Sensors and Actuators Sensors Physics

Transcription

1 Sensors and Actuators Sensors Physics Sander Stuijk Department of Electrical Engineering Electronic Systems

2 HEMOESISIVE SENSOS (Chapter 16.3)

3 3 emperature sensors placement excitation physical effect material thermal sensor contact passive thermal expansion metal bimetal contact active resistive effect metal D contact active resistive effect semiconductor silicon resistive contact active resistive effect polymer or ceramic thermistor contact passive thermoelectric effect conductor thermocouple contact active PN junction semiconductor non-contact passive pyroelectric effect pyroelectric pyroelectric non-contact active ultrasound - acoustic

4 4 hermoresistive effect resistivity of (semi)conductors depends on temperature temperature can be found by measuring resistance specific resistivity of a material m ne temperature dependency through number of free electrons (n) in semiconductors NC behavior: n ρ mean time between collisions (τ) in conductors PC behavior: τ ρ semiconductor conductor

5 5 esistance temperature detectors (Ds) specific resistivity of a material m ne mean time between collisions (τ) in conductors number of free electrons (n) in semiconductors D metal temperature sensor positive temperature coefficient (PC) relation between temperature and resistance n... ] reference temperature [ n 0 P100 D 0 resistance at 0 example P100 D α /K, α /K, α /K 3 almost linear relation between temperature and resistance

6 6 Silicon resistive sensors specific resistivity of a material m ne mean time between collisions (τ) in conductors number of free electrons (n) in semiconductors pure silicon four electrons in outer ring electrons in outer ring form covalent bonds with neighboring atoms these electrons are responsible for current +14 Si Si Si Si Si Si Si Si Si Si Si Si

7 7 Silicon resistive sensors specific resistivity of a material m ne mean time between collisions (τ) in conductors number of free electrons (n) in semiconductors Energy of electrons pure silicon four electrons in outer ring electrons in outer ring form covalent bonds with neighboring atoms these electrons are responsible for current these electrons are at = 0K in valence band increasing energy moves electrons to conduction band Si Fermi level Si Conduction band Valence band Si Si Si Si Si Si Si Si Si Si

8 8 Silicon resistive sensors specific resistivity of a material m ne mean time between collisions (τ) in conductors number of free electrons (n) in semiconductors pure silicon temperature increase lower resistance (NC behavior) n-doped silicon (Sb - Stibium) additional free electrons at given temperature which contribute to current mean time between collisions dominates resistivity device has PC behavior Si Si Si Si Si Sb Si Si Si Si Si Si

9 9 Silicon resistive sensor pure silicon has a negative temperature coefficient (NC) specific sensitivity ρ decreases when temperature increases doping with n-type impurity can change behavior to PC PC behavior only in limited range (up-to 00 C) above this temperature intrinsic behavior dominates =C n-doped pure silicon

10 10 Silicon resistive sensor silicon resistive sensor has typically a C of 0.7%/K non-linearity of the sensor is limited transfer function can be approximated with ] 0[1 1 0 example KY81-1 sensor silicon resistive sensor with n-doping range: -55 C to +150 C high long-term stability: ±0.05K/year almost linear transfer function α 1 = (Ω/Ω)/K α = (Ω/Ω)/K resistance: 1kΩ at 5 C sensitivity (at 5 C) ~ 7.9Ω/K 0

11 11 hermistor thermistor comes from thermally sensitive resistor thermistors are made by mixing doped oxides of metals leads to larger sensitivity then Ds which use only metals effect similar as seen in silicon resistive sensors temperature coefficient of thermistors PC when doping is heavy NC when doping is small only NC thermistors are useful for precision temperature measurement

12 1 NC thermistor relation between temperature and resistance is highly non-linear two different thermistors P100 D transfer function 0 reference temperature 0 e B(1/ 1/ 0 resistance at 0 (typically at 5 C) B (or β) characteristic temperature of the material 0 )

13 13 NC thermistor characteristic temperature is material and temperature dependent relation B and can be approximated as linear (small error) two-point calibration can be used to find B in certain range B ln( 1 / (1/ 1/ 0 / 1 ) ) 0 resistance at 0 1 resistance at example calibration data = 5000Ω at 5 C, = 144Ω at 60 C what is the characteristic temperature from 5 C to 60 C? 144 ln B / K 1 1 (73 60) K (73 5) K

