Slide 13 · • Work via the Seebeck effect, which states that current will ... Magnetic Field...
Transcript of Slide 13 · • Work via the Seebeck effect, which states that current will ... Magnetic Field...
Slide 1
6.071 Electronic Sensors
Electronic Sensors
Electronic sensors can be designed to detect a variety of quantitative aspects of a given physical system. Such quantitiesinclude:
• Temperatures• Light (Optoelectronics)• Magnetic Fields• Strain• Pressure• Displacement and Rotation• Acceleration
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6.071 Electronic Sensors
Thermistors
where,
β =Eg2k
.
• Consist of a semiconductor, with energy gap Eg (~1eV) attached between two leads.
• Temperature dependence given by:
R = R0 ⋅ exp βT
− βT0
β is typically between 3000 and 4000K.
Symbol:
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6.071 Electronic Sensors
Thermistors 2
• One problem: thermistors have a non-linear temperature response. This can be handled by micro-computer interpolation or parallel linearization.
R0
R
RTotal = R0RR0 + R
= R0
1+ exp −β 1T
− 1T0
≈ R0
2 −β 1T
− 1T0
≈ R012
− β∆T4T0
2
where ∆T=T-T0 is assumed to be small.
• Tradeoff is linearization reduces β sensitivity by a factor of four.
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6.071 Electronic Sensors
Resistance Temperature Detectors
σ(Τ) = n⋅q·µ(Τ),
• RTDs are resistors fabricated from a nearly pure metal.• Due to electron scattering off the metal latice, electron mobility,
µ, decreases as Temperature increases. Conductivity of thedevice is
where n is electron concentration.
• Linear over a large temperaturerange, but about 10 times less sensitive than thermistors.
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6.071 Electronic Sensors
Thermocouples
• Work via the Seebeck effect, which states that current will circulate in a loop formed by joining two segments of dissimilar wires if the two joining points are at different temperatures. This is shown in the figure below.
IT1 T2
T1 T2
metal A
metal B
emf
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6.071 Electronic Sensors
Thermocouple ClassificationsThermocouples are classified by type as in the following table:
TypeType EType JType KType T
Metal A - Metal BChromel - Constantan
Iron - ConstantanCromel - Alumel
Copper - Constantan
Temperature Range (°C)-200 to +900
0 to +750-200 to +1250-200 to +350
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6.071 Electronic Sensors
Magnetic Field Sensors - Introduction
Simple wire:
B0 = µ0 ⋅ n ⋅ I
# of turnspermeability offreespace
current
∴ B = B0 + µ0 ⋅M
Magnetization (dipoles align along B0)
B
B0
µ0
≡H magnetic intensity
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6.071 Electronic Sensors
Magnetic Field Sensors - Fluxgate Magnetometers
• Figure shows Vacquier-type fluxgate configuration.
• Central coils are driven by a time-varying current IE.
• The voltage across the pickup coil is
Vpickup = n dΦdt
where n is the number of windings and P is the magnetic flux.• With no external field (Hsig = 0), there will be no flux throughthe pickup coil since windings are in opposite directions.
one wire
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6.071 Electronic Sensors
Fluxgate Magnetometers 2
• When there is an external field the hysteresis loops (closed in the figure for simplification) get translated away from the origin; resulting in a non-zero flux for Hex that doesn’t saturate both coils.
Net flux
• As IE oscillates, Vpickup will oscillate in the presence of an external magnetic field
two hysteresis loops
In an external field
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6.071 Electronic Sensors
Vpickup
Φtime
• Note that two flux envelopes are generated for each Iex cycle. Sosensor circuits need to be tuned to second harmonic.
drive current:
Fluxgate Magnetometers 3
Saturated ∴ no external flux
At edges (with external field) there is a brief excitation
• Recall that cores are polarized in opposition and external field is in one direction.
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6.071 Electronic Sensors
Magnetic Field Sensors - Hall Effect Probes
+ -
I
B
V
(v×B)F-F+
• Most widely used sensor for magnetic fields.
• In presence of a magnetic field, Lorenz forces push chargecarriers laterally across the sample according to
FL = q(v × B).This results in a transverse electric field EH.
h
l
w
field
velocitycharge
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6.071 Electronic Sensors
Hall Effect Probes 2
• In equilibrium, q|v|·|B| = q|EH| ⇒ |EH| = |v|·|B|.
• Defining v as the drift velocity. Bias current can be written as
I = q⋅(w⋅l)⋅v⋅n : negative charge carriersI = q⋅(w⋅l)⋅v⋅p : positive charge carriers.
Thus, the Hall voltage VH (= w⋅EH) can be written as
VH = Bq ⋅ l ⋅ n
:negative charge carriers
:positive charge carriersVH = Bq ⋅ l ⋅ p
# of carriers
# of carriersl = thickness
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6.071 Electronic Sensors
Incremental Optical Shaft Encoders
• Work by chopping a light beam by means of equally spaced slots cut on a metal disk. A photodetector detects when light passes through and that signal is counted to determine angular position.
• Configuration of photodetector arrays is suchthat when one groups “sees” light, the otherdoes not. Consequently two digital signals are produced which are in quardrature which allows the direction of rotation to be determined.
