# What is a Wheatstone bridge used for?

## The Wheatstone bridge circuit

The Wheatstone bridge circuit - briefly explained

PreviousNext

The Wheatstone bridge circuit can be used to measure electrical resistance in several ways:

• for determining the absolute value of a resistor by comparing it with a resistor of known size
• to determine relative changes in resistance

The second type of application is used in DMS technology. It allows it, which is usually in the order of 10–4–10–2 Measure Ω / Ω moving relative changes in resistance of the strain gauges with high accuracy.

The figure below shows two different representations of the Wheatstone bridge circuit, which are electrically identical: Figure a) shows the usual rhombus-like representation of the Wheatstone bridge circuit; Figure b) is a representation of the same circuit that is easier for non-electricians to understand.

The four arms or branches of the bridge circuit are through the resistors R1 to R4 educated. The bridge corner points 2 and 3 designate the connections for the bridge supply voltage UB.; The bridge output voltage U is at corner points 1 and 4A. on, the measurement signal.

The bridge supply is usually carried out with a stabilized DC or AC voltage U.B..

Annotation:
Unfortunately, there is no generally applicable rule for the designation of the bridge elements and connections. The existing literature therefore has a wide variety of names, which is reflected in the bridge equations. It is therefore absolutely necessary to see the designations and indices used in the equations in connection with the position of the bridge elements within the circuit in order to avoid misinterpretations.

If you apply a bridge feed voltage U to the two bridge feed points 2 and 3B. on, then this divides into the two bridge halves R1, R2 and R4, R3 in each case in the ratio of the bridge resistances, i.e. each bridge half forms a voltage divider.

If the resistance ratios of the two bridge halves R1, R2 and R3, R4 are not the same, the bridge can be "detuned". This can be calculated as follows:

when the bridge circuit is "balanced" and

if the bridge output voltage UA. equals zero.

With a given expansion, the resistance of the strain gauge changes by the amount ΔR. The equation for this looks like this:

In the case of strain measurements, the resistances R1 and R2 be the same in the Wheatstone bridge circuit. The same goes for R3 and R4.

The following equation is obtained through a few assumptions and simplifications (further explanations can be found in the specialist book "An introduction to the technique of measuring with strain gauges" from HBM):

In the last step of the calculation, ΔR / R is replaced as follows:

Here k is the k-factor of the strain gauge, ε is the elongation. The equation for this looks like this:

The equations assume that all resistances in the bridge change. This condition can be found, for example, in measurement transducers or measurement objects that are used in a similar function. In experimental tests this hardly applies, there usually only a part of the bridge arms is occupied with strain gauges, the rest is formed by supplementary resistors. Designations such as quarter bridge, half bridge, two-quarter or diagonal bridge and full bridge are common to differentiate.

Depending on the measuring task, one or more strain gauges are used at the measuring point. Although terms such as full bridge, half bridge or quarter bridge are used to denote such arrangements, they are not correct. In fact, a complete circuit is always used for the measurements, which is either completely or partially formed by the strain gauges and the measurement object. It is supplemented by fixed resistors that are integrated into the devices.

In general, higher accuracy requirements have to be met in transducer construction than in measurements in experimental tests. A full bridge circuit with active strain gauges in all four bridge arms should therefore always be used in the transducer construction.

Full-bridge or half-bridge circuits should also be used in voltage analysis if different types of interference are to be eliminated. An important prerequisite for this is that different types of stress are clearly differentiated, such as compressive or tensile stress as well as bending, shear or torsion forces.

The table below shows the dependency of the geometric arrangement of the strain gauges, the type of bridge circuit used and the resulting bridge factor B for normal forces, bending moments, torques and temperatures. The small tables for each example indicate the bridging factor B for each type of influencing variable. The equations are used to calculate the effective strain from the bridge output signal UA./ UB..

