Making Basic Strain Measurements
using 24-Bit Hardware
INTRODUCTIONDISCUSSION

Strain gages are sensing devices used in a variety ofphysical test and measurement applications. Theychange resistance at their output terminals whenstretched or compressed. Because of this characteristic,
the gages are typically bonded to the surface of a solidmaterial and measure its minute dimensional changes
when put in compression or tension. Strain gages andstrain gage principles are often used in devices formeasuring acceleration, pressure, tension, and force.
Strain is a dimensionless unit, defined as a change inlength per unit length.

STRAIN MEASUREMENT CONFIGURATIONS
Wheatstone Bridge

For example, if a 1-m long bar stretches to 1.000002 m,
the strain is defined as 2 microstrains. Strain gages
have a characteristic gage factor, defined as the fractional change in resistance divided by the strain. For
example, 2 microstrain applied to a gage with gagefactor of 2 produces a fractional resistance changeof (2x2)10-6 = 4x10-6, or 4 µΩ/Ω. Common gage resistance values typically range from 120 to 350 Ω, butsome devices are as low as 30 Ω or as high as 3 kΩ.
In the past, strain gage data acquisition hardware has
typically provided 12- or 16-bit resolution. These devices
must utilize every part of their 12- or 16-bit resolution
to ensure accurate measurements. 24-bit analog-todigital converters (ADC) offer 256 times the resolutionof conventional 16-bit systems. Strain gage based DAQ
systems such as the IOtech 6224 from Measurement
Computing, use a 24-bit ADC per channel and no longer
operate with this disadvantage.

To make an accurate strain measurement, extremely
small resistance changes must be measured. The
Wheatstone bridge circuit is widely used to convert
the gage’s microstrain into a voltage change that canbe fed to the input of the ADC. (See 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 asignificant, measurable voltage. When used with an
instrument, a strain gage replaces one or more of theresistors in the bridge, and as the strain gage 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 circuit is the optimal
configuration for strain gages. It provides the highest sensitivity and the fewest error components, andbecause the full bridge produces the highest output,
noise is a less significant factor in the measurement.
For these reasons, the full bridge is recommended
when possible.

Figure 1: Full-Bridge Circuit
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The full-bridge circuit provides the largest output with minimum errors. All four arms of the bridge are active; twoare in tension while the two on the opposite side are in compression.

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Half-Bridge Circuits

An example of a full-bridge is the full bending bridge configuration
containing four strain gages mounted on a test member shown in
Figure 1. Two gages are mounted on the top surface to measuretension and the other two are mounted on the opposite surface
to measure compression when the beam is forced downward. As
the member deflects, the two gages in tension increase in resistance while the other two decreases, unbalancing the bridge andproducing an output proportional to the displacement. Upward
motion reverses the roles of the strain gages. The bridge output
voltage is given by:

When physical conditions do not allow mounting a full-bridge
gage, a half-bridge might fit. Typically, two strain gages aremounted on a test member, and two highly stable discrete resistors or a highly stable resistor network complete the bridge. The
output voltage is:

Equation 2: Half-Bridge Output Voltage
Vo = Vex (X/2)
Where: Vo = bridge output voltage, V

Equation 1: Full-Bridge Output Voltage
Vo = (Vex)(X)
Where: Vo = bridge output voltage, V		Vex = excitation voltage applied to the bridge, V		

X = relative change in resistance, ∆R/R		

Vex = excitation voltage applied to the bridge, V		

X = relative change in resistance, ∆R/R

For a large ∆R, half-bridge and quarter-bridge circuits can introduce an additional nonlinearity error. (See Figure 2.) Also, thereadings are not accurate when the temperature coefficientsamong the bridge completion resistors and strain gages are different and the resistances do not change proportionally withtemperature. Furthermore, bridge completion resistors are notusually located near the strain gages, so temperature differences
contribute additional errors. In systems with long lead wires,the bridge completion resistors should be attached close to thegages. However, this may not always be practical due to test
fixture limitations or other physical conditions.

