hw2 - EML 4312 Fall 2009 Block Diagram and SFG The due date...

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EML 4312 Fall 2009 Block Diagram and SFG The due date for this assignment is Wednesday 9/23. Show your work. 1. Determine the transfer function for the following block diagram. B A C D K Y R U + + - + - + + + Consider the following simpli f ed block diagram B E K Y R U + + - + + + x z A p where E = D 1+ CD p = R + UE Y = Az z = p Bx x = Y (1 + K ) Making substitutions yields Y = A ( R + B ( Y (1 + K ))) = AR + AUE ABY (1 + K ) Y (1 + AB (1 + K )) = AR + Y = A AB (1 + K ) R + AE AB (1 + K ) U 1
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2. Determine the transfer function for the following block diagram. B A C Y R - - + There are several possible ways to solve this problem. You should explore a solution with 2 cannonical loops, or using algebra, or a parallel combination. All three methods yield the same result. 2 Cannonical Loops Top Cannonical Loop = A 1+ AB then combined with second loop = μ A AB C μ A AB Y R = A AB + AC Parallel combination of B and C is B + C wh ichisinacannon ica lloopw ith A Y R = A A ( B + C ) Algebra Y = Az z = R + BY + CY Y = AR + ABY + ACY Y R = A A ( B + C ) 3. Use Mason’s Gain Formula to determine the transfer function.
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hw2 - EML 4312 Fall 2009 Block Diagram and SFG The due date...

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