1
1
PROCESS, QUANTUM, AND
ANALYTICAL SENSORS
1-0 INTRODUCTION
Automatic test systems, manufacturing process control, analytical instrumentation,
and aerospace electronic systems all would have diminished capabilities without
the availability of contemporary computer integrated data systems with multisensor
information structures. This text develops supporting quantitative error models that
enable a unified performance evaluation for the design and analysis of linear and
digital instrumentation systems with the goal of compatibility of integration with
other enterprise quality representations.
This chapter specifically describes the front-end electrical sensor devices for a
broad range of applications from industrial processes to scientific measurements.
Examples include environmental sensors for temperature, pressure, level, and flow;
in situ sensors for measurements beyond apparatus boundaries, including spectrom-
eters for chemical analysis; and ex situ analytical sensors for manufactured material
and biomedical assays such as microwave microscopy. Hyperspectral sensing of
both spatial and spectral data is also introduced for improved understanding
through feature characterization. It is notable that owing to advancements in higher
attribution sensors, they are increasingly being substituted for process models in
many applications.
1-1 INSTRUMENTATION ERROR REPRESENTATION
In this text, error models are derived employing electronic device, circuit, and sys-
tem parameter values that are combined into a unified end-to-end performance rep-
resentation for computer-based measurement and control instrumentation. This
methodology enables system integration beneficial to contemporary technologies
ranging from micromachines to distributed processes. Since the baseline perfor-
mance of machines and processes can be described by their internal errors, it is ax-
iomatic that their performance may also be optimized through design in pursuit of
Multisensor Instrumentation 6

these error budgets ably describe, including expression to 6␴ confidence.
␧
total
= ⌺ ␧
ෆ
m
ෆ
e
ෆ
a
ෆ
n
ෆ
%FS + [⌺ ␧
2
systematic
+ ⌺ ␧
2
random
]
1/2
%FS1␴ (1-1)
2
PROCESS, QUANTUM, AND ANALYTICAL SENSORS
FIGURE 1-1. Instrumentation error interpretation.
Figure 1-2 describes generic measurement elements, where the sensor represents
a physical device employed at a measurement interface, and the transducer princi-
ple the translation involved between measurand units and a corresponding signal
representation. For example, in the application of a thermocouple, the physical con-
tact of two dissimilar alloys with a thermal process constitutes the sensor, but the

3
FIGURE 1-2. Generic sensor elements.
temperature values nominally within 1°C of their true temperatures, which corre-
spond to typical errors of 0.25%FS. It is also useful to express the average of dis-
crete errors over the sensor range, obtaining a mean error value of 0
ෆ
.
ෆ
1
ෆ
1
ෆ
%FS for the
Type-J thermocouple. This example illustrates a design goal proffered throughout
this text of not exceeding one-tenth percent error for any contributing system ele-
ment. Extended polynomials permit further reduction in linearized sensor error
while incurring increased computational burden, where a fifth-order equation can
beneficially provide linearization to 0.1°C, corresponding to 0
ෆ
.
ෆ
0
ෆ
1
ෆ
%FS mean error.
y = AX + BX
3
+ intercept (1-2)
Coefficient for 10.779 mV at 200°C:

100 5.269 98 0.27
200 10.779 200 0
300 16.327 302 0.25
400 21.848 401 0.23
500 27.393 500 0
600 33.102 599 0.17
700 39.132 700 0
Y true temperature 0
ෆ
.
ෆ
1
ෆ
1
ෆ
%FS mean error
X Type-J thermocouple signal 0°C intercept
y linearized temperature 700°C full scale
temperature-to-emf junction with transfer relationships described by Figure 1-3.
Proper operation requires the use of a thermocouple reference junction in series
with the measurement junction to polarize the direction of current flow and maxi-
mize the measurement emf. Omission of the reference junction introduces an uncer-
tainty evident as a lack of measurement repeatability equal to the ambient tempera-
ture.
An electronic reference junction that does not require an isolated supply can be
realized with an Analog Devices AD590 temperature sensor, as shown in Figure 4-
5. This reference junction usually is attached to an input terminal barrier strip in or-
der to track the thermocouple-to-copper circuit connection thermally. The error sig-
nal is referenced to the Seebeck coefficients in mV/°C (see Table 1-2) and provided
as a compensation signal for ambient temperature variation. The single calibration

J Iron/constantan 0.054 0 to 700 Reducing atmospheres
K Chromel/alumel 0.040 0 to 1,200 Oxidizing atmospheres
R&S Pt-Rb/platinum 0.010 0 to 1,400 Corrosive atmospheres
T Copper/constantan 0.040 –250 to 350 Moist atmospheres
C Tungsten/rhenium 0.012 0 to 2,000 High temperature
FIGURE 1-4. RTD devices.
1-3 MECHANICAL SENSORS
Fluid pressure is defined as the force per unit exerted by a gas or a liquid on the
boundaries of a containment vessel. Pressure is a measure of the energy content of
hydraulic and pneumatic (liquid and gas) fluids. Hydrostatic pressure refers to the
internal pressure at any point within a liquid directly proportional to the liquid
height above that point, independent of vessel shape. The static pressure of a gas
refers to its potential for doing work, which does not vary uniformly with height as
a consequence of its compressibility. Equation (1-3) expresses the basic relation-
ship between pressure, volume, and temperature as the general gas law. Pressure
typically is expressed in terms of pounds per square inch (psi) or inches of water (in
H
2
O) or mercury (in Hg). Absolute pressure measurements are referenced to a
vacuum, whereas gauge pressure measurements are referenced to the atmosphere.
= Constant (1-3)
A pressure sensor detects pressure and provides a proportional analog signal by
means of a pressure–force summing device. This usually is implemented with a me-
chanical diaphragm and linkage to an electrical element such as a potentiometer,
strain gauge, or piezoresistor. Quantities of interest associated with pressure–force
summing sensors include their mass, spring constant, and natural frequency.
Potentiometric elements are low in cost and have high output, but their sensitivity to
vibration and mechanical nonlinearities combine to limit their utility. Unbonded
strain gauges offer improvement in accuracy and stability, with errors to 0.5% of full
scale, but their low output signal requires a preamplifier. Present developments in

ume per unit time, such as gallons per minute. Mass flow rate M for a gas is de-
fined, for example, in terms of pounds per second. Differential pressure flow sens-
ing elements are also known as variable head meters because the pressure
difference between the two measurements ⌬P is equal to the head. This is equiv-
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PROCESS, QUANTUM, AND ANALYTICAL SENSORS
FIGURE 1-6. Integrated pressure microsensor.
alent to the height of the column of a differential manometer. Flow rate is there-
fore obtained with the 32 ft/sec
2
gravitational constant g and differential pressure
by equation (1-4). Liquid flow in open channels is obtained by head-producing de-
vices such as flumes and weirs. Volumetric flow is obtained with the flow cross-
sectional area and the height of the flow over a weir, as shown by Figure 1-8 and
equation (1-5).
Flow rate F =
͙
2
ෆ
g
ෆ
⌬
ෆ
P
ෆ
feet/second (1-4)
Volumetric flow Q =
͙
2
ෆ

Acceleration measurements are principally of interest for shock and vibration
sensing. Potentiometric dashpots and capacitive transducers have largely been sup-
planted by piezoelectric crystals. Their equivalent circuit is a voltage source in se-
ries with a capacitance, as shown in Figure 1-9 which produces an output in
P⌬P
ᎏ
T
⌬P
0
ᎏ
⌬P
x
1-3 MECHANICAL SENSORS
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FIGURE 1-7. Basic LVDT.