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.

The two connections Us+ and Us- are used to power the bridge circuit. The voltage between Us+ and Us- is also referred to as excitation voltage Us or bridge supply or sensor input. Us- is connected to the mass GND in the many measuring amplifiers.

The voltage change is measured via the connections Ud+ and Ud- if the bridge circuit is disexcited due to strain at one or more strain gauges.
The voltage between Ud+ and Ud- is referred to as "differential voltage Ud" or "bridge output" or "sensor output".

The bridge circuit is adjusted (the voltage between Ud+ and Ud- is 0 V) if the following condition is met:

In most cases, the bridge circuit is supplied with DC voltage of 5V. Also common are 2.5V bridge power or 1.0V bridge power, e.g. when a low-impedance strain gauge with 120 ohms is used, or if the strain gauge is glued to a non-conductive material, so that a strong self-heating of the strain measuring strip must be prevented.

Bridge equation

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

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

Linearized form of bridge equation

For small changes in the difference voltage Ud, the linearized form of the bridge equation may be applied:

Relationship between resistance change 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:

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

Relationship between strain and bridge output

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

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

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

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

The output signals of the bridge circuit with quarter bridge, half bridge and full bridge are summarized on this page:

straingauge-bridge-circuit

For a full bridge with 4 active strain gauges (with ε1=ε3=-ε2=-ε4 = ε)is applied:

From equation (4b) one gets the relationship between the indication "ΔUd/Us" and the strain for a full bridge:

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.

Advantages of the bridge circuit

Benefits of the standardized display in mV/V