 Bridge configuration Measured external influences application description Advantages and disadvantages 1 Strain measurement on the tension / compression rod Strain measurement on the bending rod Simple quarter bridgeSimple quarter bridge with an active strain gauge + Easy installation- Normal and bending strain are superimposed- Temperature influences are not automatically compensated 2 Strain measurement on the tension / compression rod Strain measurement on the bending rod Quarter bridge with external dummy strain gaugeTwo quarter bridge circuits. One strain gauge actively measures elongation, the other is attached to a passive component made of the same material that is not elongated + Temperature influences are well compensated- Normal and bending strain cannot be separated (superimposed bending) 3 Strain measurement on the tension / compression rod Strain measurement on the bending rod Poisson half bridgeTwo active strain gauges connected as a half bridge, one of which is oriented 90 ° to the other + Temperature influences are well compensated if the material is isotropic 4 Strain measurement on the bending rod Half bridgeTwo strain gauges on opposite sides of the structure + Temperature influences are well compensated+ Separation of normal and bending strain (only pure bending is measured) 5 Strain measurement on the tension / compression rod Diagonal bridgeTwo strain gauges on opposite sides of the structure + Normal elongation is measured independently of bending elongation (bending is excluded) 6 Strain measurement on the tension / compression rod Strain measurement on the bending rod Full bridge4 strain gauges on one side of the structure as a full bridge + Temperature influences are well compensated+ High output signal and excellent common mode rejection (CRM)- Normal and bending strain cannot be separated (superimposed bending) 7 Strain measurement on the tension / compression rod Diagonal bridge with dummy strain gaugesTwo actively measuring strain gauges and two passive strain gauges + Normal elongation is measured independently of bending elongation (bending is excluded)+ Temperature influences are well compensated 8 Strain measurement on the bending rod Full bridgeFour active strain gauges connected as a full bridge + Separation of normal and bending strain (only pure bending is measured)+ High output signal and excellent common mode rejection (CMR)+ Temperature influences are well compensated 9 Strain measurement on the tension / compression rod Full bridgeFour actively measuring strain gauges, two of them rotated by 90 °. + Normal elongation is measured independently of bending elongation (bending is excluded)+ Temperature influences are well compensated+ High output signal and excellent common mode rejection (CMR) 10 Strain measurement on the bending rod Full bridgeFour actively measuring strain gauges, two of them rotated by 90 °. + Separation of normal and bending strain (only pure bending is measured)+ High output signal and excellent common mode rejection (CMR)+ Temperature influences are well compensated 11 Strain measurement on the bending rod Full bridgeFour actively measuring strain gauges, two of them rotated by 90 °. + Separation of normal and bending strain (only pure bending is measured)+ High output signal and excellent common mode rejection (CMR)+ Temperature influences are well compensated 12 Strain measurement on the bending rod Full bridgeFour active strain gauges connected as a full bridge + Separation of normal and bending strain (only pure bending is measured)+ Temperature influences are well compensated+ High output signal and excellent common mode rejection (CMR) 13 Measurement of torsional strain Full bridgeAs shown, four strain gauges are each installed at an angle of 45 ° to the main axis + High output signal and excellent common mode rejection (CMR)+ Temperature influences are well compensated 14 Measurement of torsional strain when space is limited Full bridgeFour strain gauges are installed as a full bridge, at an angle of 45 ° and superimposed (stacked rosettes) + High output signal and excellent common mode rejection (CMR)+ Temperature influences are well compensated 15 Measurement of torsional strain when space is limited Full bridgeFour strain gauges are installed as a full bridge, at an angle of 45 ° and superimposed (stacked rosettes) + High output signal and excellent common mode rejection (CMR)+ Temperature influences are well compensated

Annotation:
Examples 13, 14 and 15 assume a cylindrical shaft for torque measurement. Bending in the X and Y directions is permitted for reasons of symmetry. The same conditions apply to the bar with a square or rectangular cross-section.

Explanation of the symbols:

 T temperature F.n Longitudinal, normal force M.b Bending moment M.bx, Mby Bending moment for X and Y directions M.d Torque εs Apparent stretch εn Longitudinal, normal stretch εb Bending strain εd Torque load ε Effective elongation at the measuring point ν Poisson's number Active strain gauge