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Read Chapter 2 of Textbook
    1.   Displacement Sensors
•   Potentiometer (Already discussed)
•   Strain Gages
•   Inductive Sensors (LVDT)
•   Capacitive Sensors
•   Piezoelectric Sensors
=(A/V)/m = S/m
               P and N doped Silicon Strain Gages
                Gage Factor = G = (ΔR/R)/(ΔL/L)
 ---Stretching bar of N-type silicon crystal breaks electrons loose from impurity
         sites, making resistance decrease, producing large negative G.
---Stretching bar of P-type silicon crystal inhibits holes from moving away from
                  their impurity sites, producing large positive G
Unbonded Strain Gage Pressure Sensor

                            This is a deflection mode
                            instrument, so it is
                            important to choose
                            Ri >> R1=R2=R3=R4
                            To avoid bridge loading
BONDED Strain Gages
Silicon Integrated
Circuit Pressure
             Inductive Transducers
Coils must be
wound in
directions so
magnetic fluxes

            <- L   <- L
µ = magnetic permeability of core material
= µ R4π*10-7 F/m
Linear Variable Differential Transformer
       Displacement Transducer

LVDT used to measure very small displacements in a seismometer that
measures movements in the earth’s crust due to earthquakes. It consists of a
middle primary coil and two outer secondary coil. The magnetic core moves
freely without touching bobbins, and at the null (zero) position, it extends
halfway into each secondary coil.
Example Medical Applications of Linear Variable
     Displacement Transformer (LVDT)
output voltage is
actually the
PEAK voltage of
an ac sine wave
frequency is that
of the primary
excitation sine
Advantages of LVDTs as
displacement sensors
      Disadvantages of LVDTs
• All these advantages, in addition to their
  reasonable cost, have made the LVDT an
  attractive displacement measurement sensor.
  However, LVDTs for use in medical applications
  have the following disadvantages:
  – They require a high frequency, constant-amplitude ac
    sinusoidal excitation.
  – They cannot be used in the vicinity of equipment that
    creates strong magnetic fields.
  – A somewhat complicated “phase sensitive” ac-to-dc
    converter (detector) must be used if both positive and
    negative displacements from the middle (null) position
    needs to be measured.
LVDT showing AC Excitation and
 Phase Sensitive Demodulator
Phase INSENSITIVE Detector (Diode Half-
wave rectifier with capacitive filter.)
Commercial Diode
Ring Modulator (also
called “Double
Balanced Mixer”
LVDT Detector Circuit without need for a Phase-Sensitive Demodulator
LVDT Excitation Circuit (Power oscillator (1 kHz
       Power Sine Wave Oscillator)
Does not effect circuit,
since output resistance of
op amp is nearly 0 ohms
                                      L = thickness
C = q/v => v = q/C =>                 of piezo
Molecular Model of a Simple Piezoelectric Material: ZnS
How is the piezoelectric constant “k” (recall q = kF) related the constant “K”
above? Recall the definition of Young’s Modulus, Y:

                 f /A                   A Y
                            =>    f         x                A
                                                           f         x
                         A Y                                            A Y
Therefore     qk f k      x  Kx               where     K k
                          L                                               L
  Crystal                            Amplifier


                                     Ca          Ra
                 Rs   Cs    Cc
  q = Kx

is = dq/dt = Kdx/dt    R  Rs // Ra
                       C  Cs  Cc  Ca
                                                      q  C  v0
                                                      iC  C 
         q  C  v0
         iC  C 

                          iC          iS   iR

Eqn 2.19 is now written in phasor form:
C  j Vo  K  j  X 
Vo(1  j )       j  RC  X
                                 This transfer function is of the
                                 same form as that of the RC
                                 HPF 1st order filter and also
                                 the capacitive displacement
                                 So, like the capacitive
                                 transducer, it cannot
                                 transduce constant (dc)
                  100 kΩ and
                                       100k Ω) = 16 nF
                                           VCC = 1 5 V

                                       +              1
                                   2                      Vout

          R3      C1
Piezo    3.2MEG   1u F                     VEE = -15 V
Xducer                   R2                R1

