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    INTRODUCTION TO

    BIOMEDICAL ENGINEERING

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    Why Biomedical Engineering?

    Promising future developments

    Improve medicine, save lives

    Numerous possibilities based upon level of biology and

    engineering specialty

    Hybridization of skills and knowledge

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    Types of problems

    Interface between biological and non-biological materials

    Design, modeling, and construction of biologically-analogoustechnologies

    Understanding and improving upon biological limitations

    Medical tools and diagnostics

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    TerminologyBiomedical engineering

    Bioengineering

    Also, biological engineering and others . . .

    Biotechnology

    Often used interchangeably with biomedical engineering. When distinguishing

    between the two, typically bioengineering tends to refer to engineering using

    biological substances, often at a higher level of biology than biotechnology.

    The use of engineering science and math to tackle problems in medicine. When

    distinguished from bioengineering, focuses more on the machine/device/non-

    biological type of research.

    Term that is generally similar to bioengineering, but, in comparison, refers mostspecifically to direct manipulation and use of living biological substances.

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    UNIT I

    Physiology and Transducers

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    Human Anatomy & Physiology

    Cell

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    Human body develops from union ofSPERM + OVUM=FIRST CELL OF HUMAN

    BODY

    Group of cells

    Tissues

    Organs

    Systems

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    Structure of Cell

    Cell is a structural & Functional unit of human body, capable of

    carrying out functions of life independently. Nucleus

    Cytoplasm

    Cell Membrane

    Functions of Cell- Production of Bio-Energy- Storage- Multiplication

    - Specific function according to location

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    Membrane Potentials

    1. Resting Membrane Potential2. Excitatory Post-synaptic Potential (EPSP)3. Inhibitory Post-synaptic Potential (IPSP)4. Action Potential

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    Levels of Investigation

    Organism Systems(e.g. Vision)

    Cell Synapsis

    Next weeks

    Today

    Molecule

    Next weeks

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    Click on animation website or main website (here)

    Neurons have a selectively permeable membrane

    During resting conditions membrane is: permeable to potassium (K+) (channels are open)

    impermeable to sodium (Na+) (channels are closed)

    Diffusion force pushes K+ out (concentration gradient)

    This creates a positively charged extra-cellular space.

    Electrostatic force pushes K+ in

    Thus, there is a dynamic equilibrium with zero netmovement of ions.

    The resting membrane potential is negative (- 60mv)

    1. Resting Membrane Potential

    http://bcs.whfreeman.com/thelifewire/content/chp44/4401s.swfhttp://www18.homepage.villanova.edu/diego.fernandezduque/Teaching/Teach_Index.htmhttp://www18.homepage.villanova.edu/diego.fernandezduque/Teaching/Teach_Index.htmhttp://bcs.whfreeman.com/thelifewire/content/chp44/4401s.swf
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    Copyright Allyn & Bacon 2004

    Cell Membrane

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    15

    OUTSIDE

    INSIDE

    K+ = Potassium; Na+ = Sodium; Cl- = Chloride; Pr- = proteins

    Na+

    Na+

    K+

    K+

    Force of Diffusion

    Electrostatic Force

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -

    Cl-

    Force of Diffusion

    Cl-

    Electrostatic Force

    Pr-

    Closedchannel

    openchannel

    openchannel

    nochannel

    3Na/2Kpump

    Resting Membrane Potential

    - 65 mV

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    Resting membrane potential:(things you need to know)

    a. Concept of Selective membrane

    b. How permeable the membrane is to proteins, K+, andNa+

    c. Diffusion and electrostatic forces and how they act on

    K+ and Na+d. Concept of Dynamic equilibrium

    e. Concept of Membrane potential

    f. ATP Na/K pump and its role in maintaining the

    membrane potential

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    Copyright Allyn & Bacon 2004

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    Copyright Allyn & Bacon 2004

    Membrane Potentials

    1.RestingPotential(justdescribed)

    2.ExcitatoryPost-synapticpotential

    threshold4.InhibitoryPost-synapticpotential

    3.ActionPotential

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    2. Excitatory Post-synaptic Potential (EPSP)

    Post-synaptic neuron

    Pre-synaptic neuron

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    1. The pre-synaptic neuron releases aneurotransmitter.

