Resistance calibration
Resistance is the quantity tied directly to the quantum Hall effect, which is why a standard resistor kept in a bath can stay within a few ppm for years. In the field, the connection method and temperature decide the result.
Instruments and typical accuracy
| Instrument | Typical range | Typical accuracy | Where it is used |
|---|---|---|---|
| Standard resistor (1 Ω to 100 MΩ) | Fixed values | A few ppm per year when well kept | Reference in calibration labs |
| Decade resistance box | 1 mΩ to 100 MΩ in steps | 0.01 to 0.1 % | Simulating sensors and checking meters |
| 6½ digit multimeter, ohms | 10 Ω to 100 MΩ | About 0.001 to 0.01 % of reading on mid ranges | Bench measurement |
| Resistance bridge or DCC bridge | Ratio measurements | 0.1 to 1 ppm of ratio | Calibrating standard resistors and thermometry |
| Micro-ohmmeter | 1 µΩ to 10 kΩ | 0.05 to 1 % | Contacts, welds, bonding |
| Insulation resistance tester | 1 MΩ to over 1 TΩ | 2 to 5 % | Cables, motors, transformers |
High resistance and low resistance both demand special techniques. The accuracy figures are typical ranges to help you compare instruments. Always use the specification of the instrument in front of you.
Reference standards and traceability
- Quantum Hall effect. The resistance h/e² (the von Klitzing constant, 25 812.807 Ω; exact in the SI since 2019) is the primary resistance standard.
- Standard resistors. Oil-filled or air-sealed resistors of 1 Ω, 100 Ω, 10 kΩ and others are compared against quantum Hall systems.
- Scaling. Bridges transfer from a decade of resistance to the next by ratio, with uncertainties of a fraction of a ppm.
- Quality system. ISO/IEC 17025, with scope listing resistance values and bridges or meters.
How it is calibrated
Typical procedure
- Stabilise the unit and the reference in the same temperature, and note the standard resistor bath temperature.
- Connect 4-wire (Kelvin) for resistances below about 10 kΩ, and shield and guard for high values.
- Use low-power measurement so the resistor does not self-heat.
- Reverse the current or use offset compensation to remove thermal EMF.
- Measure the value, correct for temperature, and compare with the specification.
- Check several points across each range, including near the upper end.
Where it goes wrong
- 2-wire connections. Contact and lead resistance add tens of milliohms: use 4-wire.
- Self-heating. Power dissipated in the resistor changes its value, especially for low-resistance parts.
- Thermal EMF. Microvolts of offset matter at low current: reverse the current.
- Leakage on high values. Humidity and dirt create parallel paths that make a 1 GΩ resistor read low.
- Wrong temperature. A 25 ppm/°C resistor changes 125 ppm with 5 °C.
What goes in the uncertainty budget
- Reference standard uncertainty and drift.
- Temperature of the resistor and its coefficient.
- Lead and contact resistance for 2-wire connections.
- Self-heating and power coefficient.
- Thermal EMF, leakage and the resolution of the meter.
Combine the contributions as in the uncertainty budget calculator, then decide pass or fail with a guard band as explained on the calculators page.
Calculators
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