Sensor Fundamentals

National Instruments Measurement Fundamentals Series

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Sensor Fundamentals

Sensor Terminology

Sensitivity: The sensitivity of the sensor is defined as the slope of the output characteristic curve

(DY/DX in Figure 1) or, more generally, the minimum input of physical parameter that will create a

detectable output change. In some sensors, the sensitivity is defined as the input parameter

change required to produce a standardized output change. In others, it is defined as an output

voltage change for a given change in input parameter. For example, a typical blood pressure

transducer may have a sensitivity rating of 10 mV/V/mm Hg; that is, there will be a 10-mV output

voltage for each volt of excitation potential and each mm Hg of applied pressure.

Sensitivity Error

The sensitivity error (shown as a dotted curve in Figure 1) is a departure from the ideal slope of

the characteristic curve. For example, the pressure transducer discussed above may have an actual

sensitivity of 7.8 mV/V/mm Hg instead of 10 mV/V/mm Hg.

Range: The range of the sensor is the maximum and minimum values of applied parameter that

can be measured. For example, a given pressure sensor may have a range of -400 to +400 mm Hg.

Alternatively, the positive and negative ranges often are unequal. For example, a certain medical

blood pressure transducer is specified to have a minimum (vacuum) limit of -50 mm Hg (Ymin in

Figure 1) and a maximum (pressure) limit of +450 mm Hg (Ymax in Figure 1). This specification is

common, incidentally, and is one reason doctors and nurses sometimes destroy blood pressure

sensors when attempting to draw blood through an arterial line without being mindful of the

position of the fluid stopcocks in the system. A small syringe can exert a tremendous vacuum on a

closed system.


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Figure 1. Ideal curve and sensitivity error. Source: J.J. Carr, Sensors and Circuits Prentice Hall.

Dynamic Range

The dynamic range is the total range of the sensor from minimum to maximum. That is, in terms of

Figure 1, Rdyn = Ymax - l -Yminl.

Precision: The concept of precision refers to the degree of reproducibility of a measurement. In

other words, if exactly the same value were measured a number of times, an ideal sensor would

output exactly the same value every time. But real sensors output a range of values distributed in

some manner relative to the actual correct value. For example, suppose a pressure of exactly 150

mm Hg is applied to a sensor. Even if the applied pressure never changes, the output values from

the sensor will vary considerably. Some subtle problems arise in the matter of precision when the

true value and the sensor's mean value are not within a certain distance of each other

(e.g., the 1-s range of the normal distribution curve).

Resolution: This specification is the smallest detectable incremental change of input parameter

that can be detected in the output signal. Resolution can be expressed either as a proportion of

the reading (or the full-scale reading) or in absolute terms.


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Accuracy: The accuracy of the sensor is the maximum difference that will exist between the actual

value (which must be measured by a primary or good secondary standard) and the indicated value

at the output of the sensor. Again, the accuracy can be expressed either as a percentage of full

scale or in absolute terms.

Offset: The offset error of a transducer is defined as the output that will exist when it should be

zero or, alternatively, the difference between the actual output value and the specified output

value under some particular set of conditions. An example of the first situation in terms of Figure 1

would exist if the characteristic curve had the same sensitivity slope as the ideal but crossed the Y-

axis (output) at b instead of zero. An example of the other form of offset is seen in the

characteristic curve of a pH electrode shown in Figure 2. The ideal curve will exist only at one

temperature (usually 25C), while the actual curve will be between the minimum temperature and

maximum temperature limits depending on the temperature of the sample and electrode.

Figure 2. Typical pH electrode characteristic curve showing temperature sensitivity. Source: J.J. Carr, Sensors and

Circuits Prentice Hall.

Linearity: The linearity of the transducer is an expression of the extent to which the actual

measured curve of a sensor departs from the ideal curve. Figure 3 shows a somewhat exaggerated

relationship between the ideal, or least squares fit, line and the actual measured or calibration line

(Note in most cases, the static curve is used to determine linearity, and this may deviate

somewhat from a dynamic linearity) Linearity is often specified in terms of percentage of

nonlinearity, which is defined as:


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where

Nonlinearity (%) is the percentage of nonlinearity

Din(max) is the maximum input deviation

INf.s. is the maximum, full-scale input

The static nonlinearity defined by Equation 6-1 is often subject to environmental factors, including

temperature, vibration, acoustic noise level, and humidity. It is important to know under what

conditions the specification is valid and departures from those conditions may not yield linear

changes of linearity.

Hysteresis: A transducer should be capable of following the changes of the input parameter

regardless of which direction the change is made; hysteresis is the measure of this property. Figure

4 shows a typical hysteresis curve. Note that it matters from which direction the change is made.

Approaching a fixed input value (point B in Figure 4) from a higher value (point P) will result in a

different indication than approaching the same value from a lesser value (point Q or zero). Note

that input value B can be represented by F(X)1, F(X)2, or F(X)3 depending on the immediate

previous valueclearly an error due to hysteresis.

Figure 3. Ideal versus measured curve showing linearity error. Source: J J Carr, Sensors and Circuits Prentice Hall


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Figure 4. Hysteresis curve. Source: J.J. Carr, Sensors and Circuits Prentice Hall.

Response Time: Sensors do not change output state immediately when an input parameter change occurs. Rather, it will change to the new state over a period of time, called the response

time (Tr in Figure 5). The response time can be defined as the time required for a sensor output to

change from its previous state to a final settled value within a tolerance band of the correct new

value. This concept is somewhat different from the notion of the time constant (T) of the system.

This term can be defined in a manner similar to that for a capacitor charging through a resistance

and is usually less than the response time.

The curves in Figure 5 show two types of response time. In Figure 5a the curve represents the

response time following an abrupt positive going step-function change of the input parameter.

The form shown in Figure 5b is a decay time (Td to distinguish from Tr, for they are not always the

same) in response to a negative going step-function change of the input parameter.


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Figure 5. (a) Rise-time definition; (b) fall-time definition. Source: J.J. Carr, Sensors and Circuits Prentice Hall.

Dynamic Linearity: The dynamic linearity of the sensor is a measure of its ability to follow rapid changes in the input parameter. Amplitude distortion characteristics, phase distortion

characteristics, and response time are important in determining dynamic linearity. Given a system

of low hysteresis (always desirable), the amplitude response is represented by:

F(X) = aX + bX2 + cX

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+ dX4 + + K (6-2)

In Equation 6-2, the term F(X) is the output signal, while the X terms represent the input

parameter and its harmonics, and K is an offset constant (if any). The harmonics become especially

important when the error harmonics generated by the sensor action fall into the same frequency

bands as the natural harmonics produced by the dynamic action of the input parameter. All

continuous waveforms are represented by a Fourier series of a fundamental sinewave and its

harmonics. In any nonsinusoidal waveform (including time - varying changes of a physical

parameter). Harmonics present will be that can be affected by the action of the sensor.


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Figure 6. Output versus input signal curves showing (a) quadratic error; (b) cubic error. Source: J.J. Carr, Sensors and

Circuits Prentice Hall.

The nature of the nonlinearity of the calibration curve (Figure 6) tell something about which

harmonics are present. In Figure 6a, the calibration curve (shown as a dotted line) is asymmetrical,

so only odd harmonic terms exist. Assuming a form for the ideal curve of F(x) = mx + K, Equation

6-2 becomes for the symmetrical case:


4 + + K (6-3)

In the other type of calibration curve (Figure 6b), the indicated values are symmetrical about the

ideal mx + K curve. In this case, F(X) = -F(-X), and the form of Equation 6-2 is:


5 + + K (6-4)


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Now we will take a look at some of the tactics and signals processing criteria that can be adapted

to biomedical applications to improve the nature of the data collected from the sensor.

Taking Thermocouple Temperature Measurements

What Is Temperature?: Qualitatively, the temperature of an object determines the sensation of

warmth or coldness felt by touching it. More specifically, temperature is a measure of the average

kinetic energy of the particles in a sample of matter, expressed in units of degrees on a standard

scale.

What Is a Thermocouple?: One of the most frequently used temperature sensors is the

thermocouple. Thermocouples are very rugged, inexpensive devices that operate over a wide

temperature range. A thermocouple is created whenever two dissimilar metals touch and the

contact point produces a small open-circuit voltage as a function of temperature. This

thermoelectric voltage is known as the Seebeck voltage, named after Thomas Seebeck, who

discovered it in 1821. The voltage is nonlinear with respect to temperature. However, for small

changes in temperature, the voltage is approximately linear, or

(1)

where DV is the change in voltage, S is the Seebeck coefficient, and DT is the change in

temperature.