    2. Neurotransmitter diffuses acrossextra-cellular space - synaptic cleft.

    3. Neurotransmitter binds to post-synaptic receptor.

    4. Binding of neurotransmitter causes

    Na+ channels in post-synapticmembrane to open.

    5. Depolarization occurs (excitatory

    potential)

    Post-synaptic neuron

    Pre-synaptic neuron

    Excitatory Post-synaptic Potential (EPSP)

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    21

    OUTSIDE

    INSIDE

    K+ = Potassium; Na+ = Sodium; Cl- = Chloride; Pr- = proteins

    Na+

    Na+

    K+

    K+

    Force of Diffusion

    Electrostatic Force

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -

    Cl-

    Force of Diffusion

    Cl-

    Electrostatic Force

    Pr-

    Closedchannel

    openchannel

    openchannel

    nochannel

    OPEN Na+CHANNEL

    + + +

    - 65 mV- 50 mV

    1. Resting Membrane PotentialExcitatory Post-Synaptic Potential (EPSP)

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    EPSP

    EPSP is a graded potential

    Multiple EPSPs are integrated acrossspace and time.

    ExcitatoryPost-synapticpotential

    Integration

    Once the threshold isreached, voltage-dependent sodiumchannels are opened

    The cell is depolarized(action potential)

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    3. Inbibitory Post-synaptic Potential (IPSP)

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    Human Anatomy & Physiology

    Nervous System

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    Nervous system

    Central processing unit of body. Controls andbalance of body functions.

    Divisions Central nervous system (CNS)

    Peripheral nervous system (PNS)

    Autonomic nervous system (ANS)

    Components

    Nerve cell

    Sensory nerve

    Brain

    Motor nerve

    End organ

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    Functions of Nervous system

    Control over voluntary and involuntaryfunctions / actions.

    To control body movements, respiration,circulation, digestion, hormone secretion,

    body temperature To receive stimuli from sense organs,

    perceive them and respond accordingly

    Higher mental functions like memory,receptivity, perception & thinking.

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    Parts of CNS

    Cerebrum

    Cerebellum

    Mid brain

    Pones

    Medulla oblongata

    Spinal cord

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    Brain Protected by skull

    Three coverings of brain called meninges

    Dura Arachnoid

    Pia matter

    Cerebro spinal fluid (CSF) between the Pia

    meter and Arachnoid CSF acts as a shock absorber and provides

    nutrition to the brain

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    Cerebrum

    Biggest part of brain, divided into two hemispheres

    Contra lateral control

    Outer surface is grey due to cells

    Internally white due to fibers

    Surface is folded to increase the area

    Functions of cerebrum Intellect, memory, will power, imagination, emotion &

    other psychological functions

    Receive and perceive the stimuli

    To give command for reaction with the help of pastexperience

    To control over other parts of nervous system

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    Cerebellum

    Situated below and behind the cerebrum

    Functions of cerebellum Controls tone muscles

    Helps coordination of body movements

    Helps balancing the body

    Mid brain

    Underneath the cerebrum and above pons Functions of mid brain

    To control involuntary functions

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    Pons

    Below mid brain

    Functions of pons Control of consciousness

    Control level of concentration

    Medulla oblongata Lowest part of CNS just above the spinal cord

    Functions of Medulla oblongata

    Control of respiration Control of circulation

    Control of swallowing and vomiting

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    Spinal cord Located safely in spinal canal

    Length is 45cm, which extends up to firstlumber vertebra

    31 pairs of peripheral nerves starts fromspinal cord

    Functions of spinal cord To propagate sensory stimuli from organs to

    the brain

    To carry commands from the brain towardsthe organs

    Reflex action

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    Reflex action

    Protective function of the spinal cord

    Sensory organ

    Afferent nerve

    Sensory cell in posterior horn of spinal cord Connector nerve

    Motor cell in anterior horn of spinal cord

    Efferent nerve

    End organ of reaction

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    Autonomic nervous system(Involuntary nervous system) It has control over

    Digestion

    Respiration

    Circulation

    Hormone secretion

    Maintenance of body temperature

    Maintenance of water balance

    Peripheral nervous system 12 pairs of cranial nerves from brain (cranial

    nerves)

    31 pairs of spinal nerves from spinal cord

    (spinal nerves)

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    Billons of nerve cells

    Billons of connections

    Maximum utilization of brain is 10%

    90 % brain is in dormant state

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    Human Anatomy & Physiology

    Circulatory System

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    Components of blood

    Total volume of blood 5 to 6 liters

    Components Plasma 55-60 %

    Blood cells 40-45 %

    RBC

    WBC

    Platelets

    R B C (R d bl d ll )

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    R.B.C. (Red blood cells)

    Colour of blood due to RBC

    4 to 5 millions / c.c. Hemoglobin carry 90% Oxygen

    Dumbbell shaped cells with no nucleus

    W.B.C. (White blood cells) White colored

    6000 to 9000 / c.c.

