Deformation and Temperature Sensors

Transcription

1 Electronics Deformation and Temperature Sensors Alessandro Spinelli Phone: ( ) 4001 home.deib.polimi.it/spinelli

2 Disclaimer 2 Slides are supplementary material and are NOT a replacement for textbooks and/or lecture notes

3 Purpose of the lesson 3 At this point, we know how to analyze and design simple amplifiers Effective amplifier design depend upon the input signal characteristics (impedance, bandwidth, ) In this part of the class we discuss a few sensor arrangement: Wheatstone bridge (previous lesson) Deformation and temperature sensors (this lesson) Sensor technologies (optional overview)

4 Outline 4 Deformation sensors Resistive temperature sensors Seebeck effect and thermocouples Appendix

5 Stress and strain 5 For the uniform case under normal load we define the stress as σσ = FF SS Strain is the deformation per unit length εε = LL LL typical values are a few 10 3 ; the value is usually expressed in μstrain

6 Materials behavior 6 From [1] From [2] In the elastic region, the material will return to its original shape when the stress is removed

7 Hookes law 7 In the elastic region σσ = EEεε where EE = Young (or elasticity) modulus Axial strain is always accompanied by lateral strains of opposite sign in the two directions perpendicular to the axial strain Their ratio is called Poisson ratio νν = εε llllllllllllll εε aaaaaaaaaa

8 Poisson ratio and volume change 8 VV = LL εε 1 νννν 2 LL εε(1 2νν) VV VV = εε(1 2νν) If there is no volume change, νν = 0.5 From [3] Theoretical limits are 1 < νν 0.5

9 Typical values 9 For compact, weakly compressible materials such as liquids and rubbers, where stress primarily results in shape change, νν 0.5 For most well-known solids such as metals, polymers and ceramics, 0.25 < νν < 0.35 Glasses and minerals are more compressible, and for these νν 0 For gases, νν = 0 Materials with negative Poisson s ratio are called auxetic (e.g., Gore-Tex)

10 Strain gages/gauges 10 Convert strain into a resistance change: RR = ρρ LL SS Piezoresistivity RR RR = ρρ ρρ + LL LL SS SS = ρρ ρρ The gauge factor (GGGG) is defined as GGGG = RR/RR εε + εε(1 + 2νν) = 1 + 2νν + ρρ/ρρ εε

11 Typical values 11 Material GGGG Constantans (Ni-Cu alloys) Ni-Cr alloys ~1.9 Ni 12 Pt-Ir ~5 Si (with various impurities) ±100 ±200 Poly-Si ±30

12 Temperature effects 12 SG resistance and GF depend on T T-compensated gages are available, depending on the substrate material Correction curves are also available From [9]

13 Dummy gage compensation 13 The compensation gage must be unstrained or suitably mounted to increase the output signal The temperature should be the same and the two SGs identical From [9]

14 References en.wikipedia.org/wiki/poisson's_ratio

15 Outline 15 Deformation sensors Resistive temperature sensors Seebeck effect and thermocouples Appendix

16 Contact sensors 16 TT ss TT xx TT ee Goal is to make TT ss as close to TT xx as possible

17 Thermal circuit (Kelvin, 1841) 17 TT xx RR ssss CC xx TT ss RR ssss TT ee CC ss Thermal Temperature [K] Heat flow [W] Thermal resistance [K/W] Heat capacity [J/K] QQ = ΔTT RR TT dddd QQ = CC TT dddd Electrical Voltage Current Resistance Capacitance II = ΔVV RR II = CC dddd dddd

18 Isolated system + sensor 18 TT xx RR ssss TT ss ττ = RR ssss 1/CC ss + 1/CC xx CC xx CC ss TT FF = CC sstt ss 0 + CC xx TT xx 0 CC ss + CC xx A small CC ss minimizes both static and dynamic errors

19 Environment 19 RR ssss TT ss RR ssss ττ = CC ss (RR ssss RR ssee ) TT xx CC ss TT ee TT FF = TT xx + (TT ee TT xx ) RR ssss RR ssss + RR ssee A large RR ssee /RR ssss is required to improve the sensor accuracy

20 Requirements 20 Small CC ss Small sensor Small RR ssss Good thermal contact maximize contact area and (for solids) use good thermal grease Large RR ssee «Right» sensor connections use long, narrow connections with low thermal (and good electrical) conductivity (e.g., stainless steel, lead, )

21 RTDs 21 Resistance Temperature Detectors (RTDs) exploit the resistance change with temperature in certain metals They can provide highly accurate results (from 0.1 to C) and are used to assign the TP temperatures between about 14 and 1200 K Expensive!