14 14 NC thermistor characteristic temperature is material and temperature dependent relation B and can be approximated as linear (small error) two-point calibration can be used to find B in certain range B ln( 1 / (1/ 1/ 0 / 1 0 resistance at 0 1 resistance at 1 temperature coefficient of resistivity (C) ) ) C is often called relative sensitivity B(1/ 1/ 0 ) d / d 1 d0e B d non-linear - dependency 1 sensitive for low temperatures 0 0 sensitivity decreases quickly when temperature increases typical: α = -8%/ C (at cold side), α = -%/ C (at hot side)

15 15 NC thermistor characteristic temperature is material and temperature dependent relation B and can be approximated as linear (small error) two-point calibration can be used to find B in certain range B 0 resistance at 0 1 resistance at 1 temperature coefficient of resistivity (C) B(1/ 1/ 0 ) d / d 1 d0e B d example Siemens thermistor B = 4000K ln( 1 / (1/ 1/ 0 / 1 ) ) C (at 5 C): α = -4.5%/K 1 thermistor has a 1.5x larger C as a P100 D why do we prefer a large C? 0 0 larger C means larger sensitivity

16 16 NC thermistor models two-parameter model B(1/ 1/ model also known as simple model provides accuracy of ±0.7 C for 70 C range error due to non-linear relation B and 0 e 0 ) three or four parameter models exist provide higher accuracy more calibration points needed

17 17 NC thermistor models example - alternative thermistor model Ae B what value does A have when B = 400K and = 100kΩ at 5 C? B/ 5 100k 5 Ae A B/ 400K /(73K 5K) e e 5 5 what is the C of this device at 0 C and 100 C? at (0 C = 73K) it holds that B 400K 0 73K at (100 C = 373K) it holds that 400K K / K / K (relative) sensitivity decreases with increasing temperature

18 18 NC thermistor linearization relation between temperature and resistance is highly non-linear sensor will be connected to interface circuit hévenin equivalent resistance o as seen by interface circuit o V interface circuit sensor circuit o v o v m v v o B e e e B B o

19 resistance (Ω) 19 NC thermistor linearization example - resistance-temperature characteristic of sensor circuit 0 = 5kΩ, B = 4000K, =18500Ω sensor circuit V interface circuit o temperature (K) sensor circuit has smaller non-linearity error compared to thermistor reduction in non-linearity error is not for free... (why?) sensor circuit has smaller sensitivity compared to thermistor linearity and sensitivity form a trade-off

20 0 NC thermistor linearization sensitivity for temperature change of sensor circuit: o 0 e B(1/ 1/ 0 ) d o d d sensitivity of o is non-linear d d o d sensitivity for temperature change of thermistor: d d comparing sensitivity of sensor circuit and thermistor d 1 d o d d sensor circuit has lower sensitivity compared to thermistor alone non-linearity error will also be smaller

21 resistance (Ω) resistance (Ω) 1 NC thermistor linearization o o temperature (K) temperature (K) comparing sensitivity of sensor circuit and thermistor 1 d d o d d sensor circuit has lower sensitivity compared to thermistor alone non-linearity error will also be smaller

22 NC thermistor linearization linearity in range [ 1, 3 ] can be improved in measurement range by choosing constraints 1 3 o1 o o o3 it holds that o solving o for gives 1 1 Δ Δ (Ω) o1 o o3 the expression is independent from the model of this technique can be used for any nonlinear resistive sensor method minimizes non-linearity near the adjusting points Δ Δ (K)

23 9 NC thermistor self-heating current through NC thermistor causes self-heating similar to Ds P L is the thermal loss to the environment s, a thermistor, ambient temperature δ heat dissipation factor power consumption of the thermistor P D V i i C thermal capacity (mass x specific heat) steady-state condition d S dt 0 V ds C dt i V i i P L PD S heat accumulation rate heat loss rate a

24 30 NC thermistor self-heating current through NC thermistor causes self-heating similar to Ds self-heating can be minimized by minimizing current through use small supply voltage use large series resistor in front of use sensor with small duty-cycle voltage source

25 31 NC thermistor self-heating voltage-current characteristic for a thermistor in still air at 5 C constant (positive) resistance zero resistance ( current =voltage) negative resistance ( current voltage) increasing power dissipation increasing resistance negligible self-heating self-heating