The bridge nulls out potential error factors such as temperaturechanges because all four strain gages have the same temperature
coefficient and are located in close proximity on the specimen.
The resistance of the lead wire does not affect the accuracyof the measurement as long as the input amplifier has highinput impedance, and the bridge excitation is remotely sensed.
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.

Figure 2: Half-Bridge Circuit
Bridgecompletion resistors

Strain
gages

R1

R3

+



Vexc

VOUT

R1

Motion

+
R2


R4

R2

In a half-bridge circuit, only two arms are active. Two strain gages are on the specimen while the two fixed resistors
that complete the bridge are not.

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Figure 3: Quarter-Bridge Circuit

Figure 4: Kelvin Strain Gage Bridge Circuit

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A quarter-bridge circuit uses one strain gage and three bridge
completion resistors. The output voltage is:

Equation 3: Quarter-Bridge Output Voltage

two symmetrical terminals equals the value of one of the resistance arms. For example, four 350 Ohm arms make a 350 Ohm
bridge. The load current equals the excitation voltage divided by
the bridge resistance; in this case, 10V/350 Ω = 0.029 A = 29 mA.

Vo = Vex (X/4) [approximate]
Where: Vo = bridge output voltage, VX = relative change in resistance, ∆R/R

The Kelvin bridge circuit uses one pair of wires to provide theexcitation voltage directly at the bridge, and another to sense theexcitation voltage. A third pair of wires measures the bridge output
voltage. This arrangement removes the voltage-drop error in the
excitation wires from the measured strain signal.

Quarter-Bridge Circuits

		

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A quarter-bridge circuit uses only one active arm and is theleast sensitive of the three types. It is also the most prone tonoise and errors.

Vex = excitation voltage applied to the bridge, V

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Heating
Resistive heating in strain gages also should be considered because
the gages respond to temperature as well as stress. The excitation
voltage must be coordinated with the gage and the material towhich it is bonded. Like most engineering endeavors, strain measurement involves making compromises, in this case it is errors
due to self-heating versus signal to noise ratio. Higher excitation
results in a signal that is less affected by external electrical noise
sources but will result in higher errors due to self-heating. Selfheating errors are more prevalent when the strain gage is bonded
to a material that doesn’t heat quickly, such as wood, plastic,or glass materials. Also, heat can become a problem when thestrain gages are uncommonly small, or numerous gages occupy
a limited space.

This arrangement has the smallest output, so noise is a potential
problem. Furthermore, all the error sources and limitationsin the half-bridge circuit apply to the quarter-bridge circuit.
(See Figure 3).

PROCEDURE
Excitation Source
The Wheatstone bridge is a ratiometric transducer; it’s output
voltage to excitation voltage ratio is proportional to the resistive bridge unbalance. The 6224 makes use of a true ratiometricmeasurement system; it’s measured output is proportional tothe bridge output voltage to excitation voltage ratio. As such,
this instrument is not sensitive to excitation voltage changes.
The only excitation requirement is low short-term noise and thevoltage is between 2V and 10 VDC.

For full- and half-bridge configurations, 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
this drop with a pair of leads added at the excitation terminals
to measure and regulate the bridge voltage. For example, whenie = 50 mA, Rl = 5 Ω, and the combined voltage drop in the twoleads is 500 mV, no voltage drops in the sense wires.

An ideal data acquisition system provides an excitation sourcefor each channel, independently adjustable from 1.5 to 10.5V
with a current limit of 100 mA. An excitation voltage, V, usedwith a strain gage of resistance R, requires a current of I = V/R.
The resistance of a Wheatstone bridge measured between any

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Strain Gage Signal Conditioning

An MCC strain gage module uses a Kelvin connection to measure
and regulate the voltage at the bridge. It supplies the voltage tothe strain gage with one pair of leads and measures it with anotherpair as shown in Figure 5. The six wires are used in pairs for Sense,
Excite, and Measure. The Sense lead is a feedback loop to ensurethat the Excite voltage is constantly held within specifications.

Most strain gage based transducers and load cells are assigned
units of measure for weight, force, tension, pressure, torque, anddeflection with a full-scale value measured in mV/V of excitation. For example, a load cell with a 10V excitation supply anda 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 1,000
lbs. The difference is in the resolution of the system. That is, thesmall 10-lb load cell produces 0.5 lbs/mV, and the large 1,000 lb
load cell produces 50 lbs/mV.

