how to calibrate 10A range with 2A reference ?

[elianto]

I have a calibrated KEITHLEY 2001 which I use periodically to benchmark the accuracy of various other instruments, in conjunction with stable voltage and current sources.
Now I need to check the 10A current range of a multimeter but can only go up to the 2001 2A range.
Is there any approach to extend the range of the current that I can check? And what accuracy can I maintain?

[alm]

I'd use a Hamon type arrangement. Take five good quality, low tempco resistors of roughly equal value that can easily handle 2A without excessive heating. Calibrate each of them at 2A by measuring the voltage over them and the current through them (or all of them in series?). This gives you the resistance at 2A. Then put them all in parallel, and put ~10A through this combination. Each resistor is now carrying ~2A, and you can calculate the resistance of this parallel combination, and measure the voltage across this compound shunt to get the actual current.

I'm sure there will be a devil in details like wiring resistance and thermal EMF if the burden voltage is low.

[mzzj]

I'd use a Hamon type arrangement. Take five good quality, low tempco resistors of roughly equal value that can easily handle 2A without excessive heating. Calibrate each of them at 2A by measuring the voltage over them and the current through them (or all of them in series?). This gives you the resistance at 2A. Then put them all in parallel, and put ~10A through this combination. Each resistor is now carrying ~2A, and you can calculate the resistance of this parallel combination, and measure the voltage across this compound shunt to get the actual current.

I'm sure there will be a devil in details like wiring resistance and thermal EMF if the burden voltage is low.

Paralleing low-value resistors seems tricky, current distribution and unexpected voltage losses vs. original 4-wire measurement setup seem to spoil the day in paradise.
On the other hand Keithley 2001 is only about 0.1% accurate on 2A range so paralleing bunch of resistors might work.

Another alternative would be total overkill of shunt resistor that is known or can be assumed to be linear to 0.05% or so between 2A and 10A. Just calibrate it at 2A and use the resistance value to calculate current at 10 amps.
Example of suitable resistors would be metrology-grade standard resistors or large low value resistor that doesn't heat up noticeably during use. To minimize shunt heating select lowest value resistor that still gives enough voltage drop at 2 Amps to measure properly.

Keithley 2001 is good to about 1uV on voltage measurement in short-term, from there we can work out needed minimum resistance. We can measure 4 mV drop on the shunt with approx 0,025% precision or or 4 times better than the 2001 current measurement itself.
20mV @ 10A shunt resistor would minimize heating and still provide enough accuracy at 2A calibration. Now we just have to find 50W 0.002 ohm resistor 
100mV 50A shunt like this https://www.newark.com/empro/ha-50-100/base-mounted-dc-shunt-100mv-50a/dp/08R4301#anchorTechnicalDOCS might be pretty good guess and enough linear between 2A and 10A.

[bdunham7]

I have a calibrated KEITHLEY 2001 which I use periodically to benchmark the accuracy of various other instruments, in conjunction with stable voltage and current sources.
Now I need to check the 10A current range of a multimeter but can only go up to the 2001 2A range.
Is there any approach to extend the range of the current that I can check? And what accuracy can I maintain?

You don't say which multimeter you are checking, but in most cases if you simply check it at 0 and 2A and it is accurate, it should be pretty accurate over the entire scale.  That's not an ideal method, but it is more than likely good enough and also likely better than any ad-hoc methods.  If you need an exact 10A stimulus to set the calibration constant, then that is a different matter.  If you really need 10A and have a suitable PSU, you need a precision shunt with a specified tolerance and tempco, those will determine how accurately you can measure the 10A. 

[donlisms]

I agree that Hamon would be helpful, but I think you can do it even more... Hamon-y.  Keep in mind that his approach was the ratio of N resistors in series to those same resistors in parallel, giving an accurate ratio of N^2.  There are ways to get accurate ratios of N, but they seem a little harder. 

The error in the ratio is based on the square of the sum of the individual errors wrt the average, but you don't need to measure all that.  If you know the resistors are within 1% of their average, you know the ratio is within 0.01%. And 0.1% resistors, if you can manage or select them, gives you a ratio at 1ppm.  That's the magic.

So a very accurate resistive ratio of 4 or 9, with some good high-res voltage measurements across them, giving current ratios, seems helpful somehow.

IOW, I think you can avoid having to know the individual resistor values, other than their relative values to get some idea of the ratio accuracy.  Use them in series, use them in parallel, and use the ratio.  This also avoids having to know the absolute voltages, because you're only interested in their ratio.  Everything pretty much lands on the accuracy of the reference current measurement. 

