A385992265_25184_26_2019_UNIT-1b Sensor_characteristics_and_Fundamentals (1).ppt

Unit-1b: Smart Sensor
Sensor Characteristics:
There are various conversion steps which are performed before an electrical
signal is generated in a sensor from a given stimulus.
Take for example a pressure detection with optical fiber.
1. Pressure produce a strain in the fiber
2. That changes the refractive index of the fiber material
3. That changes the optical transmission and modulation of the photon
density
4. Then the modulated photon density is detected and converted into an
electrical signal using photoresistive phenomenon etc.
If there are lots of conversions, then we must have some way to
estimate the output at every conversion.

Sensor Characterization continued
)
(s
f
S 
This function can be a linear or exponential or some other complex
function. But in many cases it’s a linear function of the type
bs
a
S 

Here a is the intercept and b is the
slope or it is also called sensitivity.
s
S
Input
Output
1. Transfer function.
There is an ideal or a theoretical relationship between the stimulus and output it
generate. This ideal function could a table of values or a graph or a mathematical
equation. This ideal output-stimulus relationship is called a transfer function. This
relationship describes the dependence of the a stimulus s on the electrical signal S.

Transfer Function and Accuracy limits

2. Span (Input full scale)
The dynamic range of stimuli which may be converted by a sensor is called a
span or an input full scale (FS). It represents the highest possible input value
which can be applied to a sensor.
This dynamic range is often expressed in decibels which is a logarithmic
measure of ratios of either power or voltage.
3. Full Scale Output (FSO)
The algebraic difference between the end points of
the outputs for maximum input and lowest input
stimulus. The upper limit of a sensor output over
the measured range is called the full scale.
1
2
log
10
1
P
P
dB 
s
S
Input
Output
FSO

3. Accuracy
Accuracy of a sensor really means inaccuracy, that is
the highest deviation of a value from its ideal value.
4. Calibration Error
Calibration Error is inaccuracy
permitted by a manufacturer when a is
calibrated in the factory. This is a
systematic error which is added to all
possible real transfer function.
5. Hysteresis
The maximum difference in output, at
any measured value, within the
measured range when the value is
approached first with increasing and
decreasing measurand. It is expressed in
% of FSO during one calibration cycle.
Hysteresis

Nonlinearity error is
specified for sensors
whose transfer function
may be approximated
by a straight line. So it
measures a maximum
deviation (L) of a real
transfer function from
the approximate straight
line
The value of measurand over which the sensor is intended to measure
specified by upper and lower limits.
7. Measurand Range
6. Nonlinearity

8. Resolution.
The minimum change of the measurand value necessary to produce a
detectable change at the output.
9. Selectivity
The ability of a sensor to measure one measurand ( e,g., one chemical
component ) in the presence of others.
10. Sensitivity.
The ratio of the change in sensor output to the change in the
input of a measurand. It is the slope of the transfer curve.
o
s
s
ds
s
dS
b


)
(
11. Ambient Conditions Allowed
Ambient conditions can strongly influence the operation of a sensor.
These conditions include temperature, moisture, ambient pressure,
vibrations, shock, acceleration and EM field.

Electrical and other fundamentals:
Electric charges, field and potentials:
We consider interaction between charges mainly in the following
mediums :
• Conductors,
• Semiconductors
• Insulators
• Fluids
These materials are characterized by their electric properties, like
dielectric constant, resistivity etc.

Electric Charges, Fields, and Potentials
• Positive test charge in
vicinity of a charged object
• (a) and electric field of a
spherical object (b)
• If a small positive electric
test charge q0 is positioned
in the vicinity of a charged
object, it will be subjected
to a repelling electric force

Gauss’ law
• If we imagine a hypothetical closed surface (Gaussian
surface) S, a connection between the charge
q and flux can be established as
where the integral is equal to
If a surface encloses equal and opposite charges, the net flux is
zero. The charge outside the surface makes no contribution to the
value of q, nor does the exact location of the inside charges affect this
value.
The Coulomb law itself can be derived from the Gauss’ law.
It states that the force acting on a test charge is inversely
proportional to a squared distance from the charge

How to calculate an electric field at a given point in a medium?
The Gauss’ law
Q
dS
E
o

 .
 =total charge enclosed within that surface)
Q
E
dS
E=electric field
dS is the surface element
Examples: How to calculate the electric field of the following
charge distributions?
• Spherical symmetric charge distribution
Q
dS
E
o

 .

Q
r
E
o

2
4

Total surface
area of a
sphere = 2
4 r

+Q
2
4
1
r
Q
E o



+Q r
Inside a uniform sphere of charge Q
R

 dS
E
o
.
 charge enclosed within the radius
r of the big sphere of radius R
3
3
2
4
R
r
Q
r
E
o



3
4
1
R
Qr
E o


the electric field inside a uniform sphere of charge q is directed
radially and has magnitude

Infinite Charged Line
We construct a Gaussian surface, which is
a ring of radius r around the wire.
 is the charge per unit length of the wire.wire
Note that the electric field varies as
r
1
If the electric charge is distributed along an
infinite (or, for the practical purposes, long)
line, the electric field is directed
perpendicularly to the line and has the
magnitude
where r is the distance from the line and l is the linear charge
density (charge per unit length).

