Strain Sensor Basics and Signal Conditioning Tips

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Strain Sensor Basics and Signal ConditioningTips

June 1, 2005By: 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 whichthey are attached to undergoes tension or compression. They areavailable in three basic types: full-, half-, and quarter-bridge, eachwith 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 (). Strain gaugeshave a characteristic gauge factor, defined as the fractional change in resistance divided by the

strain. For example, 2 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 . Common gauge resistance values typically

range from 120 to 350 , but some devices can be as low as 30 or as high as 3 k.

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. Butwhen 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.

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 theother 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, R/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 thespecimen. 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 M input

Figure 1. The full-bridge circuitprovides the largest output with the

fewest errors. All four arms of thebridge are active; two are in tensionand the two on the opposite sideare in compression.
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impedance produces negligible current flow through the measurement leads, minimizing voltage

drops due to lead resistance.

Half-Bridge Circuits. When physical conditions do not allow mounting a full-bridge gauge, a half

bridge might fit. Typically, two strain gauges are mounted on a test member, and two discrete

resistors complete the bridge (see Figure 2). The output voltage is:

where:

VO = bridge output voltage, V

Vex = excitation

voltage applied

to the bridge, V


For a large R, half-bridge and quarter-bridge circuits can

introduce an additional nonlinearity error. Also, the readings

are not accurate when the temperature coefficients between

bridge completion resistors and strain gauges are different

and the resistances do not change proportionally with

temperature. Furthermore, bridge completion resistors are

not usually located near the strain gauges, so temperaturedifferences contribute additional errors. In systems with long lead wires, the bridge completion

resistors should be attached close to the gauges, but this might not always be practical due to

test fixture limitations or other physical conditions.

Quarter-Bridge Circuits.A quarter-bridge circuit uses one strain gauge and three bridge

completion resistors. The output voltage is:

where:

VO = bridge output voltage, V

Vex = excitation

voltage applied

to the bridge, V


This arrangement has the smallest output, so noise is apotential problem. Furthermore, all the error sources and

limitations in the half-bridge apply to the quarter bridge

circuit (see Figure 3).

Excitation Source

Accurate measurements depend on a stable, regulated, and low-noise excitation source. A

regulated source is necessary because the output voltage of a strain gauge is also proportional

to the excitation voltage, so fluctuations in the excitation voltage produce inaccurate output

voltages. An ideal data acquisition system provides an excitation source for each channel,

independently adjustable from 0.5 to 10.5 V with a current limit of 100 mA. An excitation voltage,V, used with a strain gauge of resistance, R, requires a current of I = V/R. The resistance of a

Wheatstone bridge measured between any two symmetrical terminals equals the value of one of

the resistance arms. For example, four 350 arms make a 350 bridge. The load current

equals the excitation voltage divided by the bridge resistance; in this case, 10 V/350 = 0.029 A =

29 mA.

HeatingResistive heating in strain gauges also should be considered because the gauges respond to

temperature as well as stress. In most standard circuits, the heat that each gauge dissipates is


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However, because materials such as wood, plastic, or glass do not conduct heat away as

rapidly, it is a good idea to use the lowest excitation voltage possible without introducing noise

problems. Heat can become a problem when the strain gauges are uncommonly small, or

numerous gauges occupy a limited space.

Consider a Kelvin connection for applying the excitation voltage. Because the excitation leads

carry a small current, they drop a correspondingly small voltage, V = I/RL, which reduces the

voltage reaching the bridge terminals. As illustrated in Figure 4 Kelvin connections eliminate thisdrop with a pair of leads added at the excitation terminals to measure and regulate the bridge

voltage.

For instance, when Ie = 50 mA, RL = 5 V, and the combined

voltage drop in the two leads is 500 mV, no voltage drops in the

sense wires.

A commercial unit uses a Kelvin connection to measure and

regulate the voltage at the bridge. It supplies the

voltage to the strain gauge with one pair of leads

and measures it with another pair (see Figure

5). The six wires are used in pairs for Sense,

Excite, and Measure. The Sense lead is a

feedback loop that ensures the Excite voltage isconstantly held within specifications.

Signal Conditioning

Most strain gaugebased transducers and load

cells are assigned units of measure for weight,

force, tension, pressure, torque, and deflection with a full-scale

value measured in mV/V of excitation. For example, a load cell

with a 10 V excitation supply and a 2 mV/V gain factor generates

an output of 20 mV at full load, whether the load cell was designed to handle 10, 100, or 1000 lb.

The difference lies in the resolution of the system, i.e., the small 10 lb. load cell produces 0.5

lb./mV, and the large 1000 lb. unit produces 50 lb./mV.

Conductors carrying such low-level signals are susceptible to noise interference and should be

shielded. Low-pass filters, differential voltage measurements, and signal averaging are also

effective for suppressing noise interference. Furthermore, instrumentation amplifiers usually

condition the extremely low strain gauge signals before feeding them to ADCs. For example, a 10

V F.S. input provides 156 V of resolution for a 16-bit ADC. The amplifier gain should be adjusted

to provide the full-scale output of the strain gauge or load cell over the converter's entire range.

Force and pressure transducers typically generate an offset output signal when no external force

is applied. Instrumentation amplifiers usually contain a control to adjust this offset to zero and let

the load cell cover the full range of the ADC. Most instruments also provide adjustable excitation,

and gain.

