2011 Final MECH 368

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Name Student #

MECH 368 Measurement and Instrumentation

Final Exam

Spring 2011

Notes:

There are 16 pages in total

Partial credit is given only when intermediate steps are shown

Problem Grade Maximum

#1 10

#2 6

#3 12

#4 12

#5 12

#6 10

#7 12

#8 6

Total 80

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1. Explain the following using clearand simple language. Use illustrations to aid your explanations

where appropriate.

1.1Provide three reasons why you may want to automate a measurement process. (3)

1.2An LED has a Vd= 2V. Why is the following not a good circuit for illuminating this LED? (3)

2V Vd=2V

1.3What is a free-wheeling diode? Why is it necessary? (4)

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2. Design an op amp filter that contains a high-pass stage with fc= 100 Hz, a low-pass stage with fc= 1

kHz, and Gain = -10. Use realistic component values, i.e. capacitors ranging from 100 pF to 1 F, and

resistors ranging from 1 k to 10 M. (6)

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3. For the circuit below, derive a general (symbolic) expression for Vout(j)/Vin(j) in terms of R1, R2,

R3, and C. Determine a numerical expression for Vout(j)/Vin(j) using the given R and C values. Draw

the Bode plot for Vout(j)/Vin(j) based on your numerical expression. Label all axes, as well as any

corner frequencies. (Hint: use Thevenin-Norton equivalents to simplify your expression) (12)

R1

20k

R2

10k

Vout

R3

20k

C

1nFVin

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4. Determine the current through each LED for all four switch states. If the LED is not turned on then

write 0 for the current. Show work to justify each value. (12)

S1 S2 LED1 current D2 current LED3 current

OFF OFFOFF ON

ON OFF

ON ON

LED1

Vd= 2V

5V

R1

100

S1

D2

Vd= 0.7V

LED3

Vd= 2V

5V

R2

200

S2

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5. For the Vin waveform shown in the graph, draw the resulting Vout waveform from t=0 to t=130ms.

Write the expression for Vout(t) for regions (1) and region (2) on the graph. Determine the value of the

time constant in both cases. (12)

C1

1 F

R2

30k

Vout

R1

10k

Vin

VF= 2V

LED1

Vd= 0.7V

D1

0ms

1V

2V

3V

4V

5V

10ms 20ms 30ms 40ms 50ms 60ms 70ms

0V

-1V

80ms 90ms 100ms 110ms 120ms 130ms

Vin

Region (1) Region (2)

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6.The photodiode circuit below is used to detect signals from a 5 kHz sinusoidal light source. The

sinusoidal light source generates a photodiode current with amplitude 0.2 A. The ambient light level

generates a photodiode current of 1 A. Draw the voltage signal you expect to see at V1, V2, V3, and

Vout on the graph below. Clearly label each signal. Fluorescent lighting in the room produces an

interference signal at 100 Hz with 0.01 A amplitude. How will this signal impact Vout? (10)

R4

1M

5V

5V

C1

0.1 F

R1

1.6k

5V

Vout

R61M

C2

0.1 F

5V

5V

10k

10k

V1

V2

V3

5V

10k

10k

R2

16kIin

0ms

1V

2V

3V

4V

5V

0.1ms 0.2ms 0.3ms

0V

-1V

0.4ms 0.5ms 0.6ms

Expected impact on Vout from fluorescent lighting:

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0ms

1V

2V

3V

4V

5V

0.1ms 0.2ms 0.3ms

0V

-1V

0.4ms 0.5ms 0.6ms

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7. You are designing a cooling system for an internal combustion engine where it is necessary to

measure coolant temperatures ranging from -50C to 200C. You decide to use an RTD sensor with

characteristics listed in the table. (12)

(1) The circuit below is used to generate a constant current for the RTD. What is IOUTas a function of

RREFand V3?

(2) What should be the value of RREFfor IOUTto be 1 mA?

(3)For temperatures ranging between -50C and 200C, what is the expected range of (V1- V2)?

(4)For this temperature range of interest, design an op amp circuit to interface the voltage across the

RTD to a 0 to 5V analog to digital converter. Assume only a single 5V power supply is available.

V3

R1

5V

R1

R1

R1

V2

RREF

RRTD

RW

RW

V1

IOUT

Temp (C) RRTD()-50 90

-25 95

0 100

25 105

50 110

75 115

100 120

125 125

150 130

175 135200 140

*Maximum RTD current = 1 mA

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8. The circuit you designed in the previous problem gave you a reading from 0 to 5V for temperatures

ranging from -50C to 200C. After testing this sensor, you realize that its output reading fluctuates by

2C at a constant temperature. Design a comparator circuit to generate the signal to activate the

cooling system at 75C with a hysteresis band equivalent to the expected fluctuations. Your answer for

Vth+and Vth-should be within 10 mV of the expected fluctuation levels. The cooling system is de-

activated with a 5V signal and is activated with a 0V output. Assume the output reading scales linearly

with the temperature change. Label all component values in your circuit. (6)