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Biomedical Instrumentation. Chapter 6 in Introduction to Biomedical Equipment Technology By Joseph Carr and John Brown. Signal Acquisition.

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biomedical instrumentation

Biomedical Instrumentation

Chapter 6 in

Introduction to Biomedical Equipment Technology

By Joseph Carr and John Brown

signal acquisition
Signal Acquisition
  • Medical Instrumentation typically entails monitoring a signal off the body which is analog, converting it to an electrical signal, and digitizing it to be analyzed by the computer.
types of sensors
Types of Sensors:
  • Electrodes: acquire an electrical signal
  • Transducers: acquire a non-electrical signal (force, pressure, temp etc) and converts it to an electrical signal
active vs passive sensors
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 energy from phenomenon being studied
      • Thermocouple
sensor error sources
Sensor Error Sources
  • Error:
    • Difference between measured value and true value.
5 categories of errors
5 Categories of Errors:
  • Insertion Error
  • Application Error
  • Characteristic Error
  • Dynamic Error
  • Environmental Error
insertion error
Insertion Error:
  • Error occurring when inserting a sensor
application error
Application Error:
  • Errors caused by Operator
characteristic error
Characteristic Error:
  • Errors inherent to Device
dynamic error
Dynamic Error:
  • Most instruments are calibrated in static conditions if you are reading a thermistor it takes time to change its value. If you read this value to quickly an error will result.
environmental error
Environmental Error:
  • Errors caused by environment
    • heat, humidity
sensor terminology
Sensor Terminology
  • Sensitivity:
    • Slope of output characteristic curve Δy/ Δx;
      • Minimum input of physical parameter will create a detectable output change
      • Blood pressure transducer may have a sensitivity of 10 uV/V/mmHg so you will see a 10 uV change for every V or mmHg applied to the system.
slide13

Output

Output

Input

Input

Which is more sensitive? The left side one because you’ll have a larger change in y for a given change in x

sensor terminology14

Ideal Curve

Output

Input

Sensitivity Error

Sensor Terminology
  • Sensitivity Error = Departure from ideal slope of a characteristic curve
sensor terminology15
Sensor Terminology
  • Range = Maximum and Minimum values of applied parameter that can be measured.
    • If an instrument can read up to 200 mmHg and the actual reading is 250 mmHg then you have exceeded the range of the instrument.
sensor terminology16
Sensor Terminology
  • Dynamic Range: total range of sensor for minimum to maximum. Ie if your instrument can measure from -10V to +10 V your dynamic range is 20V
  • Precision = Degree of reproducibility denoted as the range of one standard deviation σ
  • Resolution = smallest detectable incremental change of input parameter that can be detected
accuracy

Xi

Xo

Accuracy
  • Accuracy = maximum difference that will exist between the actual value and the indicated value of the sensor
offset error
Offset Error
  • Offset error = output that will exist when it should be zero
    • The characteristic curve had the same sensitive slope but had a y intercept

Output

Output

Input

Input

Offset Error

Zero offset error

linearity
Linearity
  • Linearity = Extent to which actual measure curved or calibration curve departs from ideal curve.
linearity20

Full Scale Input

Ideal

Measure

Output

Din(Max)

Input

Linearity
  • Nonlinearity (%) = (Din(Max) / INfs) * 100%
    • Nonlinearity is percentage of nonlinear
    • Din(max) = maximum input deviation
    • INfs = maximum full-scale input
hysteresis
Hysteresis
  • Hysteresis = measurement of how sensor changes with input parameter based on direction of change
hysteresis22

Output = F(x)

P

F2

Input = x

F1

B

Q

Hysteresis
  • The value B can be represented by 2 values of F(x), F1 and F2. If you are at point P then you reach B by the value F2. If you are at point Q then you reach B by value of F1.
response time

F(t)

Tolerance Band

Tresponse

100%

70%

Rising Response Time

Time

Ton

Response Time
  • Response Time: Time required for a sensor output to change from previous state to final settle value within a tolerance band of correct new value denoted in red can be different in rising and decaying directions
response time24

F(t)

Tolerance Band

Tresponse

100%

70%

Rising Response Time

Time

Ton

Response Time
  • Time Constant: Depending on the source is defined as the amount of time to reach 0% to 70% of final value. Typically denoted for capacitors as T = R C (Resistance * Capacitance) denoted in Blue
response time25
Response Time
  • Convergence Eye Movement the inward turning of the eyes have a different response time than divergence eye movements the outward turning of the eyes which would be the decay response time

