W09 314 HW02 solution

# W09 314 HW02 solution - V 30 OUT vs Angle 25 20 VOUT volts...

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-150 -100 -50 0 50 100 150 0 5 10 15 20 25 30 Angle / degrees V OUT / volts V OUT vs. Angle
1/19/09 2:24 PM C:\Users\jeremydg\Desktop\probset2num1.m 1 of 1 %Use values calculated for a,b above and %the formula for Vout vs angle. %Graph will be linear a = 15; b = 0.1; angle = [-150:.01:150]; Vout = a + b.*angle; plot(angle,Vout, 'linewidth' ,2.5); xlabel( 'Angle / degrees' ); ylabel( 'V_O_U_T / volts' ); title( 'V_O_U_T vs. Angle' ) grid on ;

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EECS 314 Winter 2009 Homework set 2 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above © 2009 Alexander Ganago Page 1 of 3 Solution by Idong Ebong Problem 4 Temperature controller circuit Resistive temperature sensor is a device whose resistance R T depends on the temperature; this dependence is described by the temperature coefficient dR T dT . Such sensors belong to two families: Thermistor is a semiconductor device with a negative temperature coefficient (NTC); Resistive Temperature Detector (RTD) is made of metal and has a positive temperature coefficient (PTC). Thermistors are the most popular temperature sensors. This diagram shows a temperature controller circuit with a resistive temperature sensor. You will build a similar circuit yourself in the Temperature Controller Lab. Circuit parameters: V S = +42 V V T = +3.5 V (the threshold gate voltage above which MOSFET conducts) R 1 = 120 k : R 3 = 120 k : R 4 = 91 k : . The resistance of the temperature sensor equals R T = 150 k : at 0 o F and R T = 75 k : at +100 o F; for simplicity, assume that R T is a linear function of temperature. Determine the following and write your answers below: Part 1 (5 points) The type of the temperature sensor. Your answer: ____NTC_____________ Part 1 2 3 4 5 Total Score
EECS 314 Winter 2009 Homework set 2 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above © 2009 Alexander Ganago Page 2 of 3 Solution by Idong Ebong Problem 4, continued The thermistor has a lower resistance at higher temperature, therefore NTC Part 2 (15 points) At what resistance R T is the Actuator turned on/off? Your answer: ___91 k ȍ ___________ The actuator is turned on when the MOSFET switch closes; this occurs when the V GS > V T . The comparator will make V OUT (connected to the MOSFET gate) equal to V S whenever V 2 >V 1 . Since V S = 42 V, this is sufficient to turn on the actuator. V 1 and V 2 are given by two voltage dividers: ܸ ൌܸ ܴ ܴ ൅ܴ ܸ ܴ ܴ Conveniently, R 1 = R 3 , so the on/off transition point occurs whenever R T = R 4 =91 k ȍ Since the thermistor’s resistance is a linear function of temperature, R T is given by: ܴ ൌ ͳͷͲ݇ߗ െ ܶ ͹ͷ݇ߗ ͳͲͲιܨ Solve for transition temperature by substituting R T = R 4 =91 k ȍ to get T=78.67 ° ܨ At what temperature is the Actuator turned on/off?

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W09 314 HW02 solution - V 30 OUT vs Angle 25 20 VOUT volts...

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