Fundamental Signal Conditioning
AMPLIFICATION

Data Acquisition Block Diagram

Data Acquisition Front Ends

Data acquisition systems differ from single or dualchannel instruments in several ways. They can measureand store data collected from hundreds of channels
simultaneously. However, the majority of systems contain from eight to 32 channels, typically in multiples
of eight. By comparison, a simple voltmeter that canselect a measurement among several different ranges
can be considered a data acquisition system, but theneed to manually change voltage ranges and a lackof data storage hobbles its usefulness.

AnaloginputsFigure 5.01 illustrates a simple data acquisition system consisting of a switching network (multiplexer)
and an analog-to-digital converter (ADC). The main
subject of this chapter, the instrumentation amplifier(IA), is placed between the multiplexer and ADC.
The individual circuit blocks each have uniquecapabilities and limitations, which together define
the system performance. Figure 5.01

Fig. 5.01. A simple data acquisition system iscomposed of a multiplexed input stage, followed byan instrumentation amplifier that feeds one accurate
and relatively expensive ADC. This arrangement
saves the cost of multiple ADCs.

The ADC is the last in a series of stages between theanalog domain and the digitized signal path. In any
sampled-data system, such as a multiplexed dataacquisition system, a sample-and-hold stage preceding the ADC is necessary. The ADC cannot digitize
a time-varying voltage to the full resolution of the
ADC unless the voltage changes relatively slowly
with respect to sample rate. Some ADCs have internal
sample-and-hold circuits or use architectures thatemulate the function of the sample-and-hold stage.
The discussion that follows assumes that the ADC
block includes a suitable sample-and-hold circuit(either internal or external to the chip) to stabilize
the input signal during the conversion period.
The primary parameters concerning ADCs in dataacquisition systems are resolution and speed. Dataacquisition ADCs typically run from 20 kHz to 1 MHz
with resolutions of 16 to 24 bits, and have one of two
types of inputs, unipolar or bipolar. The unipolar-typetypically ranges from 0V to a Figure
positive5.02
or negative voltage such as 5V. The bipolar-type typically ranges froma negative voltage to a positive voltage of the same
magnitude. Many data acquisition systems can readbipolar or unipolar voltages to the full resolution of the
ADC, which requires a level-shifting stage to let bipolar

Mux

IA
ADC
Digital data

Parasitic RC Time Constant
MUX

R
Rsource

+

Ron

–

A

C

Fig. 5.02. The source resistance should be as low
as possible to minimize the time constant of the
MUX’s parasitic capacitance C and series resistanceR. An excessively long time constant can adversely
affect the circuit’s measurement accuracy.
signals use unipolar ADC inputs and vice versa. For
example, a typical 16-bit, 100 kHz ADC has an input
range of -5V to +5V and a full-scale count of 65,536.
Zero volts corresponds to a nominal 32,768 count. If
the number 65,536 divides the 10V range, the quotientis an LSB (least significant bit) magnitude of 153 µv.

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Input and Source Impedance
Rs

Vsig

VADC =MUX Charge Injection Effects

Ri
Vsig
Rs + Ri

Drive signal

Ri
Mux output

Transducer

Fig. 5.03A. The sensor’s source impedance Rs should be
relatively small to increase the voltage divider drop acrossRi, the amplifier’s input. This can substantially improve thesignal-to-noise ratio for mV range sensor signals.

Fig. 5.03B. Analog-switching devices can produce spikes in
the MUX output during level transitions in the drive signal.
This is called charge-injection effect and can be minimized
with low source impedance.

Multiplexing through high source impedances does not work well.
The reason that low source impedance is necessary
in a multiplexed
Figure 5.03
B
system is easily explained with a simple RC circuit shown in Figure
5.02. Multiplexers have a small parasitic capacitance from all signal
inputs and outputs to analog common. These small capacitancevalues affect measurement accuracy when combined with source
resistance and fast sampling rates. A simple RC equivalent circuit
consists of a DC voltage source with a series resistance, a switch,
and a capacitor. When the switch closes at T = 0, the voltage
source charges the capacitor through the resistance. Whencharging 100 pF through 10 kW, the RC time constant is 1 µs. In a
10-µs-time interval (of which 2 µs is available for settling time),
the capacitor only charges to 86% of the value of the signal, which
introduces a major error. But a 1 kW resistor lets the capacitor easily
charge to an accurate value in 20 time constants.

some transducers (piezoelectric, for example) have high source
impedance and should be used with a special charge amplifier.
In addition, multiplexing can greatly reduce a data acquisition
system’s effective input impedance. The charge injection effects
are shown in Figure 5.03B.

Operational Amplifiers

Many sensors develop extremely low-level output signals. The
signals are usually too small for applying directly to low-gain,
multiplexed data acquisition system inputs, so some amplification is necessary. Two common examples of low-level sensors
are thermocouples and strain-gage bridges that typically deliver
full-scale outputs of less than 50 mV.
Most data acquisition systems use a number of different types ofcircuits to amplify the signal before processing. Modern analog
circuits intended for these data acquisition systems comprise basic
integrated operational amplifiers, which are configured easily
to amplify or buffer signals. Integrated operational amplifiers
contain many circuit components, but are typically portrayed onschematic diagrams as a simple logical functional block. A few

Figure 5.03A shows how system input impedance and the transducer’s source impedance combine to form a voltage divider,which reduces the voltage read by the ADC. The input impedance of most input channels is 1 MW or more, so it’s usually
not a problem when the source impedance is low. However,Operational Amplifiers
Rf

V in

+
–

V in

Ri

–
+

V out

A
Gain = –

Ri

Rf

Rf
Gain =

Ri

Inverting

V out

A

Rf
Ri

+1

Non-Inverting

Fig. 5.04. The two basic types of operational amplifiers are called inverting and non-inverting. The stage gain equals the ratio
between the feedback and input resistor values.

Figure 5.04

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Non-Inverting Amplifier Stage

Inverting Amplifier Stage
V(–) = V(+) = 0 V
virtual groundRi 10 kW
Ii

0A
Ed = 0V+–

Vin = 0.5V–+

IF = Ii

IF = Ii

Rf 100 kW

Rf 100 kW

A

Ii

Io

Ri 10 kW

–
0V

Vin

+

Io

A

+

0A
RL

Vin = 0.5V

Vo = VRL

Fig. 5.05. The output polarity of the inverting amplifier is
opposite to that of the input voltage. The closed-loop amplification or gain of this stage is Acl = 10, which is the ratio of Rf/Ri
or 100 kW/10 kW.

–

IL
RL 10 kWVo = VRL + Vi

Fig. 5.06. The input and output polarities of the non-inverting amplifier are the same. The gain of the stage is Acl = 11
or (Rf + Ri)/Ri.

Figure 5.06

external resistors and capacitors determine how they function in
the system. Their extreme versatility makes them the universal
analog building block for signal conditioning.

For example, for a 500 mV input signal and a desired output of -5V:

Vo = Vin(Rf/Ri)
Vo/Vin = Rf/Ri
5/0.50 = Rf/Ri = 10

Most operational amplifier stages are called inverting or
non-inverting. (See Figure 5.04.) A simple equation relating
to each configuration provides the idealized circuit gains as
a function of the input and feedback resistors and capacitors.
Also, special cases of each configuration make up the restof the fundamental building blocks, namely the unity-gain
follower and the difference amplifier.