S varies with changes in temperature, however, causing the output voltages of thermocouples to

be nonlinear over their operating ranges. Several types of thermocouples are available, and

different types are designated by capital letters that indicate their composition according to

American National Standards Institute (ANSI) conventions. For example, a J-type thermocouple

has one iron conductor and one constantan (a copper-nickel alloy) conductor. A complete list of

available thermocouples is shown in Table 1 below.

Table 1. Compositions and Letter Designations of the Standardized Thermocouples

Thermocouple

Type

Conductors Positive Conductors Negative

B Platinum-30% rhodium Platinum-6% rhodium

E Nickel-chromium alloy Copper-nickel alloy

J Iron Copper-nickel alloy

K Nickel-chromium alloy Nickel-aluminum alloy

N Nickel-chromium-silicon alloy Nickel-silicon-magnesium

alloy

R Platinum-13% rhodium Platinum

S Platinum-10% rhodium Platinum


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T Copper Copper-nickel alloy

Thermocouple Measurement and Signal Conditioning: To measure a thermocouple Seebeck

voltage, you cannot simply connect the thermocouple to a voltmeter or other measurement

system, because connecting the thermocouple wires to the measurement system creates

additional thermoelectric circuits.

Figure 1. J-Type Thermocouple

Consider the circuit illustrated in Figure 1, in which a J-type thermocouple is in a candle flame that

has a temperature you want to measure. The two thermocouple wires are connected to the

copper leads of a DAQ board. Notice that the circuit contains three dissimilar metal junctions J1,

J2, and J3. J1, the thermocouple junction, generates a Seebeck voltage proportional to the

temperature of the candle flame. J2 and J3 each have their own Seebeck coefficient and generate

their own thermoelectric voltage proportional to the temperature at the DAQ terminals. To

determine the voltage contribution from J1, you need to know the temperatures of junctions J2

and J3 as well as the voltage-to-temperature relationships for these junctions. You can then

subtract the contributions of the parasitic junctions at J2 and J3 from the measured voltage at

junction J1.

Thermocouples require some form of temperature reference to compensate for these unwanted

parasitic "cold" junctions. The most common method is to measure the temperature at the

reference junction with a direct-reading temperature sensor and subtract the parasitic junction

voltage contributions. This process is called cold-junction compensation. You can simplify

computing cold-junction compensation by taking advantage of some thermocouple characteristics.

By using the Thermocouple Law of Intermediate Metals and making some simple assumptions, you

can see that the voltage a data acquisition system measures depends only on the thermocouple

type, the thermocouple voltage, and the cold-junction temperature. The measured voltage is in

fact independent of the composition of the measurement leads and the cold junctions, J2 and J3.

According to the Thermocouple Law of Intermediate Metals, illustrated in Figure 2, inserting any

type of wire into a thermocouple circuit has no effect on the output as long as both ends of that

wire are the same temperature, or isothermal.


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Figure 2. Thermocouple Law of Intermediate Metals

Consider the circuit in Figure 3. This circuit is similar to the previously described circuit in Figure 1,

but a short length of constantan wire has been inserted just before junction J3 and the junctions

are assumed to be held at identical temperatures. Assuming that junctions J3 and J4 are the same

temperature, the Thermocouple Law of Intermediate Metals indicates that the circuit in Figure 3 is

electrically equivalent to the circuit in Figure 1. Consequently, any result taken from the circuit in

Figure 3 also applies to the circuit illustrated in Figure 1.

Figure 3. Inserting an Extra Lead in the Isothermal Region

In Figure 3, junctions J2 and J4 are the same type (copper-constantan); because both are in the

isothermal region, J2 and J4 are also the same temperature. Because of the direction of the

current through the circuit, J4 contributes a positive Seebeck voltage, and J2 contributes an equal

but opposite negative voltage. Therefore, the effects of the junctions cancel each other, and the

total contribution to the measured voltage is zero. Junctions J1 and J3 are both iron-constantan

junctions, but may be at different temperatures because they do not share an isothermal region.

Because they are at different temperatures, junctions J1 and J3 both produce a Seebeck voltage,

but with different magnitudes. To compensate for the cold junction J3, its temperature is

measured and the contributed voltage is subtracted out of the thermocouple measurement.

Using the notation VJx(Ty) to indicate the voltage generated by the junction Jx at temperature Ty,

the general thermocouple problem is reduced to the following equation:

VMEAS = VJ1(TTC ) + VJ3(Tref ) (2)

where VMEAS is the voltage the DAQ board measures, TTC is the temperature of the thermocouple at

J1, and Tref is the temperature of the reference junction.

Notice that in Equation 2, VJx(Ty) is a voltage generated at temperature Ty with respect to some

reference temperature. As long as both VJ1 and VJ3 are functions of temperature relative to the


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same reference temperature, equation 2 is valid. As stated earlier, for example, NIST

thermocouple reference tables are generated with the reference junction held at 0 C.

Because junction J3 is the same type as J1 but contributes an opposite voltage, VJ3(Tref ) = -VJ1(Tref ).

Because VJ1 is the voltage that the thermocouple type undergoing testing generates, this voltage

can be renamed VTC . Therefore, Equation 2 is rewritten as follows:

VMEAS = VTC (TTC ) - VTC (Tref ) (3)

Therefore, by measuring VMEAS and Tref , and knowing the voltage-to-temperature relationship of

the thermocouple, you can determine the temperature at the hot junction of the thermocouple.

There are two techniques for implementing cold-junction compensation - hardware compensation

and software compensation. Both techniques require that the temperature at the reference

junction be sensed with a direct-reading sensor. A direct-reading sensor has an output that

depends only on the temperature of the measurement point. Semiconductor sensors, thermistors,

or RTDs are commonly used to measure the reference-junction temperature. For example, several

National Instruments SCXI terminal blocks include thermistors located near the screw terminals to

which thermocouple wires are connected.

With hardware compensation, a variable voltage source is inserted into the circuit to cancel the

parasitic thermoelectric voltages. The variable voltage source generates a compensation voltage

according to the ambient temperature, and thus adds the correct voltage to cancel the unwanted

thermoelectric signals. When these parasitic signals are canceled, the only signal a data acquisition

system measures is the voltage from the thermocouple junction. With hardware compensation,

the temperature at the data acquisition system terminals is irrelevant because the parasitic

thermocouple voltages have been canceled. The major disadvantage of hardware compensation is

that each thermocouple type must have a separate compensation circuit that can add the correct

compensation voltage; this fact makes the circuit fairly expensive. Hardware compensation is also

generally less accurate than software compensation.

Alternatively, you can use software for cold-junction compensation. After a direct-reading sensor

measures the reference-junction temperature, software can add the appropriate voltage value to

the measured voltage to eliminate the parasitic thermocouple effects. Recall Equation 3, which

states that the measured voltage, VMEAS, is equal to the difference between the voltages at the hot

junction (thermocouple) and cold junction.

Thermocouple output voltages are highly nonlinear. The Seebeck coefficient can vary by a factor of

three or more over the operating temperature range of some thermocouples. For this reason, you

must either approximate the thermocouple voltage-versus-temperature curve using polynomials,

or use a look-up table. The polynomials are in the following form:

T = a0 + a1v + a2v2 + ... + anv

n (4)


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where v is the thermocouple voltage in volts, T is the temperature in degrees Celsius, and a0

through an are coefficients that are specific to each thermocouple type.

Eliminating Noise

Thermocouple output signals are typically in the millivolt range, making them susceptible to noise.

Lowpass filters are commonly used in thermocouple data acquisition systems to effectively

eliminate high frequency noise in thermocouple measurements. For instance, lowpass filters are

useful for removing the 60 Hz power line noise that is prevalent in many laboratory and plant

settings.

You can also significantly improve the noise performance of your system by amplifying the low-

level thermocouple voltages near the signal source (measurement point). Because thermocouple

output voltage levels are very low, you should choose a gain that optimizes the input limits of the

analog-to-digital converter (ADC). The output range of all thermocouple types falls between -10

mV and 80 mV.

Another source of noise is due to thermocouples being mounted or soldered directly to a

conductive material, like steel or water. This configuration makes thermocouples particularly

susceptible to common-mode noise and ground loops. Isolation helps to prevent ground loops

from occurring, and can dramatically improve the rejection of common-mode noise. With

conductive material that has a large common-mode voltage, isolation is required as non-isolated

amplifiers cannot measure signals with large common- mode voltages.