                         11 .1 k               10 k

                                           16 0 nF
                                           16 nF

Piezoelectric Displacement Sensor has a high pass filter step response
    Predicting Piezo Transducer Step Response Via Laplace Transforms

Replacing “jω” in Text Eqn 2.20 by the Laplace complex frequency variable “s”

                   Vo( s ) K S  s           Note that for a step input of amplitude
          H (s)                              xo, x(t) = xo u(t) => X(s) = x0/s
                    X (s)         s   1
                    K  s                K  s  xo xo  K S 
          Vo( s )  S             X ( s)  S           
                    s   1                s   1 s           s   1
          vo(t )  xo  K S e t / Note this is response only to the leading
                                   edge of the input pulse, x(t) = x0 u(t)
                                   But in reality, x(t) = x0 {u(t) – u(t-Td)}
  x(t)                  xoKS
                                      xoKSe-1 = 0.37xoKS       t=Td


                   t=0         t = τ = RC                             - xoKS
                      Operating frequency for
             +        very sensitive, narrow-
                      band signal transducer,
             vout    such as 40 kHz resonant
                         ultrasonic pulsed
             -         distance measuring
Useable Operating
Frequency Range
  for “wideband”
signal transducer,
  such as audio
General Block Diagram of a Feedback Oscillator

                                                 1. Magnitude of
                                                    voltage gain
                                                    around feedback
                                                    loop “BA” must
                                                    be > 1 at
                                                    frequency of
                                                 2. Phase shift
                                                    around feedback
                                                    loop must be an
                                                    integer multiple
                                                    of 360 degrees
                                                    so oscillations
                                                    can build up at
                                                    frequency of
  Pierce Crystal Oscillator Circuit Made from Digital Inverter Gate
Biasing Resistor R1                                             Vi   Vo
R1 acts as a feedback resistor, biasing the inverter
into its linear amplifying region of operation, and
effectively causing it to function as a high gain
inverting amplifier. To see this, assume the inverter
is ideal, with very high input impedance and very
low output resistance; this resistor forces the
inverter’s input and output voltages to be equal.
Hence the inverter will neither be fully on nor off, but
in the transition region where it has gain.
Piezoelectric Crystal Resonator
The crystal in combination with C1 and C2 forms
a Hi-Q “Pi network” bandpass filter, which provides
a 180 degree phase shift and also a voltage gain
from the output to input at approximately the
resonant frequency of the crystal. To understand the                       Vo=Vi
operation of this, it can be noted that at the             Vo            Load line
                                                                      established by
frequency of oscillation, the crystal appears                             biasing
inductive; thus it can be considered a large inductor                  resistor R1,
with a very high Q. The combination of the 180                            biases
                                                                       inverter into
degree phase shift (i.e. inverting gain) from the pi                    its analog
network and the negative gain from the inverter                         amplifying
results in a positive loop gain, making the bias point                     region
set by R1 unstable and leading to oscillation.                            Vi
8 MHz Crystal Oscillator
                RFC (RF Choke) is a 10 uH inductor
                that has a high enough reactance at
                the parallel resonant frequency of the
                XTAL (8 MHz) to guarantee a loop
                gain > 1 at 8 MHz. Note XRFC = 500
                ohms at 8 MHz. Oscillator will have
                high harmonic content with RFC, so
                RFC is sometimes replaced with
                parallel resonant circuit to encourage
                oscillation at only the harmonic
                frequency the parallel resonant
                circuit has been tuned to resonate at.