22 Resistance of metals 22 From [1] Metal resistance increases with T RR = RR 0 (1 + aa 1 TT + aa 2 TT aa nn TT nn ) For small T range, a linear approximation is used, characterized by its relative slope αα = TTTTTT = 1 RR 0 ΔRR ΔTT TTTTTT = temperature coeff. of resistance (usually computed between 100 and 0 C)

23 TCR values 23 Metal TT range [ C] TTTTTT [ C -1 ] Pt 200, Ni 100, Cu 100, W 100,

24 Pt RTD 24 Platinum is mostly used for RTDs Chemical inertness Large enough TTTTTT Strain-free fabrication and weak dependence of RR on strain Almost linear RR TT relationship Resistance at 0 C is usually 100 or 1000 Ω (PT100 or PT1000 RTDs) Expensive!

25 Thermistors 25 Made with transition metal (Cr, Co, Cu, Mn, Ni, ) oxides and showing a semiconductor-like behavior Strongly non-linear RR TT characteristic, but with high TTTTTT, either positive (PTC) or negative (NTC) NTCs only are useful as sensors

26 R-T characteristics 26 The R-T characteristics of NTC thermistors follow the intrinsic semiconductor behavior RR TT = RR TT 0 ee BB 1 TT 1 TT0 From [7] Resistance value is usually referenced at 25 C and varies between 100 Ω and 100 kω

27 TCR of NTC thermistors 27 The TTTTTT can be expressed as TTTTTT = αα = BB TT 2 Typical values are 3 to / C, i.e. about one order of magnitude larger than RTDs Owing to the large signal, 3- or 4-wire bridges are usually not necessary NTC thermistors are generally used between 50 and +150 C (up to 300 C for some glass-encapsulated units)

28 PTC thermistors 28 From [12] Polycrystalline ceramic materials made semiconductive by the addition of dopants Manufactured using compositions of Ba, Pb, and Sr titanates with additives (Y, Mn, Ta, ) Used as overcurrent protection, heaters,

29 Sensor self-heating 29 RR ssss TT ss RR ssss TT xx CC ss PP ss TT aa TT FF TT xx + PP ss RR ssss Ex. II = 1 ma, RR ssss = 1 C/mW. For a PT100 RTD, PP ss = 100 μw, i.e., ΔTT = 0.1 C If lower currents cannot be used, pulsed measurements (with synchronous detection) must be employed

30 References A. Morris, «Measurement and instrumentation principles», Butterworth (2001) 2. J. Webster (ed.), «Measurement, instrumentation and sensors handbook», CRC Press (1999) J. Fraden, «Handbook of modern sensors», Springer (2004)

31 Outline 31 Deformation sensors Resistive temperature sensors Seebeck effect and thermocouples Appendix

32 Seebeck effect 32 From [1] A temperature difference between two conductors or semiconductors generates a voltage difference or a current flow Discovered accidentally by Thomas Seebeck in 1826

33 Physical picture 33 From [2]

34 Seebeck coefficient 34 Is the ratio between voltage drop and thermal gradient Aka thermoelectric power SS = dddd dddd By convention, the sign of SS indicates the potential of the cold side with respect to the hot side

35 Typical values at 0 C 35 From [3] Metal SS [μv/k] Metal SS [μv/k] Sb 42 Bi -68 Li 14 K -13 Mo 4.7 Pd -9 Cd 2.6 Na -6.5 W 2.5 Pt -4.5 Cu 1.6 C -2 Ag 1.5 Al -1.6 Ta 0.05 Pb -1.1

36 The sign of SS 36 Low-energy electrons diffuse from C to H side High-energy electrons diffuse from H to C side The sign of SS is related to the energy dependence of the diffusion coefficient, i.e., of the scattering mechanisms