    Kills the bacteria (protective role) No specific shape, with central nucleus

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    Platelets

    1,00,000 to 2,00,000 / c.c.

    Helps in clotting of blood(Enzyme Thrombokinase)

    Circular shape

    Plasma 90 to 92 % water

    8 to 10 % dissolved organic & inorganic

    matter (proteins, glucose, salts & hormones) Presence of antibodies

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    Functions of Blood To carry Oxygen from lungs to cells and to

    carry CO2

    from cells to lungs

    To carry nutrients from Digestive system tocells

    To carry excretory products (waste material)

    from cells to excretory organs To carry hormones

    To maintain water balance in the body

    To maintain body temperature

    To protect the body from infections

    Clotting the blood after injury

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    Difference between Arteries & Veins

    Arteries

    Carry blood from heartto other organs

    Carry oxygenatedblood

    Have thick walls

    Do not have valves

    Veins

    Carry blood from otherorgans to heart

    Carry de-oxygenatedblood

    Have thin walls

    Presence of valves

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    Heart

    Situated in the rib cage of chest on the left

    side Embedded in lungs

    Size of heart is equal to the size of clenchedfist

    Connected with many big (giant )bloodvessels

    Made up of involuntary muscle

    Heart starts beating from 4th month of IU life.

    Duration of one heart beat is 0.8sec.

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    4 Chambers of Heart

    Auricles to receive blood

    Ventricles to pump blood Left side oxygenated blood

    Right side deoxygenated blood

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    Circulation of Blood

    Continuous circulation

    Force of circulation due to pumping action ofheart

    From left ventricle Aorta Branches &Sub branches Artery Small arteryArteriole Capillaries CELLSVenouls Small veins union of many veins Superior & Inferior venacava Right auricle

    Right ventricle Pulmonary arteryLungs (oxygenation) Pulmonary veins Left auricle Left ventricle

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    Human Anatomy & Physiology

    Respiratory System

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    Copyright 2004 Pearson Education, Inc., publishing as Benjamin Cummings

    Structure and function of the respiratory pumps

    How gases are exchanged with blood The role of pressures and surfactants in rate of

    exchange

    How respiration is regulated

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    Copyright 2004 Pearson Education, Inc., publishing as Benjamin Cummings

    Respiratory System: Overview

    Lungs: exchange surface

    75 m2

    Thin walled

    Moist

    Ribs & skin protect

    Diaphragm & ribs pump air

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    Copyright 2004 Pearson Education, Inc., publishing as Benjamin Cummings

    Respiratory System: Overview

    Figure 17-2 b: Anatomy Summary

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    Functions

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    Functions Supply of Oxygen

    To remove CO2 and water vapour

    Purification of blood

    Protective function- coughing, sneezing

    Talking

    Organs of Respiration Nose

    Throat

    Larynx

    Trachea with its branching system

    lungs

    (diagram of Respiratory System)

    Nose

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    Nose

    Two nasal cavities separated by nasal septum

    The Nasal Septum is made up of cartilage &bone

    Function

    Warming of Air Filtration of Air

    To keep nasal passage moist

    Sensation of smell

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    Throat & Larynx

    Throat (seven passages)

    Larynx Oesophagus

    Mouth

    Left Eustachian tube

    Right Eustachian tube

    Left nostril

    Right nostril

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    Trachea

    Made up of cartilage and muscles Two main branches- Left and Right bronchus

    Branching and sub branching ending in alveoli

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    Inspiration

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    Inspiration

    Active process by muscular action

    Contraction of diaphragm

    Increase in vertical diameter

    Contraction of intercostals muscles

    Elevation of ribs and sternum

    Increase in antero-posterior and transverse diameter

    Expansion of lungs due to negative pressure

    Air drawn inwards Expiration

    Passive process

    Elastic recoil of the lungs due to Relaxation of diaphragm andinter costal muscle.