To see how filtering and amplification can dramatically improve the accuracy of thermocouple

measurements, visit the Online Accuracy Lab.

Connecting a Thermocouple to an Instrument: For this section, consider an example using an NI

cDAQ-9172 chassis and an NI 9211 C Series thermocouple module. Similar procedures apply for

connecting a thermocouple to different instruments (see figure 4).

Required equipment includes the following:

- cDAQ-9172 eight-slot Hi-Speed USB chassis for NI CompactDAQ

- NI 9211 four-channel, 14 S/s, 24-bit, 80 mV thermocouple input module

- J-type thermocouple


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Figure 4. NI CompactDAQ System with NI 9211 Thermocouple Module

The NI 9211 has a 10-terminal, detachable screw-terminal connector that provides connections for

four thermocouple input channels. Each channel has a terminal to which you can connect the

positive lead of the thermocouple, TC+, and a terminal to which you can connect the negative lead

of the thermocouple, TC. The NI 9211 also has a common terminal, COM, which is internally

connected to the isolated ground reference of the module. Refer to Figure 5 for the terminal

assignments for each channel and Figure 6 for a connection schematic.

Figure 5. Terminal Assignments


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Figure 6. Connection Schematic

Measuring Temperature with an RTD or Thermistor

RTDs and Thermistors.

RTDS

Resistance temperature detectors (RTDs) operate on the principle of changes in electrical

resistance of pure metals and are characterized by a linear positive change in resistance with

temperature. Typical elements used for RTDs include nickel (Ni) and copper (Cu), but platinum (Pt)

is by far the most common because of its wide temperature range, accuracy, and stability.

RTDs are constructed by one of two different manufacturing configurations. Wire-wound RTDs are

constructed by winding a thin wire into a coil. A more common configuration is the thin-film

element, which consists of a very thin layer of metal laid out on a plastic or ceramic substrate.

Thin-film elements are cheaper and more widely available because they can achieve higher

nominal resistances with less platinum. To protect the RTD, a metal sheath encloses the RTD

element and the lead wires connected to it.

RTDs are popular because of their excellent stability, and exhibit the most linear signal with

respect to temperature of any electronic temperature sensor. They are generally more expensive

than alternatives, however, because of the careful construction and use of platinum. RTDs are also

characterized by a slow response time and low sensitivity; and because they require current

excitation, they can be prone to self-heating.

RTDs are commonly categorized by their nominal resistance at 0 C. Typical nominal resistance

values for platinum thin-film RTDs include 100 and 1000 . The relationship between resistance

and temperature is very nearly linear and follows the equation


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For 0 C RT = R0 [ 1 + aT + bT2 ]

Where RT = resistance at temperature T

R0 = nominal resistance

a, b, and c are constants used to scale the RTD

The resistance/temperature curve for a 100 W platinum RTD, commonly referred to as Pt100, is

shown below:

Figure 1. Resistance-Temperature Curve for a 100 Platinum RTD, a = 0.00385

The most common RTD is the platinum thin-film with an a of 0.385%/C and is specified per DIN EN

60751. The a value depends on the grade of platinum used, and also commonly include

0.3911%/C and 0.3926%/C. The a value defines the sensitivity of the metallic element, but is

normally used to distinguish between resistance/temperature curves of various RTDs.

Table 1. Callendar-Van Dusen Coefficients Corresponding to Common RTDs

Standard Temperature

Coefficient (a)

A B C

DIN 43760 0.003850

American 0.003911

ITS-90 0.003926

* For temperatures below 0 C only; C = 0.0 for temperatures above 0 C.

Thermistors

Thermistors (thermally sensitive resistors) are similar to RTDs in that they are electrical resistors

whose resistance changes with temperature. Thermistors are manufactured from metal oxide

semiconductor material which is encapsulated in a glass or epoxy bead.

Thermistors have a very high sensitivity, making them extremely responsive to changes in

temperature. For example, a 2252 W thermistor has a sensitivity of -100 W/C at room

temperature. In comparison, a 100 W RTD has a sensitivity of 0.4 W/C. Thermistors also have a

low thermal mass that results in fast response times, but are limited by a small temperature range.


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Thermistors have either a negative temperature coefficient (NTC) or a positive temperature

coefficient (PTC). The first has a resistance which decreases with increasing temperature and the

latter exhibits increased resistance with increasing temperature. Figure 2 shows a typical

thermistor temperature curve compared to a typical 100 W RTD temperature curve:

Figure 2. Resistance versus Temperature for a Typical Thermistor and RTD

RTD and Thermistor Measurement and Signal Conditioning: Because RTDs and thermistors are

resistive devices, you must supply them with an excitation current and then read the voltage

across their terminals. If extra heat cannot be dissipated, I2R heating caused by the excitation

current can raise the temperature of the sensing element above that of the ambient temperature.

Self-heating will actually change the resistance of the RTD or thermistor, causing error in the

measurement. The effects of self-heating can be minimized by supplying lower excitation current.

The easiest way to connect an RTD or thermistor to a measurement device is with a 2-wire

connection.

Figure 3. Making a 2-Wire RTD/Thermistor Measurement

With this method, the two wires that provide the RTD or thermistor with its excitation current are

also used to measure the voltage across the sensor. Because of the low nominal resistance of

RTDs, measurement accuracy can be drastically affected by lead wire resistance. For example, lead


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wires with a resistance of 1 W connected to a 100 W platinum RTD cause a 1% measurement

error.

A 3-wire or 4-wire connection method can eliminate the effects of lead wire resistance. The

connection places leads on a high impedance path through the measurement device, effectively

eliminating error caused by lead wire resistance. It is not necessary to use a 3 or 4-wire connection

method for thermistors because they typically have much higher nominal resistance values than

RTDs. A diagram of a 4-wire connection is shown below.

Figure 4. Making a 4-Wire RTD Measurement

RTD and thermistor output signals are typically in the millivolt range, making them susceptible to

noise. Lowpass filters are commonly used in RTD and thermistor data acquisition systems to

effectively eliminate high frequency noise in RTD and thermistor measurements. For instance,

lowpass filters are useful for removing the 60 Hz power line noise that is prevalent in most

laboratory and plant settings.

DAQ Systems for Measuring Temperature with RTDs and Thermistors:

Using SCXI with RTDs and Thermistors

National Instruments SCXI is a signal conditioning system for PC-based data acquisition systems.

An SCXI system consists of a shielded chassis that houses a combination of signal conditioning

input and output modules, which perform a variety of signal conditioning functions. You can

connect many different types of sensors, including RTDs and thermistors, directly to SCXI modules.

The SCXI system can operate as a front-end signal conditioning system for PC plug-in data

acquisition (DAQ) devices (PCI and PCMCIA) or PXI DAQ modules.


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Figure 5. SCXI Signal Conditioning System

SCXI offers a variety of analog and digital signal conditioning modules for various types of signals,

including RTDs and thermistors. Table 1 includes the features of SCXI modules that can be used for

RTD and thermistor measurements.

Table 1. SCXI Signal Conditioning Modules for RTDs and Thermistors

SCXI-1121 SCXI-1122 SCXI-1102 w/ SCXI

1581

Number of inputs 4 16 (devices in series)

8 (4-wire scanning mode)

32

Amplifier gains 1 to 2000 jumper

selectable

1 to 2000 jumper

selectable

1 or 100 software

selectable per

channel

Filtering options 4 Hz or 10 kHz 4 Hz or 4 kHz software

programmable

2 Hz

Isolation 250 Vrms 480 Vrms N/A

Excitation Values 3.33 V, 10 V

0.15 mA, 0.45 mA

3.33 V

1 mA

100 A

Recommended

terminal block for

RTDs/Thermistors

SCXI-1320 or SCXI-1322 SCXI-1322 SCXI-1300 or SCXI-

1303

Measuring Pressure with Pressure Sensors


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What is Pressure?: Pressure is defined as force per unit area that a fluid exerts on its

surroundings.[1] For example, pressure, P, is a function of force, F, and area, A.

P = F/A

A container full of gas contains innumerable atoms and molecules that are constantly bouncing

of its walls. The pressure would be the average force of these atoms and molecules on its walls per

unit of area of the container. Moreover, pressure does not have to be measured along the wall of

a container but rather can be measured as the force per unit area along any plane. Air pressure,

for example, is a function of the weight of the air pushing down on Earth. Thus, as the altitude

increases, pressure decreases. Similarly, as a scuba diver or submarine dives deeper into the

ocean, the pressure increases.