Therefore, the ratio between input and feedback resistors should
be 10, so Rf must be 100 kW when selecting a 10 kW resistor for
Ri. (See Figure 5.05.)
The maximum input signal that the amplifier can handle without
damage is usually about 2V less than the supply voltage. For example, when the supply is ±15 VDC, the input signal should notexceed ±13 VDC. This is the single most critical characteristic of
the operational amplifier that limits its voltage handling ability.

Inverting Amplifier Stages

The inverter stage is the most basic operational amplifier
configuration. It simply accepts an input signal referenced tocommon, amplifies it, and inverts the polarity at the output
terminals. The open-loop gain of a typical operational amplifier
is in the hundreds of thousands. But the idealized amplifier
used to derive the transfer function assumes a gain of infinity tosimplify its derivation without introducing significant errors incalculating the stage gain. With such a high stage gain, the input
voltage sees only the voltage divider composed of Rf and Ri. The
negative sign in the transfer function indicates that the output
signal is the inverse polarity of the input. Without deriving thetransfer function, the output is calculated from:

Non-Inverting Amplifier Stages

The non-inverting amplifier is similar to the previous circuit
but the phase of the output signal matches the input. Also, thegain equation simply depends on the voltage divider composedof Rf and Ri. (See Figure 5.06.)
The simplified transfer function is:
EQN 5.02. Non-Inverting Amplifier

Vo = Vin(Rf + Ri)/Ri
For the same 500 mV input signal,
Rf = 100 kW, and Ri = 10 kW:

EQN 5.01. Inverting Amplifier

Vo = –Vin(Rf/Ri)
Where:
Vo = output signal, V
Vin = input signal, V
Rf = feedback resistor, W
Ri = input resistor, W

Vo/Vin = (Rf + Ri)/Ri,
Vo = Vi(Rf + Ri)/Ri
Vo = 0.50(100k + 10 k)/10k
Vo = 0.50(110k/10k) = 0.50(11)Vo = 5.5V

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07

Differential Amplifier

Programmable-Gain AmplifierFeedback gain resistor
Rf

+
Vi

100 kW
100 kWRi
100 kW
+

V2
–

+
–

V1

Ri
Terminating
resistor

Optional
groundconnection

g=
–
+

Rf
Ri

A

–
Iin(–) = 0 A

+5 V

A
RL

Rf
100 kW

Vo =g(V1 - V2)

Three 1-kW
pull-upresistors

0.1% resistors

0
1

Fig. 5.07. The output voltage of the basic differential amplifier is the difference between the two inputs, or Acl = g(V1-V2),
where g is the gain factor. Because all resistors in this example
are of equal value, the gain is unity. However, a gain of 10
may be obtained by making the feedback resistor 10 times
larger than the input resistors, under the conditions that both
feedback resistors are equal and the input resistors are equal.

0

A2
A1
A0

TTL logic level,010, closes S2

Figure 5.08

S0
S1
S2
S3

4 kW G=1
2 kW G=2
1 kW G=4
1 kW G=8

R’F

R’i

S7

Fig. 5.08. The non-inverting amplifier is configured for programmable gain and controlled by the binary input signals
from a computer to the addressable inputs of the analog
switch.

The input voltage limitations discussed for inverting amplifiers
applies equally well to the non-inverting amplifier configuration.

Differential Amplifiers

Differential-input amplifiers offer some advantages over
inverting and non-inverting amplifiers. It appears as a
combination of the inverting and non-inverting amplifiers asshown in Figure 5.07. The input signal is impressed between
the operational amplifier’s positive and negative input terminals
and can be isolated from common or a ground pin. The optional
ground pin is the key to the amplifier’s flexibility. The output
signal of the differential input amplifier responds only to thedifferential voltage that exists between the two input terminals.
The transfer function for this amplifier is:

The major benefit of the differential amplifier is its ability to reject
any voltages that are common to both inputs while amplifying
the difference voltage. The voltages that are common to both
inputs are appropriately called common mode voltages (Vcmor CMV). The common-mode voltage rejection quality can bedemonstrated by connecting the two inputs together and to a
voltage source referenced to ground. Although a voltage is present at both inputs, the differential amplifier responds only tothe difference, which in this case is zero. The ideal operational
amplifier, then, yields zero output volts under this arrangement.
(See the following section on Instrumentation Amplifiers, HighCommon-Mode Amplifiers.)

EQN 5.03. Differential Amplifier

Vo = (Rf/Ri)(V1 – V2)
For an input signal of 50 mV, Where:

Programmable-Gain Amplifiers

Programmable gain amplifiers are typically non-inverting operational amplifiers with a digitally controlled analog switch
connected to several resistors in its feedback loop. An external
computer or another logic or binary signal controls the addressable inputs of the analog switch so it selects a certain resistor forparticular gain. (See Figure 5.08.) The data acquisition system’s
signal conditioners sense the input signal amplitude and automatically send the proper binary code to the programmablegain amplifier (PGA) to increase the gain for a low signal, or
decrease the gain for a large signal. The input signal then canbe measured and displayed without distortion.

V1 = 1.050V and V2 = 1.000V
Vo = (Rf/Ri)(V1 – V2)
Vo = (100k/100k)(0.05V)
Vo = 0.05V
For a gain of 10 where Rf = 100k and Ri = 10k:

Vo = (Rf/Ri)(V1 – V2)
Vo = (100k/10k)(0.05V)
Vo = 0.50V

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Instrument Amplifier

High Common-Mode Amplifiers
Rf

Vsignal

Vs

–
+

IA

100 kΩ

Vout = AvVsignal
100 kΩ

Vcommon-mode

+
VCM
–

Fig. 5.09. An instrumentation amplifier is typically a differential input operational amplifier with a high commonmode rejection ratio.

Ri
100 kΩ
Ri

–
+

A
RL

VoCM ≈ 0

95.3 kΩRfCommon-mode
adjustment

INSTRUMENTATION AMPLIFIERS

0.1% resistors

Fig. 5.10. The common mode voltage rejection is measured
with the two inputs shorted together and a voltage applied
to the node. The potentiometer is then adjusted for minimum (VoCM) output from the amplifier, signifying that thebest balance was reached between the two inputs.

A Fundamental Problem

Because signal levels from some transducers may be just a few
microvolts, special problems concerning ground loops andspurious interference frequently arise when amplifying
Figure 5.10them.
Other transducers provide output signals from differential signal
sources to minimize grounding problems and reduce the effectof common-mode interfering signals. Amplifiers used in theseapplications must have extremely low input current, drift, andoffset voltage; stable and accurate voltage gain; and high input
impedance and common-mode rejection.

The signal voltages measured are frequently much smaller than the
maximum allowed input of the system’s ADC. For example, a 0 to
100 mV signal is much smaller than the 0 to 5V range of a typical ADC. A gain of 50 is needed to obtain the maximum practicalresolution for this measurement. Instrumentation amplifiers arecapable of gains from 1 to more than 10,000, but in multiplexed
systems, the gains are usually restricted to a range of 1 to 1,000.

