I m. R s. Digital. R x. OhmmetersxSeries Shunt Digital. R m

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1 µa Meter I I s I m s E Digital x I Voltmeter x x E µa Meter m Is OhmmetersxSeries Shunt Digital EIx= = ()E sm x mxvi= x

2 Shunt Ohmmeter Shunt s x E µa Meter I m I m V m E ) ( v I E ) ( E v E v E I When x m x m s x m m m x m x m s x m x m x m s x m x m m s m s s m m m s m x = = = = = = =

3 Sample Problem Complete the design of the shunt ohmmeter and generate a calibration plot when m =1000 Ω and the meter has a full-scale reading of 100 µa. I s I m E µa Meter x V m m

4 Sample Problem Complete the design of the shunt ohmmeter and generate a calibration plot when m =1000 Ω and the meter has a full-scale reading of 100 µa. I s I m First step: Determine s E µa Meter x V m m

5 Sample Problem Complete the design of the shunt ohmmeter and generate a calibration plot when m =1000 Ω and the meter has a full-scale reading of 100 µa. I s 1.5 V µa Meter I m x m V m First step: Determine s When x is infinite, I = I m = 100 µa. s s m = I m E 1.5V = 100 A µ full scale = 15,000Ω = 15,000Ω 1,000Ω = 14,000Ω

6 Sample Problem Second Step: Generate a calibration curve I s I m 1.5 V µa Meter x V m m

7 Sample Problem Second Step: Generate a calibration curve I s 1.5 V µa Meter I m x m V m Make a spread sheet giving the meter current I m as a function of selected values of the unknown resistance, x Ix= ()sm x Exm

8 Sample Problem x I m Im x

9 Other Displacement Sensors Variable capacitance Linear variable differential transformer (LVDT) Variable inductance Mutual inductance Ultrasound transit time

10 Temperature Measurement Definitions Heat Form of energy of a body as an effect of their molecular motion Q Electrical Equivalent Charge Q Heat Flux Transport of thermal energy dq dt = Q Temperature The degree of heat in a body as measured on a defined scale Current dq I= dt Voltage V

11 Temperature Measurement More Definitions Heat Capacity The amount of heat to increase the temperature of a body by one unit Q = C T Specific Heat Heat capacity per unit mass C C s = m Thermal esistance A constant relating heat flux and temperature difference T = T Q Electrical Equivalent Capacitance esistance V = I

12 Sample Problem How much will a thermometer whose initial temperature is 20 C affect the temperature of the kidney? m=10g C s =1 J/g C Thermometer T =5 Cs/J T m=50g C s =4 J/g C Approach: convert to an equivalent electrical circuit

13 Heat capacity C = 50g 4 J = 200 g C J k C Heat C = 10g 1 J = 10 g C J T C C 200 J 10 J 210 C C J total = = C Q Q Q k T = 200 J 37 C = 7,400J C = 10 J 20 C = 200J C = 7,600J total Final Temperature of kidney and thermometer T Q total 7,600J = = 36.2 C C 210 J = total C m=10g C s =1 J/g C Thermometer C sk T C st m=50g C s =4 J/g C T Q k T C C sk sk C st C st T Q T T

14 Plot the Thermometer s esponse First-order dynamic system with response in the form T(t) = 20 C 16.2 C(1- e -t T C total ) Temperature Time constant 36.2 C C total = C C k k Ct C t 20 C τ Cs J = T C total = = J C 47.6s 47.6 s Time

15 esistance Temperature Detector (TD) Electrical resistance of an electrical conductor is a function of temperature L A = ρ L A ρ is temperature dependent therefore resistance will be temperature dependent [ 1 α(t T )] T = 0 0 Where α is the temperature coefficient of resistance for the material

16 esistance Temperature Examples of α Detector (TD) Material Gold Platinum Silver Nickel Nichrome Manganin α ( C -1 )

17 esistance Temperature Detector (TD) Examples Industrial Sensors Microfabricated Sensor

18 Thin-Film Gold Temperature Sensor Nasal Oral/Nasal In place on an infant ( ( T )) = 0 1 α T 0 0 is the resistance at temperature T 0 α Is the temperature coefficient of resistance

19 Thermistor Semiconductor Oxides Insulation High sensitivity Inexpensive Non-linear Moderate stability = 0 Lead Wires 1 exp β T 1 T 0 0 is the resistance at absolute temperature T 0 β Is a constant

