U210_sol05 - ECEU210 Solutions to HW#5 P 3.6 P 3.7 P 3.19 P...

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ECEU210 Solutions to HW #5 P 3.6 P 3.7
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P 3.19 P 3.22
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P 3.29 First we see, from v( ) = 10R/(100+R) that for R = 8.1 v( ) = 0.75, so the transient will never reach that value in finite time; therefore R > 8.1. The inequality is too complex for an algebraic solution, but we can solve it by “plotting” the function. This can easily be done on an Excel spreadsheet. What follows is an example of this process. To simplify the function, define a variable x = 10/(100||R) , and require F = (1 – e -x )/x 0.75 Now make a 3-column table as shown below on the left x=(100+R)/(10*R) F(R)=(1-EXP(-x))/x R x F(R) R x F(R) 2 5.1 0.194882991 19.1 0.623560209 0.744061832 4 2.6 0.356048624 19.2 0.620833333 0.744972343 6 1.766666667 0.469300917 19.3 0.618134715 0.745874961 8 1.35 0.548710918 19.4 0.615463918 0.746769788
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10 1.1 0.606480833 19.5 0.612820513 0.747656924 12 0.933333333 0.650099228 19.6 0.610204082 0.748536467 14 0.814285714 0.6840896 19.7 0.607614213 0.749408513 16 0.725 0.711276457
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This note was uploaded on 04/07/2008 for the course ECE U210 taught by Professor Shekel during the Spring '08 term at Northeastern.

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U210_sol05 - ECEU210 Solutions to HW#5 P 3.6 P 3.7 P 3.19 P...

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