Slide 1. Temperatures Light (Optoelectronics) Magnetic Fields Strain Pressure Displacement and Rotation Acceleration Electronic Sensors

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1 Slide 1 Electronic Sensors Electronic sensors can be designed to detect a variety of quantitative aspects of a given physical system. Such quantities include: Temperatures Light (Optoelectronics) Magnetic Fields Strain Pressure Displacement and Rotation Acceleration

2 Slide 2 Thermistors Consist of a semiconductor, with energy gap E g (~1eV) attached between two leads. Symbol: Temperature dependence given by: R = R 0 exp β T β T 0 where, β = E g 2k. β is typically between 3000 and 4000K.

3 Slide 3 Thermistors 2 One problem: thermistors have a non-linear temperature response. This can be handled by micro-computer interpolation or parallel linearization. R Total = R R 0 R 0 + R = R 0 1+ exp β 1 T 1 T 0 R β 1 T 1 R 0 2 β T 2 4T 0 T 0 R 0 R where T=T-T 0 is assumed to be small. Tradeoff is linearization reduces β sensitivity by a factor of four.

4 Slide 4 Resistance Temperature Detectors 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 the device is σ(τ) = n q µ(τ), where n is electron concentration. Linear over a large temperature range, but about 10 times less sensitive than thermistors.

5 Slide 5 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. metal A T 1 I T 2 metal B emf T 1 T 2

6 Slide 6 Thermocouple Classifications Thermocouples are classified by type as in the following table: Type Type E Type J Type K Type T Metal A - Metal B Chromel - Constantan Iron - Constantan Cromel - Alumel Copper - Constantan Temperature Range ( C) -200 to to to to +350

7 Slide 7 Magnetic Field Sensors - Introduction B = B 0 + µ 0 M Simple wire: B 0 = µ 0 n I current # of turns permeability of freespace Magnetization (dipoles align along B 0 ) B B 0 µ 0 H magnetic intensity

8 Slide 8 Magnetic Field Sensors - Fluxgate Magnetometers Figure shows Vacquier-type fluxgate configuration. Central coils are driven by a timevarying current I E. The voltage across the pickup coil is V pickup = n dφ dt one wire where n is the number of windings and P is the magnetic flux. With no external field (H sig = 0), there will be no flux through the pickup coil since windings are in opposite directions.

9 Slide 9 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 H ex that doesn t saturate both coils. As I E oscillates, V pickup will oscillate in the presence of an external magnetic field Net flux In an external field two hysteresis loops

10 Slide 10 At edges (with external field) there is a brief excitation Fluxgate Magnetometers 3 V pickup drive current: time Saturated no external flux Φ Recall that cores are polarized in opposition and external field is in one direction. Note that two flux envelopes are generated for each I ex cycle. So sensor circuits need to be tuned to second harmonic.

11 Slide 11 Magnetic Field Sensors - Hall Effect Probes Most widely used sensor for magnetic fields. (v B) B w h F+ F V I l In presence of a magnetic field, Lorenz forces push charge carriers laterally across the sample according to charge F L = q(v B). This results in a transverse electric field E H. field velocity

12 Slide 12 In equilibrium, Hall Effect Probes 2 q v B = q E H E H = v B. Defining v as the drift velocity. Bias current can be written as I = q (w l) v n : negative charge carriers I = q (w l) v p : positive charge carriers. Thus, the Hall voltage V H (= w E H ) can be written as l = thickness V H = V H = B q l n B q l p :negative charge carriers # of carriers :positive charge carriers # of carriers

13 Slide 13 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 such that when one groups sees light, the other does 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 anywhere from 500 to 2048 slots. Commercial units can measure rotations above 10,000 rpms.

