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## Demos: capacitor separation with distance

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Title: Demos: capacitor separation with distance

1
Lecture 3
• Demos capacitor separation with distance
• Introduce dielectrics (foam,glass) and see the
voltage decrease as the capacitance increases.

2
Electrical Sensors
• Employ electrical principles to detect phenomena.
• May use changes in one or more of
• Electric charges, fields and potential
• Capacitance
• Magnetism and inductance

3
Some elementary electrical sensors
Thermocouple
Thermistor
Variable Capacitor
4
Review of Electrostatics
• In order to understand how we can best design
electrical sensors, we need to understand the
physics behind their operation.
• The essential physical property measured by
electrical sensors is the electric field.

5
Electric Charges, Fields and Potential
Basics Unlike sign charges attract, like sign
charges repel
Coulombs Law a force acts between two point
charges, according to
The electric field is the force per unit charge
How do we calculate the electric field?
6
Electric Field and Gausss Law
We calculate the electric field using Gausss
Law. It states that
Seems very abstract, but is really useful
7
Point or Spherical charge
What is the field around a point charge (e.g. an
electron)? The electric field is everywhere
perpendicular to a spherical surface centred on
the charge.
Electric field vectors
So
Gaussian surface
We recover Coulombs Law! The same is true for any
distribution of charge which is spherically
symmetric (e.g. a biased metal sphere).
8
Line of Charge
For a very long line of charge (eg a wire), the
cylindrical surface has electric field
perpendicular to a cylindrical surface.
So
Where ? linear charge density (Coulombs/meter)
9
Plane of Charge
For a very large flat plane of charge the
electric field is perpendicular to a box
enclosing a segment of the sheet
So
Where ? Charge/Unit area on the surface
10
Electric Dipole
• An electric dipole is two equal and opposite
charges Q separated by a distance d.
• The electric field a long way from the pair is
• p Q d is the Electric Dipole moment
• p is a measure of the strength of the field
generated by the dipole.

11
Electrocardiogram
• Works by measuring changes in electric field as
heart pumps
• Heart can be modeled as a rotating dipole
• Electrodes are placed at several positions on
the body and the change in voltage measured with
time

12
Electrocardiogram
• Interior of Heart muscle cells negatively charged
at rest
• Called polarisation
• K ions leak out, leaving interior ve
• Depolarisation occurs just proir to contraction
• Na ions enter cells
• Occurs in waves across the heart
• Re-polarisation restores ve charge in interior

- - - - -
• - -
• -

Polarisation
Depolarisation
13
Electrocardiogram
• Leads are arranged in pairs
• Monitor average current flow at specific time in
a portion of the heart
• 1 mV signal produces 10 mm deflection of
recording pen
• 1 mm per second paper feed rate

A
-
A
-

B
C

-
C

B
14
Electric Potential
The ECG measures differences in the electric
potential V
The Electric Potential is the Potential ability
to do work.
Alternatively Work Q ? V Where V
For uniform electric fields
15
Electric fields on conductors.
• Conductors in static electric fields are at
uniform electric potential.
• This includes wires, car bodies, etc.
• The electric field inside a solid conductor is
zero.

16
Dielectric Materials
• Many molecules and crystals have a non-zero
Electric dipole moment.
• When placed in an external electric field these
align with external field.
• The effect is to reduce the strength of the
electric field within the material.
• To incorporate this, we define a new vector
Field, the electric displacement,

17
Electric Displacement
is independent of dielectric materials. Then the
electric field is related to by
Are the relative permittivity, the permittivity
of free space and the absolute permittivity of
the material.
As shown in the diagram, there is torque applied
to each molecule. This results in energy being
stored in the material, U. This energy is stored
in every molecule of the dielectric
18
Capacitance.
Remember that the electric field near a plane of
charge is
In the presence of a dielectric
So the Potential difference is proportional to
the stored charge.
19
Cylindrical Capacitor
Can make a capacitor out of 2 cylindrical
conductors
20
Sensing using capacitance.
So the charge Q C?V Where C Capacitance, V
Potential difference. For a parallel plate
capacitor
Area of plate
Easily Measured
Properties of Material
Distance between plates
We can sense change in A, e, or d and measure the
change in capacitance.
21
Measurement of Capacitance
Capacitors have a complex resistance
We measure capacitance by probing with an AC
signal. Directly measure current i(t) with known
V(t) and frequency ?.
For extreme accuracy, we can measure resonant
frequency with LC circuit.
22
Example water level sensor
Measures the capacitance between insulated
conductors in a water bath
Water has very different dielectric properties to
air (a large ?)
As the bath fills the effective permittivity seen
increases, and the capacitance changes according
to
23
Example The rubbery Ruler
Invented by Physicists here to measure fruit
growth. http//www.ph.unimelb.edu.au/inventions/ru
bberyruler/
Spiral of conductor embedded in a flexible
rubbery compound
As the sensor expands, the distance between the
plates increases causing capacitance to decrease.
24
The rubbery ruler
Spiral of conductor embedded in a flexible
rubbery compound
Invented by Physicists here to measure fruit
growth. http//www.ph.unimelb.edu.au/inventions/ru
bberyruler/
As the sensor expands, the distance between the
plates increases causing capacitance to decrease.
25
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26
Lecture 4
• Piezoelectric demo (stove lighter and voltmeter)

