# Thomson Bridge

The Thomson bridge , also called Kelvin bridge , is an electrical bridge circuit which is used to measure small resistance values ​​down to the range of a few 10 µΩ. Its structure is related to the Wheatstone bridge and is based on four-wire measurement in order to minimize undesired contact resistances that falsify the measurement result. The circuit is named after William Thomson, 1st Baron Kelvin .

Because of the effort involved in manually balancing the bridge, the Thomson bridge is of little importance in practical electrical measurement technology and has been replaced by digital resistance measuring devices based on four-wire measurement with a reference resistor .

## construction

Circuit of a Thomson bridge in four-wire representation
Historic Thomson measuring bridge for resistance values ​​from 0.2 mΩ to 2.2 Ω
Real circuit diagram of the RFT Thomson measuring bridge

As shown in the sketch on the right, the circuit consists of the unknown resistance Rx to be determined and a reference resistance Rn with a known resistance value . The resistors RL1 , RL2 and RL3 in series represent undesirable but unavoidable line resistances, contact resistances of terminals and similar, their value is unknown and, with small measuring ranges, the resistance value can also be greater than the resistance value of Rx to be determined . In order to avoid the undesirable influence of these line and contact resistances, the so-called four - wire measurement is used for both the resistance to be determined and the reference resistance . The reference resistor can be designed as a shunt resistor with four connections. The current path, on which a high voltage drop occurs as a result of the contact and line resistance, is separated from the voltage path with only low currents. The current path is fed by an external voltage source U.

The voltage paths supply the actual measuring bridge, consisting of the four resistors R1 , R2 , R3 and R4 . In the bridge path there is a voltage measuring device V, the displayed value of which must be adjusted to the voltage value of 0 V as a calibration condition for the circuit. The bridge is balanced by changing the four resistors R1 , R2 , R3 and R4 , where R1 to R3 and R2 to R4 change equally in percentage. For this purpose, two resistors are designed mechanically in the form of two potentiometers , whereby R1 and R3 can be adjusted together, as well as R2 and R4 . This potentiometer design, consisting of two variable resistors, is also known as a double potentiometer . Alternatively, instead of double potentiometers, switchable voltage dividers can also be used for adjustment , in which case the reference resistance Rn must also be changed.

Due to the mechanical connection of the resistors R1 , R2 , R3 and R4 described above, the following always applies:

${\ displaystyle {\ frac {\ mathrm {R1}} {\ mathrm {R2}}} = {\ frac {\ mathrm {R3}} {\ mathrm {R4}}}}$

If the bridge is balanced, this is the case when the voltage display on the measuring device shows 0 V, the following also applies:

${\ displaystyle {\ frac {\ mathrm {Rx}} {\ mathrm {Rn}}} = {\ frac {\ mathrm {R2}} {\ mathrm {R1}}}}$

With known values ​​of Rn , R2 and R1 , the resistance value Rx to be determined then has the following value:

${\ displaystyle \ mathrm {Rx} = \ mathrm {Rn} \ cdot {\ frac {\ mathrm {R2}} {\ mathrm {R1}}}}$

The unwanted line and contact resistances RL1 , RL2 and RL3 are not included in the measurement.

## literature

• Elmar Schrüfer: Electrical measurement technology. Measurement of electrical and non-electrical quantities. 5th edition. Hanser, Munich 1992, ISBN 3-446-17128-2 , pp. 228-229 .