In the quarter-bridge configuration it is not possible to remotely sense around the lead wire resistances, so a three-wireconnection is recommended. This configuration relies on theresistances of the lead wires being equal. Note, in Figure 3, that
if RL plus R3 equals RL plus R4 and R1 equals R2, then –AI equals+AI and the bridge will be balanced. The MCC CN-269 andCN-270 provide the bridge completion resistor R4. It is up to
the user to run the three wires (denoted by RL) to the gage; donot tie pins 1 and 2 together at the CN unless the gage wires
are extremely low resistance.

Conductors carrying such low level signals are susceptible to noiseinterference and should be shielded. Low-pass filters, differential
voltage measurements, and signal averaging are also effective
techniques for suppressing noise interference. Furthermore,
instrumentation amplifiers usually condition the extremely low
strain gage signals before feeding them to ADCs.

Figure 5: MCC Strain Gage Module
Ex+
VEX
Select
R2+

+
–

AI+

+

AI–

–

A

A

ADC

VREF

RS–
Ex–
SC
SC

100k

Shunt
Cal.

An MCC strain-gage module provides adjustable excitation, gain, and offset for each channel. This lets it makeuse of the instrument’s entire dynamic range.

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Figure 6: Wheatstone Bridge Circuit
Strain gage
347Ω

350Ω

+V

20 mV
350Ω

+10V

+10V

350Ω

5.02V

Figure 7: Shunt Bridge Circuit

350Ω

IA

(+)
350Ω

5.00V –V

RTN

Normally the strain gage signal in a Wheatstone bridge is superimposed on a common-mode voltage equal to half of the excitation
voltage. Consequently, a high CMRR is necessary to reject thecommon-mode voltage and amplify the strain gage signal.

Vmax/Ve = log10 -1 (dB/20)

CALIBRATION

Ve = Vmax/log10 -1 (dB/20)

The signal conditioning module also typically provides a shuntcalibration feature. See Figure 7. It lets users switch in an extremely
stable, internal shunt cal resistor. For example, a shunt resistor
can be calculated to simulate a full load. Applying a shunt resistor
is a convenient way to simulate an unbalance without having
to apply a physical load.

= 5.00/31,622= 0.158 mV%error = (Ve/Vs)100		= (0.158mV/20mV)100		= 0.79%Transducers and Load Cells
Strain gages are commercially available in prefabricated modules
such as load cells that measure force, tension, compression, andtorque. Load cells typically use a full-bridge configuration andcontain four leads for bridge excitation and measurement. The
manufacturers provide calibration and accuracy information.

Where: Ve = error voltage, V		Vs = signal voltage, 20 mV

		Vmax = maximum voltage, 5V

		

CMRR = 90 dB(–)

The 6224 utilizes a 24-bit ADC, so the old practice of adjusting
gain and offset voltages in hardware to pull out every last bit of a
16-bit ADC’s resolution is no longer necessary. The old method had
one very undesirable consequence; if one set the gain too close to
the maximum, the ADC could limit out and valuable information
would be lost. If the gain were set too low, low level signal information would be lost. The 24-bit ADC has 256 times the resolutionof the 16-bit ADC, so software offset and gain adjustments can be
employed providing great resolution and large overhead.

dB = 20log10(Vs/Ve)= 31,622

Close
to shunt

Strain gage signal conditioning modules usually provide a regulated excitation source with optional Kelvin excitation. Bridge
completion resistors may be connected for quarter and halfbridge strain gages. Instrumentation amplifiers provide input
and scaling gain.

Equation 4: Common-Mode Rejection Ratio		

Rs = 100 kΩ

By comparison, a CMRR of 115 dB introduces only 9 mV of error,
which corresponds to only 0.04% of full scale.