    Positive pressure created in lungs

    Control of Respiration

    Control of Inspiration and Expiration by medulla oblongata

    L V l

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    Lung Volumes

    Tidal capacity : 500c.c.

    Dead space : 150c.c. Vital capacity : 4500c.c.

    Total lung capacity : 6000c.c.

    Residual volume : 1350c.c. Expiratory reserve : 1500c.c.

    Inspiratory capacity : 3000c.c.

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    Analysis of gases in respiration

    O2

    N2

    CO2Inspired air 21% 79% -

    Exhaled air 16% 79% 5%

    Effects of Pranayama More oxygenation of blood

    Improvement in function of all organs

    Life span increases because of more supplyof oxygen

    F ti f th R i t S t O i

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    Copyright 2004 Pearson Education, Inc., publishing as Benjamin Cummings

    Functions of the Respiratory System: Overview

    Figure 17-1: Overview of external and cellular respiration

    Exchange O2

    Air to blood

    Blood to cells

    Exchange CO2 Cells to blood

    Blood to air

    Regulate blood pH Vocalizations

    Protect alveoli

    The Airways:C d ti f Ai f O t id t Al li

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    Copyright 2004 Pearson Education, Inc., publishing as Benjamin Cummings

    Filter, warm & moisten air

    Nose, (mouth), trachea, bronchi & bronchioles

    Huge increase in cross sectional area

    Conduction of Air from Outside to Alveoli

    Figure 17-4: Branching of the airways

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    Signal Acquisition

    Medical Instrumentation typically entailsmonitoring a signal off the body which isanalog, converting it to an electricalsignal, and digitizing it to be analyzedby the computer.

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    Types of Sensors:

    Electrodes: acquire an electrical signal

    Transducers: acquire a non-electricalsignal (force, pressure, temp etc) andconverts it to an electrical signal

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    Active vs Passive Sensors:

    Active Sensor: Requires an external AC or DC electrical

    source to power the device

    Strain gauge, blood pressure sensor

    Passive Sensor:

    Provides it own energy or derives energyfrom phenomenon being studied Thermocouple

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    Sensor Error Sources

    Error: Difference between measured value

    and true value.

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    5 Categories of Errors:1. Insertion Error

    2. Application Error

    3. Characteristic Error

    4. Dynamic Error

    5. Environmental Error

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    Insertion Error: Error occurring when inserting a

    sensor

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    Application Error: Errors caused by Operator

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    Characteristic Error: Errors inherent to Device

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    Dynamic Error: Most instruments are calibrated in static

    conditions if you are reading a thermistor ittakes time to change its value. If you readthis value to quickly an error will result.

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    Environmental Error: Errors caused by environment

    heat, humidity

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    Sensor Terminology

    Sensitivity:

    Slope of output characteristic curve y/ x; Minimum input of physical parameter will

    create a detectable output change

    Blood pressure transducer may have asensitivity of 10 uV/V/mmHg so you will see a10 uV change for every V or mmHg applied to

    the system.

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    Input

    Output

    Input

    Output

    Which is more sensitive? The left side onebecause youll have a larger change in y for agiven change in x

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    Sensor Terminology

    Sensitivity Error = Departure from ideal

    slope of a characteristic curve

    Ideal Curve

    Sensitivity Error

    Output

    Input

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    Sensor Terminology

    Range = Maximum and Minimum values

    of applied parameter that can bemeasured.

    If an instrument can read up to 200 mmHgand the actual reading is 250 mmHg then youhave exceeded the range of the instrument.

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    Sensor Terminology

    Dynamic Range: total range of sensor forminimum to maximum. Ie if your instrumentcan measure from -10V to +10 V your dynamic

    range is 20V Precision = Degree of reproducibility denoted

    as the range of one standard deviation

    Resolution = smallest detectable incrementalchange of input parameter that can bedetected

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    Accuracy

    Accuracy = maximum difference that

    will exist between the actual value andthe indicated value of the sensor

    XoXi

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    Offset Error

    Offset error = output that will exist

    when it should be zero

    The characteristic curve had the samesensitive slope but had a y intercept

    Zero offset errorOffset Error

    Input Input

    Output Output

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    Linearity

    Linearity = Extent to which actualmeasure curved or calibration

    curve departs from ideal curve.

