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Topic 6 - Sensors
6.2 Loading of the signal source
Learning Outcomes
At the end of this topic, you should be able to:
• Distinguish between primary and secondary
transducers and identify the primary detectortransducer elements for various operations
• Identify and explain the working principles of
variable-inductance transducers, capacitive
transducers, piezoelectric sensors and semiconductor
sensors
• Determine the sensitivity of the various transducers
Digital thermometer
Flow sensors
6.3 The secondary transducer
Secondary
transducer
Primary
transducer
Secondary
transducer
Strain resistance
change
6.4 Classification of first-Stage devices
Primary
transducer
http://www.transducertechni
ques.com/HSW-LoadCell.cfm
Load displacement/strain
Primary detectortransducer elements
Mechanical
Contacting
spindle, pin
Electrical
Resistive
Inductive
Elastic member
Capacitive
Class I. First-stage element used as detector only
Class II. First-stage elements used as detector and
single transducer
Class III. First-stage elements used as detector with
two transducer stages
Mass
Piezoelectric
Thermal
Hydro-pneumatic
Semi-conductor
junction
Photoelectric
Hall effect
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6.5 Variable-resistance transducer elements
Advantages of electrical elements :
1. Amplification or attenuation can be easily
obtained
2. Mass-inertia effects are minimized
3. The effects of friction are minimized
4. An output power of almost any magnitude can
be provided
5. Remote indication or recording is feasible
6. The transducers can often be miniaturized
• Resistance of an electrical conductor:
6.6 Sliding-contact devices
• Convert mechanical displacement input into
electrical output, either voltage or current
6.7 The resistance strain gage
• Application of a strain to a resistance element
changes its resistance basis for the resistance
strain gage
6.8 Thermistors
• Thermally sensitive variable resistors made of
ceramic-like semiconducting materials
http://en.wikipedia.org/
wiki/Strain_gauge
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6.10 Variable inductance transducers
6.9 The thermocouple
Inductance
— n. Physics the property of an electric conductor
or circuit that causes an electromotive force to be
generated by a change in the current flowing.
http://en.wikipedia.org/wiki/Inductor
‘Inductance is typified by the behavior of a
coil of wire in resisting any change of electric
current through the coil.’
http://hyperphysics.phyastr.gsu.edu/Hbase/magnetic/
indcur.html#c2
http://hyperphysics.phy-astr.gsu.edu/Hbase/magnetic/indcur.html#c2
Variable-Inductance Transducers
Variable selfinductance
Single coil
Two coil
Variable
mutual
inductance
Two coil
Three coil
Number of turns
Variable
reluctance
Moving iron
Inductance,
Size of coil
Moving coil
Moving magnet
Permeability of
magnetic flux path
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• Inductance of a straight, cylindrical air-core coil
• When flux path includes both magnetic material
and air gap, the inductance may be estimated as
d
l
http://info.ee.surrey.ac.uk/Worksh
op/advice/coils/air_coils.html
• In many instances, the permeability of the
magnetic material is sufficiently high that only the
air gaps need to be considered, thus
• When an a.c. excitation is used,
Inductive reactance:
Total impedance:
Let’s try
6.1.
LET’S RECALL
Consider an inductive displacement probe having
a diameter of 0.25 in. If the probe is set at a “standoff” distance of 0.050 in. relative to a shaft,
determine the probe sensitivity (mV/0.001 in.
displacement) when the probe is used as shown in
the circuit shown in Figure 6.25. Assume Eq. (6.3c)
is valid here with n = 100 and that the excitation
frequency is 1000 Hz.
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LET’S RECALL
6.10.1 Simple Self-Inductance Arrangements
• Flux path may be changed by a change in air gap
ha2
• Form of two-coil self-inductance:
ha1
6.10.2 Two-Coil Mutual-Inductance Arrangements
Pickup
6.11 The Differential Transformer
V1 – V2
V1
V2
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6.12 Variable-Reluctance Transducers
6.13 Capacitive Transducers
A
• Capacitance C is given by
εo
d
Permittivity of free
space
Dielectric constant of
medium between plates
Area of overlap
Separation of plates
• Capacitance of a stack of n equally spaced plates in
which alternate plates are connected to one another
is:
• Examples in transducer applications
εo
d
.
