The why and how of 4-wire Kelvin sensing: part 2 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.

This part continues the exploration of 4-wire Kelvin sensing. Read Part 1 here.

Q: What did Lord Kelvin do?
A: He realized that using a single combined path for forcing the current and sensing the voltage at the heart of the problem. This “simple” observation made a huge difference in instrumentation.

In a basic diagram of his scheme, there is a battery for the current and four leads, as shown in Figure 1. On the left is a battery, and below are four leads. Current from the battery reaches the resistor X via the two outer leads, while the inner leads are for the independent voltage-measured circuit.

Figure 1. Instead of a single pair of wires for current and voltage, Kelvin split the arrangement into a force pair for current and a sense pair for voltage. (Image: Maxim/Analog Devices).

The current to be measured goes from the battery through the ammeter (A), and there is a voltage drop across the resistor between leads 2 and 3. However, negligible current flows through the voltmeter circuit (V and leads 2 and 3) due to the voltmeter’s very high input impedance, so the voltmeter makes a highly accurate measurement.

Q: Can you show a less stylized, more detailed circuit diagram of the non-Kelvin and Kelvin arrangements?
A: Absolutely! Again, you desire to measure the resistance of interest, R_W, between the conductor’s two connector mating pins. However, the total loop resistance consists of the lead wires, R_L1 and R_L2, so the voltage drop includes all three of these resistances, as seen in Figure 2.

Figure 2. This is a more realistic portrayal of the basic 2-wire arrangement with connectors. (Image: CAMI Research Inc.)

Moving the voltage measurement points out to the endpoints of the mating pins bypasses any voltage drop that may occur in the lead wires, as shown in Figure 3.

Figure 3. This figure shows the physical arrangement when the 2-wire topology is expanded to 4 wires. (Image: CAMI Research Inc.)

Q: Are there any other advantages to 4-wire sensing?
A: Yes, there are. Note that the current flowing through the voltage-measuring circuit of a 4-wire system is extremely small, typically on the order of a microamp or less, and is usually orders of magnitude less than the source current), so there is near-zero voltage drop occurs across these lead wires.

Further, when there is no current flowing through a wire, there is no voltage drop across it, regardless of its length. This means that voltage-sensing lead wires may now be quite long (several meters) without having any negative effect on the measurement. This is useful to support long leads when testing large, multi-branch wire harness assemblies or using a test chamber. (Of course, the use of long leads for the current source is not an issue since the current is confined in a closed loop and does not “dissipate” over the lead-length path).

Q: Any other advantages?
A: The 4-wire arrangement allows the use of test currents well above those that would be tolerated for 2-wire testing. Using higher currents allows stress testing of wiring by driving a current of one amp or more through each conductor.

Q: Why isn’t 4-wire sensing always used?
A: It is not needed in many cases. In situations where the lead-wire resistance is several orders of magnitude less than the unknown resistance, the error caused by the lead wires is often negligible. Again, though, there are many current-sensing setups where the resistance of interest is in an ohm or much less, and often down in the milliohm region.

Figure 4. Due to the widespread use of Kelvin sensing, instruments are available designed for that situation, with independent source and sense connections on the front panel; here, the left-hand pair is for sensing voltage while the right-hand pair is for the current drive. (Image: CAMI Research Inc.)

The physical implementation

Q: How do you physically implement the 4-wire arrangement?
A: You can use a controllable current source and a voltmeter as separate instruments. You can also buy a multimeter designed for the 4-wire arrangement, which has a pair of source (force) connections and a pair of sense connections on the front panel (Figure 4).

Q: What about arranging for 4-wire sensing on a PC board?
A: If you are doing current sensing via an in-line resistor on a PC board, the source connection is already in place since the resistor is inserted in the conductor being measured. Therefore, you only need to add sensor lead “pickoffs” on either side of the resistor. These leads then go to a differential op-amp, which amplifies the sensed voltage by a known gain value, Figure 5.

Figure 5. Implementing the 4-wire arrangement on a PC board requires adding two sense leads across the resistor inserted in the conductor of interest. (Image: Maxim/Analog Devices)

Q: What about where you need to connect to discrete wires or a connection tab?
A: No worries: the problem has been addressed with special “alligator clips” (also known as “crocodile clips” in some places). In conventional-style clips, both halves of the jaw are electrically common and are usually joined at the hinge point. In what are called Kelvin clips, the jaw halves are insulated from each other at the hinge point, only contacting at the tips where they clasp the wire or terminal point (Figure 6).

Figure 6. Kelvin alligator clip ease making paired force and sense connections with one clip. (Image: Calibrators, Inc.)

These Kelvin clips are available with ratings ranging from a few amps to 50 A and wire gauges as large as 10 AWG (Figure 7).

Figure 7. Kelvin alligator-typer clips are available for currents of just a few amps (left) as well as for tens of amps (right). (Image: Adafruit Industries; RS Components Ltd.)

Q: What about sense resistors for PC boards?
A: In many low-current cases, a standard resistor could be used, but the TCR is too high and would yield an inaccurate result. For this reason, specialty sense-resistor vendors offer small resistors with the same appearance and form factor as conventional resistors but with very low-temperature coefficients.

Q: What about sense resistors for higher currents on PC boards?
A: Again, there are special low-tempco resistors that may look like a simple bent piece of metal but are very different. They are precision passive components fabricated using advanced materials and processes, using proprietary alloys with characteristics optimized for this role. They can be used by soldering to the board with a shared connection point on each side for the force and sense lead pair, while some offer separate connections for the contact points (Figure 8).

Figure 8. Specialty higher-current, sub-milliohm sense resistors offer extremely low TCR, typically 50 ppm/°C: the Bourns CSS2H-2512 Series is about 3 x 6 mm and has units up to 6 watts (left) while the 11-watt Bourns CSI4J-4026 devices measure about 7 × 10 mm and have independent source and sense contact points (right). (Image: Bourns, Inc).

Conclusion

A deep understanding of the underlying physics problem when trying to sense small currents and low resistance using a single pair of leads inspired Lord Kelvin to develop the 4-wire source/sense arrangement, which is still ubiquitous. His arrangement overcomes the limitations posed by lead-resistance interference and also allows for other instrumentation possibilities.