The SI unit for pressure is the Pascal (N/m2), but other common units of pressure include pounds

per square inch (PSI), atmospheres (atm), bars, inches of mercury (in Hg), and millimeters of

mercury (mm Hg).

A pressure measurement can be described as either static or dynamic. The pressure in cases

where no motion is occurring is referred to as static pressure. Examples of static pressure include

the pressure of the air inside a balloon or water inside a basin. Often times, the motion of a fluid

changes the force applied to its surroundings. Such a pressure measurement is known as dynamic

pressure measurement. For example, the pressure inside a balloon or at the bottom of a water

basin would change as air is let out of the balloon or as water is poured out of the basin.

Head pressure(or pressure head) measures the static pressure of a liquid in a tank or a pipe. Head

pressure, P, is a function solely on the height of the liquid, h, and weight density, w, of the liquid

being measured as shown in Figure 1 below.

Figure 1. Head Pressure Measurement

The pressure on a scuba diver swimming in the ocean would be the diver's depth multiplied by the

weight of the ocean (64 pounds per cubic foot). A scuba diver diving 33 feet into the ocean would

have 2112 pounds of water on every square foot of his body. That translates to 14.7 PSI.

Interestingly enough, the atmospheric pressure of the air at sea level is also 14.7 PSI or 1 atm.

Thus, 33 feet of water create as much pressure as 5 miles of air! The total pressure on a scuba

diver 33 feet deep ocean would be the combined pressure caused by the weight of the air and the


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water, that would be 29.4 PSI or 2 atm.

A pressure measurement can further be described by the type of measurement being performed.

There are three types of pressure measurements: absolute, gauge, and differential. Absolute

pressure measurement is measured relative to a vacuum (Figure 2). Often times, the abbreviations

PAA (Pascals Absolute) or PSIA (Pounds per Square Inch Absolute) are used to describe absolute

pressure.

Figure 2. Absolute Pressure Sensor [3]

Gauge pressure is measured relative to ambient atmospheric pressure (Figure 3). Similar to

absolute pressure, the abbreviations PAG (Pascals Gauge) or PSIG (Pounds per Square Inch

Gauge) are used to describe gauge pressure.

Figure 3. Gauge Pressure Sensor [3]

Differential pressure is similar to gauge pressure, but instead of measuring relative to ambient

atmospheric pressure, differential measurements are taken with respect to a specific reference

pressure (Figure 4). Also, the abbreviations PAD (Pascals Differential) or PSID (Pounds per Square

Inch Differential) are used to describe differential pressure.


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Figure 4. Differential Pressure Sensor [3]

The Pressure Sensor: Because of the great variety of conditions, ranges, and materials for which

pressure must be measured, there are many different types of pressure sensor designs. Often

pressure can be converted to some intermediate form, such as displacement. The sensor then

converts this displacement into an electrical output such as voltage or current. The three most

universal types of pressure transducers of this form are the strain gage, variable capacitance, and

piezoelectric.

Of all the pressure sensors, Wheatstone bridge (strain based) sensors are the most common,

offering solutions that meet varying accuracy, size, ruggedness, and cost constraints. Bridge

sensors are used for high and low pressure applications, and can measure absolute, gauge, or

differential pressure. All bridge sensors make use of a strain gauge and a diaphragm (Figure 4).

Figure 4. Cross Section of a Typical Strain Gauge Pressure Sensor [3]

When a change in pressure causes the diaphragm to deflect, a corresponding change in resistance

is induced on the strain gauge, which can be measured by a Data Acquisition (DAQ) System. These

strain gauge pressure transducers come in several different varieties: the bonded strain gauge, the

sputtered strain gauge, and the semiconductor strain gauge.


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In the bonded strain gauge pressure sensor, a metal foil strain gauge is actually glued or bonded to

the surface where strain is being measured. These bonded foil strain gauges (BFSG) have been the

industry standard for years and are continually used because of their quick 1000 Hz response

times to changes in pressure as well as their large -452F to -525F operating temperature.

Sputtered strain gauge manufacturers sputter a layer of glass onto the diaphragm and then

deposit a thing metal film strain gauge on to the transducers diaphragm. Sputtered strain gauge

sensors actually form a molecular bond between the strain gauge element, the insulating later,

and the sensing diaphragm. These gauges are most suitable for long-term use and harsh

measurement conditions.

Integrated circuit manufacturers have developed composite pressure sensors that are particularly

easy to use. These devices commonly employ a semiconductor diaphragm onto which a

semiconductor strain gauge and temperature-compensation sensor have been grown. Appropriate

signal conditioning is included in integrated circuit form, providing a dc voltage or current linearly

proportional to pressure over a specified range.

The capacitance between two metals plates changes if the distance between these two plates

changes. A variable capacitance pressure transducer (Figure 5), measures the change in

capacitance between a metal diaphragm and a fixed metal plate. These pressure transducers are

generally very stable and linear, but are sensitive to high temperatures and are more complicated

to setup than most pressure sensors.

Figure 5. Capacitance Pressure Transducer [4]

Piezoelectric pressure transducer (Figure 6) take advantage of the electrical properties of naturally

occurring crystals such as quartz. These crystals generate an electrical charge when they are

strained. Piezoelectric pressure sensors do not require an external excitation source and are very

rugged. The sensors however, do require charge amplification circuitry and very susceptible to

shock and vibration.


23

Figure 6. Piezoelectric Pressure Transducer [4]

A common cause of sensor failure in pressure measurement applications is dynamic impact, which

results in sensor overload. A classic example of overloading a pressure sensor is known as the

water hammer phenomenon. This occurs when a fast moving fluid is suddenly stopped by the

closing of a valve. The fluid has momentum that is suddenly arrested, which causes a minute

stretching of the vessel in which the fluid is constrained. This stretching generates a pressure spike

that can damage a pressure sensor. To reduce the effects of water hammer, sensors are often

mounted with a snubber between the sensor and the pressure line. A snubber is usually a mesh

filter or sintered material that allows pressurized fluid through but does not allow large volumes of

fluid through and therefore prevents pressure spikes in the event of water hammer. A snubber is a

good choice to protect your sensor in certain applications, but in many tests the peak impact

pressure is the region of interest. In such a case you would want to select a pressure sensor that

does not include overprotection. [3]

Pressure Measurement: As described above, the natural output of a pressure transducer is a

voltage. Most strain based pressure transducers will output a small mV voltage. This small signal

requires several signal conditioning considerations that are discussed in the next section.

Additionally, many pressure transducers will output a conditioned 0-5V signal or 4-20 mA current.

Both of these outputs are linear across the working range of the transducer. For example both 0 V

and 4 mA correspond to a 0 pressure measurement. Similarly, 5 volts and 20 mA correspond to the

Full Scale Capacity or the maximum pressure the transducer can measure. The 0-5V and 4-20 mA

signals can easily be measured by National Instruments Multi-function Data Acquisition (DAQ)

hardware.

Signal Conditioning for Pressure Sensors: As with any other bridge based sensor, there are several

signal conditioning considerations. To ensure accurate bridge measurements, it is important to

consider the following:

Bridge completion

Excitation

Remote sensing

Amplification

Filtering

Offset


24

Shunt Calibration

Each of these considerations are addressed thoroughly in the Measuring Strain with Strain Gauges

tutorial linked below.

Once you have obtained a measurable voltage signal, that signal must be converted to actual units

of pressure. Pressure sensors generally produce a linear response across their range of operation,

so linearization is often unnecessary, but you will need some hardware or software to convert the

voltage output of the sensor into a pressure measurement. The conversion formula you will use

depends on the type of sensor you are using, and will be provided by the sensor manufacturer. A

typical conversion formula will be a function of the excitation voltage, full scale capacity of the

sensor, and a calibration factor.

For example, a pressure trandsducer with a full scale capacity of 10,000 PSI and a calibration factor

of 3mv/V and given an excitation voltage of 10V DC produces a measured voltage of 15 mV, the

measured pressure would be 5000 PSI.

After you have properly scaled your signal, it is necessary to obtain a proper rest position. Pressure

sensors (whether absolute or gauge) have a certain level that is identified as the rest position, or

reference position. The strain gauge should produce 0 volts at this position. Offset nulling circuitry

adds or removes resistance from one of the legs of the strain gauge to achieve this "balanced"

position. Offset nulling is critical to ensure the accuracy of your measurement and for best results

should be performed in hardware rather than software.

