Electronics > Metrology

A stable batt powered 1mA current source for measrmnt of 10k standard resistors

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When measure a 10k standard resistor, the easiest way might be by means of a 8.5-digit multimeter. However, it suffers from inaccuracy and often instability against time and temperature. The current source of many such meters is 0.1mA making the output voltage of only 1V, 10% of the standard test current for 10k.

In a metrology sense for resistance measurement, a comparison method such as substitution is necessary instead of direct measurement.
While professional metrologies often use DCC(Direct Current Comparator resistance bridge) for this purpose owning to its super resolution, linearity and short term stability, the best thing that an amateur can find to serve the similar purpose is the 3458A 8.5-digit multimeter with 0.01ppm resolution, 0.01ppm noise, 0.02ppm differential linearity, and 0.05ppm+0.05ppm integral linearity/transfer in ten minutes in its 10V range.
In order to take advantage of this 10V range of this meter(or alike), we need an good 1mA current source to convert 10k to 10V.

1mA is the standard test current for 10k standard resistor.
When this 1mA current pass the resistor through the current terminals, a 10V appears on the voltage terminals that can be measured by a 3458A,.

Why measure a 10k in such precision?
 - To compare two 10k standard resistors to 0.1ppm level or better by a 2*4 switch/scanner.
 - To calibrate/transfer a standard(could be borrowed) to another.
 - To compare 8 or 16 10k resistors to 0.1ppm level by a 16*4 switch/scanner.
 - To measure the temperature coefficient of standard resistors(alpha and beta) accurately.
 - To re-measure the temperature coefficient of standard resistors to see how they drifted.
 - To determine the long time drift of 10 resistors in a relatively short period.

Part one, the principle of current source method

The principle: I/V method

This is the fundamental way of measure a resistor by Ohms-law:
R = V / I
In order to get a good result, the V and I should be equally good or better because any imperfection in the reading of V or I will directly affect the calculation of R.
That's is to say, if the numerator or the denominator changes by 1ppm, the result of a monomial equation will change 1ppm as well.

The principle: I/V substitution technique

However, we can use the substitute technique, a discipline widely used in the metrology fields.
While in the old days substitution was done manually, they only substitute once or twice(probably 10 times in extreme). Modern switches and scanners allow multiple substitutions more easily.
In the diagram I only draw one-wire substitution for simplicity, but in reality a 4-wire(4-pole) switch will be used.
The good things about substitution technique, it not only tends to cancel errors like leakage or contact, but it abolishes the requirements for accurate current source or even
Of course the requirement for current source is the short term stability(and low noise), that is a much easier task to achieve without the accuracy requirement.
We do have requirement for the voltmeter not for accuracy but for low noise and good linearity instead.
Let's assume that the current I remains the same during the measurement(if not, any variation will contribute to the resulting uncertainty), and the voltage reading for Rs and Rx are Vs and Vx.
Rx = (Rx-Rs) + Rs = (Vx-Vs)/I + Rs
Because Rx is another standard resistor, the value should be very close to nominal thus close to Rs, the first term((Vx-Vs)/I) is therefore much smaller than Rs, this will require much less for how accurate the current source and how accurate the voltage reading.
Though (Vx-Vs) is very small, it is the difference of two very large quality, any variation of Vx and Vs affects the result significantly. We need a DMM of both low noise and high linearity like 3458A to achieve the expect result. Put it in another word, we rely on precision of the DMM rather than accuracy.

The principle: I/V substitution plus voltage comparison technique

In this configuration, we use a 10V voltage standard Vr to step up the reference point of the voltmeter. Since the Vx and Vs in the previous configuration are all very close to 10V, the voltage difference between Vs/Vs and 10V is very small, allowing a reasonably good voltmeter or 5.5 digits DMM to measure in 100mV range.
Again, this 10V voltage need not to be accurate but need preciseness(stable and low noise) thus easy for us to make and there is no need to be calibrated.

Let this voltage be Vr, and the measurement of two voltage differences are dVx and dVs
Rx = (dVx-dVs)/I + Rs
(assume no change of Vr during the measurement, if it does, the sensitivity is 100%)
This looks not much change from the previous equation, but this time, dVx or dVs is much smaller than Vx or Vs allowing the lowest range of the DMM to be used. Even some hand-held DMM is capable of resolve 1uV, which equivalent to 0.1ppm resolution in the final result.

4-pole double-throw switch
It furnishes the substitution.
It can be a scanner, Dataproof type say.
It can be a DIY, like mine:
It can be a mechanical, like another one of mine:

The point is: switch quickly and repeatedly.

