Copper Wire Resistors or How to Calibrate that damn Nanovoltmeter

[Echo88]

Hi,

at the moment im working on a selfbuilt DC-nanovolt-amplifier and would like to calibrate it, without having to buy a Keithley 260 Nanovolt Source. Since nanovolt-levels demands no compromise in errors ive thought about building a copperwire-based resistor divider and using a simple current source to get me some nanovolts (later found out the K260 also does it like this, guess there arent much other ways to do it...).
But since copper is such a good conductor one would need an incredible amount of ultra-thin-wire to build the resistor divider (about 117m 0,05mm for 1kR) and theres still the problem of attaching said wire to contacts or spade lugs.
I dont really know if its feasible to build such a, say 1R to 1KR, resistor divider. Maybe it suffices to use a good PWW/foil resistor divider and mount it thermally close coupled to a big ass heatsink?

Please let me hear your opinion on this problem.

K260-Manual: https://archive.org/details/keithley_KEI_260_Instruction Basically a current source and a few cascaded copper wire resistor dividers in a a good shielded case.

PS: Does anyone know where to get affordable mu-metal cases? Maybe there are cheap old OCXOs cases made of mu-metal?

[Vtile]

Resistive wire (manganin etc.) wound on the 1m poles (zig-zag) on plywood attached with small thin coil wire etc loops? Maybe not metrology grade solution.

[Echo88]

Just had the idea to disassemble a normal tiny relay, those contain coils >= 1kR at coil voltages from 12V and above. But how to connect those tiny enamelled wires to a bigger copper wire or spade lug without damaging them? Just crimping them to a spade lug with a big vise seems no good idea, maybe capacitor-welding them?

[Vtile]

Mmm.. What accuracy are you after? I dont get your point of using copper nor coil wire. It does have like you said really high conductivity so it is a poor resistor in that sense.

Why wire divider is there any technical reason? Only advantage I can see (as a newb) is that it does have ideally the same T.C in whole divider, but you will be facing thomson effect with temperature gradients.

The enamel typically burn away in about 300 deg.C while soldering it. Apply a new solder to the tip of iron and poke the enameled wire to that drop. Then clean the irons tip and make the actual solder joint. Which do have the thermoelecrtic characteristics (the solder joint).

[MK]

The idea is to eliminate thermocouple effects.

But I suspect ordinary resistors and terminal reversal, perhaps using latching relays would be more useable, as keeping the two copper resistors at the same temperature becomes a bigger problem.

[EmmanuelFaure]

Only the lower resistor in your voltage divider need to be "nanovolt-grade", for the resistor on the top the sensivity is very low.

Let's take a numerical example : A voltage divider with a one to one million ratio. Rtop = 1 MOhm and Rbottom = 1 Ohm. Nominally, with 1Volt at the input you have 1µV at the output. With a 1µV emf on the LOWER resistor, error at the output = 1µV. With a 1µV emf on the top resistor, error at the output = ~1 picovolt.

Beware of the TCR of pure-copper made resistors : ~4000ppm/°C.

[Vtile]

I understand now.. For joinery might be a good technique to use jewelers saw (with those 'extra' thin blades precius metal even saw dust counts) and saw a small groove the end of solid 1.5mm2 mains wire and grimp the thin wire between. No oxide should be left on the surfaces as copperoxide and copper pair have relatively high thermocouble value IIRC. I wonder would boiling borax do the trick while crimping. I have no idea for the enamel (PU?) cleaning method.

[Echo88]

Thats also a good solution Emmanuel. I was just unsure wether a normal top-resistor in the divider would cause some additional thermal emf-errors. I will now use standard measured PWWs  as the first 1:1k divider and a combination of normal PWW and self wound copper wire 1R resistor.

[Vgkid]

That is how it is implemented in the k262. Info here:
https://www.eevblog.com/forum/testgear/keithley-262-low-thermal-voltage-divider-teardown/

[ap]

You can go low impedance with a copper wire (and you have to if you want to keep the source noise low) by using a current source instead of a voltage source. 1uA x 0.1 ohm = 100nV....
Also, if this is not a lw speed DC amplifier only, you could generate an AC signal, that opens up other options (see AOE).

[Echo88]

I would assume a current source directly interfaced to a 0,1R resistor would introduce error voltages trough the silicon components in the source? Theoretically it should work, but at this little voltage levels and the corresponding measurement times i rather think about everything twice, before trusting any measurement. 
Apart from that i dont have a good current source at hand (need to get my hands on a Keithley 220 or similar in the future) to realize the suggestion, but i have the resistors lying around.
Yes its a DC-0,2Hz bandwidth amplifier. Biggest enemy in this case, after getting noise bandwidth sufficiently low, is thermal drift.
I dont have the AoE-book yet, but i plan to get it.

[BU508A]

I've found the AN159 on the website of LT, it may be helpful for your project:

http://www.linear.com/docs/47682

[Echo88]

I know the AN159; ive built my shielding box according to the suggestion in the AN, but could only use tin plated steel for the outer and inner can, since i couldnt find affordable mu-metal-cases. Also: since theyve built a AC-amplifier they dont need to care about thermal emf in the calibration divider.

[BU508A]

There is this manufacturer in Germany which is producing nice cases for RF applikations. They are all magentic. Not directly a replacement for Mu-metal cases, but they are affordable and will probably do the job. Disadvantage: the website is in German only.

http://www.schubert-gehaeuse.de/prod01.htm

This is their prospect, including a price list:
http://schubert-gehaeuse.de/Prospekte/Prospekt.pdf

[Echo88]

Weissblech = tin plated steel  I already use those cases. But they arent nearly as effective in shielding as mu-metal cases regarding magnetic fields.