Tdecay

F(t)

Decaying Response Time

Toff

Time

dynamic linearity

F(x)* = ax + bx2+cx4+ . . . +K

F(x)* = ax + bx3+cx5+ . . . +K

Output

F(x)

Output

F(x)

F(x) = mx + K

F(x) = mx + K

K

K

Input X

Input X

Dynamic Linearity

Measure of a sensor’s ability to follow rapid changes in the input parameters. Difference between solid and dashed curves is the non- linearity as depicted by the higher order x terms

dynamic linearity27
Asymmetric = F(x) != |F(-x)| where F(x)* is asymmetric around linear curve F(x) then

F(x) = ax + bx2+cx4+ . . . +K offsetting for K or you could assume K = 0

Symmetrical = F(x) = |F(-x)| where F(x) * is symmetric around linear curve F(x) then

F(x) = ax +bx3 + cx5 +. . . + K offsetting for K or you could assume K =0

Dynamic Linearity
frequency response of ideal and practical system

Av

Av = Vo/Vi

1.0

Frequency (w) radians per second

Frequency Response of Ideal and Practical System
  • When you look at the frequency response of an instrument, ideally you want a wideband flat frequency response.
frequency response of ideal and practical system29

Av

Av = Vo/Vi

1.0

0.707

FL

FH

Frequency (w) radians per second

Frequency Response of Ideal and Practical System
  • In practice, you have attenuation of lower and higher frequencies
  • FL and FH are known as the –3 dB points in voltage systems.
examples of filters
Examples of Filters
  • Ideal Filter has sharp cutoffs and a flat pass band
  • Most filters attenuate upper and lower frequencies
  • Other filters attenuate upper and lower frequencies and are not flat in the pass band
electrodes for biophysical sensing
Electrodes for Biophysical Sensing
  • Bioelectricity: naturally occurring current that exists because living organisms have ions in various quantities
electrodes for biophysical sensing32
Electrodes for Biophysical Sensing
  • Ionic Conduction: Migration of ions-positively and negatively charge molecules throughout a region.
    • Extremely nonlinear but if you limit the region can be considered linear
electrodes for biophysical sensing33
Electrodes for Biophysical Sensing
  • Electronic Conduction: Flow of electrons under the influence of an electrical field
bioelectrodes
Bioelectrodes
  • Bioelectrodes: class of sensors that transduce ionic conduction to electronic conduction so can process by electric circuits
    • Used to acquire ECG, EEG, EMG, etc.
bioelectrodes35
Bioelectrodes
  • 3 Types of electrodes:
    • Surface (in vivo) outside body
    • Indwelling Macroelectrodes (in vivo)
    • Microelectrodes (in vitro) inside body
bioelectrodes36
Bioelectrodes
  • Electrode Potentials:
    • Skin is electrolytic and can be modeled as electrolytic solutions

Metal

Electrode

Electrolytic Solution where Skin is electrolytic and can be modeled as saline

electrodes in solution
Electrodes in Solution
  • Have metallic electrode immersed in electrolytic solution once metal probe is in electrolytic solution it:
    • Discharges metallic ions into solution
    • Some ions in solution combine with metallic electrodes
    • Charge gradient builds creating a potential difference or you have an electrode potential or ½ cell potential
electrodes in solution38
Electrodes in Solution

2 cells A and B, A has 2 positive ions

And B has 3 positive ions thus have a

Potential difference of 3 –2 = 1 where B

is more positive than A

A

++

B

+++

electrodes
Electrodes
  • Two reactions take place at electrode/electrolyte interface:
    • Oxidizing Reaction: Metal -> electrons + metal ions
    • Reduction Reaction : Electrons + metal ions -> Metal
electrodes40

Vae

Metal A

Vbe

Metal B

Electrolytic Solution

Electrodes
  • Electrode Double Layer: formed by 2 parallel layers of ions of opposite charge caused by ions migrating from 1 side of region or another; ionic differences are the source of the electrode potential or half-cell potential (Ve).
electrodes41
Electrodes
  • If metals are different you will have differential potential sometimes called an electrode offset potential.
    • Metal A = gold Vae = 1.50V and Metal B = silver Vbe = 0.8V then Vab = 1.5V – 0.8 V = 0.7V (Table 6-1 in book page 96)