Sensitivity analysis
Sensitivity refers to the degree that input affects output.
A sensitivity of 10% means that if one of the input or components change 20ppm, the output will change only 2ppm(10% of 20ppm).
Assume that Rs, Rx, Vref are within +-0.01% nominal, I is within +-0.2% nominal, DMM is also 0.2% in its 100mV range. These conditions are not very difficult to met.
Detailed analysis procedure is omitted(partial differential involved) but here are the results:
short term stability and noise of the 1mA current source: 100%
short term stability and noise of the 10V reference: 100%
Accuracy, noise and stability of the DMM: 0.03% (the change of 100ppm on the DMM reading will only affect 0.03ppm to the final result)
Contact and wire resistance of the switch: negligible if < 1 Ohm
Thermal EMF of the switch: 0.1ppm per 1uV
Leakage current of the switch: 0.1ppm per 100pA

Other ways to compare two 10k resistor standards
 -- Modern DCCs. They are very expensive to amateurs.
 -- Old DCC. Like Guildline 9975, I had one, specified as 0.2ppm for comparison on most of the common ranges, but is slow to operate and only compare two 10k in two wire mode.
 -- Kelvin Bridge. Like esi 242D, I had one, specified 0.2ppm for 10k comparison, similar drawbacks as 9975.
 -- Warshawsky Bridge. Like that employed at NIST, I made one with much better sensitivity but no guard, allowing me to compare 10k resistors within 0.1ppm.
 -- Direct measurement of resistors with a 8.5-digit multimeter.
Because the current source is not ideal, often 0.1mA resulting only 1V output, and the linearity etc on 1V range is worse than that of 10V, Some of the DMM and the measurement uncertainty(in parenthesis), assuming 1 year calibrate interval:
3458A(10.5ppm+3ppm, 0.1mA), 8508A(8.0ppm, 0.1mA), 2002(9.8ppm+7.8ppm, 0.096mA), 1281(9.6ppm+5.5ppm, 0.1mA), 6581(8.5ppm+3.1ppm, 1mA), 7081(9.5ppm+?, 1mA), 8081(10.3ppm+5.7ppm?, 1mA)
(Note, the two ppm in parenthesis cannot be simply added together, they should be combined in a Root-Sum-Square summation)
 -- Substitute measurement with a 8.5 digits multimeter(transfer).
Transfer uncertainty(some are estimate): 3458A(--0.5ppm), 8508A(0.5ppm), 2002(1.7ppm), 1281(--), 6581(--), 7081(0.3ppm)
the best uncertainty one can achieve is probably 0.5ppm(Fluke 8508A, with 0.1mA current). Solartron 7081 on the other hand do have a 1mA measurement current and 0.3ppm transfer stability but is too old, difficult to find, and very slow to read.

In summary, we need a good standard resistor to compare the unknown standard resistor. We also need a stable(but may not be accurate) current source and a stable 10V voltage reference(but may not be accurate) to do the comparison, apart from a 4-pole double-throw switch and a DMM.
If this properly, the transfer uncertainty can exceed 0.1ppm with ease.

Part two, design considerations of the 1mA current source

Why use 1mA to test 10k?
 - 1mA over 10k gives 10mW, and 10mW has been the standard test power for most of standard resistors in metrology.
 - 1mA over 10k gives 10V, much larger than 1V, which helps greatly to reduce thermal EMF to an insignificant level.
 - There are many good DMMs(including 3458A), they use 0.1mA in 10k range resulting 1V nominal voltage. Although the power of 0.1mW is low and heat-up effect is minimize, it different than what standard 10k were calibrated. Ideally conditions of calibration and working should be the same.
 - 10V is the usual standard for voltage, easy to compare and measure.

Why battery powered?
 - To eliminate the interference from the main.
 - To eliminate the heat source from the transformer/DC-DC.
 - Float operation, flexible, increase CMRR of the meter
 - It is recommended to battery power Fluke 732B for the comparison with Josephson voltage standard.
 - There would be four lithium cell(18650 type) in series to supply 13.2V - 16.8V, current < 9mA, providing >200 hrs operating time in one charge.
 - There is this paragraph from Datron/Wavetek(later Fluke) 7000 system application note 'A practical approach to maintaining DC reference standards', I quote:

Line power supply
Some types of voltage reference exhibit different output voltages depending on whether they are line or battery powered. This is usually caused by changes to the internal power dissipation for the different operational modes.
Additionally, line powered operation can introduce noise into the measurement system resulting in erroneous values or noisy readings. Where the reference output voltage is influenced by the operational mode, systematic errors may be introduced during the importation process.
The 7000 uses a patented high-isolation DC/DC Converter to reduce common-mode noise to extremely low levels. This means that it can be compared with a Josephson system directly and under line-power with no noise-related problems.
<end of quote>

What are the requirements?
 - 1mA current source, 0.01% tolerance
 - 0.1ppm low frequency rms noise
 - 0.1ppm short term stability in 30 seconds(after warm up)
 - setup time when load change <1ms to within 1ppm of final value
 - battery operated, automatic power off when no load(no power switch)(optional)

Simplified schematics and analysis

It is the very common current sink circuit and there is no need to explain the principle in words. Since it is battery powered, it is a two terminal device that can be regarded as current source as well.