DAQ Systems for Pressure Measurements:

C Series Hardware for a Modular, Flexible System

National Instruments C Series hardware for strain(bridge) based pressure sensors include two

modules with varying specifications and several module carriers to create a flexible, modular

system. The NI 9237 module can measure quarter, half, and full-bridge sensors including pressure

sensors. The NI 9237 is a 4 channel module that samples at 24-bits of resolution and 50kS/s/ch for

true simultaneous measurements. Another C Series module for pressure measurement is the NI

9219 which also measures quarter, half, and full bridge sensors. The NI 9219 has ch-ch isolation,

24-bit ADCs, and samples at 100S/s/ch. In addition to bridge measurements, the NI 9219 is a

universal module which means it can also measure thermocouples, RTDs, voltage, current, and

resistance. Both the NI 9237 and NI 9219 modules can power strain gages or pressure

transducers.


25

There are several options to use these modules. They are both supported by the USB single

module carrier, NI CompactDAQ chassis, and CompactRIO chassis for programming and data

storage (Figure 7). The 9219 and 9237 modules can also be used with the Ethernet or Wireless

carrier (Figure 8). Using this communication interfaces allows to implement data acquisition

systems located over a large area or where the communication though cable is inconvenient.

Figure 7. USB CompactDAQ, CompactRIO and C Series USB Carrier shown with modules

Figure 8. Ethernet C Series Single Module Carrier with NI 9219 and Wi-Fi C Series Single Module Carrier with NI 9237

Using SCXI with Pressure Measurements

National Instruments SCXI is a signal conditioning system for PC-based data acquisition systems

(Figure 9). An SCXI system consists of a shielded chassis that houses a combination of signal

conditioning input and output modules, which perform a variety of signal conditioning functions.

You can connect many different types of sensors, including absolute and gauge pressure sensors,

directly to SCXI modules. The SCXI system can operate as a front-end signal conditioning system

for PC plug-in data acquisition (DAQ) devices (PCI and PCMCIA) or PXI DAQ modules.


26

Figure 9. A Typical National Instruments SCXI System

SCXI offers an excellent solution for measuring pressure. The SCXI-1520 universal strain-gauge

module is ideal for taking strain based pressure measurements. It provides 8 simultaneous

sampled analog input channels each with bridge completion, programmable excitation (0-10 V),

remote excitation sensing, programmable gain amplification (1-1000), a programmable 4-pole

Butterworth filter (10 Hz, 100 Hz, 1 kHz, 10kHz), offset nulling, and shunt calibration. The SCXI-

1314 terminal block provides screw terminals for easy connections to your sensors. Additionally,

the SCXI-1314T includes a built-in TEDS reader for Class II bridge-based smart TEDS sensors.

Recommended starter kit for Pressure SCXI DAQ System:

1. SCXI-1600 DAQ module

2. SCXI chassis

3. SCXI-1520 modules and SCXI-1314/SCXI-1314T terminal blocks

4. Refer to ni.com/sensors for recommended sensor vendors

For a customized solution, see the SCXI Advisor linked below.

Using SC Series DAQ with Strain Based Pressure Sensors

For high performance integrated DAQ and signal conditioning, the National Instruments PXI-4220

(Figure 10), part of the SC Series, provides an excellent measurement solution. SC Series DAQ

offers up to 333 kS/s measurements with 16-bit resolution, and combines data acquisition and

signal conditioning into one plug in board. The PXI-4220 is a 200 kS/s, 16 bit DAQ board with

programmable excitation, gain, and 4-pole Butterworth filter. Each input channel of the PXI-4220

also includes a 9-pin D-Sub connector for easy connection to bridge sensors, and programmable

shunt and null calibration circuitry. The PXI-4220 provides the perfect solution for dynamic

pressure measurements with low channel counts.


27

Figure 10. National Instruments PXI-4220

Recommended starter kit for Pressure SC Series DAQ System:

1. PXI chassis

2. PXI embedded controller

3. PXI-4220 modules


Accelerometer Principles

Spring-Mass System: Newton's law simply states that if a mass, m, is undergoing an acceleration,

a, then there must be a force F acting on the mass and given by F = ma. Hooke's law states that if a

spring of spring constant k is stretched (extended) from its equilibrium position for a distance Dx,

then there must be a force acting on the spring given by F = kDx.

FIGURE 5.23 The basic spring-mass system accelerometer.


28

In Figure 5.23a we have a mass that is free to slide on a base. The mass is connected to the base by

a spring that is in its unextended state and exerts no force on the mass. In Figure 5.23b, the whole

assembly is accelerated to the left, as shown. Now the spring extends in order to provide the force

necessary to accelerate the mass. This condition is described by equating Newton's and Hooke's

laws:

ma = kDx (5.25)

where k = spring constant in N/m

Dx = spring extension in m

m = mass in kg

a = acceleration in m/s2

Equation (5.25) allows the measurement of acceleration to be reduced to a measurement of

spring extension (linear displacement) because

If the acceleration is reversed, the same physical argument would apply, except that the spring is

compressed instead of extended. Equation (5.26) still describes the relationship between spring

displacement and acceleration.

The spring-mass principle applies to many common accelerometer designs. The mass that converts

the acceleration to spring displacement is referred to as the test mass or seismic mass. We see,

then, that acceleration measurement reduces to linear displacement measurement; most designs

differ in how this displacement measurement is made.

Natural Frequency and Damping: On closer examination of the simple principle just described, we

find another characteristic of spring-mass systems that complicates the analysis. In particular, a

system consisting of a spring and attached mass always exhibits oscillations at some characteristic

natural frequency. Experience tells us that if we pull a mass back and then release it (in the

absence of acceleration), it will be pulled back by the spring, overshoot the equilibrium, and

oscillate back and forth. Only friction associated with the mass and base eventually brings the

mass to rest. Any displacement measuring system will respond to this oscillation as if an actual

acceleration occurs. This natural frequency is given by

where fN = natural frequency in Hz

k = spring constant in N/m

m = seismic mass in kg

The friction that eventually brings the mass to rest is defined by a damping coefficient , which has


29

the units of s-1

. In general, the effect of oscillation is called transient response, described by a

periodic damped signal, as shown in Figure 5.24, whose equation is

XT(t) = Xoe-t

sin(2pfNt) (5.28)

where Xr(t) = transient mass position

Xo = peak position, initially

= damping coefficient

fN = natural frequency

The parameters, natural frequency, and damping coefficient in Equation (5.28) have a profound

effect on the application of accelerometers.

Vibration Effects: The effect of natural frequency and damping on the behavior of spring-mass

accelerometers is best described in terms of an applied vibration. If the spring-mass system is

exposed to a vibration, then the resultant acceleration of the base is given by Equation (5.23)

a(t) = -w2xo sin wt

If this is used in Equation (5.25), we can show that the mass motion is given by

where all terms were previously denned and w = 2pf, with/the applied frequency.

FIGURE 5.24 A spring-mass system exhibits a natural oscillation with damping as response to an impulse input.

FIGURE 5.25 A spring-mass accelerometer has been attached to a table which is exhibiting vibration. The table peak

motion is xo and the mass motion is Dx.


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To make the predictions of Equation (5.29) clear, consider the situation presented in Figure 5.25.

Our model spring-mass accelerometer has been fixed to a table that is vibrating. The xo in Equation

(5.29) is the peak amplitude of the table vibration, and Dx is the vibration of the seismic mass

within the accelerometer. Thus, Equation (5.29) predicts that the seismic-mass vibration peak

amplitude varies as the vibration frequency squared, but linearly with the table-vibration

amplitude. However, this result was obtained without consideration of the spring-mass system

natural vibration. When this is taken into account, something quite different occurs.

Figure 5.26a shows the actual seismic-mass vibration peak amplitude versus table-vibration

frequency compared with the simple frequency squared

prediction.You can see that there is a resonance effect when the

table frequency equals the natural frequency of the accelerometer,

that is, the value of Dx goes through a peak. The amplitude of the

resonant peak is determined by the amount of damping. The seismic-

mass vibration is described by Equation (5.29) only up to about

fN/2.5.

Figure 5.26b shows two effects. The first is that the actual seismic-mass motion is limited by the

physical size of the accelerometer. It will hit "stops" built into the assembly that limit its motion

during resonance. The figure also shows that for frequencies well above the natural frequency, the

motion of the mass is proportional to the table peak motion, xo, but not to the frequency. Thus, it

has become a displacement sensor. To summarize:

1. f < fN - For an applied frequency less than the natural frequency, the natural frequency has little

effect on the basic spring-mass response given by Equations (5.25) and (5.29). A rule of thumb

states that a safe maximum applied frequency is f < 1/2.5fN.

