Signal measurement ~50 pico volts

[Paul Colby]

Hi, my question may be too open ended in which case some help defining it would be helpful. The signal I wish to measure is estimated to be ~50 pico volts in amplitude generated in an HF AT-cut quartz crystal. Basically all the signal power will be at the fundamental mode resonant frequency (lets say 4MHz) of the crystal. I can control the signal source in that I know it's precise frequency and I can turn it off and on. I would like to measure the amplitude and phase of the received signal. Any suggestions would be welcome.

 

[tech99]

You need to know the approximate resistance across which the 50pV will be developed. Then you find your signal power from V^2/R. Then you find the available noise power from the resistor at 300K, which is kTB. Then you adjust B until the signal is stronger than the noise. And it is going to be millihertz.
I suggest using an SDR type of receiver for this.
It is going to be difficult to measure phase. Why do you need such small voltages? The crystal can oscillate at a few volts, which can be displayed directly on a CRO.

 

[Paul Colby]

You need to know the approximate resistance across which the 50pV will be developed. Then you find your signal power from V^2/R

The quartz crystal is a typical At-cut one with a Q-value of 50,000 to 100,000 so it's very low loss. Typical on resonance loss is ~25 ohms maybe less maybe more (I really need to get serious and measure it). I expect the noise will be dominated by the input stage of my amplifier. I also a bit confused by what is best. This is part of a "science" experiment. Crystals have two nearby resonances, the series one is low impedance and the parallel one is very high impedance. My gut, not known for its accuracy, is leaning toward operating at the high impedance or parallel resonance. Typically, the real part of the impedance is what contributes to the noise. I'm not clear is this is still the case here.

I suggest using an SDR type of receiver for this.

I have a RFSpace SDR-IQ which is a nice unit. Sadly it's the USB version and all the software I used to use no longer functions. I'm contemplating just biting the bullet and getting one of the NetSDRs they sell. One with an auxiliary reference input I think would allow me to get phase.

It is going to be difficult to measure phase. Why do you need such small voltages? The crystal can oscillate at a few volts, which can be displayed directly on a CRO.

This is the part we all start laughing at. I've had an interest in radio frequency gravitational waves for some years now. I've looked at many schemes to generate and detect them. By far piezoelectric materials offer the most practical, for some value of practical, means of generation and detection.

Turns out generating a meaningful amount of GW radiation isn't in the cards, however, when the near field or evanescent components are computed they depend as $(kr)^{-5}$. If I have two such crystals 5mm apart this factor is in the $10^{15}$ range. This combined with Q values and such give me the pico volt signal levels in the receiving crystal. Since laboratory measurements of general relativistic effects are rare such a measurement would be of potential interest.

 

[marcusl]

I don't get it. The wavelength of a gravity wave ranges from the size of the object generating it (a black hole) up to the size of the universe, so it is at least kilometers in length. I'm curious about your thinking of detecting one with a mm long detector, at 4 MHz. And isn't a sub-gram mass too small to couple effectively? (Remember that bars of 2 metric tons, cooled to cryogenic temperatures and read out with sensors that could detect movements down to 10^-15 cm, had insufficient sensitivity to detect gravity waves. It is no accident that, LIGO, which succeeded, has arms that are 4 km in length.) And, finally, what's the thinking behind two crystals? I'm not an expert in GW, so maybe my doubts are misplaced, but I am very curious.

 

[Paul Colby]

I don't get it.

With the detection of gravitational waves by LIGO one may conclude a spectrum of GW radiation from DC to daylight and beyond just like EM waves.

And why do you think you'll couple effectively with a sub-gram mass?

Yet another misconception, one you may share with most experts. For time harmonic fields it's not the mass that generates GW is is the spatial components of the stress energy tensor. The source term for EFE is $T_{\mu\nu}$. For weak gravitational fields the field equations are linear. As linear equations it's perfectly valid to consider a single Fourier ($e^{i\omega t}$) component of the field and source. As we know the stress energy is conserved meaning, $\partial_\mu T_{\mu \nu} =0$. For a harmonic component at $\omega$ this conservation relation allows one to compute the time components from a knowledge of just the spatial components. From this it follows that the time components of the stress energy tensor scale like the ratio of the speed of sound in quartz to the speed of light. Hence, the spatial components of the stress energy are many orders of magnitude larger than the time components and, therefore, give rise to the lions share of the metric stress, what little there is at $\omega$. These spatial components also give rise to an enormous (by comparison with the radiation field components) near field stresses.