20 Thermistor Effective temperature coefficient of about 5%/ C at body temperature (37 C) Compare with TD

21 Commercial Thermistors Disk Probes Bead Chip

22 Linearizing Thermistor Characteristics Linearizing Circuits

23 Standard Thermistor Curves

24 Sample Problem A thermistor with the curve C characteristic is to be used in an autoclave sterilizer that sterilizes at a temperature of 120 C. When the autoclave is not operating, the thermistor resistance is 2,000 Ω at room temperature of 25 C. What is its resistance at the autoclave s operating temperature? First step: use the standard thermistor curve C to determine the resistance ratio between the two temperatures

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26 120 C esistance ratio = = C 120 C = x 2,000 Ω = 46 Ω

27 Thermocouple Free electrons in a metal at a temperature greater than absolute zero will have a kinetic energy associated with the metal s temperature.

28 Thermocouple When one end of the metal is heated, the electrons at that end have a higher energy than those at the cooler end and there is a pressure for them to move to the lower temperature end. In other words, a voltage is developed between the hot and the cold ends.

29 Thermocouple T 1 T 2 Material A E A E A = α A (T 1 T 2 ) α = Seebeck Coefficient

30 Thermocouple T 1 T 2 Material A E A E A = α A (T 1 T 2 ) α = Seebeck Coefficient Voltmeter reads zero!

31 Thermocouple E A Material A T 1 T 2 E A E A E A = α A (T 1 T 2 ) α = Seebeck Coefficient Voltmeter reads zero!

32 Thermocouple E A Material A T 1 T 2 E B E A E A -E B = α A (T 1 T 2 ) α B (T 1 T 2 ) = (α A α B )(T 1 T 2 ) α = Seebeck Coefficient α AB = α A α B = Seebeck Coefficient for Materials A & B

33 Thermocouple T 2 T 1 Material A Sensing Junction Material B V eference Junction V = α AB (T 1 T 2 )

34 Thermocouple T 2 T 1 Material A Sensing Junction Material B V T 3 eference Junction V = α AB (T 1 T 2 )

35 Thermocouple T 2 T 1 Material A Sensing Junction Material B Material C T 3 eference Junction V = α AB (T 1 T 2 ) The meter can be connected with wire of a third metal and located remotely T 4 V

36 Thermopile T 1 T 2 V V = Nα AB (T 1 T 2 ) Where N is the number of thermocouples

37 Thermocouple ANSI Materials Temp. Voltage Type ange (mv) T Copper Constantan -200 to 350 C to J Iron Constantan 0 to 750 C 0 to E Chromel Constantan -200 to 900 C to K Chromel Alumel -200 to 1250 C to Platinum-13% hodium Platinum 0 to 1450 C 0 to V = α(t T 2 0 ) β(t T0 )

38 Thermocouple Table for Type K (Chromel Alumel) Thermocouples Thermoelectric Voltage in mv C

39 Sample Problem A type K thermocouple is to be used to measure the temperature of an infant incubator in the Neonatal Intensive Care Unit (NICU). This incubator should be at a temperature of 35 C, and the NICU itself is kept at a temperature of 23 C. 1. If the incubator is indeed at 35 C, what will the thermocouple voltage be? 2. If the reference junction of the thermocouple is placed in an ice bath, what will the thermocouple voltage be?

40 Work the second part of the problem first: The reference junction is at 0 C and the sensing junction is at 35 C, so the voltage can be found from the table V = mv Thermocouple Table for Type K (Chromel Alumel) Thermocouples Thermoelectric Voltage in mv C

41 Now determine the voltage for a thermocouple with its reference junction at 0 C and its sensing junction at room temperature, 23 C. V = mv Thermocouple Table for Type K (Chromel Alumel) Thermocouples Thermoelectric Voltage in mv C

42 Equivalent Circuit 23 C 35 C 0 C Sensing Junction V eference Junction mv mv V = = mv V

43 Potentiometer V ref = E I = 0 when V = V x E 1 I 2 v ref µµa V x

44 Historical Potentiometer Leeds and Northrup K-2 Potentiometer Galvanometer

45 Modern Potentiometers: Analog to Digital Converters V ref V x V c - V x V ref Staircase Generator t stop Counter Time Digital output Stop

46 Application: Electronic Thermometer Easy to read digital display apid response Equilibrium indication Disposable protective sheath Inexpensive enough for home use

47 E4E 1 Wheatstone Bridge V2E1= 1 2V4V Em 2 3 = 3 2 V 1 V 2 4 Meter voltage VVm= 1 22E-4= VV m