27
Piezoelectric sensors
Mechanical stress on some crystal lattices
results in a potential difference across the
solid.
This is an extremely useful effect. Reversible
too!
28
• For quartz, stress in x-direction results in a
potential difference in the y-direction.
• This can be used as a traffic weighing and
counting sensor!
• A piezoelectric sensor can be thought of as a
capacitor, with the piezoelectric material acting
as the dielectric. The dielectric acts a
generator of electric charge resulting in a
potential V across the capacitor.
• The process is reversible. An electric field
induces a strain in the material. Thus a very
small voltage can be applied, resulting in a tiny
change in the size of the crystal.

29
Characterisation of Piezoelectrics
We quantify the piezoelectric effect using a
vector of Polarisation.
Where dmn are coefficients, i.e. numbers that
translate applied force to generated charge and
are a characteristic of the piezoelectric
material. Units are Coulomb/Newton.
30
Characterisation of Piezoelectrics
Piezo crystals are transducers They convert
mechanical to electrical energy.
Where Y is Youngs Modulus Stress/strain
31
The charge generated is proportional to the
applied force
The charge generated in the X-direction from an
applied stress in y
Using our Q CV, we get a generated voltage
The capacitance is
Thickness of crystal
32
Some piezoelectrics
33
Numerical Example.
What is the sensitivity of 1 mm thick, BaTiO3
sensor with an electrode area of 1 square cm?

So
This is a big number because the effective
capacitance is so small. In the real world the
voltage is smaller.
Very Small!
34
Atomic Scale Microscopy
Use Piezoelectric crystals as transducers to do
atomic scale microscopy
35
Piezoresistive Sensors
The stress on a material is
Strain dl/l
A cylinder stretched by a Force F keeps constant
volume but l increases and A decreases.
Sensitivity of the sensor is
Longer wires give more sensitivity
36
Characterizing Piezoresistors
Normalised resistance is a linear function of
strain
Where e is the strain, and
Semiconductor strain gauges are 10 to 100 times
more sensitive, but are also more temperature
dependent.
Usually have to compensate with other types of
sensors.
37
Piezoresistive Heat Sensors.
Resistive Temperature Detectors on demand RTDs
RTDs used at Belle
Thin platinum wire deposited on a substrate.
38
Other piezoresistive issues
• Artificial piezoelectric sensors are made by
poling apply a voltage across material as it is
heated above the Curie point (at which internal
domians realign).
• The effect is to align natural dipoles in the
crystal. This makes the crystal a Piezoelectric.
• PVDF is of moderate sensitivity but very
resistant to depolarization when subject to high
AC fields.
• PVDF is 100 times more resistant to electric
field than the ceramic PZT Pd(Ze,Ti)O3 and
useful for strains 10 times larger.

39
Example acceleration Sensor.
• Piezoelectric cable with an inner copper core.
• The piezoelectric acts as an insulator, clad by
an outer metal sheath and flexible plastic and
rubber coating.
• Other configurations exist see
• www.pcb.com/techsupport/tech_accel.aspx

Inner copper core
Piezoelectric
Outer metal sheath or braid
Plan view of cable
Remember that Fma , so if the sensor mass is
known, then the force measured can be converted
into an acceleration.
40
Applications for piezoelectric accelerometers
• Vibration monitor in compressor blades in
turboshaft aircraft.
• Detection of insects in silos
• Automobile traffic analysis (buried in
highway) traffic counting and weighing.
• Force and pressure sensors (say, monitoring
jolts to packages).
• Tactile films thin silicone rubber film (40 ?m)
sandwiched between two thin PVDF films.