Iout = Is + Ig + Ib
where Iq is the leakage current of Q1, Ib is the opamp Ib, the signs are insignificant
Is = Vs / Rsense
Vs = Vref + Vos
Iout = (Vref-Vos)/Rsense +Ig +Ib
Idealy the current should be Io = Vref/Rsense
Iout/Io = 1 + Vos/Vref + (Ig + Ib)/Io
Therefore, if the variation of Vos is less than 0.05ppm of Vref, and the variation of (Ig+Ib) is less than 0.05ppm of Io in 30 second, we can safely ignore them.
Two things that cannot be easily ignored though, are Vref and Rsense, that any change in values will reflected in the output directly.
I'll probably select 4 Vishay 10k foil resistors in parallel(or two Vishay VHP202Z 4.9995k in parallel) to minimize the temp-co. Although less than 1mW of power dissipation is not a big deal, it raise less than 0.2 degree C and account for 0.1ppm change of TCR = 0.5ppm/K.
Vref on the other hand poses a big unsteady factor at 1ppm/K temp-co and probable 20mW dissipation.

Voltage Reference
 - Should be low noise type. Any noise from Vref will contribute to the noise of the current source.
 - LTZ1000A has the lowest noise but is complex and pricy. The next lowest available is LTC6655.
 - The output of the reference will be used to compare the voltage from the sense resistor directly.
 - The voltage should not be too high as to eat up too much supply and dissipate to much heat, and not too low to minimize other noise from opamp and thermal EMF.
 - LTC6655-2.5V is the final choice, noise is 0.63uVpp or 0.042ppm rms
 - Supply should be regulated to get a better regulation and minimize the dissipation.
 - A heat sink could be necessary.
 - Pre-regulator, HT7136, output is 3.6V, low power LDO.
 - Output capacitor, 3.3uF film type, required for stability.

Current sense resistor
 - The voltage is 2.5V(same as Vref), value is 2.5V/1mA = 2.5k
 - Dissipate at 2.5mW.
 - Very low tempco is required for short time stability, if the temperature varies by 0.2deg C, a temco of 0.5ppm/K result in 0.1ppm variation.
 - Final decision: four 10k Vishay foil resistors in parallel, tempco<0.2ppm/K.

 - Noise less than half of the Vref
 - Temco of Ib < 0.05nA/K(0.05ppm of 1mA)
 - Vos variation < 0.125uV(0.05ppm of 2.5V)
 - Final choice: AD707AH, hermetic

Other considerations
 - Case, aluminium.
 - PCB, universal type for quick prototyping.
 - MOSFET, BS170, N-ch enhanced, TO92 package, small gate leakage and small input capacitance.
 - Binding posts, no requirement for low EMF

Most of the components:

Part three, making of the 1mA current source

Detailed schematics

The making is traight forward. I decide not to show the auto-power-down part because its complex and no good for the performance. I made some changes to that part and may be eliminate the auto power off feature later because it might prolong the setup time.
Thermal conductive silicone pads were added to the Vref and Rsenese.
The tricky part being the testing and pairing the sense resistors for low tempco.

Part four, test

Pass thru this 1mA to a standard resistor(an DIY,very small tempco), use 3458A to measure the sense terminal of the standard resistor.
The result is quite nice with standard deviation of about 0.04ppm for 100 consecutive reading(200 seconds)
The noise/variation of the chart is also contributed by 3458A and the standard resistor.

Next, use a stable 10V(4910-AV) to cancel most of the 10V. The result is very similar, but this time, the reading was done in 0.1V range, and there is no need for the linearity of the DMM.

The 3rd test is about the switch, but switch to nowhere but the same resistor. Most of the readings were in a 0.5ppm bracket, and the averaged difference is not larger than 0.01ppm.

The final test is similar as above but add on a stable 10V. Although reading slowly drift for 1ppm in less than an hour, the averaged difference is only 0.01ppm

Tests has passed.


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