                R1, R2, RE bias BJT CE amplifier
                into the middle of its amplifying
                Typical Values:
                Vcc = 9 V, R1 = R2 = 560 ohms,
                RE = 1 k ohm, Cb = 0.1 uF
                C1 = C2 = 30 pF (XTAL often cut to
                resonate at desired frequency with
                these external values of C1 and C2.)
                     How DLP Technology Works
DLP (Digital Light   1. The semiconductor that continues to
Processor ) IC       reinvent projection
                     At the heart of every DLP® projection
                     system is an optical semiconductor known
                     as the DLP® chip, which was invented by
                     Dr. Larry Hornbeck of Texas Instruments in
                     The DLP chip is perhaps the world's most
                     sophisticated light switch. It contains a
                     rectangular array of up to 2 million hinge-
                     mounted microscopic mirrors; each of
                     these micromirrors measures less than one-
                     fifth the width of a human hair.
                     When a DLP chip is coordinated with a
                     digital video or graphic signal, a light source,
                     and a projection lens, its mirrors can reflect
                     a digital image onto a screen or other
                     surface. The DLP chip combined with the
                     advanced electronics that surround it
                     produce stunning images and video that
                     have redefined picture quality.
2. The grayscale image
A DLP chip's micromirrors tilt either toward the light source in a DLP
projection system (ON) or away from it (OFF). This creates a light or dark
pixel on the projection surface.
The bit-streamed image code entering the semiconductor directseach
mirror to switch on and off up to several thousand times per
second. When a mirror is switched on more frequently than off, it reflects a
light gray pixel; a mirror that's switched off more frequently reflects a darker
gray pixel.
In this way, the mirrors in a DLP projection system can reflect pixels in up
to 1,024 shades of gray to convert the video or graphic signal entering the
DLP chip into a highly detailed grayscale image.
3. Adding color
The white light generated by the lamp in a DLP projection system passes through
a color filter as it travels to the surface of the DLP chip. This filters the light into a
minimum of red, green, and blue, from which a single-chip DLP projection system
can create at least 16.7 million colors.

With BrilliantColor™ Technology, additional colors are added including Cyan,
Magenta and Yellow to expand the color pallet for even more vibrant color

Some DLP projectors offer solid-state illumination which replaces the traditional
white lamp. As a result, the light source emits the necessary colors eliminating the
color filter.

In some DLP systems, a 3-chip architecture is used, particularly for high
brightness projectors required for large venue applications such as concerts and
movie theaters. These systems are capable of producing no fewer than 35 trillion

The on and off states of each micromirror are coordinated with these basic
building blocks of color. For example, a mirror responsible for projecting a purple
pixel will only reflect red and blue light to the projection surface; those colors are
then blended to see the intended hue in a projected image.
     “Single Chip” DLP Technology
Many data projectors and HDTVS using DLP technology
rely on a single chip configuration like the one described

White light passes through a color filter, causing red,
green, blue and even additional primary colors such as
yellow cyan, magenta and more to be shone in
sequence on the surface of the DLP chip.

The switching of the mirrors, and the proportion of time
they are 'on' or 'off' is coordinated according to the color
shining on them. Then the sequential colors blend to
create a full-color image you see on the screen.
“PainGone” –
A Drug Free, Battery Free Pain
Relief Piezoelectric Device
Paingone is a pocket sized pain relief device that
works by delivering a controlled electronic
frequency through the nerve pathways to the
brain. This stimulates endorphins, the body's
natural painkillers for natural pain relief wherever
and whenever you need it. It has been
successfully clinically tested by people suffering
from a number of painful conditions such as
arthritis, back pain, osteoporosis, sciatica and
inflammatory conditions. Many NHS Hospitals and
GPs use PainGone in their Pain Clinics and
recommend it to their patients as a safe, drug free
therapy. PainGone’s effectiveness has been
clinically confirmed, as independent tests show, it
stops or relieves pain quickly in up to 87% of
cases on which it is used, making it a reliable
alternative to medication.
How does it work?
PainGone works by pressing the button on
top of the device to deliver a low frequency,
gentle electrical charge produced by crystals,
straight to the point of pain. Each click sends
a pulse that will activate endorphins, the
body's natural painkillers to free you from
pain. This stimulating frequency can thus
provide prolonged and often instant relief.
This means that anywhere, at anytime, pain
relief is but a click away.

    •Used on the point of pain             •Estimated life time of over 100,000
    •No leads, pads or batteries           clicks
    •Small and lightweight                 •Over 3 million worldwide users
    •Use as often as required              •Clinically tested
    •NHS recommended                       •Drug free and safe
    •CE registered Class IIa medical       •Simple to use and no side effects
    device                                 •30 second treatment
    •Money Back Guarantee                  •Works through clothing