Although common integrated operational amplifiers with several
stages and extremely tight resistor ratios are often used, speciallydesigned instrumentation amplifiers are preferred for these applications. The high-performance operational amplifiers still
use basic circuits but ensure that they provide extremely highcommon-mode rejection and don’t need high precision matchedresistors to set the gain. Many instrumentation amplifiers aredesigned for special applications and provide unique features
to increase their accuracy and stability for those applications.

Measurement errors come from the non-ideal ON resistance ofanalog switches added to the impedance of any signal source.
But the extremely high input impedance of the IA minimizes thiseffect. The input stage of an IA consists of two voltage followers,
which have the highest input impedance of any common amplifier configuration. The high impedance and extremely low bias
current drawn from the input signal generate a minimal voltage
drop across the analog switch sections and produce a more accurate signal for the IA input.

For example, the functional block following the switching network
in a data acquisition system, Figure 5.09, is an instrumentation
amplifier with several critical functions. It rejects common-mode
voltages, amplifies signal voltages, minimizes the effect of themultiplexer on resistance, and drives the ADC input.

The instrumentation amplifier has low output impedance, which
is ideal for driving the ADC input. The typical ADC does not havehigh or constant input impedance, so the preceding stage must
provide a signal with the lowest impedance practical.

High Common-Mode Amplifiers

The common mode voltage is defined as the voltage applied fromanalog common to both inputs when the inputs are identical.
(See Figure 5.10.) However, when the two input voltages are different, 4.10 and 4.20V for example, the common mode voltage,
Vcm, is 4.10V and the differential voltage between the two is
0.10V. Ideally, the instrumentation amplifier ignores the common
mode voltage and amplifies only the difference between the two
inputs. The degree to which the amplifier rejects common mode
voltages is given by a parameter called common mode rejection
ratio CMRR. The ability of an instrumentation amplifier (IA) toreject high common mode voltages is sometimes confused with
its ability to reject high voltages.

Some instrumentation amplifiers have limitations concerning
offset voltage, gain error, limited bandwidth, and settling time.
The offset voltage and gain error can be calibrated out as partof the measurement, but the bandwidth and settling time areparameters that limit the frequencies of amplified signals andthe frequency at which the input switching system can switch
channels between signals. A series of steady DC voltages applied
to an instrumentation amplifier in rapid succession generates
a difficult composite signal to amplify. The settling time of theamplifier is the time necessary for the output to reach final amplitude to within some small error (often 0.01%) after the signal
is applied to the input. In a system that scans inputs at 100 kHz,5
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Integrated Instrumentation Amplifiers
Input 1
Vi

+
–

+
0V

R in ~
– ∞Ω

–

A1
Ri1
R

+

R

Ri2
–
Input 2
Vi

+
–

0V

+

Sense

–
V’o

Rm

Rf1

A3

Rf2

Vo

Reference

A2

R in ~– ∞Ω
Buffered input
stage

Differential amplifier output
stage

Fig. 5.11. The instrumentation amplifier exhibits extremely high impedance to the inputs V1 and V2. Resistor Rm adjusts the gain,
and the single-ended output is a function of the difference between V1 and V2.

Figure 5.11
Programmable-Gain Instrumentation Amplifiers

the total time spent reading each channel is 10 µs. If analog-todigital conversion requires 8 µs, settling time of the input signal
to the required accuracy must be less than 2 µs.

A special class of instrumentation amplifiers, called programmable-gain instrumentation amplifiers (PGIA), switch between fixed
gain levels at high speeds for different input signals delivered by
the input switching system. The same digital control circuitrythat selects the input channel also can select a gain range. The
principle of operation is the same as that described above for
Programmable Gain Amplifiers.

Although calibrating a system can minimize offset voltage and gain
error, it is not always necessary to do so. For example, an amplifier with an offset voltage of 0.5 mV and a gain of 2 measuring
a 2V signal develops an error of only 1 mV in 4V on the output,
or 0.025%. By comparison, an offset of 0.5 mV and a gain of 50
measuring a 100 mV signal develop an error of 25 mV in 5V or
0.5%. Gain error is similar. A stage gain error of 0.25% has a greater
overall effect as gain increases producing larger errors at higher
gains and minimal errors at unity gain. System software can generally handle known calibration constants with mx+b routines, butsome measurements are not critical enough to justify the effort.

FILTERING

The three most common types of filters are called Butterworth,
Chebyshev, and Bessel. (See Figures 5.12A, B, and C.) Each typehas unique characteristics that make it more suitable for one application than another. All may be used for high-pass, low-pass,band-pass, and band-reject applications, but they have different
response profiles. They may be used in passive or active filter
networks.

Integrated Instrumentation Amplifiers

Integrated instrumentation amplifiers are high-quality op ampsthat contain internal precision feedback networks. They are
ideal for measuring low-level signals in noisy environments
without error, and amplifying small signals in the midst of highcommon-mode voltages. Integrated instrumentation amplifiers
are well suited for direct connection to a wide variety of sensors
such as strain gages, thermocouples, RTDs, current shunts, andload cells. They are commonly configured with three op amps
– two differential inputs and one differential output amplifier.
(See Figure 5.11.) Some have built-in gain settings of 1 to 100
and others are programmable.

The Butterworth filter has a fairly flat response in the pass-band forwhich it is intended and a steep attenuation rate. It works quite
well for a step function, but shows a non-linear phase response.
Chebyshev filters have a steeper attenuation than Butterworth,but develop some ripple in the pass band and ring with a step
response. The phase response is much more non-linear than the
Butterworth. Finally, Bessel filters have the best step response andphase linearity. But to be most useful, Bessel filters need to havea high order (number of sections) to compensate for their slower
rate of attenuation beyond the cut-off frequency.

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Butterworth Filter

_pt1

0.5 H

V1

1.333 F

2

-5

V1

C1

C2

CN

RL

1W

RL

1W

100k

ω(rps)

0-10-2

Gain (dB)

-10
-15
-20

0.1

0.5

1.0

ωc (rps)
3.0 5.12_C_pt1
Figure2.0

Fig. 5.12A. Butterworth filter and response characteristics

V1

10k

1k

2

0.912 F

Filtered/Buffered Data
Acquisition System

Figure 5.12_C_pt2
V2

1W
RL

2’

1’

IA

Wc (rps)0

LPF

BufferMux

Inputs

-10
-18

-100

Fig. 5.12C. Bessel filter and response characteristics

0.996 H

1

-50

-140

Chebyshev Filter

Gain (dB)

1W

Even order N
LN

2’
0

Output (dB)Rs

Odd order N

L2

1

V2

1W
RL

1’

_pt1

pt2

1.5 H

1

Bessel Filter

IA

0.1

0.5

1

2

3

ωc (rps)LPF

To ADC

Buffer

Fig.5.13A. An instrumentation amplifier, a low-pass filter,
and a unity gain buffer amplifier placed between the sensor
output and MUX input transforms the sensor’s high output
impedance to a low impedance. This is required by the MUX
to maintain accuracy.