2. f > fN - For an applied frequency much larger than the natural frequency, the accelerometer

output is independent of the applied frequency. As shown in Figure 5.26b, the accelerometer

becomes a measure of vibration displacement xo of Equation (5.20) under these circumstances. It

is interesting to note that the seismic mass is stationary in space in this case, and the housing,

which is driven by the vibration, moves about the mass. A general rule sets f > 2.5 fN for this case.

Generally, accelerometers are not used near the resonance at their natural frequency because of

high nonlinearities in output.


31

FIGURE 5.26 In (a) the actual response of a spring-mass system to vibration is compared to the simple w

2 prediction In

(b) the effect of various table peak motion is shown

EXAMPLE 5.14

An accelerometer has a seismic mass of 0.05 kg and a spring constant of 3.0 X 103 N/m Maximum

mass displacement is 0 02 m (before the mass hits the stops). Calculate (a) the maximum

measurable acceleration in g, and (b) the natural frequency.

Solution

We find the maximum acceleration when the maximum displacement

occurs, from Equation (5.26).

a.


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or because

b. The natural frequency is given by Equation (5.27).

Measuring Strain with Strain Gages

What Is Strain? Strain is the amount of deformation of a body due to an applied force. More

specifically, strain (e) is defined as the fractional change in length, as shown in Figure 1.

Figure 1. Definition of Strain

Strain can be positive (tensile) or negative (compressive). Although dimensionless, strain is

sometimes expressed in units such as in./in. or mm/mm. In practice, the magnitude of measured

strain is very small. Therefore, strain is often expressed as microstrain (me), which is e x 10-6

.

When a bar is strained with a uniaxial force, as in Figure 1, a phenomenon known as Poisson Strain


33

causes the girth of the bar, D, to contract in the transverse, or perpendicular, direction. The

magnitude of this transverse contraction is a material property indicated by its Poisson's Ratio. The

Poisson's Ratio n of a material is defined as the negative ratio of the strain in the transverse

direction (perpendicular to the force) to the strain in the axial direction (parallel to the force), or n

= eT/e. Poisson's Ratio for steel, for example, ranges from 0.25 to 0.3.

The Strain Gage: While there are several methods of measuring strain, the most common is with a

strain gage, a device whose electrical resistance varies in proportion to the amount of strain in the

device. The most widely used gage is the bonded metallic strain gage.

The metallic strain gage consists of a very fine wire or, more commonly, metallic foil arranged in a

grid pattern. The grid pattern maximizes the amount of metallic wire or foil subject to strain in the

parallel direction (Figure 2). The cross-sectional area of the grid is minimized to reduce the effect

of shear strain and Poisson Strain. The grid is bonded to a thin backing, called the carrier, which is

attached directly to the test specimen. Therefore, the strain experienced by the test specimen is

transferred directly to the strain gage, which responds with a linear change in electrical resistance.

Strain gages are available commercially with nominal resistance values from 30 to 3000 , with

120, 350, and 1000 being the most common values.

Figure 2. Bonded Metallic Strain Gage

It is very important that the strain gage be properly mounted onto the test specimen so that the

strain is accurately transferred from the test specimen, through the adhesive and strain gage

backing, to the foil itself.

A fundamental parameter of the strain gage is its sensitivity to strain, expressed quantitatively as

the gage factor (GF). Gage factor is defined as the ratio of fractional change in electrical resistance

to the fractional change in length (strain):

The gage factor for metallic strain gages is typically around 2.


34

Strain Gage Measurement: In practice, strain measurements rarely involve quantities larger than a

few millistrain (e x 10-3

). Therefore, to measure the strain requires accurate measurement of very

small changes in resistance. For example, suppose a test specimen undergoes a strain of 500 me. A

strain gage with a gage factor of 2 will exhibit a change in electrical resistance of only 2 (500 x 10-6

)

= 0.1%. For a 120 gage, this is a change of only 0.12 .

To measure such small changes in resistance, strain gages are almost always used in a bridge

configuration with a voltage excitation source. The general Wheatstone bridge, illustrated in

Figure 3, consists of four resistive arms with an excitation voltage, VEX, that is applied across the

bridge.

Figure 3. Wheatstone Bridge

The output voltage of the bridge, VO, is equal to:

From this equation, it is apparent that when R1/R2 = R4/R3, the voltage output VO is zero. Under

these conditions, the bridge is said to be balanced. Any change in resistance in any arm of the

bridge results in a nonzero output voltage.

Therefore, if you replace R4 in Figure 3 with an active strain gage, any changes in the strain gage

resistance will unbalance the bridge and produce a nonzero output voltage. If the nominal

resistance of the strain gage is designated as RG, then the strain-induced change in resistance, DR,

can be expressed as DR = RGGFe, from the previously defined Gage Factor equation. Assuming

that R1 = R2 and R3 = RG, the bridge equation above can be rewritten to express VO/VEX as a function

of strain (see Figure 4). Note the presence of the 1/(1+GFe/2) term that indicates the nonlinearity

of the quarter-bridge output with respect to strain.


35

Figure 4. Quarter-Bridge Circuit

Ideally, we would like the resistance of the strain gage to change only in response to applied

strain. However, strain gage material, as well as the specimen material to which the gage is

applied, also responds to changes in temperature. Strain gage manufacturers attempt to minimize

sensitivity to temperature by processing the gage material to compensate for the thermal

expansion of the specimen material for which the gage is intended. While compensated gages

reduce the thermal sensitivity, they do not totally remove it.

By using two strain gages in the bridge, you can further minimize the effect of temperature. For

example, Figure 5 illustrates a strain gage configuration where one gage is active (RG + DR) and a

second gage is placed transverse to the applied strain. Therefore, the strain has little effect on the

second gage, called the dummy gage. However, any changes in temperature affect both gages in

the same way. Because the temperature changes are identical in the two gages, the ratio of their

resistance does not change, the voltage VO does not change, and the effects of the temperature

change are minimized. NOTE: In the Wheatstone Bridge configuration, the active gage and the

dummy gage should be on the same vertical leg of the bridge.

Figure 5. Use of Dummy Gage to Eliminate Temperature Effects

The sensitivity of the bridge to strain can be doubled by making both gages active in a half-bridge

configuration. For example, Figure 6 illustrates a bending beam application with one bridge

mounted in tension (RG + DR) and the other mounted in compression (RG - DR). This half-bridge

configuration, whose circuit diagram is also illustrated in Figure 6, yields an output voltage that is

linear and approximately doubles the output of the quarter-bridge circuit.


36

Figure 6. Half-Bridge Circuit

Finally, you can further increase the sensitivity of the circuit by making all four of the arms of the

bridge active strain gages in a full-bridge configuration. The full-bridge circuit is shown in Figure 7.

Figure 7. Full-Bridge Circuit

The equations given here for the Wheatstone bridge circuits assume an initially balanced bridge

that generates zero output when no strain is applied. In practice, however, resistance tolerances

and strain induced by gage application generate some initial offset voltage. This initial offset

voltage is typically handled in two ways. First, you can use a special offset-nulling, or balancing,

circuit to adjust the resistance in the bridge to rebalance the bridge to zero output. Alternatively,

you can measure the initial unstrained output of the circuit and compensate in software. This topic

will be discussed in greater detail later.

The equations given above for quarter-, half-, and full-bridge strain gage configurations assume

that the lead wire resistance is negligible. While ignoring the lead resistance may be beneficial to

understanding the basics of strain gage measurements, doing so in practice can be a major source

of error. For example, consider the 2-wire connection of a strain gage shown in Figure 8a. Suppose

each lead wire connected to the strain gage is 15 m long with lead resistance RL equal to 1 .

Therefore, the lead resistance adds 2 of resistance to that arm of the bridge. Besides adding an

offset error, the lead resistance also desensitizes the output of the bridge.

You can compensate for this error by measuring the lead resistance RL and accounting for it in the

strain calculations. However, a more difficult problem arises from changes in the lead resistance

due to temperature fluctuations. Given typical temperature coefficients for copper wire, a slight

change in temperature can generate a measurement error of several microstrain.


