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ECE634S09_L14_BlockDiagrams

# ECE634S09_L14_BlockDiagrams - ECE634 Signals and Systems II...

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ECE634 Signals and Systems II, Spring 2009 - Lecture 14, February 23 Daniel S. Brogan 1 4.5 Block Diagrams: Fig. 4.18 (assumes no loading between blocks) a) () Ys Hs Xs = b) () () 12 Ws Ys HsHs Xs Ws =⋅=⋅ b) Hs Hs =+ c) () () () () ( ) ( ) ( ) ( ) E sX s H s Y s H s G s E s =− 1 Es HsGs = +

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ECE634 Signals and Systems II, Spring 2009 - Lecture 14, February 23 Daniel S. Brogan 2 () () () () () 1 X sGs Ys EsGs HsGs == + () 1 Ys Gs X sH s G s = + Block Diagram Reduction Problem 4.6-13 In this problem we show how a pair of complex conjugate poles may be realized by using a cascade of two first-order transfer functions and feedback. Show that the transfer functions of the block diagrams in Fig. P4.6-13a and P4.6-13b are (a) 2 22 2 2 11 2 Hs sa s a b sa b +++ ++ (b) 2 2 2 2 s a b + + Hence, show that the transfer function of the block diagram in Fig. P4.6-13c is (c) 2 2 2 2 As B As B s a b (a) Using the form from section 4.5,
ECE634 Signals and Systems II, Spring 2009 - Lecture 14, February 23 Daniel S. Brogan 3 () () () 1 Feedback Ys Gs X sG s G s = + In this problem, 2 1 sa = + and ( ) 2 Feedback b = . Thus, 2 2 2 2 2 1 1 1 1 s a Xs sa b b + == + + + + (b) In this problem, 1 = + and 2 Feedback b = + . Thus, 2 2 2 2 1 1 1 b ++ + + + + (c) Part (c) is a combination of the previous two results. Careful inspection reveals that

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ECE634S09_L14_BlockDiagrams - ECE634 Signals and Systems II...

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