Simple inverse Laplace using PFE not so simple?

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    Inverse Laplace
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SUMMARY

The discussion centers on evaluating the step response of a circuit represented by the Laplace transform $\frac{I_{pd}}{s^2 C1 R1}$. The user initially struggles with obtaining the time-domain representation $\frac{I_{pd}*t}{C1 R1}$ using partial fraction expansion (PFE). Ultimately, the user resolves the issue independently, indicating that the correct transformation involves recognizing the expression as a step function. The key takeaway is the importance of understanding the relationship between Laplace transforms and their time-domain counterparts.

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jrive
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Hello,

When evaluating the step response of a circuit, the resulting Laplace representation is:
$\frac{I_{pd}}{s^2 C1 R1}$

If I look this up on a table of Laplace Transforms, this results in $\frac{I_{pd}*t}{C1 R1}$.

However, I'm struggling to solve this via partial fraction expansion--is there a special trick or step I need to take that would enable me to arrive at the same solution? I don't see where I'm going wrong.

Thanks!
 
Last edited:
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jrive said:
\frac{I_{pd}R,sC1R1}
I cannot read this. please write it in another way. It seems to be something like:

IR / (C1*R1) * ( 1 / s ) which is simply a step function.
 
Sorry, my latex is rusty and i can't figure out how to make it work.
So, here it is directly Ipd/(R1*C1*s^2).

In time domain, this results in t*Ipd/(R1*C1). My problem is I can't seem to get there via partial fraction expansion...
 
Last edited:
Never mind, i figured it out...
 

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