You wish to measure air temperatures over the range from 0 C to 50 C using the thermistor bridge shown below. R T Thermistor R 1 V + V R 3

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1 PROBLEM 1 (45 points) UNIVERSITY OF CALIFORNIA Electrical Engineering and Computer Sciences EECS 145L Electronic Transducer Lab MIDTERM # (100 points maximum) (closed book, calculators OK- note formulas on last page) (You will not receive full credit if you do not show your work) You wish to measure air temperatures over the range from 0 C to 50 C using the thermistor bridge shown below. V b R T Thermistor R 1 V + V R 3 R Assume the following: R = R 3 = 5 kω. You use an instrumentation amplifier with a gain of 5: V 0 = 5 (V + V ). The thermistor resistance R T vs. temperature T as shown in the table below 0 C 10 C 0 C 30 C 40 C 50 C kω kω kω kω.500 kω kω dr T /dt = 150Ω/ C at 0 C. You then perform a series of experiments to explore the thermistor self-heating of your system and to determine the best bias voltage V b. Experiment 1: With V b = 1 volt and the thermistor in water at 0 C, you adjust R 1 to make the amplifier output V 0 = volts. (Assume that there is no self heating in water with V b = 1 volt) a. (4 points) What are the values of R 1 and R T? b. (4 points) What electrical power is consumed by the thermistor? EECS 145L Midterm # page 1 Nov. 7, 1995

2 Experiment : You then move the thermistor to air at 0 C, wait a while, and find that the amplifier output V 0 = volts (V b = 1 volt). c. (5 points) What is the thermistor resistance R T? d. (4 points) What is the temperature of the thermistor? e. (4 points) What electrical power is consumed by the thermistor? Experiment 3: With the thermistor in air at 0 C, you increase V b to 10 volts, wait a while, and find that the amplifier output V 0 = volts. f. (5 points) What is the thermistor resistance R T? g. (4 points) What is the temperature of the thermistor? h. (4 points) What electrical power is consumed by the thermistor? i. (5 points) From your calculations of experiment 3, what is the thermal dissipation coefficient in mw per C? EECS 145L Midterm # page Nov. 7, 1995

3 j. (6 points) Comment on the design factors that determine the approximate minimum and maximum bias voltages or this application. PROBLEM (45 points) You are assigned the task of designing a truck scale for the North Dakota Department of Transportation. The scale consists of a large steel plate at the road level sitting on top of a large steel cylinder. When a truck drives onto the plate the steel cylinder is slightly compressed along its axis. The ambient temperature is expected to vary from 0 C to +40 C. The thermal expansion coefficient of the steel cylinder is 10 ppm/c. Design a system that meets the following requirements: The system should produce an output that is proportional to the weight of the truck. The maximum truck weight of 10,000 kg should produce an output of 10 volts. Trucks are to be weighed to an accuracy of 100 kg over the full temperature range. Assume the following: You have decided to use four metal foil strain gauges with gauge factor G S =.00 and an unstrained resistance of 100 Ω (similar to those used in the 145L lab) You may use any electronic components used in the 145L lab, but keep it simple. You cement the strain gauges (to wherever you decide to place them) at a temperature of 0 C. At this temperature, the strain is zero. EECS 145L Midterm # page 3 Nov. 7, 1995

4 The maximum truck weight of 10,000 kg produces a compressive strain L/L = 0.% The steel cylinder is hollow so the load only compresses the steel cylinder along its length and changes in diameter are negligible. All dimensions (e.g. length and diameter) change equally when the temperature changes. The steel plate weighs 1,000 kg. The resistivity ρ of the strain gauge metal foil does not depend on temperature. a. (0 points) Sketch your circuit, showing all essential components. Also, sketch the placement and orientation of the four strain gauges on the previous drawing. c. (5 points) With no load on the scale, what are the resistances of the 4 strain gauges and the voltages at 3 key points in your circuit ( bridge outputs, 1 amplifier output) at +0 C? EECS 145L Midterm # page 4 Nov. 7, 1995

5 d. (10 points) With the maximum 10,000 kg load on the scale, what are the resistances of the 4 strain gauges and the voltages at 3 key points in your circuit at +0 C? e. (10 points) With no load on the scale, what are the resistances of the 4 strain gauges and the voltages at 3 key points in your circuit at 0 C? PROBLEM 3 (10 points) a. (5 points) What function is the Ground Fault Interrupter Circuit designed to do? b. (5 points) Describe how a Ground Fault Interrupter Circuit works. EECS 145L Midterm # page 5 Nov. 7, 1995

6 Equations, some of which you may need: ( ) R(T) = R(T 0 )exp β T 1 T0 1 V(t) = V 0 sin(ωt) ω= πf V 0 = A(V + V ) G = x = e αt 1 ( ) n tan φ n 1+ f / f c = f f c V rms = [( ) + ( D 0 ) ] B D 1 G N(x) = N(0)e xµ [ Acos(ωt) + Bsin(ωt) ] = Re αt cos(ωt +δ) V = q / C v = v 0 + at x = x 0 + v 0 t at (constant a) g = 10 m s T = T (T T 1 ) e t/ τ I = I 0 e klc x = V dv / dx I rms = qi (F F 1 ) q = 1.60 x Coulombs V rms = 4kTR (F F 1 ) k = 1.38 x 10 3 Volt sec ohm 1 K 1 R T = R 3 V b R 1 V 0 ( R 1 + R ) V b R + V 0 (R 1 + R ) V 0 = G ± (V + V ) + G c (V + + V ) 1 f c = πrc R =ρa/l R R = G s L L V T = V BE V BE1 = kt q ln I 1 I P R = σat 4 σ = Wm K 4 CMRR = G ± G CMR = 0log ± 10 G c G c V 0 =V b G s L L k / q = µv/k E = hc / λ hc = 140 ev nm λ max = ( nm K)/ T η= T n+ T n +1 T equ = T n+1 + T n+ T n+1 T n+1 T n 1 η Q= πi +I R/ +K p (T s T 0 )+ K a (T a T 0 ) T equ = πi + I R/ + K p T s +K a T a K p +K a µ a = m 1 m m 1 a i σ a = m 1 a i a i=1 i=1 ( ) σ a = σ a m σ f = f f σ a1 + a 1 a σ a f + + a n σ an Johnson noise = 19 µv for 1 MHz and 1 MΩ Iron+Constantan µv/ C W+W(Rh) µv/ C EECS 145L Midterm # page 6 Nov. 7, 1995