## Half Bridge

 Us: bridge supply Ud: bridge output ε: strain k: k-factor (2,0) Ud / Us = 1/4 · (¨R1 / R1 - ΔR2 / R2) Ud / Us = 1/4 · k · (ε1 - ε2) with a k-factor k = 2.0 applies:  1000 µm / m corresponding to 1 mV / V

The active strain gauge (1.2) are supplemented by two passive resistors (3,4) for the full-bridge.

This circuit is used in the stress analysis and at low cost sensors.

## Half Bridge, longitudinal and cross strain

 Us: bridge supply Ud: bridge output ε: strain k: k-factor (approx. 2,0) ν: Poisson's ratio (approx. 0.3) Ud/Us = 1/4 · (ΔR1/R1 - ΔR2/R2) Ud/Us = 1/4 · k · (ε1 - ν ε2) with a k-factor k = 2.0 applies:  1539 µm/m corresponding to 1 mV/V

The active DMS (1) is a transversely disposed "Poisson" DMS (2) and two passive resistors (3,4) complements the full bridge.

This circuit is used in the stress analysis and at low cost sensors.

## Quarter Bridge

 Us: bridge supply Ud: bridge output ε: strain k: k-factor (approx. 2,0) Ud/Us = 1/4 · (ΔR1/R1) Ud/Us = 1/4 · k · (ε1) with a K factor k = 2.0 applies:  2000 µm/m corresponding to 1 mV / V

This is the most widely used circuit in the stress analysis.
The active DMS (1) is complemented by three passive resistors (2,3,4) for full bridge.

The nonlinearity of this circuit is small expansions in the range up to 1000 microns / m negligible.
In very high elongations up to the region of the plastic deformation may be 2% or more of the errors caused by non-linearity.

## Full Bridge

 Us: bridge supply Ud: bridge output ε: strain k: k-factor (approx. 2,0) ν: Poisson's ratio (0.3) Ud / Us = 1/4 · (ΔR1/R1 - ΔR2/R2 + ΔR3/R3 - ΔR4/R4) Ud / Us = 1/4 · k · (ε1 - ν ε2 + ε3 - ν ε4) with a k-factor k = 2.0 applies:  500 µm/m correspond to 1 mV/V

The full bridge with 4 active strain gauges in longitudinal strain is the preferred standard circuit in the sensor production.

It provides the best possible compensation of temperature influences and mechanical interference.

## Full Bridge, 2 longitudinal 2 cross grids

 Us: bridge supply Ud: bridge output ε: strain k: k-factor (approx. 2,0) ν: Poisson's ratio (approx. 0.3) Ud/Us = 1/4 · (ΔR1/R1 - ΔR2/R2 + ΔR3/R3 - ΔR4/R4) Ud/Us = 1/4 · k · (ε1 - ν ε2 + ε3 - ν ε4) with a k-factor k = 2.0 applies:  769 µm/m correspond to 1 mV / V

The two co-rotating DMS (1.3) are supplemented by two transversely arranged DMS (2.4) for the full-bridge.
This circuit is, struts preferably used in tension.
For precision sensors linearization is often provided with additional semiconductor DMS.

 Us: bridge supply Ud: bridge output ε: strain k: k-factor (approx. 2,0) ν: Poisson's ratio (approx. 0.3) Ud/Us = 1/4 · (ΔR1/R1 - ΔR2/R2 + ΔR3/R3 - ΔR4/R4) Ud/Us = 1/4 · k · (ε1 - ε2 + ν ε3 - ν ε4) with a k-factor k = 2.0 applies:  769 µm/m correspond to 1 mV / V

The two opposing DMS (1.2) are supplemented by two transversely arranged DMS (3.4) for the full-bridge.

This circuit is used in the stress analysis and at low cost sensors.

## Wheatstone Bridge

The Wheatstone bridge circuit is the preferred circuit for measuring resistances. It can be used for the absolute determination of a resistor, or for determining a relative change in resistance. In the measurement with strain gauges, the relative change of resistance is measured.

## Advantages of the bridge circuit

• In a balanced bridge circuit, the output voltage is 0 volts. The gain can be very high in order to achieve a fine resolution.
• The symmetry of the bridge circuit is utilized to compensate for the thermal expansion electrically,
• The symmetry of the bridge circuit is utilized to compensate for unwanted mechanical stretching transversely to the measuring direction electrically.