The following schematic diagrams show the relative effects of 2 ohms total wire resistance on  a RTD circuit:

Clearly, wire resistance is more problematic for low-resistance RTDs . In the RTD circuit, wire resistance counts for 1.96% of the total circuit resistance. we can eliminate this resistance using 4-wire and 3-wire methods.

  • 4 wire RTD :-

A very old electrical measurement technique known as the Kelvin or four-wire method is a practical solution to the problem of wire resistance. Commonly employed to make precise resistance measurements for scientific experiments in laboratory conditions, the four-wire technique uses four wires to connect the resistance under test (in this case, the RTD) to the measuring instrument, which consists of a voltmeter and a precision current source. Two wires carry “excitation” current to the RTD from the current source while the other two wires merely “sense” voltage drop across the RTD resistor element and carry that voltage signal to the voltmeter. RTD resistance is calculated using Ohm’s Law: taking the measured voltage displayed by the voltmeter and dividing that figure by the regulated current value of the current source. A simple 4-wire RTD circuit is shown here for illustration:

Wire resistances are completely inconsequential in this circuit. The two “excitation” wires carrying current to the RTD will drop some voltage along their length, but this voltage drop is only “seen” by the current source and not the voltmeter. The two “sense” wires connecting the voltmeter to the RTD also possess resistance, but they drop negligible voltage because the voltmeter draws so little current through them 3 . Thus, the resistances of the current-carrying wires are of no effect because the voltmeter never senses their voltage drops, and the resistances of the voltmeter’s sensing wires are of no effect because they carry practically zero current.

Note how wire colors (white and red ) indicate which wires are common pairs at the RTD. The RTD is polarity-insensitive because it is nothing more than a resistor, which is why it doesn’t matter which color is positive and which color is negative.

The only disadvantage of the four-wire method is the sheer number of wires necessary. Four wires per RTD can add up to a sizeable wire count when many different RTDs are installed in a process area.

  • 3 wire RTD

A compromise between two-wire and four-wire RTD connections is the three-wire connection, which looks like this:

In a three-wire RTD circuit, voltmeter “A” measures the voltage dropped across the RTD plus the voltage dropped across the bottom current-carrying wire. Voltmeter “B” measures just the voltage dropped across the top current-carrying wire. Assuming both current-carrying wires will have (very nearly) the same resistance, subtracting the indication of voltmeter “B” from the indication given by voltmeter “A” yields the voltage dropped across the RTD:
                                                              V RT D = V meter(A) − V meter(B)
Once again, RTD resistance is calculated from the RTD voltage and the known current source value using Ohm’s Law, just as it is in a 4-wire circuit.

If the resistances of the two current-carrying wires are precisely identical (and this includes the electrical resistance of any connections within those current-carrying paths, such as terminal blocks), the calculated RTD voltage will be the same as the true RTD voltage, and no wire-resistance error will appear. If, however, one of those current-carrying wires happens to exhibit more resistance than the other, the calculated RTD voltage will not be the same as the actual RTD voltage, and a
measurement error will result.

Thus, we see that the three-wire RTD circuit saves us wire cost over a four-wire circuit, but at the “expense” of a potential measurement error. The beauty of the four-wire design was that wire resistances were completely irrelevant: a true determination of RTD voltage (and therefore RTD resistance) could be made regardless of how much resistance each wire had, or even if the wire resistances were different from each other. The error-canceling property of the three-wire circuit,
by contrast, hinges on the assumption that the two current-carrying wires have exactly the same resistance, which may or may not actually be true.

It should be understood that real three-wire RTD instruments do not employ direct-indicating voltmeters as shown in these simplified examples. Actual RTD instruments use either analog or digital “conditioning” circuits to measure the voltage drops and perform the necessary calculations to compensate for wire resistance. The voltmeters shown in the four-wire and three-wire diagrams serve only to illustrate the basic concepts, not to showcase practical instrument designs.

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