# Four-wire measurement

The four-wire measurement , in the measurement of electrical resistance with a four-wire connection used when management and terminal resistors can falsify the measurement. With the four-wire measuring arrangement, a known electric current flows through the resistor via two of the lines . The voltage drop across the resistor is tapped at high resistance via two additional lines and measured with a voltmeter ; the resistance to be measured is calculated from this according to Ohm's law . The same principle applies to current measurement using a low-resistance shunt ; Here the unknown amperage is determined by a known resistance by means of the falling voltage . Two-wire measurement: The voltage is not measured across the resistor , but rather across the sum of the resistances or at the power source.${\ displaystyle R_ {t}}$  Four-wire measurement: the voltage across the resistor alone is measured .${\ displaystyle R_ {t}}$ The four-wire measurement was invented by William Thomson, 1st Baron Kelvin , and implemented in 1861 in the form of a Thomson bridge . This is why the type of contact required for four-wire measurement is also called Kelvin contact .

## Basics

If the current through the voltmeter is negligibly small with the four-wire measurement, which is fulfilled to a good approximation by the very large and ideally infinitely high internal resistance of the voltmeter

${\ displaystyle I_ {U} \ ll I \ qquad \ qquad \ qquad}$ (no noticeable measurement deviation due to current branching ),

and if, furthermore, the voltage loss in the measuring lines is negligibly small

${\ displaystyle 2 \ I_ {U} \ R _ {\ mathrm {Ltg}} \ ll I \ R_ {t} \ qquad}$ (no noticeable measurement deviation due to voltage division),

the resistance value results from

${\ displaystyle R_ {t} = U / I \.}$ A supply from a current source instead of a voltage source is recommended because the current is then independent of and and therefore only needs to be set or measured once. ${\ displaystyle I}$ ${\ displaystyle R_ {t}}$ ${\ displaystyle R _ {\ mathrm {Ltg}}}$ The line resistances include the resistances of the supply lines and the screw or plug connectors .

## scope of application

The four-wire measurement is mainly used when measuring small resistances when the parasitic resistances of supply lines and contact points are no longer negligibly small compared to the resistance to be measured. Examples in which the four-wire measurement is required are:

• In the case of current measuring resistors, the contact resistance can be greater than the nominal value of the resistance; In addition, the contact resistance is sometimes difficult to determine or subject to fluctuations that can hardly be estimated. A mathematical correction is not possible under these circumstances.
• In the case of resistance thermometers in industrial temperature measuring devices with copper lines outdoors, the temperature influence is considerable; this is indistinguishable from changes in the measurement object when measuring with two conductors.${\ displaystyle R _ {\ mathrm {Ltg}}}$ ${\ displaystyle R_ {t}}$ Measurement deviations that can occur despite four-wire measurement are primarily caused by thermal voltages as a result of temperature differences between the connections. However, this can be avoided by adjusting the contact point temperatures or by pairing materials with low thermal voltages.

## Kelvin clamp

An additional terminal is referred to as a Kelvin terminal , which only serves to branch off or supply a relatively small measuring current. It serves as a contacting aid to connect an electrical component for a four-wire measurement. This term is rarely used in measurement technology; rather, the term voltage clamp (as opposed to the current clamp ) is used.

In addition, measuring accessories for four-wire measurements are referred to as Kelvin terminals or (depending on the equipment) Kelvin measuring cables, for example for electrical multimeters , oscilloscopes or inductance measuring devices . Laboratory Kelvin clips are constructed similarly to alligator clips , but the two legs are isolated from each other and have their own connections. Four-pole contact is achieved with a pair of such terminals.

## Three-wire measurement Three-wire measurement with two measuring devices: The voltage drop on the live line can be calculated

In industrial temperature measuring systems, the measuring resistor and the further measuring circuit can be located far away. Then you come to savings in cabling costs with the three-wire connection . The current-carrying lines must have the same resistance (common cable); the contact resistances must be negligibly small.

The following applies to the three-wire measurement

${\ displaystyle I \ cdot R_ {t} = U_ {2} - (U_ {1} -U_ {2}) \.}$ The formation of the difference between two similar voltages from measured values ​​with two independent measuring devices is always uncertain. The difference can, however, be recorded directly with a simple measuring circuit. With the approximations usual for not overdriven and not overloaded operational amplifiers ,

• no noticeable tension between the inputs and
• no noticeable currents in the inputs (but with unhindered input quiescent current),

arises

${\ displaystyle I \ cdot (R _ {\ mathrm {Ltg1}} + R_ {t} + R _ {\ mathrm {Ltg3}}) = 2 \ cdot U_ {5} + U _ {\ mathrm {a}} \ ;. }$ With line 2 operated without current, with and with the same line resistances, this is simplified ${\ displaystyle I \ cdot R _ {\ mathrm {Ltg1}} = U_ {5}}$ ${\ displaystyle I \ cdot R_ {t} = U _ {\ mathrm {a}} \ ;;}$ ${\ displaystyle R _ {\ mathrm {Ltg}}}$ is no longer included. ${\ displaystyle U _ {\ mathrm {a}}}$ The slightly detuned Wheatstone bridge also works to create the difference. If the two resistors on the right in the circuit diagram are the same size, a bridge cross voltage is created${\ displaystyle U_ {q}}$ ${\ displaystyle U _ {\ mathrm {q}} \ sim (R_ {t} + R _ {\ mathrm {Ltg3}}) - (R_ {1} + R _ {\ mathrm {Ltg2}}) = R_ {t} - R_ {1} = \ Delta R_ {t} \.}$ This voltage is independent of a measure of a resistance deviation from a fixed reference value. Since the voltage is not proportional to , but to , changes can be seen particularly clearly. ${\ displaystyle R _ {\ mathrm {Ltg}}}$ ${\ displaystyle R_ {t}}$ ${\ displaystyle \ Delta R_ {t}}$ ## Differentiation from the four-point measurement

With the four- point measurement (also called four-point measurement ), the specific resistance of a layer is determined. It also uses separate lines for the measuring current and the voltage drop, but the contact tips are spatially separated from one another by equal distances.

## literature

• Norbert Weichert, Michael Wülker: Measurement technology and measurement data acquisition. 2nd edition, Oldenbourg Verlag, Munich 2010, ISBN 978-3-486-59773-8 .
• Christian Orgel, Rainer Rottmann: Handbook for testing electrical devices and systems. Herkert Verlag, Merching 2014, ISBN 978-3-86586-633-2 .

## Individual evidence

1. Erwin Böhmer, Dietmar Ehrhardt, Wolfgang Oberschelp: Elements of applied electronics: Compendium for training and occupation. Vieweg, 16th ed. 2010, p. 297
2. Hans-Rolf Tränkler: Pocket book of measuring technology: With a focus on sensor technology . Oldenbourg, 4th ed. 1996, p. 44
3. Kurt Bergmann: Electrical measurement technology: Electrical and electronic processes, plants and systems . Vieweg, 5th ed. 1993, p. 54
4. Rupert Patzelt, Herbert Schweinzer (Ed.): Electrical measurement technology . Springer, 2nd ed. 1996, p. 357
5. Catalog measurement accessories Touch-protected. (PDF) Test & Measureline | Test & measurement technology. Multi-Contact / Stäubli , 2017, p. 96 , accessed on July 24, 2017 .