kind of a chirp..

Regards, Dieter

[charliehorse55]

Re: Being able to measure gravity waves:

We aren't expecting to be able to measure them with this setup. 10^-20 to 10^-24 is a high bar to reach. We're aiming for something much more realistic with the first iteration of this experiment, say 10^-8 or better (10ppb). The idea is to verify the sensitivity of the instrument in stages, making improvements with each iteration. Eventually, the budget would start getting large and you'd need bigger and bigger grants. LIGO's total budget by the time it first detected gravity waves was probably over a billion dollars.

Re: Measuring capacitance change using resonant frequency:
Hadn't considered this approach, certainly seems to be worth investigating. After all, measuring time is something we can do extremely accurately. The best clocks in the world are 10^-18. That ANDEEN-HAGERLING capacitance bridge mentioned claims a resolution of 0.07ppm, about 10^-7.

Alternatively, we have been looking at directly measuring the differential change in voltage that will appear at the capacitor terminals. Given that the total amount of charge stays the same, the change in voltage should be proportional to the DC voltage across the capacitor times the change in capacitance. For the first prototype, if you could build an analog system with a 1uV noise floor, and a 10V DC bias, you'd already be at 0.1ppm. Add in some DSP techniques, which can improve SNR for a known signal by roughly sqrt(n cycles) and you're approaching 10ppb for the type of signals LIGO sees.

[dietert1]

Electromagnetic force is much stronger than the gravitational force and it's a disadvantage to use electrically charged bodies for sensing gravitational fields. If you read about LIGO, they made a strong effort to isolate their test bodies (=laser mirrors) from terrestrial forces along the sense direction. I'd guess the electrostatic force of the charged capacitor plates onto each other can already ruin the measurement and a solid body like a MLCC won't even be able to sense earth gravitation. There are many steps to take before even mentioning gravitational waves.

Regards, Dieter

[m98]

Obviously, you can't really DIY a gravitational wave detector, especially not (entirely) with capacitive sensing, as the whole principle is based on measuring miniscule distance differences between orthogonal paths over large distances. So km-scale UHV vacuum chambers, multi-ton test masses suspended with advanced vibration isolation, ...

Having worked on/with some interferometers derived from LISA Pathfinder, you definitely could build a heterodyne interferometer with sub-nm resolution for < 10k in material cost, provided you are not after the long-term stability needed for something like gravitational wave detection.

[RoGeorge]

The physics formulas we know, and use in electrical engineering (i.e. the ones related with the measuring capacitors), were all deduced by assuming timespace don't wobble.  I'm not a physicist, but I remember some of the laws of electrostatics, and later electromagnetism, explicitly assume the symmetry and homogeneity of space, for example (sorry for the video, it's an explanation following the ideas in the Feynman's lectures):

Maxwell's equations are intuitive! (Ep: 1 - Power of Gauss's Law)
FloatHeadPhysics
https://www.eevblog.com/forum/chat/fun-for-nerds/msg5130876/#msg5130876

Maxwell's equation explained logically! (Ep 2: Faraday's law powers the world)
FloatHeadPhysics
https://www.eevblog.com/forum/chat/fun-for-nerds/msg5162484/#msg5162484


The really funny question when it comes to detecting gravitational waves is which of the EE formulas will still stand true while stretching the timespace.  I guess not many of them, if any.

[rteodor]

Alternatively, we have been looking at directly measuring the differential change in voltage that will appear at the capacitor terminals. Given that the total amount of charge stays the same, the change in voltage should be proportional to the DC voltage across the capacitor times the change in capacitance. For the first prototype, if you could build an analog system with a 1uV noise floor, and a 10V DC bias, you'd already be at 0.1ppm. Add in some DSP techniques, which can improve SNR for a known signal by roughly sqrt(n cycles) and you're approaching 10ppb for the type of signals LIGO sees.

I guess there would be additional gain from the amplitude of the resonant circuit (assuming this method would be used). If that can be increased to 1 kV for example instead of 10 V there are two orders of magnitude gain right there. Same principle as in LIGO's detector.

Later edit: ... and after seeing RoGeorge's post, assuming that there is capacity change. I do not understand what G waves are changing in terms of 1/sqrt (e_0 * u_0).

