Transcript Biomedical Instrumentation Tara Alvarez Ph.D.

Biomedical
Instrumentation
Chapter 6 in
Introduction to Biomedical
Equipment Technology
By Joseph Carr and John Brown
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:

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 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

Error:
•
Difference between measured value
and true value.
5 Categories of Errors:
1.
2.
3.
4.
5.
Insertion Error
Application Error
Characteristic Error
Dynamic Error
Environmental Error
Insertion Error:
•
Error occurring when inserting a
sensor
Application Error:
•
Errors caused by Operator
Characteristic Error:
•
Errors inherent to Device
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:
•
Errors caused by environment
•
heat, humidity
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.
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 Terminology

Sensitivity Error = Departure from ideal
slope of a characteristic curve
Output
Ideal Curve
Input
Sensitivity Error
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 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

Accuracy = maximum difference that
will exist between the actual value and
the indicated value of the sensor
Xi
Xo
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
Zero offset error
Input
Offset Error
Linearity

Linearity = Extent to which actual
measure curved or calibration
curve departs from ideal curve.
Linearity

Nonlinearity (%) = (Din(Max) / INfs) * 100%
• Nonlinearity is percentage of nonlinear
• Din(max) = maximum input deviation
• INfs = maximum full-scale input
Full Scale Input
Output
Din(Max)
Input
Hysteresis

Hysteresis = measurement of how sensor
changes with input parameter based on
direction of change
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.
Output = F(x)
P
F2
Input = x
F1
B
Q
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
F(t)
Tresponse
100%
70%
Tolerance Band
Rising Response Time
Ton
Time
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
F(t)
Tresponse
100%
70%
Tolerance Band
Rising Response Time
Ton
Time
Response Time
F(t)
Tdecay
Decaying Response Time
Toff

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
Dynamic Linearity
Measure of a sensor’s ability to follow rapid
changes in the input parameters. Difference
between solid and dashed curves is the nonlinearity as depicted by the higher order x terms
F(x)* = ax + bx2+cx4+ . . . +K
F(x)* = ax + bx3+cx5+ . . . +K
Output
F(x)
Output
F(x)
K
K
Input X
Input X
Dynamic Linearity


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
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.
Av
Av = Vo/Vi
1.0
Frequency (w) radians per second
Frequency Response of Ideal
and Practical System

In practice, you have attenuation of
lower and higher frequencies
Av
Av = Vo/Vi
1.0
0.707
FL
FH
Frequency (w) radians per second

FL and FH are known as the –3 dB points in voltage systems.
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

Bioelectricity: naturally occurring current
that exists because living organisms
have ions in various quantities
Electrodes for Biophysical
Sensing

Ionic Conduction: Migration of ionspositively and negatively charge
molecules throughout a region.
• Extremely nonlinear but if you limit the region
can be considered linear
Electrodes for Biophysical
Sensing

Electronic Conduction: Flow of electrons
under the influence of an electrical field
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.
Bioelectrodes

3 Types of electrodes:
• Surface (in vivo) outside body
• Indwelling Macroelectrodes (in vivo)
• Microelectrodes (in vitro) inside body
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

Have metallic electrode immersed in
electrolytic solution once metal probe is in
electrolytic solution it:
1. Discharges metallic ions into solution
2. Some ions in solution combine with metallic
electrodes
3. Charge gradient builds creating a potential
difference or you have an electrode potential or
½ cell potential
Electrodes in Solution
A
++
B
+++
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
Electrodes

Two reactions take place at
electrode/electrolyte interface:
• Oxidizing Reaction: Metal -> electrons +
metal ions
• Reduction Reaction : Electrons + metal
ions -> Metal
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).
Metal A
Vae Vbe
Electrolytic Solution
Metal B
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)
Metal A
Vae Vbe
Electrolytic Solution
Metal B
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)
Electrode A
Cellular
Resistance
Cellular
Potentials
Rsa
Rc
Mass
Tissue
Resistance
Vd +
Rsb
Ionic Conduction