Fig. 5.12B. Chebyshev filter and response characteristics

Low-Pass Filters

Low pass filters attenuate higher frequencies
in varying
Figure5.13 degrees
depending on the number of stages and the magnitude of thehigh frequency relative to the corner frequency. An amplifier stage
doesn’t need high bandwidth when the measured signal is at amuch lower frequency. In fact, the design is intended to eliminate
excessive bandwidth in all circuits, which reduces noise. One
major benefit of individual signal conditioning stages for low-levelsensors (as opposed to multiplexed stages) is to include low-passfiltering on a per-channel basis in the signal path. In a multiplexed
circuit (an amplifier which is being shared by multiple low-levelDC signals), the main signal path generally cannot operate as a

low-pass filter due to the fast settling time necessary in multiplexed
systems. (See Figure 5.13A.)
The best place for low-pass filters is in the individual signal pathbefore buffering and multiplexing. (See Figure 5.13B.) For small
signals, amplifying with an instrumentation amplifier prior tofiltering lets an active low-pass filter operate at optimum signalto-noise ratios. Figure 5.13C illustrates a typical amplifier-filtermultiplexer configuration.

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High-Pass Filter

Simple RC Filter
Vin

R

+

C

–

A

C1

To Mux
Vi

RI

C2

R1

C3

R2

R3 Vo

RL

Fig.5.13B. Low-pass filters inserted in each channel as
needed simultaneously reduce the bandwidth and noise
while passing the targeted, lower frequency signals.
Fig. 5.14. The high-pass filter is designed to have a lower
corner frequency near zero and the cutoff frequency at somehigher value. The number of capacitor/resistor pairs determines the number of poles and the degree of cutoff sharpness.

Amplifier/Filter/MUX CombinationIA

Low-pass filter
per channelIA

Low-pass filter
per channel

Ch 3

IA

Low-pass filter
per channel

Ch 4

IA

Low-pass filter
per channel

Ch 1
Ch 2

Switched bias resistors(per channel)

characteristics. The advantages of such a filter is; it is easier todesign, and it has finer tuning, fewer parts count, and improved
filter characteristics.

Figure 5.14

Mux

To A/D

Switched-Capacitance Filters

Although active filters built around operational amplifiers aresuperior to passive filters, they still contain both integrated anddiscrete resistors. Integrated-circuit resistors occupy a large spaceon the substrate and their values can’t be made easily to hightolerances, either in relative or absolute values. But capacitorswith virtually identical values can be formed on integrated
circuits more easily, and when used in a switching mode, they
can replace the resistors in filters.

2

Channel address lines

Fig. 5.13C. A typical production type data acquisition
system contains an instrumentation amplifier and a lowpass filter in each channel preceding the MUX. The amplifier boosts low-level signals sufficiently well to let the active
filter work at an optimum signal-to-noise ratio.

The switched-capacitor filter is a relatively recent improvement
over the traditional active filter. James Clerk Maxwell compareda switched capacitor to a resistor in a treatise in 1892, but only
recently has the idea taken hold in a zero-offset electronic switch
and a high input impedance amplifier. The switched-capacitor
concept is now used in extremely complex and accurate analog
filter circuits.

High-Pass Filters

High-pass filters operate in reverse to low-pass filters. They attenuate
the lower frequencies and are needed when low-frequency
interference can mask high-frequency signals carrying thedesired information or data. Low frequency electrical interference
sometimes couples into the system from 50 or 60 Hz power lines.
Similarly, when analyzing a machine for vibration, the desired
signals can be corrupted by low frequency mechanical interference
from the vibrating laminations of a power transformer mounted
to its frame. Moreover, a combination of high-pass and low-passfilters may be used to create a notch filter to attenuate a narrow
band of frequencies, such as 50 to 60 Hz and their first harmonic.
A 3-pole high-pass filter is shown in Figure 5.14.

The theory of operation is depicted in Figure 5.16. It shows thatwith S2 closed and S1 open, a charge from V2 accumulates on
C. Then, when S2 opens, S1 closes, and the capacitor transfers
the charge to V1. This process repeats at a particular frequency,
and the charge becomes a current by definition, that is, current
equals the transfer of charge per unit time.
The derivation of the equation is beyond the scope of thishandbook, but it can be shown that the equivalent resistor
may be determined by:

Passive vs. Active Filters

EQN 5.04 Switched-Capacitance Filters

Passive filters comprise discrete capacitors, inductors, andresistors. As the frequencies propagate through these networks,
two problems arise: the desired signal is attenuated by arelatively small amount, and when connected to a load, theoriginal filtering characteristics change. However, active filters
circumvent these problems. (See Figure 5.15.) They comprise
operational amplifiers built with both discrete and integrated
resistors, capacitors, and inductors. They can provide the proper
pass-band (or stop-band) capability without loading the circuit,attenuating the desired signals, or changing the original filtering(V2 – V1)/i = 1/(fC) = R
Where:
V2 = voltage source 2, V
V1 = voltage source 1, Vi = equivalent current, A
f = clock frequency, Hz
C = capacitor, FR = equivalent resistor, W

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Active Filters

R1
C

Vi

R2

–
+

C1
R1

A

C2

Vi

Vo

R2

–
+

Vo
ActualIdeal

Stopband

A

Vo

Vo
Ideal

Passband_Af

High-Pass Filter

Passband

Stop

Figure 5.15 E

fL

0

C

0

fL

fr

Stop
ActualfH

f

R1

Band-Pass Filter

R2

Vi

–
+

A

Vo

Fig. 5.15. Passive filters tend to change in frequency-cutoff
characteristics with a change in load. To prevent this, anactive device such as a transistor or op amp isolates the lastpole from the load to maintain stable filter characteristics.

Figure 5.15_F

Vo
Ideal
ActualPassband

StopbandC0reading 50V. If a 900 kW and a 100 kW resistor are chosen toprovide a 1 MW load to the source, the impedance seen by theanalog multiplexer input is about 90 kW, still too high for themultiplexed reading to be accurate. When the values are bothdownsized by a factor of 100 so the output impedance is lessthan 1 kW, the input impedance seen by the measured sourceis 10 kW, or 2 kW/V, which most instruments cannot tolerate
in a voltage measurement. Hence, simple attenuation is notpractical with multiplexed inputs.

fH

f

Low-Pass Filter

Buffered Voltage Dividers

The above equation states that the switched capacitor is identicalto a resistor within the constraints of the clock frequency and fixedcapacitors. Moreover, the equivalent resistor’s effective value isinversely proportional to the frequency or the size of the capacitor.

The low impedance loading effect of simple voltage dividers
can be overcome using unity-gain buffer amplifiers on divider
outputs. A dedicated unity-gain buffer has high-input impedance in the MW range and does not load down the source, as
does the network in the previous example. Moreover, the buffers’ output impedance is extremely low, which is necessary
for the multiplexed analog input. (See Figure 5.18.)

ATTENUATION

Voltage Dividers

Most data acquisition system inputs can measure voltages only
within a range of 5 to 10V. Voltages higher than this must be
attenuated. Straightforward resistive dividers can easily attenuate any range of voltages (see Figure 5.17), but two drawbacks
complicate this simple solution. First, voltage dividers present
substantially lower impedances to the source than direct analog inputs. Second, their output impedance is much too highfor multiplexer inputs. For example, consider a 10:1 divider

Balanced Differential Dividers

Not all voltage divider networks connect to a ground or a common
reference point at one end. Sometimes, a balanced differential
divider is a better solution for driving the data acquisition system’s input terminals. (See Figure 5.19.) In this case, the CMRR ofthe differential amplifier effectively reduces the common-mode
noise that can develop between different grounds in the system.