[RoGeorge]

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

If you mean they added a frequency shift to make it audible, they probably didn't.  Saying this because of a YT comment I've just read this morning (the comment seems to be coming from somebody who works at LIGO):

@K8URChannel
1 year ago
How are we sure Ligo is detecting gravitational cosmic waves and not an earthquake, a bird strike or a lightning strike somewhere???
1
Reply
Craig Cahillane
·
@craigcahillane1063
1 year ago
Mostly because the gravitational-wave signal has a very distinct signature.  According to numerical relativity simulations, we expect the gravitational-wave emission to increase in frequency and amplitude, producing a chirp effect that increases from very low frequency to around 100 Hz or so (depending on the black hole masses).  An earthquake is certaintly detected, but looks more like a low frequency rumbling that shakes the detectors around.  A bird strike would look like an impulse with some slow decay, same as a lightening strike.  Our black hole merger signals actually increase in frequency and amplitude, until they merger with a huge energy emission in GWs, then the final black hole wobbles as it decays to it's smooth final form.
If we could hear it, the GW signal would probably sound something like this: https://youtube.com/watch?v=ug2bKCG4gZY
Also, we have two detectors that are a thousand miles apart, and if they see the same chirping signal within a couple of milliseconds we can be really, really sure it came from an astrophysical source.

Quoted text is from the comments in this YouTube video:

How does LIGO detect gravitational waves?
Craig Cahillane
https://youtu.be/X7RJHxeCulY

My understanding is the signal produced by LIGO detector goes up to 100Hz or so, and that signal is in sync with the space wobbling, so no frequency shift, but I don't really know any details about how they post-process the detected signal.

[rteodor]

Meanwhile, in a completely unrelated thread:

I was successfully measuring to 0.1pF resolution in the '80s. And with a little effort, it is simple to get to tens of fF (femtofarad, 10^-15 range) resolution. You need to pay special attention to temperature stability of the parts. The below circuit is good to 10fF resolution using TLC555 timers and careful part selection. A modern circuit with crystal control should be able to do even better.

https://www.eevblog.com/forum/metrology/millimeter-range-water-level-sensor/msg5533791/#msg5533791

[dietert1]

..
If you mean they added a frequency shift to make it audible, they probably didn't.  Saying this because of a YT comment I've just read this morning (the comment seems to be coming from somebody who works at LIGO):
..

You shouldn't insist on your mistake. Why don't you just read at the LIGO website (link above)? They explicitly demonstrate that they apply signal processing to make the signal audible. They have a video that contains the original signal and the transposed signal. What you remember as audible is the treated signal. They don't say though whether they always have to do that or not..

Regards, Dieter

[RoGeorge]

Meanwhile, in a completely unrelated thread

Another topic with a very sensitive capacitors-bridge was this one
https://www.eevblog.com/forum/projects/suggestions-for-high-resolution-tiltmeter-(inclinometer)-sensor/msg1565554/#msg1565554

[iMo]

We have to to place beacons on several bodies in our Solar system (ie. Mars, asteroids, moons of Jupiter/Saturn). Beacons with high stability, sending signals we can then evaluate and based on the phase differences we may get better info on the space-time wobbling..

[babysitter]

The planned LISA is a array of 3satellites, intending exactly to realize a extremley-long-baseline interferometer.
The TO setup might, howver, be interesting for seismic research.

BR
Hendi

[iMo]

..How does LIGO detect gravitational waves?
Craig Cahillane
https://youtu.be/X7RJHxeCulY
..

So they indeed use the multiplicative effect of the "roundtrips between the mirrors" - not in form I thought above ("the bouncing N-times between the mirrors") but in form of the Q of the cavity where the Q depends on the mirrors reflectivity (13:21)..

[RoGeorge]

...
If you mean they added a frequency shift to make it audible, they probably didn't.
...

You shouldn't insist on your mistake.
...

Indeed, I was wrong about that one, sorry.  Sometimes they do shift the frequency to make it more audible, even if the detected signal of LIGO is still in the audio range.  Found such an evidence starting from the Caltech link, and searching for other signals on the same YT channel, there is this half minute video where the detected signal vs the audio-enhanced signal are shown side by side:  https://youtube.com/watch?v=JKBBVgR991s

Meanwhile they improved on the lower detectable frequency, too, from 40Hz minimum to only 10Hz now.