A high common-mode rejection ratio (CMRR) is essential forstrain gage amplifiers. A strain gage signal in a Wheatstonebridge is superimposed on a common-mode voltage equal tohalf the excitation voltage. CMRR is a measure of how well theamplifier rejects common-mode voltages. For example, consider a 10V excitation supply (Vmax = 5V) for a strain gage 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 mVof error, corresponding to about 0.80% full scale, which may
not be acceptable:= log10 -1 (90/20)

350Ω

A bridge may be calibrated with a shunt resistor, which is switchedwith a software command into either one of the two lower legs.

Common-mode rejection ratio

		

350Ω

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Strain Diaphragm Pressure Gagesof the strain gages themselves. Transducers must contain temperaturecompensation circuits to maintain accurate pressure measurements
in environments with widely varying temperatures.

A strained diaphragm pressure gage consists of two or four strain
gages mounted on a thin diaphragm. The gages are wired in a
Wheatstone bridge circuit, including bridge completion resistors
when needed, so the pressure gage is electrically equivalent to aload cell. The output voltage is specified in mV/V of excitation
for a full-scale pressure differential across the diaphragm.

All strained diaphragm pressure gages require a regulated excitation
source. Some gages contain internal regulators, so users can connect
an unregulated voltage from a power supply. Some strained
diaphragm pressure gages also employ internal signal conditioning,which amplifies the mV signal output of the Wheatstone bridge
to a full-scale voltage from 5 to 10V. Gages of this type have lowimpedance outputs. In contrast, other pressure gages have nointernal signal conditioning so their output impedance equals
the Wheatstone bridge resistance (several kΩ for semiconductor
types), and their full-scale output is in mV.

When one side of the diaphragm (called the reference pressureside) is open to the ambient atmospheiore, the gage compares theinlet pressure to the ambient pressure, which is about 14.7 psi at
sea level. When the gage measures ambient pressure, the referencechamber must be sealed with either a vacuum reference (near zeropsi) or the sea-level reference.

MCC Contact Information

Temperature variations can affect the accuracy of strained diaphragmpressure gages. A pressure gage with a sealed non-zero reference
pressure exhibits temperature variations consistent with the ideal
gas law. For example, a 5˚C change in ambient temperature nearnormal room temp (25˚C) produces an error of 1.7% in the pressure
measurement. Temperature variations can also affect the performance

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6224 Strain Measurement Module - Learn more online
The IOtech 6224 module from MCC combines an accurate, instrument class, Ethernet-based module with powerful, easy-to-use
software. It is a major advancement in ease-of-use and functionality. The 6224 features integrated signal conditioning and a
modular design that allows for system expansion. Because it uses an Ethernet connection, modules can be connected directly toa PC or used in remote configurations utilizing multiple modules. Included with each module is Encore interactive measurement software, which couples ease-of-use with advanced functionality.

Features

The 6224 with
Encore software
is a portable,
strain gage
measurement
solution• 12 strain gage inputs• 24-bit/delta-sigma ADC per channel• 50-kHz per channel sample rate
• User programmable excitation• Simultaneous sampling• Shunt calibration• Eight digital I/O• Multiple trigger modes• Compact, portable design• Expandable using multiple modules• Combine with other 6000 Series modules to measure
voltage or temperature

Software• Includes Encore interactive measurement software for
setup, acquisition, display, logging, analysis, and reporting• Advanced feature set with no programming required• True drag-and-drop functionality• Easy-to-use set-up wizards• Drag data directly to Excel®
• Included data analysis tools• Playback mode
• Sophisticated test report capability• Incorporate multiple 6224 devices into one application• Supported Windows® Operating Systems:
Windows 7 and Windows Vista (32-bit or 64-bit),Windows XP SP2 (32-bit), Windows 2000 SP4

Software Overview
Encore is the premier Out-of-the-Box data acquisition software
package and is included with each 6224 module. Encore
combines ease of use with advanced functionality, including
customizable data layouts, powerful analysis, and reporting
capabilities. Instead of having a program to log data, anotherto analyze, and a third to develop report data, Encore includes
the functionality of all three into one package, thus shortening
the learning curve, and saving time and cost.
6000 Series, 6224, and Encore software, are the property of MCC. All other trademarks andtradenames are the property of their respective holders.

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