It is my opinion that a listening experience deserves whatever I can do to make it as good as possible, i.e. lowest noise , lowest distortion (within reason), lowest order of distortion series, fast slew rate, etc. Sure, one can save money and make something passable, but why waste your time making it? Just buy something already produced in mass production. Mediocre is the right word for it, and for many things, it's just enough for me, but not for audio reproduction.
Scott,
As usual I don't think we are on the same page.
Perhaps we can approach something.
I see that such a unit may have a reference that can swing from -10 to +10 volts. This can be metered to a silly degree of accuracy. This reference feeds a multi-stage resistive divider that ends in a .01 ohm resistor with a peak voltage of 100 pV. Multi-stage is used to avoid any extraordinary parts.
There is a reed relay that swings between the output of the voltage divider and the input ten times per second. (This should keep us above the 1/f limits of the following stages.) This feeds a capacitor. The capacitor feeds a step up transformer. (I think you are right a transformer is the best way to do this.) This should produce a square wave into the circuitry.
Now the transformer to meet the noise spec of less than a .03 ohm resistor must be very low input impedance. As the bandwidth of the gain chain needs only be .005 Hz, the transformer needs an input impedance less than .42 ohms. Now a standard ribbon microphone transformer would step this up to 250-500 ohms. However as we do not need a frequency response much exceeding 20 Hz we could use a special to do .25 to 1000 ohms.
Now at 1000 ohms there are a number of monolithic amplifiers to do much better than the 4 nV/rt Hz. The following tuned amplifier stages would have a center frequency of 10 hz. and a bandwidth of say .01 Hz. These could amplify our error signal to a level high enough for a multiplier also fed by our 10 hz. clock (with appropriate phase compensation to account for the error amplifier chains delay) to provide a vector signal to drive our reference supply.
I think this example of a design would meet the specifications. Of course actually doing it in practice would be non-trivial.
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I was only saying the reading does not bounce back and forth +-4pV it wanders randomly around 0 so 8pV p-p is 1.5 or so pV rms.
And no the transformer needs a DCR in the primary of <.03 Ohms in fact all the total DCR of the switches, cap, and transformer need to be <.03 Ohms. You're confused about how the bandwidth factors in, the nV/rt-Hz is not reduced by BW limiting, 22pV/rt-Hz stays 22pV/rt-Hz as the resolution limit the BW only gives the p-p or rms uncertainty of the reading. As the data sheet says you should be able to measure the thermal noise of .1 Ohms.
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Still not there... As I see the noise is filtered by the gain stage so it won't be a crest factor of 2 for a square wave but should approach 2.8 of a sine wave. I just don't see very narrow band noise having a crest factor higher than that.
Have you ever built an RTA? (I see you edited, so I will also!) I think the issue is actually the noise modulating the signal. I'll try the math on that, give me some time as I suspect it is not a simple problem.
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Jeez Ed, I've only looked at low frequency noise behavior for 40yr. Go get Rice's Bell Labs treatise on the statistics of noise and read it. It's a gaussian process with a standard deviation the time scale of the expected crest factor depends on the BW and time you observe over. 3.1 is a good rule of thumb.
Okay you have paid more attention to the data sheet than I did. If you want to measure the nose of a .1 ohm resistor then the noise needs to be under 41 pV/ rt Hz.
Not really an issue on the transformer you can get the primary down to almost 0. As a ribbon transformer is typically .12 and has a 20 kHz bandwidth, easily doable. So just drop the transformer input impedance down to zero! Err maybe a bit higher...
But I though this started as you wondering how such results could be achieved..
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Your probably envisioning a .005Hz filter centered at 100Hz or whatever but in a chopper amp you would need to get back to baseband and it turns back into a DC to .005 Hz signal.
See we really don't communicate. I don't see a classic chopper amp. I see turning DC into AC and keeping it as AC. When there is a difference between the reference and the signal this will offset the zero crossing and can be detected as a phase change. Using a multiplier at the output against the switching clock allowing for the amplifier chain delay should give polarity. Amplitude is a given.
Then on noise. My question about the RTA was that when you actually build a filter bank version it turns out you can use a 1/2 wave rectifier to get an accurate level. So having looked at the math but not yet worked all of it I can see where you might be.
That's an automated Kelvin Varley with a null galvanometer, that's actually one of the applications for this instrument. I'm assuming this instrument gives as output the baseband DC to .005Hz voltage after offset removal, noise per root Hz would be meaningless otherwise.. There's no way to beat the noise.
We agree you are always going to have noise.
I would have though the output would be from the higher voltage reference, which could then be low pass filtered if required. But I suspect the reference voltage would already be very slow to change anyways.
Then again this is a perception issue. The reference voltage is the output of the system, but is not the output of the error amplifier. (Although driven by it so it could be considered the output....)
Anyways such a system exists, the only real magical part as far as I can tell is the capacitor, everything else requires careful engineering from commodity parts.
Just for kicks if you used an even higher step up transformer you might be able to even use 741s as the op-amp!
Did you ever use the first JBL one? Told it was a deal at under $200,000!
We actually have about one shop fire a year around here! So far good luck in keeping them contained and extinguished before anything really happens.
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