26 3 NC thermistor self-heating voltage-current characteristic for a thermistor in still air at 5 C Δ=50 C Δ=100 C Δ=00 C Δ 0 C self-heating can lead to thermal run-away and destruction of sensor some applications use self-heating to get maximal voltage drop across sensor (e.g. flow rate sensor)

27 33 NC thermistor self-heating voltage-current characteristic for a thermistor in still air at 5 C V max voltage drop, max sensitivity V max I o I small current (negligible heating) use Ohm s law to find temperature increasing current: I P D Δ V

28 34 hermal flow sensors example - wind chill factor when cycling on a cold day, your hands are colder then when standing still air flow causes the hands of the cyclist to cool down by measuring the temperature of his hands, the cyclist can get a good measure of the air flow

29 35 hermal flow sensors construction three tubes immersed into a moving medium two tubes contain temperature detectors ( 0 and S ) detectors thermally coupled to medium detectors thermally isolated from structural elements mass equalizer ensures that medium moves through the detectors without turbulence

30 36 hermal flow sensors operation detector 0 measures the temperature of the flowing medium medium heated with heater detector S measures the elevated temperature

31 37 hermal flow sensors still medium heat dissipated from heater to both detectors heat moves out of the heater by thermal conduction and gravitational convection heater is closer to S then to 0 S will register a higher temperature then 0

32 38 hermal flow sensors moving medium heat dissipation increased due to forced convection increasing flow rate, leads to the higher heat dissipation this leads to a lower temperature registered by S thermal flow sensor measures the heat loss and converts it into the flow rate of the medium

33 39 hermal flow sensors non-linear relation between flow velocity v and temperature difference relation between flow velocity v and temperature difference K dq 1 v dt s 0 K calibration constant, ρ density of the medium, Q heat transfer Q depends on dissipation factor (velocity) 1.87

34 40 hermal flow sensors heater can be integrated into S by using it in self-heating mode relation between voltage across self-heating detector (e) and velocity of the flow (v) given by v K e S s K calibration constant ρ density of the medium

35 41 hermal flow sensors relation between voltage across self-heating detector (e) and velocity of the flow (v) suggests two method to measure flow v K e S s method 1 voltage (e) and resistance of detector S are kept constant and temperature difference is outputted method temperature difference is kept constant by a control circuit which regulates voltage (e) of the heater voltage (e) is output of the sensor method is easier to realize in miniature sensors

36 4 hermal flow sensors method 1 thermal flow sensor can be placed in a bridge circuit bridge is imbalanced at low flow rate high output voltage increasing flow heats detector S its temperature comes closer to temperature of 0 balances the bridge and decreases the output voltage voltage outputted by the sensor depends on the flow velocity on the medium

37 46 PC thermistors PC thermistor NC behavior till some temperature (point m) PC thermistors show abrupt change in resistance switch occurs around Curie temperature C temperature coefficient of resistivity (C) can be 00%/ C transfer function is not suitable for precision temperature measurement

38 47 PC thermistors example PC thermistor PC thermistor modeled with K 98.15K.3 what is the C for this PC thermistor at 5 C? C is defined as d d derivative of the given equation yields d 73.15K d 98.15K K at 5 C it holds that 1.3 d d 5 C K / K 98.15K 98.15K 98.15K

39 48 PC thermistors example PC thermistor PC thermistor modeled with K 98.15K.3 what is the C for this PC thermistor at 5 C? therefore C(5 C) d d 5 C d d 5 100% 0.77%/ K % is used to indicate the fractional change in resistance when a unit change in the temperature occurs

40 49 PC thermistors application: circuit protection short circuit of load causes PC to get very large resistance current in circuit goes to zero circuit resets itself when short circuit is removed PC characteristic provides build-in protection against overheating overheating will increase resistance increasing resistance will decrease current decreasing current will decrease self-heating

41 50 Comparing NC, PC thermistors and Ds NC thermistors versus Ds (+) higher resistivity (small lead-wire error) (+) higher sensitivity (up-to 1000x) (-) larger self-heating effect (-) smaller operating range (-) higher non-linearity (-) lower accuracy (±0.7 C) PC versus NC (+) build-in self-protection against overheating (-) complex temperature-resistance relation (partially NC behavior) (-) smaller operating range (some types only usable as switch) (-) not suitable for precision temperature measurement