If tactile sandwich is compressed, the mechanical
coupling in the PVDF/rubber/PVDF sandwich
changes, the measured AC signal changes, and the
demodulation voltage changes
41
Lecture 5
42
Pyroelectric Effect.
Generation of electric change by a crystalline
material when subjected to a heat flow.
Closely related to Piezoelectricity.
BaTiO3, PZT and PVDF all exhibit Pyroelectric
effects
43
Primary Pyroelectricity.
Temperature changes shortens or elongates
individual dipoles.
This affects randomness of dipole orientations
due to thermal agitation.
44
Secondary Pyroelectricity
45
Quantitative Pyroelectricity.
Pyroelectric crystals are transducers they
convert thermal to electrical energy.
The Dipole moment of the bulk pyroelectric is
M ? A h
Where ? is the dipole moment per unit volume, A
is the sensor area and h is the thickness
From standard dielectrics, charge on electrodes,
Q ? A
The dipole moment, ?, varies with temperature.
46
Is the pyroelectric charge coefficient, and Ps is
the spontaneous polarisation
The generated charge is ?Q PQ A ?T
Pv is the pyroelectric voltage
coefficient and E is the electric
Field.
The generated voltage is ?QV Pv h ?T (h is the
thickness)
The relation between charge and voltage
coefficients follows directly from Q CV
47
Seebeck and Peltier Effects.
Seebeck effect Thermally induced electric
currents in circuits of dissimilar material.
Peltier effect absorption of heat when an
electric current cross a junction two dissimilar
materials
The dissimilar materials can be different
species, or the the same species in different
strain states.
The Peltier effect can be thought of as the
reverse of the Seebeck effect
48
Seebeck effect
Free electrons act as a gas. If a metal rod is
hot at one end and cold at the other, electrons
flow from hot to cold.
Where ? is the absolute Seebeck coefficient of
the material.
When two materials with different ? coefficients
are joined in a loop, then there is a mis-match
between the temperature-induced voltage drops.
?AB ?A - ?B
The differential Seebeck coefficient is
49
Thermocouples
The net voltage at the junction is
So the differential Seebeck coefficient is also
This is the basis of the thermocouple sensor
Thermocouples are not necessarily linear in
response. E.g. the T type thermocouple has
characteristics
Where the as are material properties
50
The sensitivity is the differential Seebeck
coefficient
Independent of geometry, manufacture etc. Only a
function of materials and temperature.
Seebeck effect is a transducer which converts
thermal to electrical energy.
Can be used as solid state thermal to electrical
energy converter (i.e. engine)as well as an
accurate temperature sensor.
Seebeck engines are currently not very efficient
but are much more reliable than heat engines.
They are used by NASA for nuclear powered
deep-space probes.
51
Peltier Effect.
If electric current is passed through a
dissimilar material junction, then the heat may
be generated or absorbed.
The change in heat dQ ?p I dt (where p is the
Peltier constant (unit of voltage))
52
Can be used to produce heat or cold as required.
Eg. Cooling high performance Microprocessors.
53
Lecture 6
54
Magnetism
The density of a magnetic field (number of
magnetic field lines passing through a given
surface) is the magnetic flux
Units of flux are Webers. Tesla/m2
55
Photos of flux gate magnetometers, used for
sensing magnetic fields down to a few microtesla,
which is about the size of the earths magnetic
field.
56
Sources of Magnetism
A solenoid produces lines of flux as shown (in
blue).
Note that the magnetic field lines are continuous
with no source or sink
57
Inside the solenoid the magnetic flux density is
Where n number of turns of wire. ?
permeability of the core material. I current
through the core.
Active solenoids have many uses in sensor
technologies.
Solenoids make inductive sensors which can be
used to detect motion, displacement, position,
and magnetic quantities.
There are permanent magnets (ferromagnets) too
these are very useful for small compact sensors..
58
Magnetic fields increase inside a permanent
magnet.
The magnetic field inside a magnetic material is
usually denoted H.
Magnetisation (M) is the average magnetic moment
of the magnet. It is a measure of how much all
the domains are pointing in the same direction.
59
Residual inductance in Gauss how strong the
magnet is. Also called remanence or retentivity
Characteristics of permanent magnets
B
H
Coercive force in Oersteds -Resistance to
demagnetization
60
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61
We can also plot magnetisation instead of flux
density to get a similar hysteresis curve.
62
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63
Some other figures of merit for permanent
magnets- these are commonly listed in data tables
Maximum Energy Product (MEP), (B x H) in
gauss-oersteds times 106. The overall figure of
merit for a magnet.
Temperature coefficient /C, how much the
magnetic field decreases with temperature.
64
Some common permanent magnets.
65
Typical Magnetic and Physical Properties of Rare
Earth Magnet Materials
66
Some rare earth magnets-notice how the small
spheres are strong enough magnets to support the
weight of the heavy tools.
67
These structures were created by the action of
rare earth magnets on a suspension of magnetic
particles (a ferrofluid).
68
A movie of ferrofluid reacting to a magnetic
field from a rare earth magnet.
69
70
Note that the hysteresis curves for magnetisation
(J or M) and flux density (B) are slightly
different.
The maximum energy product is the maximum energy
that can be obtained from the magnet. In
practice, it is the strength of a permanent
magnet.
71
Magnetic Induction
Time varying fluxes induce electromotive force
(emf, i.e. a voltage difference) in the circuit
enclosing the flux FBS
The sign of the voltage is such as to make a
current flow whose magnetic field would oppose
the change in the flux.
72
Induced currents also happen for solid
conductors- they are called eddy currents
Small current loops are set up in the material to
create a magnetic field that opposes the applied
field.
73
We can add a second solenoid to intercept the
flux from the first
Assuming the same cross section area and no flux
leakage, a voltage is induced in the second coil
N number of turns in the solenoid coil
74
Assuming B is constant over area A gives a more
useful relation
This second coil is called the pickup circuit. We
get a signal in this circuit if the magnitude of
the magnetic field (B) changes or if the area of
the circuit (A) changes.
We get an induced voltage if we
• Move the source of the magnetic field (magnet,
coil etc.)
• Vary the current in the coil or wire which
produces the magnetic field
• Change the orientation of the magnetic field in
the source
• Change the geometry of the pickup circuit, (eg.
stretching or squeezing)