37

Using a 3-wire connection can eliminate the effects of variable lead wire resistance because the

lead resistance affects adjacent legs of the bridge. As seen in Figure 8b, changes in lead wire

resistance, RL2, do not change the ratio of the bridge legs R3 and RG. Therefore, any changes in

resistance due to temperature cancel out each other.

Figure 8. 2-Wire and 3-Wire Connections of Quarter-Bridge Circuit

Signal Conditioning for Strain Gages: Strain gage measurement involves sensing extremely small

changes in resistance. Therefore, proper selection and use of the bridge, signal conditioning,

wiring, and data acquisition components are required for reliable measurements. To ensure

accurate strain measurements, it is important to consider the following:

Bridge completion

Excitation

Remote sensing

Amplification

Filtering

Offset

Shunt calibration

Bridge Completion Unless you are using a full-bridge strain gage sensor with four active gages,

you need to complete the bridge with reference resistors. Therefore, strain gage signal

conditioners typically provide half-bridge completion networks consisting of high-precision

reference resistors. Figure 9a shows the wiring of a half-bridge strain gage circuit to a conditioner

with completion resistors R1 and R2.


38

Figure 9a. Connection of Half-Bridge Strain Gage Circuit

Excitation Strain gage signal conditioners typically provide a constant voltage source to power

the bridge. While there is no standard voltage level that is recognized industry wide, excitation

voltage levels of around 3 and 10 V are common. While a higher excitation voltage generates a

proportionately higher output voltage, the higher voltage can also cause larger errors because of

self-heating.

Remote Sensing If the strain gage circuit is located a distance away from the signal conditioner

and excitation source, a possible source of error is voltage drop caused by resistance in the wires

connecting the excitation voltage to the bridge. Therefore, some signal conditioners include a

feature called remote sensing to compensate for this error. Remote sense wires are connected to

the point where the excitation voltage wires connect to the bridge circuit, as seen in Figure 9b. The

extra sense wires serve to regulate the excitation supply through negative feedback amplifiers to

compensate for lead losses and deliver the needed voltage at the bridge.

Figure 9b. Remote Sensor Error Compensation

Amplification The output of strain gages and bridges is relatively small. In practice, most strain

gage bridges and strain-based transducers output less than 10 mV/V (10 mV of output per volt of

excitation voltage). With 10 V excitation, the output signal is 100 mV. Therefore, strain gage signal

conditioners usually include amplifiers to boost the signal level to increase measurement

resolution and improve signal-to-noise ratios.

Filtering Strain gages are often located in electrically noisy environments. It is therefore essential

to be able to eliminate noise that can couple to strain gages. Lowpass filters, when used with

strain gages, can remove the high-frequency noise prevalent in most environmental settings.


39

Offset Nulling When a bridge is installed, it is very unlikely that the bridge will output exactly

zero volts when no strain is applied. Slight variations in resistance among the bridge arms and lead

resistance will generate some nonzero initial offset voltage. Offset nulling can be performed by

either hardware or software:

1. Software Compensation With this method, you take an initial measurement before strain

input is applied, and use this offset to compensate subsequent measurements. This method is

simple, fast, and requires no manual adjustments. The disadvantage of the software compensation

method is that the offset of the bridge is not removed. If the offset is large enough, it limits the

amplifier gain you can apply to the output voltage, thus limiting the dynamic range of the

measurement.

2. Offset-Nulling Circuit The second balancing method uses an adjustable resistance, a

potentiometer, to physically adjust the output of the bridge to zero. By varying the resistance of

potentiometer, you can control the level of the bridge output and set the initial output to zero

volts.

Shunt Calibration The normal procedure to verify the output of a strain gage measurement

system relative to some predetermined mechanical input or strain is called shunt calibration.

Shunt calibration involves simulating the input of strain by changing the resistance of an arm in the

bridge by some known amount. This is accomplished by shunting, or connecting, a large resistor of

known value (Rs) across one arm of the bridge, creating a known DR as seen in Figure 9c. The

output of the bridge can then be measured and compared to the expected voltage value. The

results are used to correct span errors in the entire measurement path, or to simply verify general

operation to gain confidence in the setup.

Figure 9c: Shunt Resistor connected across R3

DAQ Systems for Strain Gauge Measurements:

Using cDAQ with Strain Gages

NI CompactDAQ hardware provides the plug-and-play simplicity of USB to sensor and electrical

measurements. The NI CompactDAQ system consists of an NI cDAQ-9172 8-slot USB 2.0-compliant


40

chassis that can hold up to eight C Series I/O modules and connect to a PC using a 1.8 m USB cable.

NI CompactDAQ delivers fast and accurate measurements with more than 45 self-contained

measurement modules available. Since all circuitry required for the specific measurement is

contained in the C Series I/O module itself, you can connect many different types of sensors,

including strain gages, directly to the modules.

Figure 10: NI CompactDAQ cDAQ-9172 Chassis with C Series I/O Modules

The NI 9219 is a 4-channel universal C Series module designed for multipurpose testing in any NI

CompactDAQ or CompactRIO chassis. With the NI 9219, you can measure several signals from

sensors such as strain gages, RTDs, thermocouples, load cells, and other powered sensors. The

channels are individually selectable, so you can perform a different measurement type on each of

the four channels. The NI 9219 uses 6-position spring terminal connectors in each channel for

direct signal connectivity and contains built-in quarter, half, and full-bridge support.

For C Series I/O modules specifically designed for the measurement of strain gages, National

Instruments offers the NI 9235, NI 9236, and the NI 9237. These bridge modules contain all the

signal conditioning required to power and measure bridge-based sensors simultaneously. The NI

9235 and NI 9236 are for high count applications with completion for quarter bridge sensors. The

NI 9237 supports up to four full and half bridge sensors and can measure from quarter bridge

strain gages using a completion accessory.

The NI 9237 can perform offset/null as well as shunt calibration and remote sense, making the

module the best choice for strain and bridge measurements.

Recommended Starter Kit for Strain Gage NI CompactDAQ System:

1. cDAQ-9172 chassis

2. NI 9237 with an RJ50 cable and an NI 9949 (full and half bridge) or NI 9944/NI 9945 (quarter

bridge)


Using SCXI with Strain Gages


41

National Instruments SCXI is a signal conditioning system for PC-based instrumentation

applications. An SCXI system consists of a shielded chassis that houses a combination of signal

conditioning input and output modules, which perform a variety of signal conditioning functions.

You can connect many different types of sensors, including strain gages, directly to SCXI modules.

The SCXI system operates as a front-end signal conditioning system for PC plug-in Data Acquisition

devices (USB, PCI, and PCMCIA) or PXI DAQ modules.

Figure 11. SCXI Signal Conditioning System

The SCXI-1520 is an 8-channel universal strain gage input module that offers a variety of features

for strain measurements. With this single module, signals from strain, force, torque, and pressure

sensors can be easily read. The SCXI-1520 also offers a programmable amplifier and programmable

4-pole Butterworth filter on each channel, and simultaneous sampling with track-and-hold

circuitry. In addition, the SCXI-1520 system offers a half-bridge completion resistor network in the

module and a socketed 350 W quarter-bridge completion resistor. Table 1 summarizes some

additional features of the SCXI-1520 that relate to strain gage measurements.

Table 1. SCXI-1520 Features for Strain Gages

Number of channels 8

Multiplexer scan rate Up to 333 kS/s1

Amplifier gain 1 to 1000


42

Excitation voltage source 0.0 to 10.0 V in 0.635 V

increments

Excitation current drive 29 mA throughout

excitation voltage range

Half-bridge completion Yes

Offset nulling Yes

Shunt calibration Yes

Remote excitation sensing Yes

1 Multiplexer scan rate depends on the DAQ device.

Recommended Starter Kit for Strain Gage SCXI DAQ System:

1. USB-1600 USB Data Acquisition and Control Module for SCXI

2. SCXI-1000 chassis

3. SCXI-1520 with SCXI-1314 terminal block


Using SCC with Strain Gage Measurements

National Instruments SCC provides portable, modular signal conditioning for DAQ systems. SCC can

condition a variety of analog I/O and digital I/O signals. SCC DAQ systems include an SC-2345

Series shielded carrier, SCC modules, a cable, and a DAQ device. Figure 12 illustrates an SC-2345

carrier with SCC modules.


43

Figure 12. SC-2345 with SCC Modules

SCC-SG Series modules can be used for conditioning quarter-, half-, and full-bridge strain gages.