[ap]

I would assume a current source directly interfaced to a 0,1R resistor would introduce error voltages trough the silicon components in the source? Theoretically it should work, but at this little voltage levels and the corresponding measurement times i rather think about everything twice, before trusting any measurement. 
Apart from that i dont have a good current source at hand (need to get my hands on a Keithley 220 or similar in the future) to realize the suggestion, but i have the resistors lying around.
Yes its a DC-0,2Hz bandwidth amplifier. Biggest enemy in this case, after getting noise bandwidth sufficiently low, is thermal drift.
I dont have the AoE-book yet, but i plan to get it.

Error voltages through the silicon components? What do you mean? If the circuitry is well done it shoudl work well and you can assess the error sources. Building a 1uA source is not that difficult, you can do it with an opamp and a precision resistor.

[tszaboo]

I would assume a current source directly interfaced to a 0,1R resistor would introduce error voltages trough the silicon components in the source? Theoretically it should work, but at this little voltage levels and the corresponding measurement times i rather think about everything twice, before trusting any measurement. 
Apart from that i dont have a good current source at hand (need to get my hands on a Keithley 220 or similar in the future) to realize the suggestion, but i have the resistors lying around.
Yes its a DC-0,2Hz bandwidth amplifier. Biggest enemy in this case, after getting noise bandwidth sufficiently low, is thermal drift.
I dont have the AoE-book yet, but i plan to get it.

Error voltages through the silicon components? What do you mean? If the circuitry is well done it shoudl work well and you can assess the error sources. Building a 1uA source is not that difficult, you can do it with an opamp and a precision resistor.

He means, that things, like CMRR of opamp or input bias current. These will change the output of your current source. Like, you calibrate your current source with a 100K precision resistor for 1uA, and when you change the resistor for another one, the current will change. Because the common mode voltage on the opemp will be different.
Maybe some of these effects can be avoided, if you are careful.

[coppice]

Beware of the TCR of pure-copper made resistors : ~4000ppm/°C.

This is a killer when doing anything with copper as a resistor. Put differently, that's 0.4% per degree. I experimented with dynamically self calibrating shun sensors, and the shift with temperature is so strong its hard to made the calibration keep up with the changes unless you put the resistors in a very precisely controlled temperature chamber.

In a divider you don't really care about the divider's resistance changing with temperature, as long as you can keep the whole divider at the same temperature. However, keeping even fairly small objects consistent across their entire area to within, say, 0.01C (which would keep the divider within 0.004%) is a challenge.

[Echo88]

Indeed i have to watch out for the TC of the 1R copper resistor i use and a divider would cancel that effect. But i hope through good thermal isolation and concurrent temperature measurement near the divider to see this effect and maybe cancel it sufficiently.
In the end the divider is just used to check if the amplification is correct and maybe to check the bandwidth.
Also my amplifier alone drifts way too much as it is now (need better collector resistors 1,5kR), so i thought about inputting a low frequency square wave (say 20nV 0.01Hz) using the divider instead of a steady voltage, which will avoid drift-errors.

[MK]

use a latching relay to reverse the contacts, .01 Hz could easily be done with relays. look at the HP low ohm meter that uses AC to measure the resistance, I cant remember the part number?

[Echo88]

The 1R resistor will be connected directly via copper wire and copper spade lugs to the nV amplifier. If you add a latching relay between the 1R resistor and the nV amplfier you will inevitably produce massive thermal emf-errors compared to the nV-resolution theoretically (we will see...) possible with just the 1R resistor. Even the best latching relays need to be soldered and then they consist of different metals which will produce easily tens to hundreds of nV.
Theres no problem to produce a .01Hz square wave with a few mV amplitude, i have a DAC-board which is capable of that.

[Echo88]

Short Feedback: The 1R copper resistor solution works beautifully. 1mV at the input of the 1M:1-divider yields reproducible visible 1nV-changes in the 4nVpp-noise-band of the amplifier. 
Following updates on the amplifier in the next weeks:
Compensating the offet-drift by an autozero-function and exchanging the SSM2212 against MAT-03. This should yield even lower noise and better measurement stability.

[Conrad Hoffman]

How much bandwidth can the meter be made to have, even temporarily? I'm thinking it's not difficult to wind ratio transformers with ppm level accuracy, but I don't know if the frequency can be low enough for what you're doing.

[Mickle T.]

I'm missing the schematic diagrams? 

[Echo88]

http://www.analog.com/media/en/technical-documentation/data-sheets/MAT03.pdf The amplifier is basically the one on page 8, but i use 3x SSM2212 instead of the 3x MAT-03 (the modern MAT-02-substitute) because the MAT-03 is obsolete and pricey. Of course i exchanged the supply-voltages +-15V, rotated the red LED and the current source-transistor Q4 became a npn-type, to make the circuit work with the SSM2212 which are dual-npn instead of the MAT-03-dual-pnp. The amplifier is followed by a fourth order Butterworth filter with a cutoff-frequency of 0.2 Hz.

The 1:1Mio divider is the same as in the schematic of Keithley 260 mentioned in the first post: a 1R:1k-divider while the 1R-voltage-drop supplys the second 1R:1k-divider.

@Mr. Hoffman: Since i dont have much experience with signal-transformers, especially in this low frequency range, i avoided this design-possibility. But it may be doable.