9
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Switched-Capacitor Filters
V2

Buffered Voltage Dividers
Vin

V1
S2

S1

RA

C

+

Fig. 5.16. Because resistors have wider tolerances andrequire more substrate area than capacitors, a technique thatuses multiple precision capacitors to replace resistors in filters
is called a switched capacitor circuit.

–

RB

Vout

A

RL
Vout =RBV
RA + RB in

Attenuator/Buffer
Vin

6

Vin
R1

900 kW

RA

+Vc

9 kW

Figure 5.18 A
Vout

ZS = Source
100 kW
R2

1 kW

com.

Vout

ZL = Mux input

RL

RB

RE

RL

com.
1 Meg
90 kW

ZS
ZL

10 kW
1 kW

Fig. 5.18. An op amp or a transistor serves as an impedance
matching buffer to prevent the load from affecting the divider’soutput voltage.

Fig. 5.17. When the input signal exceeds about 10V, thedivider drops the excess voltage to prevent input amplifier
damage or saturation.

Figure 5.18_B
High-Voltage Dividers

Some data acquisition systems employ special input modules
containing high-voltage dividers that can easily measure up to
1,200V. They are properly insulated to handle the high voltage
and have resistor networks to select a number of different divider
ratios. They also contain internal trim potentiometers to calibrate
the setup to extremely close tolerances.

of tolerance by as much as 5%. This is because the lead capacitanceenters into the divider equation. One way around the problem
is to shunt the data acquisition input terminals (or the divider
network) with a compensating capacitor. For example, oscilloscopeprobes contain a variable capacitor precisely for this purpose.
The probe capacitor is adjusted to match the oscilloscope’s input
impedance and as a result, it faithfully passes the leading edgeof the oscilloscope’s built-in 1,000 Hz square-wave generator
without undershoot or overshoot.

ISOLATION

Compensated Voltage Dividers and Probes

Voltage divider ratios applied to DC voltages are consistently
accurate over relatively long distances between the divider network and data acquisition system input when the measurement
technique eliminates the DC resistance of the wiring and cables.
These techniques include a second set of input measuring leads
separate from those that apply power to the divider.
Voltage dividers used on AC voltages, however, must always
compensate for the effective capacitance between the conductors
and ground or common, even when the frequency is as low as
60 Hz. It’s not uncommon to find that when the AC voltages arecalibrated to within 0.01% at the divider network, the voltages
reaching the data acquisition system input terminals may be out

When Isolation Is Required

Frequently, data acquisition system inputs must measure low-levelsignals where relatively high voltages are common, such as inmotor controllers, transformers, and motor windings. In thesecases, isolation amplifiers can measure low-level signals amonghigh common-mode voltages, break ground loops, and eliminate
source ground connections without subjecting operators andequipment to the high voltage. They also provide a safe interface
in a hospital between a patient and a monitor or between thesource and other electronic instruments and equipment. Yetother applications include precision bridge isolation amplifiers,
photodiode amplifiers, multiple-port thermocouple and summing
amplifiers, and isolated 4 to 20 mA current-control loops.

10
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Compensated High-Voltage Dividers
2.49 M

Hi

2M

50V

249 K

Compensation
capacitors

220 pF

249 K

220 pF

249 K

+
A
–

100V
50V

2M

2.49 M

+
A
–

100V

249 K

Lo

Select divider ratios

10V

Out

+
–A

10V

Input channel (typ. of 8)

Fig. 5.19. A typical high-voltage input card for a data acquisition system contains a balanced differential input and jumpers forselecting an input voltage range of 10 V, 50 V, or 100 V. The input circuit also compensates for long lead wire capacitance that tends
to form an AC voltage divider, which would reduce accuracy.

Figure 5.19
Isolation Amplifiers

Isolation amplifiers are divided into input and output sections,galvanically isolated from each other. Several techniques provide
the isolation; the most widely used include capacitive, inductive,
and optical means. The isolation voltage rating is usually 1,200
to 1,500 VAC, at 60 Hz with a typical input signal range of ±10V.
They normally have a high isolation mode rejection (IMR) ratioof around 140 dB. Because the primary job of relatively low-cost

amplifiers is to provide isolation, many come with unity gain.
But more expensive units are available with adjustable or programmable gains. (See Figure 5.20.)
One benefit of an isolation amplifier is that it eliminates groundloops. The input section’s signal-return, or common connection
is isolated from the output signal ground connection. Also, two

Isolation

Input

OutputC1
C1H

C2
Isolation barrier

C1L
Ia
X

Vin

–
+

Signal
Com 2
Ext
Osc

C3

R1

R2

A1

1pF

A
1pF

1pF

C2H

Ia

1pF

A
Sense
Ib

C2L

X

Sense

C5
Ib
A2

R3
R4

–
+

S/H
G=1

C4

R5

Sense

Vout

Signal
Com 2
S/H
G=6

Adjustable
gain stages+V2 Gnd -V2+V1 Gnd -V1
1

2

Fig. 5.20. A differential isolation amplifier’s front end can float as high as the value of the common mode voltage (CMV) rating
without damage or diminished accuracy. The isolation barrier in some signal conditioners can withstand from 1,500 to 2,200 VDC.

Figure 5.20

11

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Galvanic Isolation AmplifierHigh
voltage+
200 VDC
–

50 mV
Shunt

Load

Capacitive Isolation Amplifier
Input

Input

Output

VCC1+

Differential V
CC2isolation+
amplifier
G=1

+

+VC

–
–
VCC1

Sync

Duty cycle
demodulator
C2
T1
Oscillator
driverRectifiers
Filters

Ps GndGroundisolation

200 VDC

Duty cycle
modulator

-VC
Com 1
Gnd 1
+VCC1

–
VCC2

Sense

C1

Vin
To ADC
andcomputer

Output-VCC1

Isolation barrier

Vout
Com 2
-VCC2
Sync
+VCC2
EnableGnd 2Isolation

Fig. 5.22. The isolation barrier in this amplifier protects
both the signal path and the power supply from CMV breakdown. The signal couples through a capacitor and the power
through an isolation transformer.

Fig. 5.21. Galvanic isolation can use any one of several techniques to isolate the input from the output circuitry. The goal is
to allow the device to withstand a large common mode voltage(CMV) between the input and output signal and power grounds.

Figure 5.22

are fabricated, a laser trims both stages to precisely match theirperformance characteristics. Then they are mounted on either endof the package separated by the isolation capacitors. Although theschematic diagram of the isolation amplifier looks quite simple, it
can contain up to 250 or more integrated transistors.

different power supplies are used, Vcc1 and Vcc2, one for eachsection, which further helps isolate the amplifiers. (See Figure 5.21.)

