F07 314 HW 02 all - EECS 314 Fall 2007 HW 02 Problem 1...

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EECS 314 Fall 2007 HW 02 Problem 1 Student's name ___________________________ Discussion section # __________ (Last name, first name, IN INK) © 2007 Alexander Ganago Page 1 of 2 The big picture A potentiometer (pot) shown on the first diagram is basically a resistor with three connectors: in addition to the end connectors A and B, there is a movable tap C. The resistance between the potentiometer’s ends is fixed R AB = R P The resistance R X = R AC between the end and the tap is variable so that the resistance between the tap and the other end connector equals (R P - R X ) Thus the potentiometer is equivalent to two resistors as shown on the second diagram. The circuit diagram below (under the Problem section) shows that a potentiometer can be used as a sensor with voltage readout proportional to the variable resistance R X Potentiometers come in various packages. In some of them, the tap moves when you move a linear slide: they can be used as sensors for linear displacement, for example, in an electronic balance. In others, you move the tap by rotating the shaft: these can be used as sensors for angular displacement such as rotation of a throttle valve in an internal combustion engine, position of the flap on the airplane wing, etc.: see the example below. Problem The circuit shown on this diagram shows a potentiometer used as a sensor for the angular position (angle α ) of a robotic arm. At α = 0, the potentiometer’s tap is in its middle position so that R X = R 0 = R P /2 At an arbitrary, non-zero angle α (in degrees) the resistance equals R X = R P /2 + K α where K is constant measured in k Ω /degrees. As shown in lectures, the output voltage is a linear function of the angle: V OUT = a + b α The coefficients a and b depend on the source voltage and the potentiometer.
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EECS 314 Fall 2007 HW 02 Problem 1 Student's name ___________________________ Discussion section # __________ (Last name, first name, IN INK) © 2007 Alexander Ganago Page 2 of 2 Part 1 (20 points) Assume R P = 200 k Ω , K = 2.0 k Ω /degree, V S = 12 V 1. Calculate a in volts and b in volts/degree a = ______________ volts b = _______________ volts/degree 2. Make a computer-generated plot of V OUT vs. the angle α over the interval from – 75 degrees to +75 degrees; attach your computer code or show your work in hand-written form. 3. Determine the angles in degrees: α 4 corresponding to V OUT = 4 V and α 7 corresponding to V OUT = 7 V α 4 = ____________˚ α 7 = ____________˚ 4. Assume that the error of readout of V OUT is 10 mV and calculate the error Δα of readout of the angle α . Δα = ____________˚ 5. Briefly discuss how to reduce the error of readout of the angle α : increase/decrease R P ; increase/decrease K; increase/decrease V S , etc. Part 2 (5 points)
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This note was uploaded on 10/25/2008 for the course EECS 314 taught by Professor Ganago during the Fall '07 term at University of Michigan.

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F07 314 HW 02 all - EECS 314 Fall 2007 HW 02 Problem 1...

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