How 4-terminal resistors work

In a 4-terminal resistor, an ultra-precise resistor (green) is connected to 4 terminals through small, but unknown, resistors (red).
These unknown resistors are the combination of lead resistance, screw terminal resistance, connection wire resistance, and other sources of errors.
Typical values for these unknown resistors range from 0.01 ohms to 0.2 ohms, and the values are often unstable
The values can change when you loosen or tighten a screw, for example, or if you substitute a longer test lead.

4-terminal resistor
Power Standard Lab's
ultimate resistance standard:
0.09999863 ohms

To use a 4-terminal resistor, we force a current from Terminal 1 to Terminal 2. It's current, so the unknown resistances attached to Terminal 1 and Terminal 2 don't affect the amount of the current. The same number of electrons per second flow through from T1 to T2, regardless of the resistance.

A voltmeter measures the resulting voltage drop across the ultra-precise resistor, measuring through the unknown resistors attached to Terminal 3 and Terminal 4. The voltmeter's input impedance is very, very high compared to the unknown resistors, so the unknown resistors have essentially zero effect (typically less than 0.1 parts-per-million).

So the current flows through the 0.100 ohm resistor, unaffected by the unknown resistors, and we measure the voltage across the 0.100 ohm resistor, unaffected by the unknown resistors.

And that's how a 4-terminal resistor works!

So what errors do we worry about when we're using this type of resistor? We typically measure these errors in parts-per-million, or PPM (one PPM = 0.0001%).

There are five major sources of errors: calibration uncertainty, inductance, temperature, aging, and metal-to-metal contacts.

  1. The United States National Institute of Standards and Technology calibrates the PSL standard resistor to an uncertainty of 0.5 PPM - this sets an absolute floor for measurement uncertainty at PSL
  2. The resistor is typically made of a length of wire wrapped around a spool; in most precision resistors, the direction of wrapping is reversed after half the turns to minimize the inductance. Still, optimal accuracy is achieved at 0 Hertz, or DC. Even at typical power frequencies of a few tens of hertz, the inductance can contribute errors of a few PPM.
  3. The wire is made of a material that has minimal temperature coefficient. Still, a change of a degree or two can contribute errors of tens to hundreds of PPM. It's not just the ambient temperature of the oil bath, either; we have to worry about self-heating when we pass current through the resistor. So temperature control plays a major role
  4. All resistors change values when they age. Most studies show that there is an initial aging during the first few years of a resistor's life (sometimes this is intentionally accelerated with heat), then the resistor settles into a stable value. For this reason, PSL prefers calibration resistors that are at least 25 years old
  5. It's important to consider the galvanic voltages generated by the contact between dissimilar metals. Although the value of the unknown resistors has no effect on the function of the calibration resistor, even a microvolt of galvanic voltage on Terminal 3 or Terminal 4 will affect the reading by 10 PPM at 1 amp. So we're very careful to use the correct types of test lead connectors on these terminals (and on the terminals of the voltmeter).

Questions? Please e-mail Alex McEachern for more information. Or you can telephone...

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