ECE 202 Lesson 18

# ECE 202 Lesson 18 - ECE 202 Circuit Theory 2 Lesson 18...

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ECE 202 Circuit Theory 2 Lesson 18 Partial Fraction Expansion for Multiple-Order Real Poles

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Multiple-Order Real Pole ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 1 3 1 2 2 3 1 1 ! 0,1, , 1 m s a m m m s a F s F s s a F s K K K K F s s a s a s a s a d F s K ds m s - - - = + = + + + + + + + + + = = - l l l K K l l K Pole of order m at s = -a 2
The Time Function f(t) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 3 1 2 2 3 1 2 1 1 1 1 2 3 2! 1 ! 1 1 ! m m n at n m at m m K K K K F s s a s a s a s a t e u t n s a f t K K t K t K t e u t - + - - - = + + + + + + + + + + = + + + + + K K K K 3

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Class Problem ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 3 3 1 2 4 2 3 1 2 3 1 2 3 4 4 3 4 4 Solve for , , s s F s s s K K K K F s s s s s K K K + + = + + = + + + + + + + 4
Pole of Order 3 at s = -4 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 3 1 1 3 1 2 3 4 1 2 3 1 ! 0,1,2 s a s s F s s s s s F s s d F s K ds - - + + = + + + + = + = = l l l l l 5

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( 29 ( 29 ( 29 ( 29 1 3 4 3 1 4 1 2 4 2 1 1 1 2 2 4 1 ! 0,1,2
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## This note was uploaded on 03/12/2009 for the course ECE 202 taught by Professor Deanschmidlin during the Fall '08 term at UMass Dartmouth.

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ECE 202 Lesson 18 - ECE 202 Circuit Theory 2 Lesson 18...

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