slide 13 · • work via the seebeck effect, which states that current will ... magnetic field...

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


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:


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.


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.


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


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


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


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


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


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.


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


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


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.


Micromachined Angular Rate Sensor


Micromachined Angular Rate Sensor 2


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.


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.


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


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.


LVDTs 3: Conceptual Layout


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


• 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.


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


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


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


Bonded Metal Films 2

unstrained: Rstrain = R

VoutVbias

=−∆Rstrain

R4 + 2 ∆Rstrain

R


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


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.


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


Resistive Strain Gages

An important sensor parameter is the so-called Gage Factor (G), which is defined as

G =δRR

δLL

= (1+ 2ν ) + 1εl

δρρ

.

slide 13 · • work via the seebeck effect, which states that current will ... magnetic field...

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