Now some numbers. For quartz resonator, $T_{n,m} \approx 3.36\times 10^{6} \times Q$ Pa for a 0.5 Amp driving current. Typical Qs are 50000 to 100000 (sometimes more). This stress number is independent of the mass of the crystal. It depends on the stiffness of quartz which for the mode of interest is some 30 GPa. These largish numbers eventually erode the $4.1\times 10^{-43}$ gravitational coupling yielding the pico volt values I estimate for a signal.

Do you think you'll detect something with a mm long detector? And at 4 MHz

The radiation field of a driven crystal is undetectably small. However, for a crystal in the extreme near field of another the metric strain is $10^{15}$ times stronger than one would expect based on a far field calculation. Evanescent fields couple just like freely propagating ones, just over shorter distances. The same principle holds for EM except the near fields are typically smaller.

And, finally, what's the thinking behind two crystals?

One transmit the other receive.

 

[marcusl]

Well, at least something I said agrees with experts!

EDIT: BTW, I think it will be challenging if not impossible to reduce acoustic coupling below the nearly infinitesimal levels you are considering.

 

[Vanadium 50]

This isn't going to work.

First, if you're requiring near fields, that's not radiation. It's just gravity. It's not a test of GR, since in this regime GR and Newton make the same predictions.

Second, 1 pV at 25 ohms = 250000 electrons per second. At 4 MHz that means that you don't even get one signal electron 94% of the time.

Third, because Newton and Coloumb follow the same r dependence, you need to ensure that both crystals are exactly neutral. Otherwise the EM signal drowns out the gravitational. And neutral means neutral. Not a single additional electron on them. Worse, you need to ensure this throughout the crystal - an extra electron in one spot and a hole in the other and now you have a dipole. This condition is only satisfied at T = 0.

 

[Paul Colby]

This isn't going to work.

Hey, most things don't.

First, if you're requiring near fields, that's not radiation. It's just gravity. It's not a test of GR, since in this regime GR and Newton make the same predictions.

Okay, this is what others are saying and it's clearly as wrong for gravity as it is for EM. It's like saying every field at 4MHz is either a radiation field or a rapidly changing static one. Look, were there's a $k=2\pi/\lambda$ there's a wave. $k$ just doesn't appear in a Newtonian argument. Near fields occur because in a plane wave expansion of the field there are evanescent plane wave components. In principle these should be "measurable".

It's completely unclear I have the near fields correctly computed.
https://www.physicsforums.com/threads/are-evanescent-gravitational-waves-measurable.915226/

 

[Vanadium 50]

Okay, this is what others are saying

And there's a reason for that.

 

[Baluncore]

If the Q of the 4 MHz crystal is 100,000 then the bandwidth of the crystal will be 40 Hz.
R is specified as 25 ohms, so for a 0 dB signal to noise ratio, the Johnson noise will be about 50 pV.
The temperature required will be 0.045 Kelvin.
The front-end of the LNA will need to be at a similar temperature.
I do wonder if a quartz crystal in the presence of superconducting metallisation, will maintain it's mechanical properties at that temperature.

 

[nikpav73]

First, I would recommend to go through some literature on low noise signal processing, just get well ground in the ideology there:

The questions asked there are usually something like: can the energy below Boltzmann kT/2 be detected? - Yes, it can be.
And commercial charge sensitive amplifiers routinely demonstrate noise well bellow kT/2. Why? Usually, the signal energy is released in much shorter time than thermal (dissipation) time constant of the system.

Can you detect 2.7K of microwave background using antenna and cabling at 300K? - Yes, as far as they have very losses.
But if you have 10% power loss in the antenna fider cable that will give you extra ~30K of the noise temperature.

Can very low signal be detected, e.g. 50pV - yes, depending on the effective bandwidth or same to say - integration time.

So systems having "low dissipation" (keyword corresponding to some books) can be used to detect very low signals, well below thermal noise (the important parameter being duration-bandwidth and characteristics of thermal= disspative coupling).

Sorry for long wandering around.
Coming to you case - I guess you right regarding parallel mode resonance. I guess you should connect your device to low noise RF MOSFET of capacitance comparable to static capacitance of your crystal. I would consider BF1207 Dual N-channel dual gate MOSFET or similar as the preamplifier. You may even consider several of them in parallel. One may also think of GaAs FET but their low frequency performance is questionable and they much harder to work with.
One may also consider JFETs like Moxtek's or low cost BF862 but at 4MHz they have no advantage over MOSFET (at lower frequency they would be preferred because of lower 1/f noise).