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    Linearity

    Nonlinearity (%) = (Din(Max) / INfs) * 100%

    Nonlinearity is percentage of nonlinear Din(max) = maximum input deviation

    INfs = maximum full-scale input

    Input

    Output Din(Max)

    Full Scale Input

    Transducers and other Sensors

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    Transducers and other Sensors

    Transducers: sensors and are defined asa device that converts energy from someone form (temp., pressure, lights etc) into

    electrical energy where as electrodesdirectly measure electrical information

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    Wheatstone Bridge

    Basic Wheatstone Bridge uses one resistor ineach of four arms where battery excites thebridge connected across 2 opposite resistor

    junctions (A and B). The bridge output Eoappears across C and D junction.

    Es

    R1

    R2R4

    R3

    EC ED+-

    A

    B

    Eo

    Eo

    R1R3

    R2 R4

    EC ED

    Es

    + -

    + -

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    Strain Gauges

    Definition: resistive element thatchanges resistance proportional to an

    applied mechanical strain

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    Strain Gauges

    Compression = decrease in length by DL andan increase in cross sectional area.

    Rest ConditionL = length

    L - DL = length Compression

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    Strain Gauges

    Tension = increase in length by DL and adecrease in cross section area.

    Rest ConditionL = length

    TensionL + DL = length

    Resistance of a metallic bar is

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    Resistance of a metallic bar is

    given in length and area

    where R = Resistance units = ohms () = resistivity constant unique to type of

    material used in bar units = ohm meter (m) L = length in meters (m) A = Cross sectional area in meters2 (m2 )

    A

    pLR

    Resistance of a metallic bar is

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    Resistance of a metallic bar is

    given in length and area

    Example: find the resistance of a copper bar that has a crosssectional area of 0.5 mm2 and a length = 250 mm note the resistivityof copper is 1.7 x 10-8m

    - 0085.0

    1000

    15.0

    1000

    1250

    10*7.12

    2

    8

    mm

    mmm

    mm

    mmm

    mA

    LR

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    Piezoresistivity

    Piezoresistivity = change in resistance for agiven change in size and shape denoted as h

    Resistance in tension =

    Resistance increases in tension

    L = length;L = change in L; = resistivityA = Area;A = change in A

    DDAALLhR

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    Resistance in compression =

    Resistance decreases in compression

    L = length;L = change in L; = resistivity

    A = Area;A = change in A

    DDAA

    LLhR

    Note: Textbook forgot the in equations 6-28 and 6-29 on page 110

    Gauge Factor

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    Gauge Factor

    Gauge Factor (GF) = a method of comparing onetransducer to a similar transducer

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    Gauge Factor

    where

    GF = Gauge Factor unitless

    R = change in resistance ohms ()

    R = unstrained resistance ohms () L = change in length meters (m) L = unstrained length meters (m)

    DD

    L

    LR

    R

    GF

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    Gauge Factor

    Where strain which is unitless GF gives relative sensitivity of a strain gauge where the

    greater the change in resistance per unit length thegreater the sensitivity of element and the greater thegauge factor.

    LL

    RR

    GF

    D

    D

    T f St i G U b d d d

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    Types of Strain Gauges: Unbonded and

    Bonded

    Unbonded Strain Gauge: resistanceelement is a thin wire of special alloystretch taut between two flexiblesupports which is mounted on flexiblediaphram or drum head.

    Types of Strain Gauges: Unbonded and

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    Types of Strain Gauges: Unbonded and

    Bonded

    When a Force F1 is applied todiaphram it will flex in a manner thatspreads support apart causing anincrease in tension and resistance

    that is proportional to the forceapplied.

    When a Force F2 is applied todiaphram the support ends will more

    close and then decrease the tensionin taut wire (compression force) anddecrease resistance will decrease inamount proportional to applied force

    Types of Strain Gauges: Unbonded and

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    Types of Strain Gauges: Unbonded and

    Bonded

    Bonded Strain Gauge:made by cementing athin wire or foil to a diaphragm thereforeflexing diaphragm deforms the element

    causing changes in electrical resistance insame manner as unbonded strain gauge

    Types of Strain Gauges: Unbonded and

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    Types of Strain Gauges: Unbonded and

    Bonded

    When a Force F1 is applied todiaphram it will flex in amanner that causes anincrease in tension of wirethen the increase in resistanceis proportional to the forceapplied.

