## Construction of the bridge circuit

The two terminals are used to supply the Us bridge circuit. The voltage Us is also called excitation voltage or excitation voltage or sensor input.

Usually the bridge circuit with DC voltage of 5V is supplied. Are also common 2.5V bridge supply or 1.0V bridge supply if, for example, a low strain gauges is (DMS) with 120 Ohm used, or if the DMS is bonded to a non-conductive material, so that a strong self-heating of the strain gage must be prevented.

About the two other terminals Ud is the voltage at the output of the DMS measured.
The voltage Ud is called "differential voltage" or "bridge output" or "sensor output".

In the usual range of strain gauges is a linear relationship between the voltage Ud and the change in resistance or the elongation.

The relationship between the bridge output Ud and the resistance change ΔR/R is for the full-bridge:

Ud / Us = 1/4 (¨R1 / R1 - ΔR2 / R2 + ΔR3 / R3 - ΔR4 / R4) (Equation 1)

where:
ΔR/R: relative change in resistance
Ud / Us: relative bridge output
Derivation of the equation for the bridge circuit: Wheatstone bridge.pdf

## Task of a measuring amplifier

The relative bridge output Ud/Us is usually less than 0.1%. At 5V bridge excitation voltages Ud therefore must be measured from -0.5 to +0.5 mV. Therefore, a sense amplifier is used.
The amplifier has several functions:

• it provides a bridge supply voltage Us with highest stability available,
• it amplifies the difference voltage Ud and transforms them into an appropriate display value.

A measuring amplifier shows the basic setting usually the relative bridge output Ud/Us at.
The unit of the display is then mV/V.

By standardizing the bridge output Ud on the supply voltage Us, the display values ​​on measuring amplifiers with different supply voltage Us directly comparable. The default setting of the unit on the display of many measuring amplifier is therefore mV/V.

## Strain and bridge output

The relationship between bridge output, supply voltage and strain follows from equations (1) and (2):

Ud/Us = 1/4 k (ε1 - ε2 + ε3 - ε4) (Equation 3)

For one quarter bridge is due ε2 = ε3 = ε4 = 0:

Ud/Us = 1/4 k ε1 (Equation 4)

From equation (4) gives the relationship between display Ud / Us and strain ε for a quarter bridge:

ε1 = Ud/Us 4/k (Equation 5)

In a k-factor of 2.0 an indication Ud/Us of 2.0 mV/V (= 0.002 V/V = 2.0E-3) means:

0.002 x 4/2.0 = ε1 = 0.004 = 4 ‰ = 4000 µm/m

2 mV/V therefore correspond to 4000 µm/m strain at a quarter bridge with k-factor. 2

## Basics of bridge circuit

The bridge circuit allows the determination of very small changes in resistance.
At the same temperature-induced changes in resistance and other interference are compensated for.
However, a prerequisite for a good compensation of interferences that the disorder equally affecting two adjacent resistors of the bridge circuit.

## Advantages of the bridge circuit

With adjusted bridge circuit (R1/R2 = R4/R3) is the differential voltage between + Ud and -Ud equal to 0 volts. Since only resistance changes are recognized starting from 0 volts, the measuring range can be adapted to the requirements. "The gain can be as high as desired selected"

The different signs in equation (3) allow the compensation of disturbance:

1. the thermal expansion can be compensated: ε1 - ε2 + ε3 - ε4 = 0
2. mechanical strains that are not desired in the measuring direction are, can be compensated. This can be used, by detecting specific strains of opposite signs with strain gauges.
3. For each load case (bending, torsion, compression, shear) there are wiring diagrams that capture only the strain in a certain measuring direction.

## Benefits of the standardized display in mV/V

• when displaying the absolute bridge output always takes an additional indication of the supply voltage used to be made,
• for calculating the expansion only the knowledge of the relative bridge output is required (see equation 5)
• through the calibration of measuring instruments for strain gages in mV / V, the measuring amplifiers from different manufacturers with different bridge supply voltages are interchangeable.

## Change in resistance and strain

The relationship between resistance change ΔR/R and strain ε is defined by the k-factor of the strain gauge.

If the elongation of an electrical conductor, a change in cross section of the electrical conductor to the sequence. The change in cross section of the electrical conductor is in turn connected to a change in electrical resistance.

From the condition that an "elongation" (positive elongation) of a conductor in volume still remains constant, resulting in a "necking" of the conductor. Conversely, results from an "upsetting" (negative strain) a "thickening" of the conductor.

This, purely geometrical effect results under the condition constant conductor volume to a linear relationship between resistance change and expansion:

ΔR1/R1 = k ε (Equation 2)

The Propotionalitätsfaktor is referred to as k-factor of the strain gauge. For alloys whose volume remains constant while stretching (and this applies to all electrical conductor) results in a k-factor of 2.

1 ‰ elongation corresponds to 2 ‰ change in resistance, or
1000 .mu.m / m elongation corresponding 2 ‰ change in resistance, or
1000 e 6 strain corresponding 2000 E-6 resistance change