So after some pre-amplifier (you can use e.g. low cost MiniCircuits ZFL1000LN as the second stage after the MOSFET), you can use some high frequency lock-in amplifier, e.g. http://www.thinksrs.com/products/SR844.htm.
If it is too expensive you can down-convert your signal using some simple I/Q mixer to some very low frequency (KHz) and sample it into the PC by some low cost DAQ. The mixer can be get at low cost as eval board. You can use low cost DDS synthesizer eval board to generate the signals.

To put rough estimate, you are starting with the noise level of ~ 0.5...1nV /sqrt(hz) vs 50pV signal, that means that integrating signal for ~100 sec you can get signal/noise ~1. So after averaging for an hour or so you may see clear signal.Important to note - the signal have to stay coherent (no much phase drift).

It is very critical to minimize interconnection of the quartz to mosfet - any extra capacitance, especially lossy one (like common FR-4 PCB material) will be a killer.

 

[Paul Colby]

If the Q of the 4 MHz crystal is...

Yes, that's what it looks like to me as well. The greater question for me is whether my approach to the physics is valid. The knee jerk reaction seems to involve whacking me over the head with rubber chickens. Counter arguments based on power series evaluated well inside their radius of convergence or using coordinate systems in which the material equations of motion I'm using are invalid aren't really counter arguments. On the flip side there is something off on what I'm doing that I need to get clear.

 

[Paul Colby]

So after some pre-amplifier (you can use e.g. low cost MiniCircuits ZFL1000LN as the second stage after the MOSFET),

Wow, thanks for the input. I have a Jfet preamp (unit voltage gain buffer) with a 50 ohm output impedance I built for this purpose and I happen to have 2 ZFL1000LNs on my work bench. I also have some ancient WJ-1 double balanced mixers. The thought was to build a Dickie interferometer where one differences signal on from signal off and averages for a fortnight.

So after averaging for an hour or so you may see clear signal.Important to note - the signal have to stay coherent (no much phase drift).

I also have a rather nice Hp3325B synthesizer with very good frequency control and (I think) phase stability which I was planning to drive the transmit crystal.

For now I need to address my uncertainty with the estimated signal strength. I want to understand what is being looked for before I start trying to measure anything even at the nano volt level.

 

[Paul Colby]

EDIT: BTW, I think it will be challenging if not impossible to reduce acoustic coupling below the nearly infinitesimal levels you are considering.

In any serious experiment this and stray electrical coupling will be very important noise sources to eliminate and or control. All materials are extremely lossy for sound waves at 4MHz. In addition the parts I'm using aren't microphonic at measurable levels, I know I've tried. Also coupling into sound is as inefficient as coupling back out. The same comment applies to stray electromagnetic coupling. For there to be direct coupling then the available signal exterior to the transmit and receive crystals must be many Db above the stuff that gets through both. I'm a long way from making this the primary concern.

 

[Paul Colby]

you can use some high frequency lock-in amplifier, e.g. http://www.thinksrs.com/products/SR844.htm.

Dearly love to have one of these puppies.

 

[Vanadium 50]

The knee jerk reaction seems to involve whacking me over the head with rubber chickens.

Stop it. You have been treated in no way unfairly.

 

[Paul Colby]

Stop it. You have been treated in no way unfairly.

Didn't say I was. Sometimes a good whack is helpful. This was clearly said in jest.

 

[f95toli]

Hi, my question may be too open ended in which case some help defining it would be helpful. The signal I wish to measure is estimated to be ~50 pico volts in amplitude generated in an HF AT-cut quartz crystal.

This can't be done. At 50 ohm this corresponds to -200 dBm; meaning it is about 20 dB lower than what would be practically possible even at GHz frequencies (with cryogenic amplifiers etc) even in a dilution refrigerator at 10mK; at 4 MHz you would be completely swamped by the white noise of even the best amplifier (including quantum limited ones).

Note that cooling the amplifier does not work; the noise temperature of cryogenic LNAs bottom out at about 2K at 15-20K bath temperature (and they mostly work at higher frequencies). Near-quantum limited parametric amplifiers are about one order of magnitude better than this but they only operate at GHz frequencies and would still not be good enough.

Also, try re-calculating 50 pV at 50Ohm into the average number of 4 MHz photons per second...

Hence, it is impossible for technical reasons.

 

[Paul Colby]

Hence, it is impossible for technical reasons.