14 Slide 14 Micromachined Angular Rate Sensor

15 Slide 15 Micromachined Angular Rate Sensor 2

16 Slide 16 Accelerometers Capacitor plates When sensor is accelerated, the beam will deflect, changing the capacitance of the device. The beam s movement is Mechanically equivalent to the system below. Flexible beam Direction of acceleration

17 Slide 17 Accelerometers 2 The general equation of motion of this system is M d 2 y m + G d ( y dt 2 m y b )+ ky ( m y b L)= a b (t) dt Where y m,y b, and L are the mass displacement, base displacement and spring relaxation values respectively. a b (t) is the acceleration of the base (this is what we want to determine). The sensor will read out the solution to this differential equation, from that, a b (t) will need to be determined. This can be made a lot easier in practice if one knows something about a b (t) beforehand. i.e. a b (t) is constant or oscillating.

18 Slide 18 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. connection to object mobile ferromagnetic core The pickup coils are wound opposite each other so their EMFs subtract. The core is mechanically coupled to the system via a pushrod extending out one end of the sensor (not shown).

19 Slide 19 LVDTs 2 V 1 -V V 1 -V 2 = 0 when core is in center position (by design). V 1 -V 2 will vary according the position of the magnetic core because of changing mutual inductances between pickup and excitation coils. M 1 M 2 (i.e. if core moves left V 1 -V 2 increases and becomes positive, and vice-versa.) Output will be modulated on top of the oscillating current driving 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.

20 Slide 20 LVDTs 3: Conceptual Layout

21 Slide 21 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 internal directions. Resistivity will have a tensor dependence on the applied strain tensor. With proper alignment, strain in one direction of the resistor will cause a change in resistance in the material in that same direction. Then strain could be measured using the following configuration. Resistor imbedded in semi-conductor δr R = ε l 1+ 2ν ( )+ δρ ρ for silicon this is strain-dependent

22 Slide 22 Piezoresistive Devices 2 Have very large gage factors so they are sensitive Strain is actually nonlinear and for silicon can be approximated as δr =120ε + 4ε2 : p-type, R δr = 110ε +10ε2 : n-type. R Maximum permitted strain for these gauges is 10x smaller than that of metal-foil devices. Also exhibit strong temperature dependences.

23 Slide 23 Pressure Sensors Modern solid-state sensors consist of a membrane which gets deformed when a pressure gradient is present. This deformation is then measured by strain sensors on the membrane. Piezoresistors Si diaphragm vacuum chamber

24 Slide 24 Pressure Sensor Classifications There are four main pressure chamber/membrane configurations used for pressure measurement. P 1 P 2 0 P 2 test differential vacuum reference ambient test P 1 P 2 P 1 P 2 test gage sealed reference

25 Slide 25 Bonded Metal Films In these sensors, resistivity doesn t change with applied strain, i.e. δr R = ε l( 1+ 2ν). Fabricated by photo-etching a thin film of metallic alloy to a desired shape and then backing that with a plastic insulating layer. Typically, the metal is etched in a folded pattern so that a large equivalent length is present in one direction so as to increase sensitivity. L equivalent length = 8L

26 Slide 26 Bonded Metal Films 2 unstrained: R strain = R V out V bias = R strain R R strain R

27 Slide 27 Bonded Metal Films 3 Typical Bonded Sensor: 10mm sensor (actual size 0.5mm) 1-2% strain ν = 0.3 R = 120Ω Gage factor = 2 ε l = 10-5 R = Ω or at a voltage of 10V, V out = -50µV

28 Slide 28 Strain Sensors Define longitudinal strain as ε L L L, and transverse strain as ε t = W W. F L + L F W - W Poisson s ratio is simply the negative ratio of these two quantities. ν = ε t ε l ν =.5 volume is constant under strain. Metals typically have ν range from ν <.5 volume is increases when stretched, decreases when compressed.

29 Slide 29 Strain Sensors 2 With net resistance R = ρ L A, resistivity Then the resistance changes with strain. If ρ does not vary, then we have a simple relation δr R = ε l 1+ 2ν ( )+ δρ ρ.

30 Slide 30 Resistive Strain Gages An important sensor parameter is the so-called Gage Factor (G), which is defined as δr G = R = (1 + 2ν) + 1 δρ δl ε L l ρ.

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