What is the Kelvin four-terminal measurement?

Early electricity investigators cleverly solved the challenge of measuring milliohm resistances or microvolt changes in voltage across a resistor over 150 years ago.

Engineers, scientists, and researchers must often reduce imperfections and associated inaccuracies in test and measurement situations. Among the techniques they have used to do this are:

Use better, more accurate components with tighter tolerances or lower temperature coefficients.
Performing one-time or ongoing calibration using comparison with a better standard.
Devising simple yet clever topologies that inherently self-cancel many errors, such as the Wheatstone bridge.
Or develop a “workaround” that transforms the problem into a non-problem or minor problem.

This FAQ will examine one such workaround: using 4-wire sensing rather than 2-wire when measuring very small voltage drops.

Q: What is the problem here?
A: In many applications, it’s essential to measure the amount of current flowing in a conductor. This current can be in the power-supply lead, through a system load, or even from a sensor. While there are several ways to do this, one of the most common and attractive ways is to insert an accurate, known resistor in the current-carrying conductor of interest and measure the voltage drop across the leads. By simple application of Ohm’s Law (I=V/R), the current can be determined, as shown in Figure 1.

Figure 1. Basic electricity: Ohm’s law shows the relationship between voltage V, current I, and resistance R; knowing two of these values allows you to easily determine the value of the third variable. (Image: ThoughtCo/Dotdash Meredith)

Q: Do you always want to measure current as the unknown variable?
A: No, there are times when you want to. instead, you need to measure small resistance values such as contact or solder-joint resistance (often well under an ohm). In this case, the arrangement is the same, but instead, you inject an accurate, known current into the conductor. Again, you measure the voltage drop developed along the current loop, and Ohm’s law solves the problem using R= V/I.

Q: Sounds like there is no problem here — so what is the issue here?
A: The problem is the resistance of the test leads is usually on the order of magnitude of the resistance in the center of the loop. The voltage drops across the resistance, and the test leads add together. In many such situations, the resistance is on the order of a milliohm (mΩ) or less, and the voltage drop is around 100 millivolts (mv) or less. Therefore, the lead resistance has a major effect on the integrity of the measurement.

Q: Can’t you just use test leads of known resistance or measure their resistance and compensate?
A: That’s very hard in practice.

First, measuring the lead resistance is a problem, as a typical benchtop-instrument test lead pair that is 24” in length with banana plugs at both ends will typically have a resistance of about 0.2 Ω.
Second, what is your switch to a new pair of leads?
Third, even that resistance can change. Something as minor as fingerprint oil on the contacts on the lead plugs or at the test instrument can change the resistance value by just a few milliohms, which is enough to significantly increase the overall loop resistance.

Q: Is that all there is to worry about?
A: It’s never that simple in the real world. The other factor is the change in lead resistance due to temperature changes. Copper, the material of standard leads and wiring, has a temperature coefficient (tempco) of resistance (TCR) of about 3900 parts per million (ppm) per degree Celsius (C), or roughly 0.4% per degree C, meaning that for every 1°C rise in temperature, the resistance increases by 0.4%. Do the math, and you’ll see how temperature-induced changes can become a significant problem.

Q: But can’t you factor all of this into account with some sort of calibration scheme?
A: Yes and no. You might be able to do this for wire leads on the test bench, but what about a current-sensing resistor buried on a circuit board? It is heated by ambient air from other components and self-heating from dissipating due to I²R Joule heating. The self-induced tempco error would render any reading nearly meaningless.

Historical context

Q: Is this a new problem?
A: Actually, it’s a very old one. In the mid-1800s, when “electricity” was just beginning to be understood as we know it today, prominent investigators observed this problem. They were puzzled and intrigued by their sometimes confusing findings and strived to understand them.

The relationship between voltage, current, and resistance was not even well understood until 1827. That’s when German physicist, mathematician, and schoolteacher George Ohm described the relationship between electromotive force, current, and resistance, which we know as Ohm’s law, while experimenting with the new electrochemical cell (what we call a battery), developed by Italian scientist Alessandro Volta.

Q: What’s “electromotive force” doing here? What happened to volts?
A: in electricity’s early days, voltage was known as electromotive force (EMF), ppotential difference, and other names, and those terms are still used today. The term “potential difference” reminds engineers that saying the voltage is “x volts” is a meaningless characterization, as voltage can only be defined as the potential difference between two points, not at a single point.

Q: How was the resistance-sensing problem resolved?
A: Lord Kelvin (William Thomson) invented the Kelvin bridge in 1861 by developing what is called four-terminal sensing, also known as Kelvin sensing.

Q: What was Lord Kelvin trying to accomplish?
A: He was attempting to measure current and voltage with accuracy and precision. Remember, in those days, voltmeters and ammeters as we know them did not exist.

Q: How did they make measurements?
A: Before the invention of the voltmeter, the voltage of a battery was measured using an arrangement called a galvanometer, an instrument that detects and measures small electric currents. By connecting a known resistance in series with the galvanometer and the battery, the deflection of the galvanometer could be used to determine the battery’s voltage.

This method allowed for the measurement of voltage before the invention of the voltmeter. Despite the crudeness from our perspective, many of their instruments were amazingly accurate and precise.

Q: In addition to measuring the voltage across very low ohm values to implement current sensing, what are some situations where it is important to measure these values accurately?
A: Milliohm-range measurement can be used to locate bad solder joints, faulty crimps, recessed pins, pin-contact contamination, improper wire gauge, and stress-extruded wire which may fracture prematurely. In some cases, it is not the actual value that matters as much as changes in value.

The next part of this article looks at the problem and solution in more detail.