Vae

Metal A

Vbe

Metal B

Electrolytic Solution

electrodes42
Electrodes
  • Two general categories of material combinations:
    • Perfectly polarized or perfectly nonreversible electrode: no net transfer of charge across metal/electrolyte interface
    • Perfectly Nonpolarized or perfectly reversible electrode: unhindered transfer of charge between metal electrode and the electrode
      • Generally select a reversible electrode such as Ag-AgCl (silver-silver chloride)
slide43
Rt= internal resistance of body which is low

Vd = Differential voltage Vd

Rsa and Rsb = skin resistance at electrode A and B

Electrode A

C1a

Vea

+

-

Rsa

Cellular

Resistance

R1a

Rc

-

Vo

Mass

Tissue

Resistance

Rt

Vd

Cellular

Potentials

+

Electrode B

C1b

Veb

+

-

Rsb

R1b

Ionic Conduction

Electronic Conduction

  • R1A and R1B = resistance of electrodes
  • C1A and C1B = capacitance of electrodes
electrode potentials cause recording problems
Electrode Potentials cause recording Problems
  • ½ cell potential ~ 1.5 V while biopotentials are usually 1000 times less (ECG = 1-2 mV and EEG is 50 uV) thus have a tremendous difference between DC cell potential and biopotential
  • Strategies to overcome DC component
    • Differential DC amplifier to acquire signal thus the DC component will cancel out
    • Counter Offset-Voltage to cancel half-cell potential
    • AC couple input of amplifier (DC will not pass through) ie capacitively couple the signal into the circuit
electrode potentials cause recording problems45
Electrode Potentials cause recording Problems
  • Strategies to overcome DC component
    • Differential DC amplifier to acquire signal thus the DC component will cancel out
    • Counter Offset-Voltage to cancel half-cell potential
    • AC couple input of amplifier (DC will not pass through)
      • Capacitively couple the signal into the circuit
medical surface electrodes

Binding Spot

Pin-Tip

Connector

Shielded Wire

Electrode Surface

Medical Surface Electrodes
  • Typical Medical Surface Electrode:
  • Use conductive gel to reduce impedance between electrode and skin
  • Schematic:
medical surface electrodes47
Medical Surface Electrodes
  • Have an Ag-AgCl contact button at top of hollow column filled with gel
    • Gel filled column holds actual metallic electrode off surface of skin and decreases movement artifact
      • Typical ECG arrangement is to have 3 ECG electrodes (2 differentials signals and a reference electrode)
problems with surface electrodes
Problems with Surface Electrodes
  • Adhesive does not stick for a long time on sweaty skin
  • Can not put electrode on bony prominences
  • Movement or motion artifact significant problem with long term monitoring results in a gross change in potential
  • Electrode slippage if electrode slips then thickness of jelly changes abruptly which is reflected as a change in electrode impedance and electrode offset potential (slight change in potential)
potential solutions for surface electrodes problems
Potential Solutions for Surface Electrodes Problems
  • Additional Tape
  • Rough surface electrode that digs past scaly outer layer of skin typically not comfortable for patients.
other types of electrodes
Other Types of Electrodes
  • Needle Electrodes: inserted into tissue immediately beneath skin by puncturing skin on an angle note infection is a problem.
  • Indwelling Electrodes: Inserted into layers beneath skin -> typically tiny exposed metallic contact at end of catheter usually threaded through patient’s vein to measure intracardiac ECG to measure high frequency characteristics such as signal at the bundle of His
other types of electrodes51
Other Types of Electrodes
  • EEG Electrodes: can be a needle electrode but usually a 1 cm diameter concave disc of gold or silver and is held in place by a thick paste that is highly conductive sometimes secured by a headband
microelectrode
Microelectrode
  • Microelectrode: measure biopotential at cellular level where microelectrode penetrates cell that immersed in an infinite fluid
    • Saline.
microelectrode53
Microelectrode
  • Two typical types:
    • Metallic Contact
    • Fluid Filled
microelectrode equivalent circuit
Microelectrode Equivalent Circuit

R1

RS = Spreading Resistance of the electrode and is a function of tip diameter

R1 and C1 are result of the effects of electrode/cell interface

C2 = Electrode Capacitance

RS

C2

C1

Vo

V1

calculation for resistance rs
Calculation for Resistance Rs

Rs in metallic microelectrodes without glass coating:

  • where Rs = resistance ohms (Ώ)
    • P = Resistivity of the infinite solution outside electrode = 70 Ώcm for physiological saline
    • r = tip radius ( ~0.5 um for 1 um electrode) = 0.5 x10-4 cm
calculation for resistance rs56
Calculation for Resistance Rs
  • Rs of glass coated metallic microelectrode is 1-2 order of magnitude higher:
  • where Rs = resistance ohms (Ώ)
  • P = Resistivity of the infintie solution outside electrode) = 3.7 Ώcm for 3 M KCl
  • r = tip radius typically 0.1 u m = 0.1 x 10-4 cm
  • a = taper angle (~ p/ 180)
capacitance of microelectrode
Capacitance of Microelectrode

Capacitance of C2 has units pF/cm

  • Where e = dielectric constant which for glass = 4
  • R = outside tip radius
  • r = inside tip radius
capacitance of microelectrode58
Capacitance of Microelectrode
  • Find C of glass microelectrode if the outer radius is 0.2 um and the inner radius = 0.15 um
transducers and other sensors
Transducers and other Sensors
  • Transducers: sensors and are defined as a device that converts energy from some one form (temp., pressure, lights etc) into electrical energy where as electrodes directly measure electrical information
wheatstone bridge
Wheatstone Bridge

Es

  • Basic Wheatstone Bridge uses one resistor in each of four arms where battery excites the bridge connected across 2 opposite resistor junctions (A and B). The bridge output Eo appears across C and D junction.

A

R1

R3

R1

R3

+

-

Eo

EC

ED

+

Eo

+

-

Es

ED

EC

-

R2

R4

R4

R2

B

finding output voltage to a wheatstone bridge
Finding output voltage to a Wheatstone Bridge
  • Ex: A wheatstone bridge is excited by a 12V dc source and has the following resistances R1 = 1.2KΏ R2 = 3 K Ώ R3 = 2.2 K Ώ; and R4 = 5 K Ώ; find Eo
finding output voltage to a wheatstone bridge62
Finding output voltage to a Wheatstone Bridge
  • A wheatstone bridge is excited by a 12V dc source and has the following resistances R1 = 1.2KΏ R2 = 3 K Ώ R3 = 2.2 K Ώ; and R4 = 5 K Ώ; find Eo
null condition of wheatstone bridge
Null Condition of Wheatstone Bridge
  • Null Condition is met when Eo = 0 can happen in 2 ways:
    • Battery = 0 (not desirable)
    • R1 / R2 = R3/ R4
null condition of wheatstone bridge65
Null Condition of Wheatstone Bridge
  • When R1 = 2KΏ; R2 = 1K Ώ; R3 = 10K Ώ; R4 = 5K Ώ
null condition of wheatstone bridge66
Null Condition of Wheatstone Bridge
  • Key with null condition is if you change one of the resistances to be a transducer that changes based on input stimulus then Eo will also change according to input stimulus
strain gauges
Strain Gauges
  • Definition: resistive element that changes resistance proportional to an applied mechanical strain
strain gauges68

L = length

Rest Condition

L - DL = length

Compression

Strain Gauges
  • Compression = decrease in length by DL and an increase in cross sectional area.
strain gauges69

L + DL = length

Tension

Strain Gauges
  • Tension = increase in length by DL and a decrease in cross section area.

L = length

Rest Condition

resistance of a metallic bar is given in length and area
Resistance of a metallic bar is given in length and area
  • where
    • R = Resistance units = ohms (Ώ)
    • ρ = resistivity constant unique to type of material used in bar units = ohm meter (Ώm)
    • L = length in meters (m)
    • A = Cross sectional area in meters2 (m2 )
resistance of a metallic bar is given in length and area71
Resistance of a metallic bar is given in length and area
  • Example: find the resistance of a copper bar that has a cross sectional area of 0.5 mm2 and a length = 250 mm note the resistivity of copper is 1.7 x 10-8Ώm
piezoresistivity
Piezoresistivity
  • Piezoresistivity = change in resistance for a given change in size and shape denoted as h
  • Resistance in tension =
  • Resistance increases in tension

