Memorandum. September 21. To: Terry Cool, Project Manager From: Brian Lim, Lead Scientist Re: Progress Report on Temperature Controllers

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1 Memorandum September 21 To: Terry Cool, Project Manager From: Brian Lim, Lead Scientist Re: Progress Report on Temperature Controllers Summary I propose using an inexpensive NTC thermistor to maintain the temperature of the alexandrite laser rod. Through simple experiments, I hope to demonstrate that it can regulate some specified temperature within the range of 30 C to 100 C, to an accuracy of ±3 C. Stage 1, of the 2-stage project, to calibrate the thermistor, has been completed; I hope to complete stage 2, involving prototyping the temperature controller, by Sep 28 well before our Oct 18 deadline. Project Description The goal of this assignment is to identify an inexpensive scheme to maintain the alexandrite laser rod at some specified temperature between 30 C and 100 C, accurate to ±3 C. I have chosen the easily available and affordable NTC thermistor as the temperature controller, and have divided the project into two stages: the first to calibrate the transducer, and the second to determine its proficiency in regulating temperature. Stage 1 First, the behavior of the thermistor is verified against the relation of resistance, R T, as a function of temperature in Kelvin, T, defined by T0 R T = R0 exp, (1.1) T where R 0 and T 0 are physical constants specific to the thermistor used. This equation holds over a moderate range of temperature, for which 303K < T < 373K should be valid. To calibrate the thermistor, the values of R 0 and T 0 have to be determined, and this is done by following the procedure: i) Set up the computer system and diagnostic circuit ii) Write a controlling program iii) Test the circuit, and read R T values for various T values iv) Analyze the data and determine R 0 and T 0 Stage 2 Next, the thermistor is integrated into a temperature control system and tested on whether it can regulate temperature specified within the range of 30 C to 100 C, to an accuracy of ±3 C, following this procedure: v) Modify the computer system and circuit for prototyping vi) Write another controlling program vii)test the circuit, for some chosen temperature, T SET, to regulate at, and record changes in T viii)analyze the data and verify sufficient temperature control

2 Work Completed Stage 1 is complete, and stage 2 is in development. i) Using the circuit set-up of Diagram 1, the voltage across the thermistor, V T, was read into ADC2 of the National Instruments Lab-PC + microprocessor. I could not use ADC0, because it was faulty. ii) Using the relation determined from the circuit diagram (Diagram 1), =, (1.2) and equation 1.1, a C program was written to calculate R T from varying T. iii) iv) The circuit was run by raising T, in 3.0 C increments, from 30.0 C to 89.0 C and then lowering it to 29.0 C. Using a Matlab routine to analyze and plot the data, and accounting for systematic errors, I found the thermistor behavior to agree appreciably with the equivalent form of equation 1.1, T0 ln R T = ln R0 +, (1.3) T with ln R 0 = and T 0 = K. The R T T plots with theoretical approximation can be seen in Graph 1. As illustrated in that and Graph 2, the cooling and heating plots form a hysteresis loop around the mean regression line, possibly due to the slow response time of the mercury thermometer used in the calibration. Eliminating this systematic error, I find an uncertainty in T of ΔT = 5.10K. Work Remaining Stage 2 has been planned and will be conducted on Sep 28. I will set up an experiment to prototype the thermistor as a temperature controller and determine if it can regulate temperature at T SET ±3 C. v) Employing a HEXFET as a program controllable switch, I will set up the circuit as in Diagram 2, and read V T into ADC2. Switch control will be directed through PA0. vi) vii) viii) I will write a C program to turn the heater on when T < T SET δt and off when T > T SET + δt, where δt 1 C, measuring and recording T every 2 seconds. The circuit will be run for a few minutes, raising T to T SET and allowing it to fluctuate about that temperature for at least 3 oscillations, measuring T regularly. T vs time, t, plots will be collected and analyzed, using Matlab, to check whether the final temperature deviates far from T SET.

3 Conclusions and Recommendations Broadly, the project looks in good shape, with the thermistor obeying theory (equation 1.1) and final testing scheduled for Sep 28. If all goes well, I should have an inexpensive, functioning temperature controller well before the Oct 18 deadline. However, since the uncertainty of temperature, ΔT exceeds 3 C, my concern is that, currently, my results cannot guarantee temperature regulation to within the bounds of ±3 C. Nonetheless, there is no strong reason for them to deviate far from the true values. So if the temperature is regulated tightly (<< 3 C) over long periods at T SET, it should function fairly accurately. Another concern is that since the calibration of the thermistor was carried out up to 89 C, temperature readings above that to 100 C may diverge more from what is expected. But it should be possible to attenuate this problem by reducing ΔT. To that end, stage 1 can be repeated several times to improve accuracy. This should be quick, since the procedure has been tried and tested. Attachments Appendix A Graphs Graph 1: Heating and Cooling Curves and Mean of R vs T Graph 2: Heating and Cooling Curves of ln R vs 1/T Appendix B Circuits Diagram 1: Circuit for Stage 1 to Calibrate Thermistor Diagram 2: Circuit for Stage 2 to Prototype Temperature Moderator

4 Appendix A Graphs H e a t i n g a n d C o o l i n g a n d M e a n C u r v e s o f R v s T h e a t i n g p l o t s c o o l i n g p l o t s m e a n l i n e a r f i t h e a t i n g l i n e a r f i t c o o l i n g l i n e a r f i t R ( O h m ) a p p a r e n t t e m p e r a t u r e, T 1 ', w h i l e h e a t i n g t r u e t e m p e r a t u r e, T 1, w h i l e h e a t i n g t r u e t e m p e r a t u r e, T 2, a p p a r e n t t e m p e r a t u r e, w h i l e c o o l i n g T 2 ', w h i l e c o o l i n g T ( K ) Graph 1 Systematic errors in temperature reading due to slow response of mercury thermometer. Mean linear fit line shows the theoretical average of the plots. 9 H e a t i n g a n d C o o l i n g C u r v e s o f l n R v s 1 / T l n R h e a t i n g p l o t s c o o l i n g p l o t s m e a n l i n e a r f i t h e a t i n g l i n e a r f i t c o o l i n g l i n e a r f i t / T ( 1 / K ) x Graph 2 Linear fits for heating and cooling curves and their mean. Neglecting systematic error, it can be seen that the data is well-fit, suggesting that the relation is indeed ln R α 1/T.

5 Appendix B Circuit Diagrams Circuit for Stage 1 to Calibrate Thermistor 50Ω 6.7Ω Heater = 1kΩ 5V To ADC2 Thermistor Push button switch Diagram 1 Lab-PC + reads V T at input ADC2 for the program to determine R T using equation 1.2. Circuit for Stage 2 to Prototype Temperature Moderator 50Ω 6.7Ω Heater = 1kΩ 5V To ADC2 Thermistor From PA0 Gate Drain IRF 510 Or IRF Ω Source Diagram 2 Lab-PC + generates a signal voltage at PA0, to turn the HEXFET on, when it detects, from ADC0, that T < T SET δt, and turns it off when detects T > T SET + δt, thus regulating T at T SET.