• Codewheels are 1-2in. in diameter with anywherefrom 500 to 2048 slots.• Commercial units can measure rotations above 10,000 rpms.
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6.071 Electronic Sensors
Accelerometers
Capacitor platesFlexible beam
Direction ofacceleration
• When sensor is accelerated,the beam will deflect, changingthe capacitance of the device.• The beam’s movement is Mechanically equivalent to the system below.
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6.071 Electronic Sensors
Accelerometers 2• The general equation of motion of this system is
M d2ymdt 2
+G ddtym − yb( )+ k ym − yb −L( )= −ab (t)
Where ym, yb, and L are the mass displacement, base displacementand spring relaxation values respectively. ab(t) is the acceleration ofthe base (this is what we want to determine).
• The sensor will read out the solution to this differential equation, from that, ab(t) will need to be determined. This can be made a loteasier in practice if one knows something about ab(t) beforehand.i.e. ab(t) is constant or oscillating.
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6.071 Electronic Sensors
Displacement Detectors - LVDTs
• Stands for Linear Variable Differential Transformer• Consists of two pickup coils located on either side of an excitation
coil, as in the following picture.
mobile ferromagnetic core
• The pickup coils are wound opposite each other so their EMFssubtract.
• The core is mechanically coupled to the system via a pushrod extending out one end of the sensor (not shown).
connection to object
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6.071 Electronic Sensors
LVDTs 2
M1 M2
1 2
V1-V2
• V1-V2 = 0 when core is in center position(by design).
• V1-V2 will vary according the position ofthe magnetic core because of changing mutual inductances between pickup and excitation coils.(i.e. if core moves left V1-V2 increases and becomes positive, and vice-versa.)
• Output will be modulated on top of the oscillating currentdriving the excitation coil.
• Typically, driving current oscillates at about 10x the rate of the mechanical system.
• These sensors are precision instruments, yet are very rugged.
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6.071 Electronic Sensors
Piezoresistive Devices
• Made of semi-conductor material such as silicon.• Applied Forces deform the atomic lattice resulting in current
being able to flow with greater ease along certain internaldirections.
• Resistivity will have a tensor dependence on the applied straintensor. With proper alignment, strain in one direction of theresistor will cause a change in resistance in the material in that same direction. Then strain could be measured using the followingconfiguration.
Resistor imbeddedin semi-conductor
δRR
=εl 1+ 2ν( )+ δρρ
for silicon this isstrain-dependent
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6.071 Electronic Sensors
• Have very large gage factors so they are sensitive• Strain is actually nonlinear and for silicon can be approximated as
Piezoresistive Devices 2
δRR
=120ε + 4ε2
δRR
= −110ε +10ε2
: p-type,
: n-type.
• Maximum permitted strain for these gauges is 10x smaller than that of metal-foil devices.
• Also exhibit strong temperature dependences.
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6.071 Electronic Sensors
Pressure Sensors• Modern solid-state sensors consist of a membrane which getsdeformed when a pressure gradient is present. This deformationis then measured by strain sensors on the membrane.
Piezoresistors Si diaphragm
vacuumchamber
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6.071 Electronic Sensors
Pressure Sensor Classifications• There are four main pressure chamber/membrane configurations used for pressure measurement.
test
ambient
P1 P2
P1 P2 P1 P2
0 P2
test
test
differential
gage sealed reference
vacuum reference
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6.071 Electronic Sensors
Bonded Metal Films
δRR
=εl 1+ 2ν( ).
L
• In these sensors, resistivity doesn’t change with applied strain,i.e.
• Fabricated by photo-etching a thin film of metallic alloy toa desired shape and then backing that with a plastic insulatinglayer.
• Typically, the metal is etched in a folded pattern so that a large equivalent length is present in one direction so as to increasesensitivity.
equivalent length = 8L
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6.071 Electronic Sensors
Bonded Metal Films 2
unstrained: Rstrain = R
VoutVbias
=−∆Rstrain
R4 + 2 ∆Rstrain
R
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6.071 Electronic Sensors
Bonded Metal Films 3
Typical Bonded Sensor:10mm sensor (actual size 0.5mm)
1-2% strainν = 0.3
R = 120ΩGage factor = 2εl = 10 -5
∴∆ R = 2.4×10-3Ωor at a voltage of 10V, Vout = -50µV
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6.071 Electronic Sensors
Strain Sensors
εL ≡ ∆LL
,
εt = −∆WW
.
ν = −εtεl
L + ∆L
F F
W - ∆W
• Define longitudinal strainas
and transverse strain as
Poisson’s ratio is simply the negative ratio of these two quantities.
• ν = .5 ≡ volume is constant under strain. • Metals typically have ν range from 0.3 → 0.4• ν < .5 ≡ volume is increases when stretched, decreases when compressed.
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6.071 Electronic Sensors
δRR
=εl 1+ 2ν( )+ δρρ
.
Strain Sensors 2
With net resistance
R = ρ LA
,
resistivity
Then the resistance changes with strain. If ρ does not vary, then we have a simple relation