L = length; ΔL = change in L; ρ = resistivity

A = Area; ΔA = change in A

slide73
Resistance in compression =
  • Resistance decreases in compression

L = length; ΔL = change in L; ρ = resistivity

A = Area; ΔA = change in A

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

example of piezoresistivity
Example of Piezoresistivity
  • Thin wire has a length of 30 mm and a cross sectional area of 0.01 mm2 and a resistance of 1.5Ώ.
  • A force is applied to the wire that increases the length by 10 mm and decreases cross sectional area by 0.0027 mm2
  • Find the change in resistance h.
    • Note: ρ = resistivity = 5 x 10-7 Ώm
example of piezoresistivity76
Example of Piezoresistivity
  • Note: Change in Resistance will be approximately linear for small changes in L as long as ΔL<<L.
  • If a force is applied where the modulus of elasticity is exceeded then the wire can become permanently damaged and then it is no longer a transducer.
gauge factor
Gauge Factor
  • Gauge Factor (GF) = a method of comparing one transducer to a similar transducer
gauge factor78
Gauge Factor
  • where
    • GF = Gauge Factor unitless
    • ΔR = change in resistance ohms (Ώ)
    • R = unstrained resistance ohms (Ώ)
    • ΔL = change in length meters (m)
    • L = unstrained length meters (m)
gauge factor79
Gauge Factor
      • Where ε strain which is unitless
  • GF gives relative sensitivity of a strain gauge where the greater the change in resistance per unit length the greater the sensitivity of element and the greater the gauge factor.
example of gauge factor
Example of Gauge Factor
  • Have a 20 mm length of wire used as a string gauge and has a resistance of 150 Ώ.
  • When a force is applied in tension the resistance changes by 2Ώ and the length changes by 0.07 mm.
  • Find the gauge factor:
types of strain gauges unbonded and bonded
Types of Strain Gauges: Unbonded and Bonded
  • Unbonded Strain Gauge : resistance element is a thin wire of special alloy stretch taut between two flexible supports which is mounted on flexible diaphram or drum head.
types of strain gauges unbonded and bonded82
Types of Strain Gauges: Unbonded and Bonded
  • When a Force F1 is applied to diaphram it will flex in a manner that spreads support apart causing an increase in tension and resistance that is proportional to the force applied.
  • When a Force F2 is applied to diaphram the support ends will more close and then decrease the tension in taut wire (compression force) and decrease resistance will decrease in amount proportional to applied force
types of strain gauges unbonded and bonded83
Types of Strain Gauges: Unbonded and Bonded
  • Bonded Strain Gauge: made by cementing a thin wire or foil to a diaphragm therefore flexing diaphragm deforms the element causing changes in electrical resistance in same manner as unbonded strain gauge
types of strain gauges unbonded and bonded84
Types of Strain Gauges: Unbonded and Bonded
  • When a Force F1 is applied to diaphram it will flex in a manner that causes an increase in tension of wire then the increase in resistance is proportional to the force applied.
  • When a Force F2 is applied to diaphram that cause a decrease the tension in taut wire (compression force) then the decrease in resistance will decrease in amount proportional to applied force
comparison of bonded vs unbonded strain gauges
Comparison of Bonded vs. Unbonded Strain Gauges
  • Unbonded strain gauge can be built where its linear over a wide range of applied force but they are delicate
  • Bonded strain gauge are linear over a smaller range but are more rugged
    • Bonded strain gauges are typically used because designers prefer ruggedness.
typical configurations
Typical Configurations

A

R1 = SG1

R3 = SG3

+

Vo

ES

C

D

-

R4 = SG4

R2 = SG2

B

Mechanical Configuration

Electrical Circuit

  • 4 strain gauges (SG) in Wheatstone Bridge:
strain gauge example
Strain Gauge Example
  • Using the configuration in the previous slide where 4 strain gauges are placed in a wheatstone bridge where the bridge is balanced when no force is applied,
  • Assume a force is applied so that R1 and R4 are in tension and R2 and R3 are in compression.
  • Derive the equation to depict the change in voltage across the bridge and find the output voltage when each resistor is 200 Ώ, the change of resistance is 10 Ώ and the source voltage is 10 V

+

strain gauge example88
Strain Gauge Example

Derivation:

Circuit

A

R1 = R +h

R3= R-h

Es

+

-

Eo

+

C

D

-

R2 = R - h

R4 = R +h

B

Note: Text book has wrongly stated that tension decreases R and compression increases R on page 112

transducer sensitivity
Transducer Sensitivity
  • Transducer Sensitivity = rating that allows us to predict the output voltage from knowledge of the excitation voltage and the value of the applied stimulus units = μV/V*unit of applied stimulus
transducer sensitivity90
Transducer Sensitivity
  • Example if you have a force transducer calibrated in grams (unit of mass) which allows calibration of force transducer then sensitivity denoted as φ = μV/V*g (another ex φ = μV/V*mmHg)
transducer sensitivity91
Transducer Sensitivity
  • To calculate Output Potential use the following equations:
    • where
      • Eo = output potential in Volts (V)
      • E = excitation voltage
      • φ = sensitivity μV/V*g
      • F = applied force in grams (g)
transducer sensitivity92
Transducer Sensitivity
  • Example: Transducer has a sensitivity of 10 μV/V*g, predict the output voltage for an applied force of 15 g and 5 V of excitation.
  • note book has typo where writes μV/V/g for sensitivity
inductance transducers
Inductance Transducers
  • Inductance Transducers: inductance L can be varied easily by physical movement of a permeable core within an inductor 3 basic forms:
    • Single Coil
    • Reactive Wheatstone Bridge
    • Linear Voltage Differential Transformer LVDT:
slide94

