# Strain Sensor Basics and Signal Conditioning Tips

June 1, 2005 By: John R. Gyorki, Iotech, Inc., Inc. Sensors

### Strain gauges are fairly straightforward devices that output a voltage signal based on a change in resistance when the object to which they are attached to undergoes tension or compression. They are available in three basic types: full-, half-, and quarter-bridge, each with its own requirements.

Strain gauges are sensing devices that change resistance at their output terminals when stretched or compressed. They are typically bonded to the surface of a solid material to measure its minute dimensional changes when put into compression or tension. Strain gauges and their underlying principles are often used in devices for measuring acceleration, pressure, tension, and force. Strain is a dimensionless unit, defined as a change in length per unit length. For example, if a 1-m-long bar stretches to 1.000002 m, the strain is defined as 2 microstrain (µε). Strain gauges have a characteristic gauge factor, defined as the fractional change in resistance divided by the strain. For example, 2 µε applied to a gauge with gauge factor of 2 produces a fractional resistance change of (2 × 2) 10-6 = 4 3 10-6, or 4 µΩ. Common gauge resistance values typically range from 120 to 350 Ω, but some devices can be as low as 30 or as high as 3 kΩ.

## Strain Gauge Configurations

To obtain accurate strain data, extremely small resistance changes must be measured. A Wheatstone bridge circuit is widely used to convert the gauge's microstrain into a voltage change that can be fed to the input of the A/D converter (ADC), as shown in Figure 1. When all four resistors in the bridge are absolutely equal, the bridge is perfectly balanced and Vout = 0. But when any one or more of the resistors change value by only a fractional amount, the bridge produces a significant, measurable voltage. When used with an instrument, a strain gauge replaces one or more of the resistors in the bridge, and as the strain gauge undergoes dimensional changes (because it is bonded to a test specimen), it unbalances the bridge and produces an output voltage proportional to the strain.

 Figure 1. The full-bridge circuit provides the largest output with the fewest errors. All four arms of the bridge are active; two are in tension and the two on the opposite side are in compression.

Full-Bridge Circuits. Although half-bridge and quarter-bridge circuits are often used, the full bridge is optimal for strain gauges. This circuit has the highest sensitivity, the fewest error components, and the highest output that reduces the effects of noise on the measurements.

A full-bridge circuit contains four strain gauges mounted on a test member: two on the surface under tension and the other two on the opposite surface under compression, as shown in Figure 1. As the member deflects, the two gauges in tension increase in resistance while the other two decrease, unbalancing the bridge and producing an output proportional to the displacement. The bridge output voltage is given by:

where:
V O = bridge output voltage, V

Vex = excitation voltage applied to the bridge, V

X = relative change in resistance, ΔR/R

The bridge nulls out potential error factors such as temperature changes because all four strain gauges have the same temperature coefficient and are located close to one another on the specimen. The resistance of the lead wire does not affect measurement accuracy so long as the input amplifier has high input impedance. For example, an amplifier with a 100 MΩ input impedance produces negligible current flow through the measurement leads, minimizing voltage drops due to lead resistance.

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