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Consider the following partial fraction expansion: $$ H ( s ) = \sum _ { k = 1 } ^ 2 \frac { A _ k } { s - p _ k } = \frac { A _ 1 } { s - p _ 1 } + \frac { A _ 2 } { s - p _ 2 } $$ $$ \frac { 0.264 } { s ^ 2 + 0.513 s + 0.33 } = \frac { A _ 1 } { s - ( - 0.256 + j 0.514 ) } + \frac { A _ 2 } { s - ( - 0.256 - j 0.514 ) } \\ = \frac { 0.257 j } { s - ( - 0.256 + j 0.514 ) } - \frac { 0.257 j } { s - ( - 0.256 - j 0.514 ) } $$

When I solved I got $ A _ 1 = - 0.257 j $ and $ A _ 2 = 0.257 j $.

For finding $ A _ 1 $, I put $ s - ( - 0.258 + 0.514 j ) = 0 $.

For finding $ A _ 2 $, I put $s - ( - 0.258 - 0.514 j ) = 0 $.

Am I right or wrong? Please tell.

Mohsen Shahriari
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abdulkhan
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1 Answers1

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Your answer is correct, you should obtain $A_1= -0.257j$ and $A_2=-A_1=0.257j$.

For the solving itself, I do not quite understand what you mean by "I put $s-(-0.258+0.514)=0$" as you cannot put a denominator equal to zero. Anyway, in this case, you find easily $A_1$ and $A_2$ by comparing the first and second lines of the right-hand side of your equation, and matching the numerators of the fractions with the same denominator.

user115805
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