Diaphragm

L2

AC Excitation

L1

External

Load

Core

L3

Axis of Motion

LVDT:
capacitance transducers
Capacitance Transducers
  • Quartz Pressure Sensors: capacitively based where sensor is made of fused quartz
  • Capacitive Transducers: Capacitance C varies with stimulus
capacitive transducers
Capacitive Transducers:
  • Three examples:
    • Solid Metal disc parallel to flexible metal diaphragm separated by air or vacuum (similar to capacitor 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 Plate placed between 2 stationary Places where you have 2 capacitors: C1 between P1 and P3 and C2 between P2 and P3 where when a force is applied to diaphragm P3 moves closer to one plate or vice versa
temperature transducers
Temperature Transducers
  • 3 Common Types:
    • Thermocouples
    • Thermistors
    • Solid State PN Junctions
thermocouple
Thermocouple:
  • Thermocouple: 2 dissimilar conductor joined together at 1 end.
  • The work functions of the 2 materials are different thus a potential is generated when junction is heated (roughly linear over wide range)
thermistors
Thermistors:
  • Thermistors: Resistors that change their value based on temperature where
    • Positive Temperature Coefficient (PTC) device will increase its resistance with an increase in temperature
    • Negative Temperature Coefficient (NTC) device will decrease its resistance with an increase in temperature
    • Most thermistors have nonlinear curve when plotted over a wide range but can assume linearity if within a limited range
bjt bipolar junction transistor

+

VCB

+

IB

-

VCE

+

-

VBE

-

IE

BJT = Bipolar Junction Transistor

IC

  • Transistor = invented in 1947 by Bardeen, Brattain and Schockley of Bell Labs.

B = Base

C = Collector

E = Emitter

IE = I B + I C

bjt bipolar junction transistor101
BJT = Bipolar Junction Transistor
  • Transistor rely on the free travel of electrons through crystalline solids called semiconductors. Transistors usually are configured as an amplifier or a switch.”
solid state pn temperature transducers

VCC+

+

+

VCB

Ic1

Ic2

VCB

-

+

+

VBE

DVBE

VBE

-

-

ccs1

ccs2

VEE-

Solid State PN Temperature Transducers

Solid State PN Junction Diode: the base emitter voltage of a transistor is proportional to temperature. For a differential pair the output voltage is:

K = Boltzman’s Constant = 1.38 x10-23J/K

T = Temperature in Kelvin

IC1 = Collector current of BJT 1 mA

IC2 = Collector current of BJT 2 mA

q = Coulomb’s charge = 1.6 x10 -19 coulombs/electron

example of temperature transducer
Example of temperature transducer
  • Find the output voltage of a temperature transducer in the previous slide if IC1 = 2 mA; IC2 = 1 mA and the temperature is 37 oC
homework
Homework
  • Read Chapter 7
  • Chapter 6 Problems: 1, 3 to 6, 9
    • Problem 1: resistivity = 1.7 * 10-8Ώm
    • Problem 4: sensitivity = 50 μV/(V*mmHg)
    • Problem 4: 1 torr = 1 mmHg
    • Problem 6: sensitivity = 50 μV/(V*g)
review
Review
  • What are two types of sensors?
  • List 5 categories of error
  • How do we quantify sensors?
  • What is an electrode?
  • How do you calculate Rs and C2 of a microelectrode that is metal with and without glass coating?
  • What is a transducer?
  • What is a Wheatstone Bridge? How do you derive the output voltage
  • Find resistance of a metallic bar for a given length and area
  • How does resistance change in tension and in compression and how do you calculate resistance
review106
Review
  • How do you find resistance change in piezoresistive device
  • How do you determine gauge factor
  • What is the definition of a strain gauge and what is difference between bonded and unbonded strain gauge.
  • Determine the output potential given a transducer’s sensitivity.
  • What are inductance, capacitance, and temperature transducers?
  • How do you calculate the temperature for a solid state PN Junction Diode?