Physical Principles of
Sensing
SOPHOMORE CLINIC I
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Definition

A sensor is a device that receives a stimulus and
responds with an electrical signal.
Fig 1.1
Level control system. A sight tube and the
operator’s eye form a sensor.
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What are some quantities
that can be sensed?





Motion, position,
displacement
Velocity and
acceleration
Force, strain
Pressure
Flow






Sound
Moisture
Light
Radiation
Temperature
Chemical presence
These quantities are the stimulus.
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The Response is an
Electrical Signal

When we say electrical we
mean a signal which can
be channeled, amplified
and modified by electronic
devices:

• Voltage
• Current
• Charge
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The voltage, current or
charge may be describe
by:
•
•
•
•
Amplitude
Frequency
Phase
Digital code
4
Any sensor is an energy converter

This conversion can be direct or it may
require transducers.
Fig 1.2

Example:
• A chemical sensor may have a part which
converts the energy of a chemical reaction into
heat (transducer) and another part, a
thermopile, which converts heat into an
electrical signal.
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Physical Principles of Sensing






Charges, fields &
potentials
Capacitance
Magnetism
Induction
Resistance
Piezoelectric effect
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


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Seebeck and
Peltier effects
Thermal properties
of materials
Heat transfer
Light
6
Types of Sensor

Direct
• A sensor that can convert a nonelectrical stimulus into an electrical
signal with intermediate stages.


Thermocouple (temperature to voltage)
Indirect
• A sensor that multiple conversion steps
to transform the measured signal into
an electrical signal.
A fiber-optic displacement sensor:
 Current photons current

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Today’s Topic:
Physical Principles that are Used to
Effect a Direct Conversion of
Stimuli into Electrical Signals
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Electric Charges, Fields, &
Potentials

Any charged object is subject to a force when in
the region of an electric field.
• A field can be used to detect the presence of charge or
the opposite can be true and the force on a charge
determined to detect a field.
f
E
q0
E
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q
4 0 r
2
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Other Geometries

E
2 0 r
=charge/unit length
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
E
2 0
The field is strongest at
areas of highest
curvature
=charge/unit area
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Electric Dipole

Dipoles are found in crystalline materials and form a
foundation for piezoelectric and pyroelectric detectors.
• The dipole is a combination of 2 opposite charges placed 2a
apart. The electric field is the vector sum to the two fields.
E
qa
p

4 0 r 3 8 0 r 3
p represents the
dipole moment
In the presence of an E
field the dipole will
develop a torque
  pE
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Capacitance

Two isolated conductive objects of
arbitrary shape which can hold an electric
charge is called a capacitor.
• An E field is developed between the two conductors.
q 0 A
C 
V
d
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Capacitor as Displacement Sensor

If the inner conductor can be moved
in and out, the measured
capacitance will be a function of l.
2 0l
C
ln b / a 
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Dielectric Constant

The material between the plates of the capacitor can also
be used to sense changes in the environment.
• When vacuum (or air) is replaced by another material, the
capacitance increases by a factor of , known as the dielectric
constant of the material
• The increase in C is due to the polarization of the molecules of
the material used as an insulator.
q  0 A
C  
V
d
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Example – A Water Level Sensor

The total capacitance of the coaxial sensor shown below is
the capacitance of the water-free portion plus the
capacitance of the water-filled portion. As the level of the
water changes, the total capacitance changes.
Ch  C free  C filled
Ch 
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2 0
H  h1   
lnb / a 
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Magnetism

There are two methods of generating a magnetic
field:
• Permanent magnets (magnetic materials).
• The magnetic field generated by a current.
Force is
generated on a
test magnet in
the field of
magnetic
materials.
A compass
needle will
respond to the
magnetic field
generated by a
current.
Magnetic field, B
“flux” is the field density, B
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Sources of Magnetic Field
Electric current sets a
circular magnetic field
around a conductor.
Moving electron sets
a field,
superposition of
field vectors results
in a combined
magnetic field of a
permanent magnet.
Magnets are useful for fabricating magnetic sensors for the detection
of motion, displacement, and position.
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Induction

A phenomenon related to magnetism is induction,
the generation of voltage from a changing
magnetic field.
• If the coil has no magnetic core, the flux is proportional
to current and the voltage proportional to di/dt.
v
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d n B 
dLi
di

 L
dt
dt
dt
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Resistance

If we apply a battery across two points of a piece of
material, an E field will be set up where E=V/l
V
i
E V
1
Va
  

j l i / a  li
Va l
l
R
 
il a
a
R
The tendency of the material
to resist the flow of electrons
is called its resistivity, , and
we say that the material has
a particular electrical
resistance, R.
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Sensitivity of Resistance

