# Wheatstone Bridge

## Strain gauges conditioning circuit

The Wheatstone bridge is a signal conditioning circuit, commonly used with strain gauges.
Indeed, it is one of the most suitable circuits when it comes to measuring very small resistance variations. Especially useful for getting a better sensitivity.

## Wheatstone Bridge principle for measuring strain

This circuit consists of four bridge-connected resistors (R1, R2, R3, R4), a power supply Vin (DC or AC) and an output voltage Vout (Measurable using a voltmeter for example).

Applying Millman’s theorem in B and D leads to the following equation:

We say that the bridge is balanced when the output voltage Vout is zero.
Or when R2.R3 = R1.R4
That is to say when the products of opposite resistors are equal.

When performing a strain measurement, we usually take R1=R2=R3=R4 to balance the bridge.

In practice, those resistors are replaced by strain gauges (one, two or four / Quarter, half or full Wheatstone bridge) having a variable resistor (particularly to strain and to temperature).

Once the bridge is balanced, the potential difference between B and D is zero. If one of the resistors changes slightly, this variation can be directly collected by measuring the output signal Vout.

We can notice one fundamental Wheatstone bridge property: The resistors R2 and R3 act in the positive direction (increasing resistance) whereas R1 and R4 act in the opposite direction (decreasing resistance).
Thereby, the two adjacent resistors act in opposite directions and the two opposite resistors act in the same direction. (This allows the elimination of parasitic variations in order to, for example, self-compensate the gauges in temperature).

## Operating principle of the quarter Wheatstone bridge

This circuit consists of three precision resistors (R2=R3=R4=R) and of one active strain gauge, that we can note J1 with a resistance = R + α R. Where α is the relative resistance variation.
This circuit only allows you to collect the variation resistance of the gauge J1 at the output.
The output value V out is:

## Operating principle of the half Wheatstone bridge

It consists of two precision resistors (R3=R4=R) and of two active strain gauges J1 et J2 (both having a nominal resistance which is equal to R)
The two active strain gauges are either arranged opposite to one another or arranged side by side, depending on the requirements.

If you want to self-compensate your gauges in temperature you will arrange them side by side. One of the two will undergo a mechanical strain ( such as its resistance is R + α R) and the other won’t and will be used as an indicator. Indeed, both will undergo the same temperature variation but, due to their disposition, their resistance variation linked to this temperature will be opposed.

The bridge output will only depend on the active gauge deformation; the effect of the temperature will be compensated.

This circuit sensitivity is twice this of the quarter Wheatstone bridge.
The output value V out is:

If you arrange the two gauges opposite to one another, they won’t be self-compensated in temperature but the sensitivity will be increased.

## Operating principle of the full Wheatstone bridge

It consists of four active gauges having an equal nominal resistance (J1=J2=J3=J4=R).
These four gauges undergo a mechanical strain such as their resistance is R+ α R
Thanks to the circuit layout, those gauges are automatically self-compensated in temperature and this is the circuit that allows the optimal sensitivity. Here, the output value V out is:

## Conditioning principle of the nano strain gauges

Our nano strain gauges distinguish themselves by their high gauge factor (G=30). Our gauge sensitivity is self-sufficient.
The only benefits of using a Wheatstone bridge in nano gauge conditioning is to self-compensate the gauges in temperature with a half or a full bridge.

The quarter bridge does not have particular benefit. Therefore, the easiest way to collect the resistance variation with our gauges is to use a voltage divider bridge.

This is on this circuit that is based our nano strain gauges conditioner: the NanoDAQ. It allows you to collect your data directly on a serial output.