# Wheatstone Bridge Test Applications

## The Wheatstone bridge circuit is ideal for many accurate test applications and as a result various formats have been developed to enable its use in many ways.

Wheatstone Bridge For Test Includes:
Wheatstone bridge test applications basics     Strain gauge

The Wheatstone bridge has been used for many years to provide a very accurate means of measuring resistance.

Although many people may think its use is confined to demonstrations in school physics laboratories, nothing could be further from the truth.

Wheatstone bridges can be found in high accuracy resistance measuring instruments and in addition to this they are finding increasing use in sensors from strain gauges to load cells as we as many more.

There are several variants on the basic Wheatstone bridge theme including four wire and six wire variants as well as having multiple measurement active elements.

## Wheatstone bridge measurement basics

The basics of the Wheatstone bridge have been used for many years. In its early days it was used mainly to determine the resistance of a single unknown resistor by having two fixed resistors and a third calibrated variable resistor or potentiometer.

To understand the operation of the bridge, it can be considered as two parallel potential dividers consisting of R1 and R4 and then R2 and R3.

Typically R1 and R2 would be the same value, and therefore when there is a balance, i.e. no potential difference between the two points "b: and "d: on the diagram, the unknown resistance is the the same as that of the potentiometer which may be calibrated so its resistance is known for any position.

### Note on the Wheatstone Bridge:

The Wheatstone bridge circuit consists of four resistors, two in each arm, with meter bridging the centres of the two arms. Although it appears to be a basic circuit, it is widely used in measurement systems, and the fundamental electrical calculations are easy to understand.

When used for measurement systems, the basic way in which the bridge circuit is used can be slightly different.

For modern measurement systems, the Wheatstone bridge may be operated in what may be termed an out of balance condition.

Here the bridge circuit may be almost in balance for the basic condition and any deviation will result in a potential difference change across the centre of the bridge circuit which can be denoted as ΔV.

It is possible to easily calculate the change in voltage acros the points between 'b' and 'd' giving a way of determining the resistance and hence any change in R3.

This method is far more preferable than having to vary another resistor to achieve a full balance within the bridge circuit.

It is possible to calculate the voltage across the points 'b' and 'd' quite easily.

${V}_{\mathrm{out}}={V}_{\mathrm{in}}\left(\frac{r+\Delta R}{2R+\Delta R}\right)$

This simplifies down to:

${V}_{\mathrm{out}}=\frac{{V}_{\mathrm{in}}}{2}\left(\frac{\Delta R}{2R+\Delta R}\right)$

Where:
R is the value for R1, R2, and R4 which are all equal
ΔR is the small change in value of R3 from R to ΔR as a result of the changes in the sensor causing the resistance to change.
Vin is the supply voltage to the Wheatstone bridge
Vout is the output voltage across the points 'b' and 'd'.

For small changes in the sensor resistance, ΔR there is a virtually linear change on the output voltage Vout because R dominates over ΔR on the denominator of the equation.

However for the small changes normally encountered in sensors such as strain gauges, load cells, etc using a Wheatstone bridge, the non-linearity is not an issue.

For systems where larger changes in ΔR are encountered it is possible to correct this using processing.

## Two active elements: half bridge

The example above looked the situation where only one of the resistors varied - the remaining three resistors all remained constant.

It is possible to have two resistors change - for example R1 and R3 may both change, and this can be used in some sensors to advantage, especially where the resistance changes are small.

This type of bridge circuit is often referred to as a half bridge.

To see how this affects the circuit, it cna be deduced in a similar way to the single variable Wheatstone bridge:

${V}_{\mathrm{out}}={V}_{\mathrm{in}}\left(\frac{\Delta R}{2R+\Delta R}\right)$

It can be seen in this instance that the change in output voltage is twice what it was before for a given change in resistance.

This can be very important when the changes may only be very small. It can help with reducing errors caused by noise and transients, etc as well as accommodating a larger signal that is easier to measure.

It's also possible to place two active elements within the same branch. This is still referred to as a half bridge because there are two active elements.

In this case the active elements should act in the opposite direction to each other, one increasing in resistance while the other decreases.

If they both acted in the same sense, then the effects would nullify each other as they are effectively in the same potential divider.

${V}_{\mathrm{out}}={V}_{\mathrm{in}}\left(\frac{\Delta R}{2R}\right)$

Note that in this case the equation is rather different to that of the example where they are in different legs and acting in the same sense.

## Four active elements: full bridge

The logical extension of the half bridge is to extend the number of variable or active elements to four in what is known as a full bridge.

For the benefits of this topology to be gained, the resistors in each branch must act in opposite directions and then the other branch must act in the opposite sense to the first one as shown in the diagram.

It is found that the sensitivity of this type of bridge is better than any version of the half bridge.

${V}_{\mathrm{out}}={V}_{\mathrm{in}}\left(\frac{\Delta R}{R}\right)$

It is possible to see from this that the full bridge has double the sensitivity of the half bridge circuits and four times that of the single active element bridge.

This is hardly surprising seeing that four active elements are going to be better than one.

There are several variations on the basic Wheatstone bridge that can all be used with various forms of measurement and sensing.

The bridge is becoming particularly widespread with the huge number of sensors that are being incorporated into automated control and monitoring systems as well as accurate sensing technologies.

Even though many might feel the Wheatstone bridge had been consigned to the basic experiments for school physics laboratories, nothing could be further from the truth.