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This question is inspired by some basic questions on resistors I've read here lately.

What's the most accurate/precise technique for measuring the value of a resistor you can think of? What level of precision can be practically achieved? Can you repeatably measure a resistance to +/- 1 micro-ohm? +/- milli-ohm? Can you somehow distinguish between a resistor of a given value and equivalent series resistors? equivalent parallel resistors?

Not to limit answers too much, but I'd be interested in using a microcontroller plus external circuitry to take the measurements. Sorry if this is too vague of a question, I struggled to narrow down the scope. I'm thinking of techniques that incorporate GPIO pins and onboard peripherals like ADC and Analog Comparators.

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    \$\begingroup\$ How much money do you have? \$\endgroup\$ – Connor Wolf Dec 17 '10 at 21:33
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A common accurate method to resistance is the 4-point probe. The issue with a standard resistance measurement, using 2 probes, is that it uses the same contacts to deliver current and measure voltage. This means there is a voltage drop in the probes themselves (as well as contact resistance, but that isn't overcome with a 4-point). To get around this, 4 probes are used: 2 of them deliver current, the other two measure voltage.

This is commonly done using expensive bench-type multimeters, but can also be performed with 2 decent multimeters, a current source, and a pocket calculator. Use the current source to drop a voltage across the resistor in question, and measure this current with one meter. Beware that meters have a burden voltage, and often cannot measure low currents accurately (Dave Jones makes the uCurrent to combat this). With the other meter measure voltage drop across the resistor. Calculate resistance with your calculator with Ohm's Law: R = V/I. This method will be limited by your current meter's burden voltage. You'll find that it will give resistance measurements slightly lower than if you simply measure with 1 meter alone.

The 4-point probe technique is often used to characterize Si wafers, whose resistivity ranges from 10^12 to 10^18 Ωm!

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  • \$\begingroup\$ @tyblu, good answer, I've actually used a 4-wire meter... are you suggesting that this technique can provide 12-18 significant digits of precision (i.e. detect variations in excess of pico-Ohms for small resistances)? \$\endgroup\$ – vicatcu Dec 17 '10 at 19:06
  • \$\begingroup\$ @vicatu, Unfortunately even thermal noise overcomes measurements in that range. The devices used in fab houses don't have wires, but do the measurements right at the 'tips'. They are well-protected against EMI as well. This is the one I used. \$\endgroup\$ – tyblu Dec 17 '10 at 19:10
  • \$\begingroup\$ @tyblu fascinating, the meter looks pretty big (similar to what I've used), have you ever heard of implementations of the components involved in a 4-wire measurement directly 'in circuit' to avoid all the issues associated with probes? \$\endgroup\$ – vicatcu Dec 17 '10 at 19:25
  • \$\begingroup\$ @tyblu yea, i agree nobody would probably ever care about that kind of accuracy, i was just asking out of curiosity what level of accuracy is practically possible. \$\endgroup\$ – vicatcu Dec 17 '10 at 19:32
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    \$\begingroup\$ @vicatcu: There's no environment where you can measure 18 significant digits where the last digit is indeed significant. Just think of keeping temperature constant to within 1/1000th of a degree. It's just not possible. I can see no reason why somebody would want to measure with such accuracy either. You never need more than 4 significant digits. \$\endgroup\$ – stevenvh Jun 22 '11 at 6:54
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In addition to tyblu's answer regarding 4-lead measurement, to get good precision you are going to need excellent temperature stability/reproduction, as coefficients can range from 5 to 250 ppm/K[1], depending on composition.

Furthermore, regarding:

Can you somehow distinguish between a resistor of a given value and equivalent series resistors? equivalent parallel resistors?

Resistors could be considered to have millions (billions, etc) of tiny resistors with in them, in a mix of series and parallel. Defining a "discrete resistor" is fairly arbitrary, based on mechanical properties, not electrical.

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  • \$\begingroup\$ right I wasn't talking about distinguishing them physically/visually, I meant could you somehow tell the differnece indirectly through measurement. \$\endgroup\$ – vicatcu Dec 17 '10 at 19:16
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    \$\begingroup\$ @vicatcu: That's my point, you can't determine it from a two-terminal measurement of a "black-box" Sure, you could CAT scan it... \$\endgroup\$ – Nick T Dec 17 '10 at 19:18
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    \$\begingroup\$ The volt is defined down to about 1nV. Current measurement accuracy depends on the shunt resistor; let's say it's a "6.5 digit" meter that gives 0.5nA precision. This gives a maximum resistance accuracy of 1.5nΩ. Seems kinda low. Thermal noise is 1nV/50Ω over 1Hz bandwidth, which will dominate the measurements. \$\endgroup\$ – tyblu Dec 17 '10 at 20:15
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use of a wheatstone bridge will be able to give you far greater accuracy than four point probes. It is what is used to instrument strain guages where mechanical change in stress and strain results in very low change in resistance. The only way to measure these small changes in resistance is to use a wheatstone bridge.

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    \$\begingroup\$ @shashtastic interesting, can you elaborate on your claim that it is more accurate than a 4-wire measurement? \$\endgroup\$ – vicatcu Dec 19 '10 at 23:29
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    \$\begingroup\$ -1: Wheatstone bridges give very good relative accuracy (and in strain gauges can multiply the signal x 4 if all resistors are strain-dependent), but don't provide any advantage in absolute accuracy unless you know the reference resistors in the bridge. They also provide no help with low-ohm resistance measurements, where connection resistance can be signification. \$\endgroup\$ – Jason S Feb 3 '11 at 1:21
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  • Top accuracy of resistance measurement is limited by Quantum Hall based Resistance Standard (now accepted internatiolally), which is now about 0.02 ppm (part per milion) = 2/100 000 000; = 0.000002%.
  • Good National laboratories, for example NIST, measure customer's special (stability) 1 Ohm and 10 kOhm resistors to 0.05ppm (I have one, calibrated to 0.05ppm :-) ). Stabilty of best Primary Standard Resistors is 0.05 ..0.2ppm/year, when properly handled (not exposed to elevated temperature and thermal/mechanical schock). The price of resistor /measurement is of the order of 1.5k$. To avoid influence of temperature, manganin resistors are kept at 25.00'C temperature bath during measurement.
  • Good quality bridges and 8.5 digit mutimeters allow for measurement with 3..15ppm accuracy (limited by drift with time 3..10ppm/year). But they allow for comparison of resistors with 0.1 ..0.5ppm uncertainty. So having Good Resistor Standard allows for better accuracy. Secondary Standard resistors (eg Rosa Type (made of manganin), old sells for about 80$) have annual drift 0.3 ...3ppm/year, TC -20 ...+20ppm/deg (depending on temperature). Resistors made of Evanohm have lower temp coefficient <3ppm, but have higher EMF to copper.
  • Main limits of accuracy in resistance measurements are due to drift of resistors with time, temperature and humidity. For low value resistors <10 kOhm) four wire connections and methods must be used to avoid voltage drops on connecting wires. Precision Measurement of High value resistors (>1MOhm) requires special guarding circuits to avoid leakage.
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