Electric field near an infinite sheet
The electric field due to an infinite
sheet of charge is perpendicular to
the plane of the sheet and has
magnitude

Electric filed between the two charged sheets or
between parallel plate condensers
++
+
+
+
+
+
-
-
-
-
-
-
-
Electric field E is directed from one sheet
to another
o
o
o
E
E
E










 

2
2

Electric dipole (a); an electric dipole in an electric
field is subjected to a rotating force (b)
An electric dipole is a combination
of two opposite charges which are
placed at a distance 2a apart.
Each charge will act on a test
charge with force which defines
electric fields E1 and E2 produced
by individual charges.
A combined electric field of a
dipole, E, is a vector sum of two
fields. The magnitude of the field is
where r is the distance from the center of the
dipole
Where dipole moment p =2qa

Electric potential:
It is the amount of work done per unit charge against the external electric field to
bring a charge to a particular point r in a medium. That defines the electric
potential associated with that point.
A
Charge Q
B
Electric field E

 B
A V
V
-work done =-F.dr =- E.dr









  B
A
o
B
A
o
r
r
Q
r
Q
dr
V
1
1
4
4
1
2


Potential at a distance r from the charge +Q is
r
Q
V o

4
1

One can obtain this if we take the
point B to infinity and assume rA = r
Units of the potential are
Volt = Joule/Coulomb dr
E
V .



Since E
dr
dV


Gradient of potential
gives the electric field

Capacitance
V
Q
C 
Capacitance
is defined as
On what factors the value of C
depends?
Medium between the plates,
shape of the plates,
distance between the plates
Fluctuating
current
C
j
i
V

1


Electric field E
A= area
of the
plate
+
+
+
+
+
+
-
-
-
-
-
-
+Q -Q
Voltage applied =V
+ -
d
The phenomenon of a
capacitance is used in many
sensors.

Capacitance continued
Capacitance between the two parallel plates can also be defined as
d
A
C 0


It is the capacitance dependence of the
above factors which is exploited in most of
the sensors design.
For a cylindrical capacitor
a
b
L
C
ln
2
0 


L
+Q
-Q
a
b

Dielectric Constant
The presence of a medium between the plates of a capacitor
modifies the electric field between the plates.
So the effective dielectric
constant becomes
d
A
C
V
Q
C
0
0






One can think of making a
sensor where k is changes by
a stimulus.
Think also of series and
parallel capacitors

Dielectric Constant of Water vs
Temperature

Capacitive water level sensor
(A); capacitance as function of the water level

Another Example of Capacitor
• Another example of a capacitive
sensor is a humidity sensor.
• In such a sensor, a dielectric
between the capacitor plates is
fabricated of a material that is
hygroscopic, that is, it can
absorb water molecules.
• Material dielectric constant
varies with the amount of
absorbed moisture, this changes
the capacitance that can be
measured and converted to a
value of relative humidity
The dependence is not perfectly linear but
this usually can be taken care of during the
signal processing

RH estimation by Dry & Wet Bulb
Relative Humidity - RH (%)
Tdb -
Twb
(oC)
Dry Bulb Temperature - Tdb (oC)
15 18 20 22 25 27 30 33
1 90 91 91 92 92 92 93 93
2 80 82 83 84 85 85 86 87
3 71 73 75 76 77 78 79 80
4 62 65 67 68 70 71 73 74
5 53 57 59 61 64 65 67 69
6 44 49 52 54 57 59 61 63
7 36 42 45 47 51 53 55 58
8 28 34 38 41 45 47 50 53
9 21 27 31 34 39 41 45 48
10 13 20 25 28 33 36 40 43

Resistance
Resistance of a material is
defined as
i
V
R 
a = area of cross-section of
the material
Temperature dependence of resistivity
 
)
(
1 o
o T
T 

 


•Resistivity of a material can be
expressed through
•mean time between collisions, τ,
•the electronic charge, e,
•the mass of electron, m, and
•a number of conduction electrons
per unit volume, n

Specific Resistance of Materials

Moisture Sensitivity
• By selecting material for a resistor, one
can control its specific resistivity and
susceptibility of such to the
environmental factors.
• One of the factors that may greatly
affect r is the amount of moisture that
can be absorbed by the resistor.
• A moisture-dependent resistor can be
fabricated of a hygroscopic material
whose specific resistivity is strongly
influenced by concentration of the
absorbed water molecules.
• This is the basis for the resistive
humidity sensors, which are called
hygristors.
A typical hygristor is comprised of a ceramic
substrate that has two silk-screen printed
conductive inter-digitized 7 electrodes

Piezoelectric effect
It is generation of electric charge by a crystalline material when
subjected to an external stress.
Example of materials: Quartz ( chemical formula SiO2, , man made
ceramics and some polymers, such as PVDF
How the charges are created?
To pick up the electric field, conductive electrodes must be applied
to the opposite side of the crystal cut. As a result a piezoelectric
material becomes a capacitor with voltage V across the capacitor.