Analog Isolation Modules

Analog isolation amplifiers use all three types of isolation between
input and output sections: capacitive, optical, and magnetic. One
type of capacitively coupled amplifier modulates the input signal
and couples it across a capacitive barrier with a value determined by
the duty cycle. (See Figure 5.22.) The output section demodulates
the signal, restores it to the original analog input equivalent, andfilters the ripple component, which resulted from the demodulation
process. After the input and output sections of the integrated circuit

Another isolation amplifier optically couples the input section tothe output section through an LED transmitter and receiver pairas shown in Figure 5.23. An ADC converts the input signal to atime-averaged bit stream and transmits it to the output section
via the LED. The output section converts the digital signal backto an analog voltage and filters it to remove the ripple voltage.

Optical Isolation Amplifier
Input

OutputIsolation

IREF1

Rin
+
–

+In

Vin

I
-In

IREF2

Input

Output

I

I

–
+

Rf

–

A
Opticalcouplers

+

D1

D2

A

Vout

Vout = IinRf

LED

Common 1

Common 2

Fig. 5.23. This is a simplified diagram of a unity gain current amplifier using optical couplers between input and output stages to achieveisolation. The output current passing through the feedback resistor (Rf) generates the output voltage.

Figure 5.23

12

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Magnetic Isolation Amplifier
Input

OutputVc

VαSignaltransmitted
by magnetic
field

A

Vin

Iin

Planarcoil

H

Isolated
outputA

Galvanic
isolationby thin-film
dielectric

GMR resistors

Isolation

Fig. 5.24A. Magnetic couplers transfer signals through a magnetic field across a thin film dielectric. In this case, a magnetoresistance bridge circuit sensitive to the field exhibits a large change in resistance when exposed to the magnetic field from a small
coil sitting above it.

Figurecoupled
5.24 A isolation amplifiers come in two types.
Magnetically
One contains hybrid toroid transformers in both the signal andpower paths, and the other contains one coil that transmits thesignal across a barrier to a giant magnetoresistor (GMR) bridge
circuit. (See Figure 5.24A.) In the transformer type, Figure 5.24B,
the rectified output of a pulse generator (T1) supplies power to the
input and output stages (T3). Another winding of the transformer(T2) operates a modulator and demodulator that carry the signal
across the barrier. It provides from 1,000 to 3,500 VDC isolation
among the amplifier’s three grounds, as well as an isolated output signal equal to the input signal with total galvanic isolation
between input and output terminals.
The second type, the giant magnetoresistor amplifier uses thesame basic technology as does high-speed hard disc drives. The

coil generates a magnetic field with strength proportional to its
input drive current signal, and the dielectric GMR amplifies andconditions it. Ground potential variations at the input do not
generate current so they are not detected by the magnetoresistor
structure. As a result, the output signal equals the input signal withcomplete galvanic isolation. These units are relatively inexpensive,and can withstand from 1,000 to 3,500 VDC. Full-power signal
frequency response is less than 2 kHz, but small signal response
is as much as 30 kHz.

Digital Method of Isolation

Digital isolation packages are similar in many respects to analog
amplifiers. They transmit digital data across the isolation barrier
at rates up to 80 Mbaud, and some can be programmed to transmit

Transformer-Type Isolation Amplifier
Input

OutputInput
Demodulator

T1

Pulse
generatorA

Modulator

T2

OutputDemodulator

Input
power

Rectifiers
and filters

T3

Rectifiers
and filters

+Vs
–Vs

R2
R1

–
+

Vin
R3

–
+

A

Vout

Outputpower

Isolation

Fig. 5.24B. The transformer-coupled isolation amplifier uses separate power supplies for the input and output stages, which are isolated by virtue of the individual transformer windings. This provides the input and output stages with decoupled ground or common
returns. In addition, the modulator/demodulator transfers the measured signal across the barrier via other transformer windings forcomplete galvanic isolation between input and output.

Figure 5.24 B

13

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Input

VDD1
Data
in

OutputEncodeGap

VDD2

Permanent
magnetHall-effectsensorData
out

Decode

Gap

Tone
wheel
Gnd

Gnd
Air coretransformer

Rotation

Isolation

Vsens

Fig. 5.25. Yet another isolation method specifically intended
for digital circuits employs a high-speed CMOS encoder anddecoder at the input and output, coupled with a monolithic
air-core transformer.

5

N
Rotation

N
S

Target
wheel

3 mV

0

t

-3 mV

Input
Magnetic poleFig. 5.26B. This Hall-Effect sensor configuration uses abias magnet and a tone wheel that modulates the magnetic
field intensity to produce an output signal.

Figure 5.26 B
Hall-effectsensor

Amplifier,comparator

N
S

A

OutputBridge circuit

Conditioned Output
10 mA
Current

Conditioned output

IL

Magnetic field
S

Iout

IH

Isolated Sensors – Hall Effect

26 A pt 1

t2

Isolated Sensors – Hall Effect

Digital Method of Isolation

5 mA

Wheel position

Fig. 5.26A. This Hall-Effect sensor is switched with a seriesof alternating magnets in a target wheel. Each pass between
N and S magnets changes the sensor’s state.

data in either direction, that is, through input to output or output
to input terminals. Data, in the form of complementary pulses,
couple across the barrier through high-voltage capacitors or aircore inductors. Faraday shields usually surround the inductors
or capacitors to prevent false triggering from external fields. The
receiver restores the pulses to the original standard logic levels.
As with analog amplifiers, the power supplies for each section
are also galvanically isolated. (See Figure 5.25.)

Inherently Isolated Sensors

In addition to directly measuring voltage, current, and resistance, which require some degree of isolation, certain sensors
that measure other quantities are inherently isolated by virtueof their construction or principle of operation. The most widelyused sensors measure position, velocity, pressure, temperature,acceleration, and proximity. They also use a number of different
devices to measure these quantities, including potentiometers,
LVDTs (linear variable differential transformers), optical devices,Hall-effect devices, magnetic devices, and semiconductors.
Hall-effect devices, for example, measure magnetic fields, and areelectrically insulated from the magnetic source that they are designed to measure. The insulation may be air or another material
such as plastic or ceramic, and the arrangement essentially isolates
them from ground loops and high voltages. Figures 5.26A and B
illustrate two applications where Hall-effect devices measure speed.
The first senses the alternating magnetic field directly from the

14
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Isolated Sensor –Variable Reluctance/Magnetic

Isolated Sensor – Current Transformer

Antilock brake
controller

To data acquisition system

Variablereluctancewheel speed
sensorRs
Ammeter

AC inputfrom sensor

ACDCreference

To ammeter orshunt resistor, Rs

AC inputfrom sensor

Donut-shaped
current transformer
220 VAC
power
input

Gear
wheel

50 to 100A
load

1 turn

1.70V

15 mA

1.0V

5 mA

I
I

Digital output signal

Figure 5.28 A

Common or return

TargetRatio 1:1

2 turns

Wire coil

MagnetAnalog in
Signalprocessing

I
I
Common or return

VR transducer

Figure 5.28 B

Fig. 5.28. Variable reluctance sensors comprise a coil of wire
wound around a magnetic core. As a ferrous metal passes near
one pole it disturbs the magnetic field and induces a small
voltage in the coil. In this example, the voltage is amplified,shaped, and converted to a digital signal for indicating vehicle
wheel speed.

Ratio 2:1

4 turns
I

I

gure 5.27 B,C,D

Common or return

DigitaloutputFigure 5.28 C

insulation between primary and secondary can be made towithstand thousands of volts and have extremely low leakage
values. The turns ratio also is easy to select for stepping down ahigh voltage to a lower standard voltage of 5 to 10 VAC.

