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Measure Small Resistances
Jon Titus, Contributing Writer -- Design News, February 16, 2009
Engineers often must measure small resistances between relay contacts, in power cables, at cable junctions, across connectors, along railway rails and so on. Motor manufacturers, for example, measure the small resistance in motor windings after the motor runs at full load. This value and the temperature-resistance coefficient of the copper wire lets them calculate the motor’s internal temperature.
Common instruments such as DMMs or VOMs measure resistance by forcing a current through an unknown resistance and measuring the voltage across it. Meters convert the measured voltage into — and display — a resistance value. This resistance value includes the resistances in the two instrument-probe wires. That technique will work for a 10KΩ resistor but not for micro- or milli-ohm measurements.
Instead, you make a four-wire measurement, also called a Kelvin resistance measurement, named after William Thompson (Lord Kelvin), who devised the technique. In a four-wire measurement setup, two wires supply current that flows through the unknown resistance while two separate wires connect the resistance to a voltmeter with high-impedance inputs. You might think we compound the lead-resistance problem in this setup, but we actually diminish its effects.
In the circuit diagram, above, the same current appears across any component in the current loop, so we know the current that flows through the device under test (DUT). The separate high-impedance voltmeter draws negligible current through its leads, so negligible voltage drops occur — usually not enough to affect the measurements. By knowing the current and voltage, you can calculate the unknown resistance. Some instruments measure the voltage across a resistance standard and then across a DUT, both in the same current loop. In this case, you don’t need an accurate current measurement, but the current must remain stable during a measurement sequence. The ratio of voltages and the standard resistance provides the unknown resistance value. Removing the current measurement eliminates it as an error source.
You can purchase low-resistance ohmmeters that provide four-wire connections and many precision DMMs come equipped for four-wire measurements, too. To preserve the separate connections of the current source and voltmeter, you should use special Kelvin probes that maintain the separate voltage and current circuits right up to the DUT. Each probe contacts the DUT at two places. The separate connections minimize errors due to stray voltages or resistances at the current-connection points. You place the current connections farther away from the unknown resistance than the voltage connections.
The 10.06.08 Tips from Titus column, “Sample Rates Revisited,” contains a mathematical error that will be corrected in the online version of that column.
Measurement of a low resistance in this cable junction requires a separate current source and voltmeter that minimize errors due to stray voltages or resistances at contact points for the current circuit.
