me_96_sol

# me_96_sol - MS-1 MS-1 Problem 1 The temperature dierence...

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MS-1 MS-1 Problem 1 The temperature difference between position 1 and position 2 is to be found. Let x 1 [290 K , 310 K] denote the temperature at po- sition 1 and x 2 [290 K , 310 K] denote the temperature at po- sition 2. Temperature at position 1 is to be measured using an integrated temperature sensor with model function H t - ITS ( x ) = x μ A K and temperature at position 2 is to be measured using a thermistor with model function H t - thm ( x ) = R 0 e β/x , where R 0 = 0 . 075 Ω and β = 3000 K . (a) Show the linear form of the thermistor model function for the given temperature range in which the thermistor is placed in parallel with a linearizing resistor. Thermistor with linearizing resistor: T Formula (from Set 7): H t4 ( x ) = R M 2 1 + α 2 ( x - T M ) , where R M is resistance at center of temperature range and α is related to slope at center of temperature range. Call center temp, T M . From problem statement T M = 300 K . Using (provided) exponential thermistor model: R M = R 0 e β T M = 1652 Ω . From Set 7: α = - β T 2 M = - 0 . 03333 / K . MS-1 EE 4770 Lecture Transparency. Formatted 13:10, 15 March 1998 from me˙96˙sol. MS-1

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MS-2 MS-2 Using the linear thermistor model function obtained above, design a circuit to convert the temperature difference Δ x = x 1 - x 2 to voltage H x ) = Δ x V 2 K . Show all component and source values. Use a summing amp since x 1 - x 2 is needed. + - + - R A R M R T v c2 v o R R c2 i 1 i 2 i 3 v c3 R c3 v c1 Observations: i 1 is a simple linear function of x 1 . i 2 is a linear function of x 2 plus a constant current . (See the thermistor’s linear model function.) A 1 Kelvin change in x 1 causes 1 μ A change in i 1 .
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