ECE 202 Lesson 17

ECE 202 Lesson 17 - ECE 202 Circuit Theory 2 Lesson 17...

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Unformatted text preview: ECE 202 Circuit Theory 2 Lesson 17 Partial Fraction Expansion: Distinct Complex Conjugate Poles Initial Problem of Interest f ( t ) = Ae - t cos ( t + ) u ( t ) Find F ( s ) 2 Problem 2 from Lesson 14 A cos ( t + ) u ( t ) ( A cos ) s - ( A sin ) s2 + 2 e - at f ( t ) F ( s + a ) Ae - t cos ( t + ) u ( t ) ( A cos ) ( s + ) - ( A sin ) 2 s + ) + 2 ( 3 Partial Fraction Expansion ( A cos ) ( s + ) - ( A sin ) = ( A cos ) ( s + ) - ( A sin ) 2 ( s + - j ) ( s + + j ) s + ) + 2 ( ( A cos ) ( s + ) - ( A sin ) = K K* + s + - j s + + j ( s + - j ) ( s + + j ) ( A cos ) ( s + ) - ( A sin ) K = lim s + - j s - j + ( s + - j ) ( s + + j ) 4 Determination of K ( A cos ) ( s + ) - ( A sin ) K = lim s + - j s - j + ( s + - j ) ( s + + j ) ( A cos ) ( s + ) - ( A sin ) = ( A cos ) ( j ) - ( A sin ) K = lim s - j + 2 j ( s + + j ) A cos + jA sin A A j K= = ( cos + j sin ) = e 2 2 2 5 The Values of A and K= A j e = K 2 A=2 K K = K f ( t ) = Ae - t cos ( t + ) u ( t ) f ( t ) = 2 K e - t cos ( t + K ) u ( t ) 6 Final Result K K* + 2 K e - t cos ( t + ) u ( t ) K s + - j s + + j p. 488, Eq. (12.64) 7 ...
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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 17 - ECE 202 Circuit Theory 2 Lesson 17...

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