To Temperature:
Specific resistivity of
tungsten as a function
of temperature.
  0 1   t  t0 
 is the temperature
coefficient of resistivity.
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Application for Temperature Indication using a
Laminate of Materials with Two Different ’s.
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To Strain:

Strain changes the
geometry of a conductor
and its resistance.
F
dl
 E  Ee
a
l
Stress = Young’s Modulus x strain

(1)
R
(2)
dR

 Se l
dl
v
(3)
dR  S e
(4)
dR
R  R1
 See  2
R
R1
v
l2

v
ldl  S e 
l
l
dl
 dl 
dl   S e  R S e 
a l
a
l
 l 
Since length is changing the factor of 2 in the second equation
becomes a variable which depends on the material.
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To Moisture:
For the hygristor, the resistance of the polymer changes with the
absorption of water molecules.
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The Piezoelectric Effect

The piezoelectric effect is the generation
of electric charge by a crystalline material
upon subjecting it to stress.
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Piezoelectric Sensor
Because a crystal with deposited
electrodes forms a capacitor the
voltage developed can be
expressed as:
Qx d x
V

Fx
C
C
Piezoelectric crystals are
direct converters of
mechanical energy into
electrical energy.
Where dx is the piezoelectric
coefficient in the x direction and
Fx is the applied force in the x
direction.
Laminated 2-layer piezoelectric sensor
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Pyroelectric Effect
dPs
PQ 
dT
PQ is the pyroelectric charge
coefficient and Ps is related to
the charge developed on the
electrodes when the sensor is
subjected to heat flow.
If the sensor has the “capacitor”
form:
Pyroelectric materials are
crystals capable of generating
an electrical charge in response
to heat flow.
Q  PQ AT
Q  r  0 A

V
h
then
C
PQ AT
Q PQ AT
h
V 


 PQ
T
C
C
 r 0 A / h
 r 0
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The material loses its
usefulness at the Curie Temp –
the point at which polarization
disappears.
The electric charge reaches its
peak nearly instantaneously and
then decays with a thermal time
constant, T
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Seebeck and Peltier Effects

The Seebeck effect is a direct conversion of
thermal energy into electric energy.
The varying temperature
along the bar is a source of
electromotive force
(voltage) and current will
flow.
This is the principle behind
the thermocouple.
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Thermoelectric Loops
VAB   A   B T 
If a loop of conductor has
points at 2 different
temperatures, current flows.
But if there is a single
conductor no measurable net
current flows.
If a loop of conductor has
points at 2 different
temperatures, again current
flows. If the loop is composed
of 2 different conductors,
measurable net current flows
due to a difference in the
Seebeck coefficients.
A and B are the Seebeck coefficients
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Output Voltage from Standard
Thermocouples
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TYPES – MATERIALS – TEMP RANGES
Thermocouple Type
Names of Materials
Useful Application Range
B
C
E
J
K
N
R
S
T
Platinum30% Rhodium (+)
Platinum 6% Rhodium (-)
2500 -3100F
1370-1700C
W5Re Tungsten 5% Rhenium (+)
W26Re Tungsten 26% Rhenium (-)
3000-4200F
1650-2315C
Chromel (+)
Constantan (-)
200-1650F
95-900C
Iron (+)
Constantan (-)
200-1400F
95-760C
Chromel (+)
Alumel (-)
200-2300F
95-1260C
Nicrosil (+)
Nisil (-)
1200-2300F
650-1260C
Platinum 13% Rhodium (+)
Platinum (-)
1600-2640F
870-1450C
Platinum 10% Rhodium (+)
Platinum (-)
1800-2640F
980-1450C
Copper (+)
Constantan (-)
-330-660F
-200-350C
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The Peltier Effect
The Peltier effect concerns the reversible absorption of heat which
usually takes place when an electric current crosses a junction
between 2 dissimilar metals.
It can produce heat or cold depending on the direction of electric
current through the junction.
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Light
(Electromagnetic Radiation)
E  h  h
c

E is the energy of the
radiation
c = c x 108 m/s
h = 6.63 x 10-23 J-s
 is the wavelength of the
radiation
UV and visible photons have relatively high energy levels and are easily
detected. In the far IR the energies become very small and thermal
detectors are used.
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Conclusions
A sensor is a device that receives a
stimulus and responds with an
electrical signal.
 The final stage of any sensor is
dependent upon the electrical
properties of the sensor materials.
 The materials introduced today are
used in the design and fabrication of
many different types of sensors.

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