The word piezo comes
from the Greek meaning “to press.”
• The Curie brothers discovered the piezoelectric effect in
quartz in 1880, but very little practical use was made until
1917 when another Frenchman, professor P. Langevin used
x-cut plates of quartz to generate and detect sound waves
in water.
• His work led to the development of sonar.

Piezoelectric effect is a
reversible phenomenon.
Which means that the
applied voltage across
the material will
produce a strain.
The polarization vector P is given
by
zz
yy
xx P
P
P
P 


Piezoelectric effect
Piezoelectric sensor is formed by applying electrodes
to a poled crystalline material

zz
yy
xx
xx d
d
d
P 

 13
12
11 


zz
yy
xx
yy d
d
d
P 

 23
22
21 


zz
yy
xx
zz d
d
d
P 

 33
32
31 


When we apply a stress  to the crystal we generate
polarization.
Let dij are the piezoelectric coefficient along the orthogonal
directions. Then
Charge generated by a piezoelectric crystal is proportional to
applied force.
x
x F
d
Q 11
 For x-direction
Voltage generated in a Piezoelectric crystal

So the voltage developed will be
x
F
C
d
C
Qx
V 11


l
a
C o


Capacitance can be written in terms of the
electrode surface area , a, and thickness l
Then the output voltage
becomes x
o
x F
a
l
d
F
C
d
V

11
11



Piezoelectric Sensor is AC or DC Device?
• When stress is applied, or air blows near its surface the balanced
state is degraded and the piezoelectric material develops an
electric charge.
• If the stress is maintained, the charges again will be neutralized
by the internal leakage.
• Thus, a piezoelectric sensor is responsive only to a changing
stress rather than to a steady level of it.
• In other words, a piezoelectric sensor is an AC device, rather
than a DC device.
• The three most popular materials are zinc oxide (ZnO),
aluminum nitride (AlN), and the so-called solid solution system
of lead-zirconite-titanium oxides Pb(Zr,Ti)O3 known as PZT
ceramic

A385992265_25184_26_2019_UNIT-1b Sensor_characteristics_and_Fundamentals (1).ppt

Piezoelectric Sensor for Sound
waves

Which material preferred?
• Zinc oxide in addition to the piezoelectric properties also is
pyroelectric. It was the first and most popular material for
development of ultrasonic acoustic sensors, surface acoustic
wave (SAW) devices, microbalances, etc. One of its advantages
is the ease of chemical etching. The zinc oxide thin films are
usually deposited on silicon by employing the sputtering
technology.
• Aluminum nitride (AlN) is an excellent piezoelectric material
because of its high acoustic velocity and its endurance in
humidity and high temperature. Its piezoelectric coefficient is
somewhat lower than in ZnO but higher than in other thin-film
piezoelectric materials, excluding ceramics. The high acoustic
velocity makes it an attractive choice in the GHz frequency
range.

• Usually, the AlN thin films are fabricated by using the
chemical vapor deposition (CVD) or reactive molecular
beam epitaxy (MBE) technologies. However, the drawback
of using these deposition methods is the need for high
heating temperature (up to 1,300C) of the substrate.
• The PZT thin films possess a larger piezoelectric coefficient
than ZnO or AlN, and also a high pyroelectric coefficient,
which makes it a good candidate for fabrication of the
thermal radiation detectors.
• A great variety of deposition techniques is available for the
PZT, among which are the electron-beam evaporation [11],
RF sputtering [12], ion-beam deposition [13], epitaxial
growth by RF sputtering [14], magnetron sputtering [15],
laser ablation [16], and sol-gel [17]
Which material preferred?

Polymer Piezoelectric Films
• In 1969, H. Kawai discovered a strong piezoelectricity in
polyvinylidene fluoride (PVDF) and in 1975 the Japanese
company Pioneer, Ltd. developed the first commercial
product with the PVDF as a piezoelectric loudspeakers and
earphones.
• PVDF is a semicrystalline polymer with an
approximate degree of crystallinity of 50%

Some unique properties of the piezoelectric films are
(from Measurement Specialties Inc., www.msiusa.com)
• Wide frequency range - 0.001 Hz to 109 Hz.
• Vast dynamic range (10-8 to 106 psi or micro-torr to Mbar).
• Low acoustic impedance – close match to water, human tissue and adhesive
systems.
• High elastic compliance.
• High voltage output – 10 times higher than piezo ceramics for the same force
input.
• High dielectric strength – withstanding strong fields (75 V/micro-m) where
most piezo ceramics depolarize.
• High mechanical strength and impact resistance (109—1010 Pascal
modulus).
• High stability—resisting moisture (<0.02% moisture absorption), most
chemicals, oxidants, and intense ultraviolet and nuclear radiation.
• Can be fabricated into many shapes.
• Can be glued with commercial adhesives.

Pyroelectric
Sensor
Piezo- and pyroelectric materials such as lithium tantalate and polarized
ceramics are typical materials to produce the pyroelectric sensors

A385992265_25184_26_2019_UNIT-1b Sensor_characteristics_and_Fundamentals (1).ppt

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