[GigaJoe]

would it be better to have \ build a resistor shunt and measure voltage drop , then calculate a current flow

it seems build something with liquid cooling , pass approx 10A , then measure resistance \ temco if it warm up, would give you much better then 0.1%

[Berni]

Yep if you really want to test it at 10A then get a high quality shunt resistor. Calibrate it at 2A then raise the current until the voltage across it is 5 times larger so the current is then 10A

That's similar to what i did when i needed an accurate 300A of current. Except that shunts become a bit of a problem at currents that high due to the amount of self heating even if you use very very tiny resistance shunts (at what point they make a tiny signal that has tons of thermal EMF issues). So i been using a Danfysik ULTRASTAB flux gate current transducer in place of the shunt. It is basically a "DC current sense transformer" where the magnetic field is sensed in the core, this drives a coil around the core with a feedback loop in such a way that cancels the field out to 0, this makes the ratio of current trough the sense wire and driven coils exactly the turns ratio. Since it works like a null meter it is very accurate. (but is likely only accurate at large currents)

EDIT:
Tho i suppose you could wind 10 turns of wire around a current transducer to 'amplify' your measured current to 100A to where these things work well. But still easier and cheaper to simply get a good shunt resistor.

[mzzj]

Yep if you really want to test it at 10A then get a high quality shunt resistor. Calibrate it at 2A then raise the current until the voltage across it is 5 times larger so the current is then 10A

That's similar to what i did when i needed an accurate 300A of current. Except that shunts become a bit of a problem at currents that high due to the amount of self heating even if you use very very tiny resistance shunts (at what point they make a tiny signal that has tons of thermal EMF issues). So i been using a Danfysik ULTRASTAB flux gate current transducer in place of the shunt. It is basically a "DC current sense transformer" where the magnetic field is sensed in the core, this drives a coil around the core with a feedback loop in such a way that cancels the field out to 0, this makes the ratio of current trough the sense wire and driven coils exactly the turns ratio. Since it works like a null meter it is very accurate. (but is likely only accurate at large currents)

EDIT:
Tho i suppose you could wind 10 turns of wire around a current transducer to 'amplify' your measured current to 100A to where these things work well. But still easier and cheaper to simply get a good shunt resistor.

Ultrastab flux gate transducers  scale remarkably well also to small currents thanks to very large dynamic range and good linearity.
Keithley 2001 is specified only 0.1% accuracy on 2A range. 600A flux gate sensor gives similar accuracy down to 0.6 A if you pay some attention to nulling offsets and keeping the fluxgate sensor orientation fixed during the measurement.
Winding 10 turns gives you 0.1% accuracy down to 0.06A. Even 30 turns around fluxgate wont take more than minute or two and gives you 0.1% accuracy down to 20mA.
 600A ultrastab with 30 turns around the core gives you sensible 20A maximum range and it was pretty easy to resolve currents to  1 uA resolution.

[Berni]

Ultrastab flux gate transducers  scale remarkably well also to small currents thanks to very large dynamic range and good linearity.
Keithley 2001 is specified only 0.1% accuracy on 2A range. 600A flux gate sensor gives similar accuracy down to 0.6 A if you pay some attention to nulling offsets and keeping the fluxgate sensor orientation fixed during the measurement.
Winding 10 turns gives you 0.1% accuracy down to 0.06A. Even 30 turns around fluxgate wont take more than minute or two and gives you 0.1% accuracy down to 20mA.
 600A ultrastab with 30 turns around the core gives you sensible 20A maximum range and it was pretty easy to resolve currents to  1 uA resolution.

Good to know they work well down so low. I have always assumed that they wouldn't work that well for low currents because that tends to be a weak point for magnetic current measurement, also it sounded like miliamps are too tiny for something that that has a measurement range of 600A (that's like working with just the last 2 digits on a 6.5 digit DMM). Maybe il use it for some accurate , super low burden voltage current measurements at lower currents too then.

Zero offset is indeed there weakpoint in these. If the split rail supply to it is not brought up nicely and evenly that puts a bit of a pulse into the output and this magnetizes the core slightly, so every power on can slightly move the zero. Same likely happens if you put current trough the middle of it without it powered on to cancel the magnetic field. I just hit the NULL button on my DMM every time i turn it on to take care of that. Easy enough to do when used on the bench.