HW04_solutions

# HW04_solutions - EECS 460 Homework#4 Solutions 1(Problem...

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EECS 460 Homework #4 Solutions 1. (Problem 3-10) Use Mason’s Rule to obtain the transfer function from Y 1 (s) to Y 3 (s) as follows: (a) Direct Paths P 1 = G Single Loops L 1 = -GH (b) The direct path and loop gain is the same (apply Mason’s Rule, and you will get the same result). Therefore, the two are equivalent. Alternatively, you could use block diagram reduction to show that the two systems are equivalent. Draw the block diagram from the signal flow graph in (a) as follows: GH G Y 1 Y 2 Y 3 _ Reduce the diagram to a final feedback form as follows: H G Y 1 Y 2 Y 3 _ So, the block diagram can be redrawn as: H G Y 1 Y 2 Y 3 _ Drawing the block diagram from the signal flow graph in (b) you obtain the same feedback block diagram. Therefore the two systems are equivalent. ## 3 1 1 () () 1 GH Ys G Y s GH ∆= + ⇒= +

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2. (Problem 3-11) Using Mason’s Rule, you obtain different ’s for the two signal flow graphs. For part (a), 11 22 33 1212 1313 2323 123123 1 GH GH GH GGHH GGGHHH ∆= + + + + + + + , whereas for the signal flow graph in part (b) 1 1 2 2 3 3 13 1 3 1 + + + + .
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## This note was uploaded on 04/13/2010 for the course CS 235 taught by Professor Sabnis during the Spring '10 term at Punjab Engineering College.

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HW04_solutions - EECS 460 Homework#4 Solutions 1(Problem...

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