    When a Force F2 is applied todiaphram that cause a

    decrease the tension in tautwire (compression force) thenthe decrease in resistance willdecrease in amountproportional to applied force

    Comparison of Bonded vs Unbonded

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    Comparison of Bonded vs. Unbonded

    Strain Gauges

    1. Unbonded strain gauge can be builtwhere its linear over a wide range ofapplied force but they are delicate

    2. Bonded strain gauge are linear over asmaller range but are more rugged

    Bonded strain gauges are typically usedbecause designers prefer ruggedness.

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    Typical Configurations

    R2 = SG2R4 = SG4

    R3 = SG3

    C+

    -

    A

    B

    Vo

    R1 = SG1

    DES

    Electrical Circuit MechanicalConfiguration

    4 strain gauges (SG) in Wheatstone Bridge:

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    Transducer Sensitivity

    Transducer Sensitivity = rating thatallows us to predict the output voltagefrom knowledge of the excitation

    voltage and the value of the appliedstimulus units = V/V*unit of appliedstimulus

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    Transducer Sensitivity

    Example if you have a force transducer calibrated ingrams (unit of mass) which allows calibration of forcetransducer then sensitivity denoted as = V/V*g(another ex = V/V*mmHg)

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    Transducer Sensitivity

    To calculate Output Potential use thefollowing equations:

    where Eo = output potential in Volts (V)

    E = excitation voltage

    = sensitivity V/V*g F = applied force in grams (g)

    FEEo **

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    Inductance Transducers

    Inductance Transducers: inductance L canbe varied easily by physical movement of apermeable core within an inductor 3 basic

    forms: Single Coil Reactive Wheatstone Bridge Linear Voltage Differential Transformer LVDT:

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    LVDT:

    Diaphragm

    Core External

    Load

    L2

    L3

    L1

    Axis of Motion

    AC Excitation

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    Capacitance Transducers

    Quartz Pressure Sensors: capacitivelybased where sensor is made of fusedquartz

    Capacitive Transducers: Capacitance Cvaries with stimulus

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    Capacitive Transducers:

    Three examples: Solid Metal disc parallel to flexible metal

    diaphragmseparated by air or vacuum (similar tocapacitor microphone) when force is applied they

    will move closer or further away. Stationary metal plate and rotating moveable plate:

    as you rotate capacitance will increase or decrease

    Differential Capacitance:1 Moveable metal Plateplaced between 2 stationary Places where youhave 2 capacitors: C1 between P1 and P3 and C2between P2 and P3 where when a force is appliedto diaphragm P3 moves closer to one plate or viceversa

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    Temperature Transducers

    3 Common Types: Thermocouples Thermistors Solid State PN Junctions

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    Thermocouple:

    Thermocouple: 2 dissimilar conductor joinedtogether at 1 end.

    The work functions of the 2 materials are different

    thus a potential is generated when junction isheated (roughly linear over wide range)

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    Thermistors:

    Thermistors: Resistors that change their valuebased on temperature where

    Positive Temperature Coefficient (PTC) device willincrease its resistance with an increase intemperature

    Negative Temperature Coefficient (NTC) device willdecrease its resistance with an increase intemperature

    Most thermistors have nonlinear curve when plottedover a wide range but can assume linearity if within alimited range

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    BJT = Bipolar Junction Transistor

    Transistor = invented in 1947by Bardeen, Brattain andSchockley of Bell Labs.

    IC

    VCB

    VCE

    VBE+

    ++

    -

    -

    -IB

    IE

    B = BaseC = CollectorE = Emitter

    IE = I B + I C

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    BJT = Bipolar Junction Transistor

    Transistor rely on the free travel ofelectrons through crystalline solids calledsemiconductors. Transistors usually areconfigured as an amplifier or a switch.

    Solid State PN Temperature

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    Solid State PN Temperature

    Transducers

    Solid State PN Junction Diode: thebase emitter voltage of a transistor isproportional to temperature. For adifferential pair the output voltage is:

    q

    IIKT

    VC

    C

    BE

    D2

    1ln

    K = Boltzmans Constant = 1.38 x10-23J/K

    T = Temperature in KelvinIC1 = Collector current of BJT 1 mA

    IC2 = Collector current of BJT 2 mA

    VCB

    VEE-

    VBE+

    +

    +

    - -

    -VCB

    VCC+

    VBE

    +

    ccs1 ccs2

    Ic1 Ic2

    DVBE