Common Mode Rejection Ratio

A high common mode rejection ratio (CMRR), a measure of how well the amplifier rejects

common mode voltages, is essential for strain gauge amplifiers. A strain gauge signal in a

Wheatstone bridge is superimposed on a common mode voltage equal to half the excitation

voltage. For example, consider a 10 V excitation supply (Vmax = 5 V) for a strain gauge with 2

mV/V (Vs = 20 mV) at full scale and an amplifier with a CMRR of 90 dB (see Figure 6). The

amplifier can introduce 0.158 mV of error, corresponding to ~0.80% F.S.,

Figure 4. The Kelvin bridgecircuit uses one pair of wires toprovide the excitation voltagedirectly at the bridge, andanother to sense the excitationvoltage. A third pair of wiresmeasures the bridge outputvoltage. This arrangementremoves the voltage-drop errorin the excitation wires from themeasured strain signal.

Figure 5. A commercial strain gaugemodule provides adjustableexcitation, gain, and offset for eachchannel, so it can make use of theinstruments entire dynamic range.


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which may not be acceptable:

where:

Ve = error voltage, 0.158 mV

Vs = signal voltage, 20 mV

Vmax = maximum voltage, 5 V

CMRR = 90 dB

By comparison, a CMRR of 115 dB

introduces only 9 V of error, which

corresponds to only 0.04% of full

scale.

Strain gauge signal-conditioning

modules usually provide a regulated

excitation source with optional

Kelvin excitation.

Onboard bridge completion resistors

may be connected for quarter- and

half-bridge strain gauges.Instrumentation amplifiers provide

input and scaling gain adjustments,

and an offset adjustment nulls large quiescent loads.

This allows input signals to use the full range of the

data acquisition system, and the measurements

cover the full resolution of the ADC.

Some strain gauge signal conditioners provide fixed

gain, offset, and excitation settings, but fixed settings

do not take advantage of the ADC's maximum

dynamic range. Rather, they decrease the actual

available resolution of the measurement. For

example, many generic strain gauge signal conditioner modules can be set to a fixed 3 mV/Vrating. At 10 V, the excitation, offset, and gain trimming are all fixed and no adjustments can be

made.

An excitation adjustment lets users set the excitation voltage to the maximum allowed by the

manufacturer, which maximizes the bridge's output. Also, the offset adjustment lets users zero

the output offset produced by either a small bridge imbalance or a quiescent deformation of the

mechanical member. And the gain adjustment lets users set a gain that provides a full-scale

output under maximum load, which optimizes the dynamic range of the ADC.

Calibration

The signal-conditioning module also typically provides a shunt calibration feature (see Figure 7)that lets users switch their own shunt resistors into either one of the two lower legs of the bridge

under software control.

For example, a shunt resistor can be calculated to simulate

a full load, which is a convenient way to simulate an

imbalance without having to apply a physical load. For any

balanced bridge, a specific resistor can be connected in

parallel with one of the four bridge elements to obtain a

predictable imbalance and output voltage. For example, a

350 V, 2 mV/V strain gauge delivers full output when one

leg drops by 0.8% to 347.2 V. A 43.75 k resistor shunted

across one or the other lower bridge elements swings the

output to full positive or full negative. An equation for

calculating the shunt calibration resistor value is:

Figure 6. The strain gauge signal ina Wheatstone bridge is usuallysuperimposed on a common modevoltage equal to half the excitationvoltage. Consequently, a highcommon mode rejection ratio isnecessary to reject the common

mode voltage and amplify the straingauge signal.

Figure 7. A bridge may be

calibrated with a shunt resistor thatis switched by means of a softwarecommand into either of the twolower legs.


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where:

Rs = shunt resistor,

Rba = bridge arm resistor,

Rs >> Rba

Vex = excitation voltage, V

VO = bridge output voltage, VMany products include calibration software with a Windows-based program that provides several

calibration methods, online instruction, and a diagnostic screen for testing the calibrated system.

Applications of the Technology

Transducers and Load Cells. Strain gauges are commercially available in prefabricated

modules such as load cells that measure force, tension, compression, and torque. Load cells

typically use a full-bridge configuration and contain four leads for bridge excitation and

measurement. The manufacturers provide calibration and accuracy information.

Strained-Diaphragm Pressure Gauges.

These devices consist of two or four strain gauges mounted on a thin diaphragm. The gauges

are wired in a Wheatstone bridge circuit, including bridge completion resistors when needed, so

the pressure gauge is electrically equivalent to a load cell. The output voltage is specified in

mV/V of excitation for a full-scale pressure differential across the diaphragm.

When one side of the diaphragm (the reference pressure side) is open to the ambient

atmosphere, the gauge compares the inlet pressure to the ambient pressure, ~14.7 psi at sea

level. When the gauge measures ambient pressure, the reference chamber must be sealed with

either a vacuum reference (near zero psi) or the sea level reference.

Temperature variations can affect the accuracy of these gauges. A pressure gauge with a sealed

non-zero reference pressure exhibits temperature variations consistent with the ideal gas law.

For example, a 5C change in ambient temperature near normal room temperature (25C)

produces an error of 1.7% in the pressure measurement. Temperature variations can also affect

the performance of the strain gauges themselves. Transducers must contain temperature

compensation circuits to maintain accurate pressure measurements in environments with widely

varying temperatures.

All strained-diaphragm pressure gauges require a regulated excitation source. Some gauges

contain internal regulators that allow users to connect an unregulated voltage from a power

supply. Some also have internal signal conditioning that amplifies the millivolt signal output of the

Wheatstone bridge to a full-scale voltage from 5 to 10 V.

Gauges of this type have low-impedance outputs. In contrast, other pressure gauges have no

internal signal conditioning; their output impedance equals the Wheatstone bridge re

(several kilohms for semiconductor types), and their full-scale output is in millivolts.

This article was adapted from the Signal Conditioning & PC-Based Data Acquisition Handbook,

3rd Ed., 2004, ed. John R. Gyorki, $29.95, available from IOtech, Inc.John R. Gyorki is Senior Project Engineer, IOtech, Inc., Cleveland, OH; 440-703-

2307,[email protected],www.iotech.com.
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