#### Transcript Department of Optical Engineering Zhejiang University

```Advanced Sensor Technology
Lecture 4
Jun. QIAN
Department of Optical Engineering
Zhejiang University
A Review of Lecture 3
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Background on electrical measurement of
sensor outputs
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Resistive
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Capacitive
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Voltage divider
Bridge circuit
Inductive
Temperature Effect and Compensation
Provide an overview of piezoresistive
devices. Some examples are worked out
using this sensing technique
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A Review of Lecture 3

Strain gauge
Strain
 Poisson’s ratio
 Gauge factor
 Mercury tube/metal wire
 Resistance change 1%-0.001%
 Various bridge circuits
 Temperature Effect

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Lecture 4: Basic Intent
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Overview of the use of capacitance
measurements in sensors
Describe the fundamentals of
accelerometers.
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Capacitance measuring systems,
Limiting factors of the measurement, and
obtainable performance levels.
Fundamentals of accelerometer operation,
including
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The relationship between the mechanical characteristics
of the sensor and its performance,
The limitations of the performance of most
accelerometers.
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Capacitive Sensing
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The capacitance
C=Q/V
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If the capacitance is large, more
charge is needed to establish a
given voltage difference.
In practice, capacitance between
two objects can be measured
experimentally.
Predicting the capacitance between
a pair of arbitrary objects is very
complicated,
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to know the electric field throughout
the space between the objects.
The field distribution is affected by
the charge distribution, which is, in
turn, affect the field distribution.
Iterative analytical techniques are
generally required, and accurate
calculations are very costly.
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One application: proximity sensing
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Capacitors with Simple Geometry
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Parallel plates
Electrodes
with area 10mm x 10mm,
 separation 1m.
 C~ 1000 pF,
which isn't very big but still
would ever expect to find in
a real sensor !
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More generally,
capacitive sensors have
capacitance closer to 100
pF or less.
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Change in Capacitance due to
the Lateral Movement
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The capacitance signal changes linearly with
displacement.
To implement such a sensor, it is necessary
to guarantee that the lateral motion does not
also affect the separation between the
electrodes, d.
Difficult to use for measurement of very small
lateral displacements,
A 1um lateral displacement would cause only
100 PPM change in the capacitance of the
capacitor geometry worked out earlier.
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Lateral displacement capacitive transducers
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Useful for many
applications
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Rotary capacitive
transducers for
positioning
High precision monitoring
system
Military application
140 ± 8 mV/degrees of shaft rotation
Manufacturer: Bently, USA
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Lateral displacement capacitive
transducers
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Zhejiang University
Capacitance Change v.s. Plate Separation
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change in capacitance isn't
obviously linear,
but for small changes in
separation,
If the initial separation ~ a few
microns, a 1% change in the
capacitance  displacement
of a few tens of nanometers,
Such a measurement should
be considered well within the
capabilities of capacitive
sensing.
Department of Optical Engineering
Zhejiang University
Capacitance Change v.s. Plate Separation
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Nice features associated with such a
measurement include
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good sensitivity to very small deflections
Precision fabrication is required, since it is
necessary to produce electrodes which are very
close to one another and highly parallel
Capacitive sensing is generally used for
situations in which a precision measurement is
required, and the expense associated with the
sensor fabrication is acceptable.
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Zhejiang University
Differential Capacitor
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One technique for reducing
the effect of the nonlinearity :
differential capacitor
The circuit is set up to
measure the difference
between the two
capacitances,
the nonlinearity associated
with the term 2/d2 is
subtracted away, and the
first nonlinearity appears as
a cubic term 3/d3 ,
substantially smaller than the
squared term.
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Zhejiang University
Linearity
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Why do we care so much about linearity in
capacitive sensors?
Generally, capacitive measuring techniques
are only applied in cases where precision
measurement is necessary
 Otherwise, a strain gauge based
measurement would suffice.
 One example of such a measurement is the
measurement of acceleration for inertial
navigation applications. A common problem in
navigation situations is due to vibrations of the
vehicle.

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In geomatics engineering sense, navigation is
understood as (quasi-) continuous positioning of
a moving object
Modern navigation makes use of the so-called
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two or more electronic sensing devices (sensors) are
used together to collect the information necessary to
find the position of the object.
These systems can then be installed on-board
vehicles, ships, aircraft, or missiles.
Some of the sensors that are being part of such
systems are:
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Doppler Velocity Sensors (DVS),
laser-ranging devices, barometric altitude-meters, etc
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
Three main forces that an INS has to take into
account are:
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(a) Gravitational acting down;
(b) Centrifugal due to Earth’s rotation and sensed
by gyros – a radial force acting outward from the
object, unlike centripetal that acts toward the object;
and
(c) Coriolis force in the direction of the movement,
coming from compound acceleration of coriolis (in
navigation: Coriolis correction of the sensed
acceleration) :
ac = 2v’,
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Zhejiang University
Nonlinearity Problem
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In inertial navigation, offset errors in the
output of the accelerometer accumulate as
errors in position as t2:
d 2 si
2
ai 
,
s

a
dt
i
 i
dt 2
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If an accelerometer with a small nonlinearity
in the form of a term 2:
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in a situation which includes a vibration, there
will be a displacement of the form sin(t).
There will be a term in the output of the sensor
of the form
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Vibration Rectification
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This expression includes
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an oscillating term
a static term.
Generally, this phenomenon is referred to as
vibration rectification - the process of generating a dc
offset signal from a vibration signal.
As described above, inertial navigation is one
application which is particularly concerned about
such phenomena, and so cancellation of
nonlinearities in capacitive sensing is very important
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for such applications.