R1a
Rt
Electrode B

C1a Vea
- +
Rt= internal resistance of body which is low
Vd = Differential voltage Vd
Rsa and Rsb = skin resistance at electrode A
and B
C1b
Vo
Veb
- +
R1b
Electronic Conduction
•R1A and R1B = resistance of electrodes
•C1A and C1B = capacitance of electrodes
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
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



Typical Medical Surface Electrode:
Use conductive gel to reduce impedance
between electrode and skin
Schematic:
Pin-Tip
Connector
Binding Spot
Shielded Wire
Electrode Surface
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
1. Adhesive does not stick for a long time on
sweaty skin
2. Can not put electrode on bony prominences
3. Movement or motion artifact significant
problem with long term monitoring results in
a gross change in potential
4. 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
1. Additional Tape
2. Rough surface electrode that digs past scaly
outer layer of skin typically not comfortable for
patients.
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 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: measure biopotential at
cellular level where microelectrode
penetrates cell that immersed in an
infinite fluid
•
Saline.
Microelectrode

Two typical types:
1. Metallic Contact
2. Fluid Filled
Microelectrode Equivalent
Circuit
R1
RS
V1
C1
C2
Vo
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
Calculation for Resistance Rs
Rs in metallic microelectrodes
without glass coating:
P
Rs 
4r
70cm
Rs 
43.14 0.5 * 10-4 cm
 111.4 K


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 Rs

Rs of glass coated metallic
microelectrode is 1-2 order of magnitude
higher:
2P
Rs 
r 
Rs 
23.7cm
3.140.1 * 10-4 cm 3.14 180
 13.5M
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
 = taper angle (~ / 180)
Capacitance of Microelectrode
Capacitance of C2 has units pF/cm
C2 
0.55e 
R
ln  
r
Where e = dielectric constant which for
glass = 4
R = outside tip radius
r = inside tip radius
Capacitance of Microelectrode

Find C of glass microelectrode if the outer radius is
0.2 um and the inner radius = 0.15 um

0.55e 
C2 

 R
ln  
r
(0.55)( 4)
pF
 7.7
cm
 0.2m 

ln 
 0.15m 
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
A
R1
R1
Es +
-
R3
R3
+ Eo -
EC
Es
ED
EC
R2
R2
+ Eo -
ED
R4
R4
B

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.
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


R2  
R4
 - 
 
Eo  Es 
 R1 + R 2   R 3 + R4  

3 * 10 3 
Eo  12V 
3
3
 1.2 * 10  + 3 * 10 
5 
 3
Eo  12V 
  0.24V
 4.2 7.2 


 
5 * 10 3 
-
  2.2 * 10 3  + 5 * 10 3 
 





 
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
Eo  EC - ED
 R2 
EC  Es 

R
1
+
R
2


 R4 
ED  Es 

R
3
+
R
4




R2  
R4
 - 
 
Eo  Es 
 R1 + R 2   R 3 + R4  

 
3 * 10 3 
5 * 10 3 


Eo  12V 
3
3
3
3
 
 1.2 * 10  + 3 * 10    2.2 * 10  + 5 * 10 

5 
 3
Eo  12V 
  0.24V
 4.2 7.2 






 
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 Bridge

When R1 = 2KΏ; R2 = 1K Ώ; R3 = 10K Ώ; R4
= 5K Ώ
R2
R4

R1 + R 2 R3 + R 4
R 2R3 + R 4   R 4R1 + R 2 
R 2 * R3 + R 2 * R 4  R 4 * R1 + R 4 * R 2
R 2 * R3  R 4 * R1
R1 R3

R2 R4
2 K 10 K

2
1K 5 K
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

Definition: resistive element that
changes resistance proportional to an
applied mechanical strain
Strain Gauges

Compression = decrease in length by DL and
an increase in cross sectional area.
L = length
Rest Condition
L - DL = length
Compression
Strain Gauges