May depend on how one defines "it". nikpav73 (post #11) outlined something similar to what I had in mind. I completely agree with your assessment, the S/N looks abysmal. The signal is very narrow band and I have the driving source signal. nikpav73 lock in amplifier approach appears to offer some hope. I think you are correct given the specifics crystals I've been discussing. nikpav73 pointed out how critical managing the losses in the "antenna" connections will be. Much depends on how much effort one wishes to expend. The dominant opinion is the effect I'm discussing is just the Cavendish experiment at 4MHz which arguably doesn't warrant much effort. I'm still working on understanding this viewpoint. There is a paper in Phys Rev. D

https://arxiv.org/abs/1410.2334

which I find impressive. The measurement is completely dominated by thermal noise but they measure that noise to like 20 Db S/N. They also achieve astounding Q-values.

 

[Baluncore]

The experiment is possible. Firstly, the synchronous down conversion of the 4 MHz signals to a few hundred hertz or less will make 20 to 24 bit A-D conversion possible. The conversion noise floor will then be below –120 dB, which an FFT will give you a process gain. Power spectrum accumulation over the fortnight might yield another 60 dB or more.
Cooling the front end amplifier will certainly help.

 

[Paul Colby]

The "real" answer is to buy a real kickass lock in amplifier like nikpac73 suggested (and cool and reduce loss, etc..). If I read the Wiki page on lock in amplifiers correctly it's possible (limit of the technology) to extract S/N ~ $10^{-6}$. Judging by the look my wife[1] gave me when I said I need to spend 9k on some equipment so I can win an argument on the internet, that's not in the cards quite yet.

[1] Also has a Ph.D. in physics.

 

[marcusl]

You assumed a peak drive current of 0.5 A into 50 ohms, for a drive power of 6.25 W or 38 dBm. Your expected receive power is -196 dBm, giving a power transfer factor of -234 dB. The mechanical isolation between your crystals must be small compared to this number. Your crystals will couple strongly with the cans touching, as you specify in your other thread. Even separating them by 1 mm (how much does that weaken your signal?) and putting them in a vacuum, I can't see how you can suppress acoustic conduction through the mounting apparatus and electrical leads to order 250 dB (that's isolation of $10^{-25}$). BTW, 6.25 W exceeds manufacturer's maximum ratings for a typical crystal by more than 3 orders of magnitude, so reduce the drive and add another 38 dB to the required isolation. Your lock-in will find a signal--it just won't be gravitational.

EDIT: There's also the problem of providing electrical isolation between drive and receive circuits to the same level, but the mechanical problem makes that one look easy.

 

[f95toli]

The "real" answer is to buy a real kickass lock in amplifier like nikpac73 suggested (and cool and reduce loss, etc..). If I read the Wiki page on lock in amplifiers correctly it's possible (limit of the technology) to extract S/N ~ $10^{-6}$. Judging by the look my wife[1] gave me when I said I need to spend 9k on some equipment so I can win an argument on the internet, that's not in the cards quite yet.

[1] Also has a Ph.D. in physics.

The Sr844 is not great, it is quite noisy ( I have one in my lab but I no longer use it) and is an old design. More modern designs from e.g Zurich Instruments are better (and is what I use) but are more expensive. It will still not get you anywhere near the noise level you would need.

Note also that there are some very practical limits when it comes to integrating out noise. In any real measurement you will in addition to the white noise also have some 1/f^a noise which does NOT average out, you will inevitable also have instrument drift. I sometimes work with single microwave photons (using cryogenic LNAs with noise temperatures of 2-4K) and I know from experience that trying to use long integration(days) to get a clean signal is very tricky. Having a good first stage amplifier is critical even when using look-in amplifiers and other "tricks".

 

[Paul Colby]

You assumed a peak drive current of 0.5 A into 50 ohms,

Just the dissipated heat is very problematic for the toy example. Much depends on the level of effort to be expended. One need not be married to a particular crystal or configuration.

I can't see how you can suppress acoustic conduction through the mounting apparatus and electrical leads to order 250 dB (that's isolation of 10−2510−2510^{-25}).

If one computes the wavelength of sound in steel one gets 1mm which is longer than I would have expect. The loss tangents at these frequencies I would expect to be high but I'm always willing to be surprised. One could arrange the acoustic path to be quite large (and lossy) by proper experiment design.

 

[marcusl]

Spoken like a true theoretician...

 

[Paul Colby]

Spoken like a true theoretician...

Who earned his Ph.D. doing experimental work. I know this stuff is hard.