37 Seebeck effect in semiconductors 37 From [3] Semiconductor SS [μv/k] Se 900 Te 500 Si 435 Ge 300 PbTe -180 PbGeSe BiTe -230 Much larger than in metals because of the exponential dependence of carrier concentration on temperature

38 Measurement of S 38 VV AA TT 2 TT 0 TT 1 AA VV AA VV 2 VV 1 VV = SS TT = 0

39 Measurement of S 39 VV AA TT 2 TT 1 TT 0 BB VV BB VV 2 VV 1 VV = SS AA TT SS BB TT = SS AAAA TT

40 In brief 40 A circuit made with one conductor will not generate any emf irrespective of the thermal gradient A circuit made with two conductors will not generate any emf when isothermal Different materials and different temperatures are needed!

41 Thermocouples are emf sources! 41 AA AA VV VV AA = TT 2 TT 1 TT 2 TT 1 BB VV BB BB VV

42 Law of intermediate temperatures 42 VV = SS AAAA TT 2 TT 1 = SS AAAA TT 2 TT 0 + TT 0 TT 1 = SS AAAA TT 2 TT 0 SS AAAA TT 1 TT 0 If the emfs with respect to a reference temperature TT 0 are known, they can be used to compute the emf for any TT Conversely, we only need to know TT 1 to measure SS(TT 2 ) Also valid if SS = SS(TT)

43 Law of intermediate metals 43 VV = SS AA SS BB TT = SS AA SS MM + SS MM SS BB TT = SS AA SS MM TT SS BB SS MM TT Is the emfs with respect to a reference electrode MM are known, they can be used to compute the emf for any couple of metals Also valid if SS = SS(TT)

44 Thermocouple measurements 44 AA CC TT 2 TT 1 TT 0 VV ΔVV = CC SS AAAA (TT 2 TT 1 ) BB Soldering metals will not generate any emf if isothermal Connecting wires of the same material will not generate any emf

45 The ice bath 45 TT 2 TT 1 = 0 C TT 0 CC BB TT 1 is kept stable by using an ice bath and the constant offset is then subtracted Impractical in modern systems AA CC VV ΔVV = SS AAAA (TT 2 TT 1 )

46 Cold junction compensation 46 AA CC TT 2 BB TT 1 CC ΔVV = SS AAAA (TT 2 TT 1 ) TT 1 is measured by a thermistor or RTD and its contribution is subtracted (e.g., via SW) Single reference can be used for multi-point

47 A few notes 47 Open-circuit voltage must be measured Thin thermocouple wires are used to reduce CC ss high resistance and noise keep the TC short and use thicker connection wires TCs decalibrate over time due to chemical contamination (recalibration may not be easy) Grounded, ungrounded or exposed TC junctions are available

48 Thermocouple standards 48 From [6] Av. S [μv/k] Noble metals High sensitivity Inexpensive, accurate, most common Noble metals (high T, high accuracy, low S) Low T

49 Typical data 49 From [7]

50 Sensor comparison 50 From [6]

51 References Y. Pei et al., Energy Env. Sci. 5 (2012) 5. M. McGuire et al., J. Solid-State Chem. 184 (2001) 6. df 7.

52 Outline 52 Deformation sensors Resistive temperature sensors Seebeck effect and thermocouples Appendix

53 Seebeck effect in metal: model 53 Average energy of electrons in metals EE = 3 5 EE FF The increase in energy after TT is 1 + 5ππ2 12 kk BB TT EE FF 2 TT EE = TT = ππ2 kk BB TT, 2EE FF balanced by the electrostatic energy qq VV. Then 2 TT SS = VV TT = ππ2 kk BB 2qqEE FF 2

54 Seebeck effect in semiconductors: model 54 Drift-diffusion current density: where dddd = nn + nn dddd xx TT dddd JJ nn = qqqqμμ nn FF + qqdd nn dddd dddd = nn + nn EE CC EE FF ddxx xx kk BB TT 2 JJ nn = qqqqμμ nn dddd dddd FF + EE CC EE FF qqqq dddd dddd JJ nn = 0 SS = dddd dddd = EE CC EE FF qqqq