Zhejiang University
Capacitance Measurement: bridge circuit
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Sensors using cap measurement
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Pressure sensors, accelerometers, position
detectors, level sensors, …
A good way to measure displacement. If
implemented carefully, very small displacements
may be measured.
Best suited to applications which require better
performance than can be obtained from a strain
gauge, and where the added cost of the
capacitance detection is allowed.
However, the output of a capacitive transducer is
not immediately linear. If linearity is important,
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Accelerometer overview
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Accelerometers: devices that produce
voltage signals in proportion to the
acceleration experienced.
Techniques for converting an acceleration
to an electrical
Spring-mass+cap measurement
 Potentiometric
 Variable Reluctance
 Piezoelectric
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General Accelerometer
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The most general way:
suspend a mass on a
linear spring from a frame
which surrounds the
mass,
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When the frame is shaken,
it begins to move, pulling
the mass along with it.
If the mass is to undergo
the same acceleration as
the frame, there needs to
be a force exerted on the
mass, which will lead to an
elongation of the spring.
We can use any of a
number of displacement
transducers (such as a
capacitive transducer) to
measure this deflection.
A
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General Accelerometer: Oscillatory force
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impose an acceleration
by forcing X to take the
form:
If we assume all the time
varying quantities also
oscillate,
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General Accelerometer: Amplitude
Response of Vibration-measuring Instruments
If b = 0 (no damping),
signal at the resonance can lead to
infinitely large signals, generally
impose finite damping on the system.
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If < < 0, this expression simplifies to
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the displacement of the mass
is proportional to the acceleration
of the frame. This is the response
we would hope for from an accelerometer.
If > > 0, then
For high frequency signals, during which the mass remains stationary, and
the accelerometer frame shakes around it. The displacement is the same
size as the motion of the frame. This mode of operation is generally
referred to as `seismometer mode'. Seismometers are instruments which
attempt to measure ground motion, rather than ground acceleration.
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An Example
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EXAMPLE
An accelerometer has a seismic mass of 0.05 kg and a spring
constant of 3.0 X 103 N/m Maximum mass displacement is
±0.02 m (before the mass hits the stops). Calculate (a) the
maximum measurable acceleration in g, and (b) the natural
frequency.
Solution
We find the maximum acceleration when the maximum
displacement occurs
a.
b. The natural frequency
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Accelerometer Selection based on
Applications
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Applications
 Vibration
 Shock
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
 a measure of acceleration that may vary in time but
that is nonperiodic.
 the stop-go motion of an automobile is an example
 we select a sensor having
(1) adequate range to cover expected acceleration
magnitudes
(2) a natural frequency sufficiently high that its period is
shorter than the characteristic time span over which
the measured acceleration changes.
(3) By using electronic integrators, the basic
accelerometer can provide both velocity (first
integration) and position (second integration)
information.
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
An accelerometer outputs 14 mV per g. Design a
signal-conditioning system that provides a velocity
signal scaled at 0.25 volt for every m/s, and
determine the gain of the system and the feedback
resistance ratio.
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Solution
We chose T = RC = 1 so that the integrator output is scaled at
We pick R = 1 M and C = 1uF
and make R2 = 175 k R1 = 1 k 
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Vibration
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The application of accelerometers for
vibration
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first requires that the applied frequency is less
than the natural frequency of the accelerometer.
Second, one must be sure the stated range of
acceleration measured will never exceed that of
the specification for the device.
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This assurance must come from a consideration of
the following equation under circumstances of
maximum frequency and vibration displacement.
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Shock
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The primary elements of
importance in shock
measurements are that the
device
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have a natural frequency that
is greater than 1 kHz and
a range typically greater than
500 g.
The primary accelerometer that
can satisfy these requirements
is the piezoelectric type
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COLD ATOMS : Atomic Interferometer
The atom as a measuring device
λ=h/P=h/mv
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Atoms also have mass, which enables them to interact
with the gravitational field, just as any other body with
mass.
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Their high thermal agitation speed (several hundreds of
metres or even kilometres per second) generally means that
this interaction cannot be perceived.
Now know how to slow atoms down with laser beams to speeds
of a few mm.s-1,  interaction with the gravity field can now be
observed.
The atoms' mass also makes them sensitive to inertial fields
(Coriolis force, centrifugal force) which occur in non-Galilean
reference frames.
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Zhejiang University
COLD ATOMS : Atomic Interferometer
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For about twenty years, the development of laser
techniques for manipulating atoms has made it
possible to determine more easily the wave nature of
atoms and has yielded a whole range of applicable
tools for these atomic waves.
Steven Chu
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know how to make mirrors, beam splitters, diffraction arrays,
lenses and all sorts of other tools for developing operational
instruments for atomic optics.
Given these many possible interactions, the atom
thus appears to be an ideal tool for probing the
external environment.
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
The phase induced by the gravity field on an
atomic wave varies rapidly with the value of this
field. This phase may be very precisely
measured using an atomic interferometer of the
temporal Mach-Zehnder type for instance.
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possible to measure gravity (terrestrial potential or
any other gravitational potential) very precisely.
The latest experiments conducted have revealed high
sensitivity which corresponds typically to a variation of
about one centimeter of the gravity field on the
ground. (resolution: 10-9 g)
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Department of Optical Engineering
Zhejiang University
Summary
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Capacitive measurement
Features:
High precision/resolution: nanometer
 Suit for displacement sensing
 Switched cap circuit for measurement
 Cost more than strainresistive type
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Accelerometer overview
General accelerometer principle
 Applicability
 Examples
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Atomic gravitational sensingDepartment of Optical Engineering
Zhejiang University
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