Ratio 4:1

Fig. 5.27. Because it does not need a ground connection, acurrent transformer is isolated from both the input and outputof the signal conditioner.
revolving wheel. In the second application, a permanent magnet
sitting behind the Hall effect device supplies the magnetic field.
The gear teeth passing by the unit disturb the field, and the Halldevice senses the resulting fluctuations. In addition, see Figure
4.08. It shows a third example, where the Hall-effect device isused in a wattmeter circuit.
Current transformers and potential transformers for measuring
AC voltage and current are also inherently isolated between
primary and secondary windings. (See Figure 5.27.) Transformer

Other sensors include magnetic pickups composed of wire coils
wound around a permanent magnetic core. A ferrous metal
passing over one end of the coil disturbs the magnetic flux andgenerates a voltage at the coil terminals. The sensor does not
require a separate power supply, and the output voltage is typically small enough to require only ordinary signal conditioners.
(See Figure 5.28.)
Piezoelectric materials and strain gages are typically used formeasuring acceleration, and are inherently isolated from theobjects on which they are mounted by virtue of their protective
housings. High-voltage insulation and magnetic shielding may be
added to the mounting base if needed in some rare applications.

15
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Seebeck Coefficient Plot

Thermocouple Output Voltage
80

E

100
K

40

T

J
R

20
0

500˚
TYPE
E
J
K
R
S
T

Seebeck Coefficient µV/˚C

Millivolts

60

1000˚
1500˚
Temperature ˚C

S

2000˚

2500˚

METALS+–
Chromel vs. Constantan
Iron
vs. Constantan
Chromel vs. Alumel
Platinum vs. Platinum
13% Rhodium
Platinum vs. Platinum
10% Rhodium
Copper
vs. Constantan

80

E
J

T

60

Linear region

40

K

20

R
S

0
-500˚

0˚

500˚

1000˚

Temperature ˚C

1500˚

2000˚

Fig. 5.30. The slope of the Seebeck coefficient plotted against
temperature clearly illustrates that the thermocouple is a nonlinear device.

Fig. 5.29. Although some thermocouples must be both therFigure 5.30
mally and electrically connected to the specimen under test,
many may be purchased with insulated junctions, which isolates them from making high-voltage and ground-loop connections to the signal conditioner.

of a light beam between an optical transmitter and receiver. A
revolving opaque disc with multiple apertures placed between thetransmitter and receiver alternately lets light through to generate
pulses. Usually, LEDs generate the light and a photo diode on the
opposite side detects the resulting pulses, which are then counted.
The pulses can indicate position or velocity.

LVDTs contain a modulator and demodulator, either internally or
externally, require some small DC power, and provide a small AC
or DC signal to the data acquisition system. Often they are scaled to
output 0 to 5V. LVDTs can measure both position and acceleration.
Optical devices such as encoders are widely used in linear androtary position sensors. The possible configurations are many, butbasically, their principle of operation is based on the interruption

LINEARIZATION
Why Linearization Is Needed

The transfer function for many electronic devices, which relates
the input to output, contains a nonlinear factor. In most cases
this factor is small enough to be ignored. However, in some
applications it must be compensated either in hardware or software.

Temperature Conversion Table in ˚C (IPTS 1968)
mV

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

.10

mV

0.00
0.10
0.20
0.30
0.40

0.00
1.70
3.40
5.09
6.78

0.17
1.87
3.57
5.26
6.95

0.34
2.04
3.74
5.43
7.12

0.51
2.21
3.91
5.60
7.29

0.68
2.38
4.08
5.77
7.46

0.85
2.55
4.25
5.94
7.62

1.02
2.72
4.42
6.11
7.79

1.19
2.89
4.58
6.27
7.96

1.36
3.06
4.75
6.44
8.13

1.53
3.23
4.92
6.61
8.30

1.70
3.40
5.09
6.78
8.47

0.00
0.10
0.20
0.30
0.40

0.50
0.60
0.70
0.80
0.90

8.47
10.15
11.82
13.49
15.16

8.63
10.31
11.99
13.66
15.33

8.80
10.48
12.16
13.83
15.49

8.97
10.65
12.32
13.99
15.66

9.14
10.82
12.49
14.16
15.83

9.31
10.98
12.66
14.33
15.99

9.47
11.15
12.83
14.49
16.16

9.64
11.32
12.99
14.66
16.33

9.81
11.49
13.16
14.83
16.49

9.98
11.65
13.33
14.99
16.66

10.15
11.82
13.49
15.16
16.83

0.50
0.60
0.70
0.80
0.90

1.00
1.10
1.20
1.30
1.40

16.83
18.48
20.14
21.79
23.44

16.99
18.65
20.13
21.96
23.60

17.16
18.82
20.47
22.12
23.77

17.32
18.98
20.64
22.29
23.93

17.49
19.15
20.80
22.45
24.10

17.66
19.31
20.97
22.62
24.26

17.82
19.48
21.13
22.78
24.42

17.99
19.64
21.30
22.94
24.59

18.15
19.81
21.46
23.11
24.75

18.32
19.97
21.63
23.27
24.92

18.48
20.14
21.79
23.44
25.08

1.00
1.10
1.20
1.30
1.40

Fig. 5.31. Because thermocouple outputs are non-linear, a table is an accurate method for converting a voltage reading to temperature
for a specific type of thermocouple.

16
Figure 5.31

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NIST Polynomial Coefficients

a0
a1
a2
a3
a4
a5
a6
a7
a8
a9

TYPE E

TYPE J

Nickel-10% Chromium(+)
VersusConstantan (–)

Iron (+)
VersusConstantan (–)

TYPE K

TYPE R

TYPE STYPE T-100˚C to 1000˚C±0.5˚C
9th order

0˚C to 760˚C±0.1˚C
5th order

0˚C to 1370˚C±0.7˚C
8th order

0˚C to 1000˚C±0.5˚C
8th order

0˚C to 1750˚C±1˚C
9th order-160˚C to 400˚C±0.5˚C
7th order

0.104967248
17189.45282-282639.0850
12695339.5-448703084.6
1.10866E + 10
-1.76807E + 11
1.71842E + 12
-9.19278E +12
2.06132E + 13

-0.048868252
19873.14503-218614.5353
11569199.78-264917531.4
2018441314

0.226584602
24152.10900
67233.4248
2210340.682-860963914.9
4.83506E + 10
-1.18452E + 12
1.38690E + 13
-6.33708E + 13

0.263632917
179075.491-48840341.37
1.90002E + 10
-4.82704E + 12
7.62091E + 14
-7.20026E + 16
3.71496E + 18
-8.03104E + 19

0.927763167
169526.5150-31568363.94
8990730663-1.63565E + 12
1.88027E + 14
-1.37241E + 16
6.17501E + 17
-1.56105E + 19
1.69535E + 20

0.100860910
25727.94369-767345.8295
78025595.81-9247486589
6.97688E + 11
-2.66192E + 13
3.94078E + 14

Copper (+)
Nickel-10% Chromium (+) Platinum-13% Rhodium (+) Platinum-10% Rhodium
Versus Nickel-5% (–)
VersusVersusVersus(Aluminum Silicon)
Platinum (–)
Platinum (–)
Constantan (–)