Each module has two strain gage input channels, offset nulling circuitry for each channel, and a 2.5

V excitation circuit. Each input channel includes an instrumentation amplifier with differential

inputs and a fixed gain of 100. The output of each amplifier is filtered and buffered to prevent

settling time delays. The SCC-SG01 works with 120 quarter-bridge strain gages, and the SCC-

SG02 works with 350 quarter-bridge strain gages. The SCC-SG03 works with half-bridge strain

gages and the SCC-SG04 works with full-bridge strain gages. Figure 12 illustrates the block diagram

of the SCC-SG01/01 modules.

Figure 12. Block Diagram of the SCC-SG01, SCC-SG02 Quarter-Bridge Modules


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The SCC-SG11 is a dual-channel shunt calibration module for use with the SCC-SG series modules.

Each channel includes two terminals for wiring a switched 301 k, 1 percent, 1/4 resistor across

both channels of a module by writing a logic high to the digital line controlling the SCC-SG11. You

can disable shunt calibration by writing a logic low to the same digital line. Figure 14 illustrates an

example of using the SCC-SG11 shunt calibration module with the SCC-SG02 module.

Figure 13. Using the SCC-SG11 Shunt Calibration Module with the SCC-SG02

Recommended Starter Kit for Strain Gage SCC DAQ System:

1. PCI-6221 DAQ board

2. SC-2345 module carrier

3. SCC-SG01/02 (quarter-bridge), SCC-SG03 (half-bridge), or SCC-SG04 (full-bridge)

4. SCC-SG11 (shunt calibration)

5. Refer to ni.com/sensors for recommended strain gages and full-bridge sensors.

Voltage Measurements: How-To Guide

Voltage Measurement Overview

Voltage is the difference of electrical potential between two points of an electrical or electronic

circuit, expressed in volts.It measures the potential energy of an electric field to cause an electric

current in an electrical conductor.

Most measurement devices can measure, or read, voltage. Two common voltage measurements

are direct current (DC) and alternating current (AC).

Although voltage measurements are the simplest of the different types of analog measurements,

they present unique challenges due to noise considerations.

How to Make a DC Voltage Measurement

Although many sensors output DC voltages that you can measure with a data acquisition device,

the primary concern of this white paper is to examine general DC measurements that do not

involve an intermediary sensor setup.

Voltage Measurement Fundamentals


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To understand how to measure voltages, it is essential to understand the background of how you

take the measurement. Essentially, voltage is the electrical potential difference between two

points of interest in an electrical circuit. However, a common point of confusion is how the

measurement reference point is determined. The measurement reference point is the voltage

level at which the measurement is referenced to.

Reference Point Methods

There are essentially two methods to measure voltages: ground referenced and differential.

Ground Referenced Voltage Measurement

One method is to measure voltage with respect to a common, or a ground point. Oftentimes,

these grounds are stable and unchanging and are most commonly around 0 V. Historically, the

term ground originated from the usual application of ensuring the voltage potential is at 0 V by

connecting the signal directly to the earth.

You can use ground referenced input connections for any channel that meets any of the following

conditions:

The input signal is high-level (greater than 1 V)

The leads connecting the signal to the device are less than 10 ft (3 m)

The input signal can share a common reference point with other signals

The ground reference is provided by either the device taking the measurement or by the external

signal being measured. When the ground is provided by the device, this setup is called ground

referenced single-ended mode (RSE), and when the ground is provided by the signal, the setup is

called nonreferenced single-ended mode (NRSE).

Most instruments offer similar pin configurations for analog input measurements. The following

example demonstrates this type of measurement using an NI CompactDAQ chassis and an NI 9205

analog input module (see Figure 1).

Figure 1. NI CompactDAQ Chassis and NI 9205 Analog Input Module


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Figure 2 shows the connection diagram for RSE voltage measurements using an NI cDAQ-9172

chassis with an NI 9205 as well as the pinouts for the module. In Figure 2, Pin 1 corresponds to the

Analog Input 0 channel and Pin 17 corresponds to the common ground.

Figure 2. Ground Referenced Single-Ended Mode

Figure 3 shows the connection diagram for NRSE voltage measurements using a cDAQ-9172 with

an NI 9205. In the figure, Pin 1 corresponds to the Analog Input 0 channel and Pin 35

corresponds to the Analog Input Sense channel. This channel, specifically for NRSE

measurements, can detect the ground voltage provided by the signal.

Figure 3. Non-referenced Single-Ended Mode


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Differential Voltage Measurement

Another method of measuring voltage is to determine the differential voltage between two

separate points in an electrical circuit. For example, to measure the voltage across a single

resistor, you measure the voltage at both ends of the resistor. The difference between the

voltages is the voltage across the resistor. Usually, differential voltage measurements are useful in

determining the voltage that exists across individual elements of a circuit, or if the signal sources

are noisy.

You can use differential input connections for any channel that meets any of the following

conditions:

The input signal is low-level (less than 1 V)

The leads connecting the signal to the device are greater than 3 m (10 ft)

The input signal requires a separate ground reference point or return signal

The signal leads travel through noisy environments

Figure 4 illustrates the connection diagram for differential voltage measurements using a cDAQ-

9172 with an NI 9205. In the figure, Pin 1 corresponds to the Analog Input 0 channel and Pin 19

corresponds to the Analog Input 8 channel.

In differential mode, the negative signal is wired to the analog pin directly facing the analog

channel that is connected to the positive signal. For example, Analog Input 0 would be

connected to positive, and Analog Input 8 would be connected to the negative signals, and

Analog Input 1 for positive and Analog Input 9 for negative and so on. The disadvantage of

differential mode is that it effectively reduces the number of analog input measurement channels

by half.


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Figure 4. Differential Mode

Types of Signal Sources

Before configuring the input channels and making signal connections, you must determine

whether the signal sources are floating or ground referenced.

Floating Signal Sources

A floating signal source is not connected to the building ground system but has an isolated ground

reference point. Some examples of floating signal sources are outputs of transformers,

thermocouples, battery-powered devices, optical isolators, and isolation amplifiers. An instrument

or device that has an isolated output is a floating signal source. The ground reference of a floating

signal must be connected to the ground of the device to establish a local or onboard reference for

the signal. Otherwise, the measured input signal varies as the source floats outside the common-

mode input range.

Ground Referenced Signal Sources

A ground referenced signal source is connected to the building system ground, so it is already

connected to a common ground point with respect to the device, assuming that the measurement

device is plugged into the same power system as the source. Non-isolated outputs of instruments

and devices that plug into the building power system fall into this category. The difference in

ground potential between two instruments connected to the same building power system is

typically between 1 and 100 mV, but the difference can be much higher if power distribution

circuits are improperly connected. If a grounded signal source is incorrectly measured, this

difference can appear as measurement error. Following the connection instructions for grounded

signal sources can eliminate the ground potential difference from the measured signal.

Figure 5 shows the different types of signal source types as well as the optimal connection

diagrams based on the individual measurement method. Please note that depending on the type

of signal, a particular voltage measurement method may provide better results than others.


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Figure 5. Common Signal Source Types versus Recommended Input Configurations

High-Voltage Measurements and Isolation

There are many issues to consider when measuring higher voltages. When specifying a data

acquisition system, the first question you should ask is whether the system will be safe. Making

high-voltage measurements can be hazardous to your equipment, to the unit under test, and even

to you and your colleagues. To ensure that your system is safe, you should provide an insulation

barrier between the user and hazardous voltages with isolated measurement devices.

Isolation, a means of physically and electrically separating two parts of a measurement device, can

be categorized into electrical and safety isolation. Electrical isolation pertains to eliminating

ground paths between two electrical systems. By providing electrical isolation, you can break

ground loops, increase the common-mode range of the data acquisition system, and level shift the

signal ground reference to a single system ground. Safety isolation references standards that have

specific requirements for isolating humans from contact with hazardous voltages. It also

characterizes the ability of an electrical system to prevent high-voltage and transient voltages to


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be transmitted across its boundary to other electrical systems with which the user may come in

contact.

Incorporating isolation into a data acquisition system has three primary functions: preventing

ground loops, rejecting common-mode voltage, and providing safety.

Ground Loops

Ground loops are the most common source of noise in data acquisition applications. They occur

when two connected terminals in a circuit are at different ground potentials, causing current to

flow between the two points. The local ground of your system can be several volts above or below

the ground of the nearest building, and nearby lightning strikes can cause the difference to rise to

several hundreds or thousands of volts. This additional voltage itself can cause significant error in

the measurement, but the current that causes it can couple voltages in nearby wires as well. These

errors can appear as transients or p

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Sensor Fundamentals