The seismic isolation system is built on the initial LIGO piers and support tubes but otherwise is a complete replacement, required to bring the seismic cutoff frequency from 40 Hz (for initial LIGO) to 10 Hz. RMS motions (frequencies less than 10 Hz) are reduced by active servo techniques. The result is to render the seismic noise negligible at all observing frequencies.

Quote from:  https://advancedligo.mit.edu/summary.html

I was curious about the exact frequency range of the signal produced by LIGO, but could find any clear specification, only indirect hints.

So they indeed use the multiplicative effect of the "roundtrips between the mirrors"

You assumed correctly. 

Maybe the Fabry-Perot cavity is not stressed enough in most popular videos about LIGO.  I didn't register an optical cavity was inserted in the LIGO arms, until watching that video.

This is funny, you can drag the mirrors and observe the effect live:  https://ccahilla.github.io/fabryperot.html 

[iMo]

Yep, the "megawatt pulses" mentioned in the above YT video was for me the first indication they have been using a strong multiplicative effect of some kind, otherwise there will no need for such power in a 4km long arm. I have to refresh my math - as what could be the transformation between the Fabry-Perot equations and the simple N*arm_length path multiplicative effect..

That reminds me on the "superregenerative" receivers (I built several in my teen age for my RC models) where in the single transistor stage you may get X million amplification. Similar with "audion" (the "regenerative" receivers)..

PS: having a supercapacitor in X and a superinductor in Y, both creating LC in a superregenerative receiver as a g-wave detector

[RoGeorge]

the "megawatt pulses" mentioned in the above YT video

My understanding is that the MW of power do not enter into the interferometer.  The guy in the Veritasium's video (iphcyNWFD10) is the manager/PR, note how he rants childish and laughs at his own joke.  Instead of answering, he is saying something like "if all contracts [including the space and the wavelength] then we can't detect anything, so it can not work, let's all go home now". 

Anyway, from the other video (X7RJHxeCulY), the one with some math in it, the mentioned power is kW, not MW, and somebody in the comments asked about the power discrepancy, MW vs kW.  IIRC the explanation was that the LASER did shoot a MW power pulse, but the light enters first in the triangular-shaped formation of mirrors on the left, which is supposed to clean the frequency and the amplitude variations in the light coming from the LASER (input cleaner), and after this operation, only a fraction of the power is left to enter into the interferometer.  Note that there is an output beam cleaner, too, not only an input cleaner.

Another aspect is the "MW" might seem huge, but that is not continuous power.  The number is that big because it's a very short pulse.  IIRC the continuous power would be something like 200W for the LASER, not kW, not MW, but there were many upgrades over decades, both in power, in mirrors and in the detected frequency range, so the specs were quite fluid over time.

The LIGO is more elaborated that it appears in either of those YT videos, pretty sure there are a lot of crucial details that are inside knowledge only, and not even mentioned.  I know nothing about optics or physics (I'm an electronist who loves physics as an amateur only), only talking about the detail after searching and browsing a few PDFs last week, might have got it all wrong, so don't take as correct what I was writing.  My impressions are after browsing (brief preview only, I didn't read them in full) files like these:

DC readout experiment in Enhanced LIGO, Fricke et al., arXiv:1110.2815v2
https://arxiv.org/pdf/1110.2815  <---  has a more detailed diagram of the optical path in the LIGO detector

Commissioning the Advanced LIGO L1 Input Mode Cleaner
https://dcc-llo.ligo.org/public/0058/T1100201/004/L1_InputModeCleanerIntegration.pdf  <---  has some numbers and specs in it, to make an idea about the orders of magnitude

These and a few more were some random PDFs that popped in the first page when searching about LIGO, no idea if they were relevant, or still valid today after so many upgrades over the years.

[Doctorandus_P]

We aren't expecting to be able to measure them with this setup. 10^-20 to 10^-24 is a high bar to reach. We're aiming for something much more realistic with the first iteration of this experiment, say 10^-8 or better (10ppb). The idea is to verify the sensitivity of the instrument in stages, making improvements with each iteration.

You want to bridge 12 orders of magnitude through "iterative improvements"?
That is like building a tesla coil when you need a micro volt power supply. And then you already start at the "sensitive" part of the bar and have to extend it.