Temperature Conversion Equation: T = a0 + a1x + a2x2 + ...+ anxn
Nested Polynomial Form: T = a0 + x(a1 + x(a2 + x(a3 + x(a4 + a5x)))) (5th order)

Fig. 5.32. The NIST polynomial table is a more accurate means of calculating a linearizing function for a particular thermocouple than a single coefficient, even though it uses a polynomial equation.
Figure 5.32 (6.04 B)

solve a polynomial equation. The equation describing thisrelationship is:Curve Divided into Sectors
Temp

EQN 5.05. Temperature Polynomiala

T = ao + a1x + a2x2 + a3x3 + ...anxn
Where:
T = temperature, ˚C
x = thermocouple voltage, V
a = polynomial coefficients unique to each type ofthermocouple
n = maximum order of the polynomial

Voltage

Ta = bx + cx2 + dx3

The accuracy increases proportionally to the order of n. For example,
when n = 9, a ±1˚C accuracy may be realized. But because highorder polynomials take time to process, lower orders may be usedover limited temperature ranges to increase the processing speed.

Fig. 5.33. Although a computer usually finds the solution to
the NIST polynomial, breaking the curve into sections representing lower order polynomials can accelerate the process.
Thermocouples, for example, have a nonlinear relationship from
input temperature to output voltage, severe enough to requirecompensation. Figure 5.29 shows the output voltage for several
types of thermocouples plotted against temperature. Thermocouple
output voltages are based on the Seebeck effect. When the slopeof the Seebeck coefficient is plotted vs. temperature, the output
response is clearly nonlinear as shown in Figure 5.30. A linear
device, by comparison, would plot a straight horizontal line. Only
the K type thermocouple most readily approaches a straight linein the range from about 0 to 1,000˚C.
The curve shows that one constant scale factor is not
sufficient over the entire temperature range for a particular
thermocouple type to maintain adequate accuracy. Higher
accuracy comes from reading the thermocouple voltage witha voltmeter and applying it to the thermocouple table fromthe National Institute of Standards and Technology as shownin Figure 5.31. A computer-based data acquisition system,in contrast, automates the temperature conversion processusing the thermocouple voltage reading and an algorithm toSoftware Linearization

The polynomials are put to work in the data acquisition system’s
computer to calculate the real temperature for the thermocouple
voltage. Typically, the computer program handles a nested polynomial to speed the process rather than compute the exponents
directly. Nested polynomials are the only practical way of dealing
with complicated equations. Without such techniques it is difficult
to handle large state tables that have more than a few hundred
entries. (See Figure 5.32.) Also, high order polynomials can becomputed faster when the thermocouple characteristic curve canbe divided into several sectors and each sector approximated bya third order polynomial as shown in Figure 5.33.

Hardware Linearization

Hardware also may be designed to accommodate the nonlinearityof a thermocouple, but the circuitry becomes complex and
expensive in order to reduce its susceptibility to errors from outside
influences such as electrical noise and temperature variations
within the circuits. The compensating circuitry is nonlinear,

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Isolation from High Voltage
Isolation
Ch 0
Isolation
Ch 1

Out
Mux Addr
Enb

Isolation
Ch 2
InputsIsolation
Ch 3
Isolation
Ch 4
Isolation
Ch 5
Isolation
Ch 6
Isolation
Ch 7

I/O
Gain
config.
µP–15 +15+5

DC/DC DC/DC
5 VDC
To DC/DC converters
in each channel
Isolation
amplifier

Input

Programmableattenuator2
andamplifier
Isolated supply
+15
–15

9-20
VDC
supplyWide range
regulator

BypassLow
passfilter2-bit opto-iso

DC/DC

To
analogmux

From
on-boardµP
5 VDC

Fig. 5.34. The isolated voltage-input modules let data acquisition systems isolate several channels of analog input, up to 500V
channel-to-channel and channel-to-system.

Figure 5.34

and contains breakpoints programmed with diodes, resistors,
and reference voltages, all subject to errors that are avoided insoftware compensation methods. However, several modules arecommercially available with excellent, stable, built-in linearizing
circuits. The thermocouple voltage is extremely small and mostsignal conditioners concentrate less on compensation and moreon amplifying the signal while rejecting common-mode noise.
Alternative digital hardware methods use a look-up table to convert
the thermocouple voltage to a corresponding temperature.

Overload Protection

CIRCUIT PROTECTION
Hazards to Instrumentation Circuits

Another consideration often overlooked is connecting active inputs
to an unpowered data acquisition system. Common safety practice
calls for all signals connected to the input of the unpowered dataacquisition system to be disconnected or their power removed. Frequently, de-energized data acquisition system signal conditioners
have substantially lower input impedances than when energized,
and even low voltage input signals higher than 0.5 VDC can damage
the signal conditioners’ input circuits.

Many data acquisition systems contain solid-state multiplexing
circuits to rapidly scan multiple input channels. Their inputs are
typically limited to less than 30V and may be damaged when
exposed to higher voltages. Other solid-state devices in a measurement system including input amplifiers and bias sources also arelimited to low voltages. However, these inputs can be protectedwith a programmable attenuator and isolation amplifiers thatisolate the high voltage input stage from the solid-state circuitry.
(See Figure 5.34.)

Several methods are used to protect signal conditioner inputs
from damage when exposed to transients of 10 to 100V. Often,
a 1,000 W, current-limiting resistor is in series with the input
when no voltage is applied to the instrument amplifiers’ input.
For transient input voltages to 3,000V and above, a series resistor
and a transient voltage suppressor are installed across the input
terminals. (See Figure 5.35.)

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A

ESD Protection

Overload Protection
Circuit A

D1
1 kW

+V
–

Input
signal+D2

Circuit B

Output

-V

2 kW
G

Input
signal

A

D

FET
S

–
+

A

OutputElectrostatic discharge damage is a special problem that can
be avoided by handling individual circuit boards carefully andproviding proper shielding. ESD comes from the static charge
accumulated on many different kinds of materials, which finds
a return to ground or a mass that attracts the excess electrons.
The charge can create potential differences that can eventuallyarc over large distances. An arc containing only several microjoules of energy can destroy or damage a semiconductor device.
Grounding alone is not sufficient to control ESD build up, it
only ensures all conductors are at the same potential. Controlling humidity to about 40% and slightly ionizing the air are themost effective methods of controlling static charge.
A discharge can travel one foot in one nanosecond and could riseto 5 A. A number of devices simulate conditions for static discharge
protection, including a gun that generates pulses at a fixed voltage
and rate. Component testing usually begins with relatively low
voltages and gradually progresses to higher values.

Fig. 5.35. Certain CMOS multiplexers may be protectedagainst overvoltage destruction with diode and resistor networks
that shut down any parasitic transistors in the device, limit thecurrent input to a safe level, and shunt input signals to groundwhen the power supplies are turned off (Circuit A). JFET
transistors also protect multiplexer inputs when they areconnected as diodes. The JFET clamps at about 0.6V, protecting
the sensitive op amp input from destruction (Circuit B).

B

19
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20
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