75
Self Induction.
The magnetic field generated by a coil also
induces an emf in itself. This voltage is given
by
Note that the voltage is only induced for a
changing flux.
The number in parenthesis is called the flux
linkage, and is proportional to the current in
the coil.
76
The constant of proportionality is labeled the
inductance, L.
Most induction sensors measure the change in L
e.g. as a result of motion.
We can therefore define the inductance
77
Induction notes.
The defining equation is
Induced voltage is proportional to current change
Voltage is zero for DC (inductors look like short
circuit to DC)
Voltage increases linearly with rate of change of
coil current
Voltage polarity different for increased and
decreased current in same direction
Induced Voltage in direction which acts to oppose
change in current
78
Calculating inductance
Inductance can be calculated from geometry
For a closely packed coil it is
If n is the number of turns per unit length, the
number of flux linkages in a length l is
Plugging in the expression B for a solenoid gives
Note that lA is the volume of the solenoid, so
keeping n constant and changing the geometry
changes L
79
Inductors and complex resistance
In an electronic circuit, inductance can be
represented as complex resistance, like
capacitance.
i(t) is a sinusoidal current having a frequency
?2?f
Two coils brought near each other one coil
induces an emf in the other
Where M21 is the coefficient of mutual inductance
between the coils.
80
Mutual inductance.
For a coil placed around a long cylinder
For a coil placed around a torus, mutual
inductance is
81
Example Motion Sensor.
Pickup coil with N turns, moves into the gap of a
permanent magnet
Flux enclosed by the loop is
The induced voltage is
82
Cross-section of a magnetic position sensor
83
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84
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85
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86
The Hall Effect.
When an electron moves through a magnetic field
it experiences a sideways force
q is electron charge v is the electron
velocity B is the magnetic field
This gives rise to an potential difference across
an appropriate sensor.
87
Qualitative Hall effect
The direction of the current and magnetic fields
is vital in determining size of the potential
difference.
The deflecting force shifts the electrons in the
diagram to the right side.
This deflection produces the transverse Hall
potential VH
88
Quantitative hall effect
At fixed temperature, VH h I B sin(?)
I is the current, B is the magnetic field, ? is
the angle between the magnetic field and the Hall
plate, h is the Hall coefficient.
h depends on the properties of the material and
is given by
• N is the number of free charges per unit volume
• c is the speed of light
• q is the charge on the carrier (ve if holes).

89
Control current flows through the control
terminals
Ri is the control resistance
Ro is the differential output resistance
Output is measured across the differential output
terminals
90
Hall effect sensors are almost always
Semiconductor devices.
Parameters of a Typical sensor.
Note the significant temperature sensitivity.
Piezoresistance of silicon should be remembered
makes semiconductor sensors very sensitive to
shocks.
Also note need to use a constant current source
for control.
91
End of Electrical sensors
Summary
• Magnetism essentials
• Permanent Magnets
• Inductance
• Hall effect