Tension = increase in length by DL and a
decrease in cross section area.
L = length
L + DL = length
Rest Condition
Tension
Resistance of a metallic bar is
given in length and area
• where
 pL 

R  
A 
• 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 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


1
m


 250mm
 

 L
 1000mm    0.0085
R      1.7 *10 -8 m
2 
A
 
 0.5mm2  1m  


1000
mm

 



Piezoresistivity

Piezoresistivity = change in resistance for a
given change in size and shape denoted as h

 L + DL 
Resistance in tension = R + h   

 A - DA 

Resistance increases in tension
L = length; ΔL = change in L; ρ = resistivity
A = Area; ΔA = change in A

 L - DL 
Resistance in compression = R - h   

 A + DA 

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



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 Piezoresistivity
 L + DL 
R + h  

 A - DA 


1
m


(30 + 10)mm *


-7
1000
mm
R + h  5 *10 m
2 
 (0.01 - 0.0027)mm2 *  1m  


1000
mm




1.5 + h  2.74
h  1.24
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 (GF) = a method of comparing one
transducer to a similar transducer
Gauge Factor
 DR 
R
GF  
 DL 
L


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 Factor
 DR 
R
GF  
  


  DL L
• 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



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:

 DR   2




150

R
GF 


3
.
71

 DL 
0.07mm
L 

20mm 
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
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
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
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
1. Unbonded strain gauge can be built
where its linear over a wide range of
applied force but they are delicate
2. 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
A
R1 = SG1
ES +
-
R3 = SG3
Vo
C
R2 = SG2
B
Electrical Circuit

D
R4 = SG4
Mechanical
Configuration
4 strain gauges (SG) in Wheatstone Bridge:
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 Example
Derivation:
Circuit
A
R1 = R +h
Es
+
C +
-
R3= R-h
Eo
R2 = R - h
B
-
D
 R 2   R 4 
Eo  Es 
-

R
1
+
R
2
R
3
+
R
4
 



 



R - h
R + h
 - 

Eo  Es 
 R + h  + R - h    R - h  + R + h  
h
 R - h  R + h  
 - 2h 
Eo  Es 

Es

Es
 2R 
2 R 
R
 2R


R4 = R +h
 10 
Eo  -10V 
 -0.5V

 200 
Note: Text book has wrongly stated that tension decreases R and compression increases R on page 112
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 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 Sensitivity

To calculate Output Potential use the
following equations:
• where
Eo   * E * F
• Eo = output potential in Volts (V)
• E = excitation voltage
• φ = sensitivity μV/V*g
• F = applied force in grams (g)
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.
 10V 
5V 15 g   750V
Eo  EF  
 Vg 
•note book has typo where writes μV/V/g for sensitivity
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:
LVDT:
Diaphragm
AC Excitation
L1
Core
L2
L3
Axis of Motion
External
Load
Capacitance Transducers


Quartz Pressure Sensors: capacitively
based where sensor is made of fused
quartz
Capacitive Transducers: Capacitance C
varies with stimulus
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

3 Common Types:
• Thermocouples
• Thermistors
• Solid State PN Junctions
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: 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

Transistor = invented in 1947
by Bardeen, Brattain and
Schockley of Bell Labs.
IC
+
IB
B = Base
C = Collector
E = Emitter
IE = I B + I C
VCB
+
VBE
IE
+
VCE
-
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
Solid State PN Junction Diode: the
base emitter voltage of a transistor is
proportional to temperature. For a
differential pair the output voltage is:
DVBE



 KT ln  I C1  
 I 

 C2 

q
VCC+
+
VCB
+
VBE
ccs1
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
Ic1
Ic2
DVBE
VEE-
+
VCB
+
VBE
ccs2
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
DVBE

 I C1  
 KT ln 

 I  

 C2 

q
DVBE 
1.38 *10
DVBE  0.0185V

 2mA 
J / K 37 + 273K  ln 

 1mA 
1.6 *10 -19 Coulombs
- 23
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









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
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?