# hw2sol - ELEC 7770-001, Spring 2010 Homework # 2 Solution...

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Homework # 2 Solution Assigned: Wednesday, March 1, 2010 Due: Wednesday, March 15, 2010 Problem 1: Using the Elmore delay formula, show that the delay of a long interconnect of length s is proportional to s 2 . Solution: To use the Elmore delay formula, we consider the interconnect as a cascade of n sections of resistance rs/n and capacitance cs/n, where r and c are the per unit length resistance and capacitance of the interconnect. See the following schematic. From Elmore delay formula, the time constant (i.e., delay from source to node n, without the constant 0.69) of the distributed interconnect is: Τ = R1C1 + (R1+R2)C2 + . . . + (R1+R2+ . . . +Rn)Cn = (rc + 2rc + 3rc + . . . + nrc)(s/n) 2 = rc[n(n+1)/2](s/n) 2 = rcs 2 (n+1)/(2n) rcs 2 /2 as n The delay of interconnect is 0.69rcs 2 /2 and is proportional to the square of the length s. Problem 2: A long interconnect has a delay D. To reduce the delay, the interconnect is split into n equal length segments. The segments are joined by n – 1 buffers, each having a delay 0.1D. Find the value of n that will minimize the buffered interconnect delay. What is the percentage reduction in delay? ELEC7770

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## This note was uploaded on 09/16/2011 for the course ELEC 7770 taught by Professor Agrawal,v during the Spring '08 term at Auburn University.

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hw2sol - ELEC 7770-001, Spring 2010 Homework # 2 Solution...

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