.
.
.
.
.
1
Changing Dielectric Constant
n
• Examples in transducer applications
2
Changing Dielectric Constant
Changing Area
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d1
1
Changing Area
d1
1
Changing Distance
Let’s try
6.3. For a capacitive displacement transducer whose
behavior can be represented by Eq. (6.6a),
determine an expression for the sensitivity deo/d(d)
for an excitation frequency f if the transducer is used
as shown in Fig. 6.26.
Let’s try
6.6. Consider the capacitive displacement transducer in
Fig. 6.26 to be governed by the following relationship:
where
C = capacitance (pF),
A = cross-sectional area of transducer tip (in.2),
d = air-gap distance (in.)
Determine the change in eo when the air gap changes
from 0.010 in. to 0.015 in.
6.14 Piezoelectric Sensors
• Equivalent circuit for a piezoelement:
• In terms of the stress
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6.15 Semiconductor Sensors
Let’s try
6.2. It is desired to construct a dynamic
compression force cell capable of measuring forces
in the range of ±1000 N. If a quartz disk 1.0 mm
thick and 10 mm in diameter is used as the sensing
element, determine the force cell sensitivity (mV/N).
• Semiconductor technology has produced compact
and inexpensive sensors:
Piezoresistive pressure sensor
Capactive pressure sensor
6.15.1 Electrical Behavior of Semiconductors
Accelerometer
• Semiconductors also respond to strain:
• Number of charge carriers, nc, is a function of
temperature, T :
• Since the resistivity of material is proportional to
1/nc, a semiconductor’s resistance decreases
rapidly with increasing temperature
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6.15.2 pn-Junctions
• Most semiconductor devices involve a junction,
at which n-type and p-type doping meet:
• When a voltage is applied to the junction, the current
through it varies as shown:
6.15.3 Photodiodes
• Irradiating light produces an additional current, Iλ,
at the junction:
• Photocurrent, Iλ, is directly proportional to the
intensity, H, of the incoming light (in W/m2):
• Voltage-current characteristics of a photodiode:
6.16 Light-Detecting Transducers
(Self-study)
• Two-dimensional arrays of photodetectors allow
the contruction of digital cameras
Image sensor
(CCD)
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6.17 Hall-Effect Sensors
• Hall effect - appearance of transverse voltage
difference on conductor carrying current
perpendicular to magnetic field:
• Because the electrons carry a charge -q, they
experience a magnetic force FB in the z-direction:
• Charge distribution creates an electric field, E,
whose force in steady state is equal and opposite the
magnetic force on the electrons:
• The magnitude of the electric field is E = vdB
• Voltage difference across a conductor of height l is
6.18 Some Design-Related Problems
Self-study
Let’s try
6.10. The circuit of Figure 6.28 may be used to operate a
photodiode. The voltage Vr is a reverse-bias voltage large
enough to make diode current, i, proportional to the incident
light intensity, H. Under this condition, i/H = 1µA/(W/m2).
(a) Show that the output voltage, Vout, varies linearly with H.
(b) If H = 1000 W/m2, Vr = 5 V, and an output voltage of 1 V is
desired, determine an appropriate value of Rload.
LEARNING POINTS
1. Fill in the table below:
Element
Load cell (compression)
Operation
Force to linear displacement
Bourdon tube
Torsional spring
Seismic mass
Thermocouple
Thermistor
Venturi
Variable inductance coil
Changing area capacitor
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LEARNING POINTS
2. List FOUR factors that affect the inductance of a
coil whose flux path includes both a magnetic
material and an air gap
3. List THREE methods that can be used to
change the capacitance of a capacitive transducer
4. What is meant by ‘Hall effect’?
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