Simple inverse Laplace using PFE not so simple?

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    Inverse Laplace
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Discussion Overview

The discussion revolves around the evaluation of the step response of a circuit using Laplace transforms and partial fraction expansion. Participants are exploring the relationship between the Laplace representation and its time-domain equivalent, as well as the challenges faced in applying partial fraction expansion to arrive at the correct solution.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant presents the Laplace representation of the step response as $\frac{I_{pd}}{s^2 C1 R1}$ and notes that it corresponds to $\frac{I_{pd}*t}{C1 R1}$ in the time domain.
  • Another participant requests clarification on the expression due to difficulties in reading the notation, suggesting it resembles a step function.
  • A later post clarifies the expression as $\frac{Ipd}{R1*C1*s^2}$ and reiterates the time-domain result of $t*Ipd/(R1*C1)$, while expressing difficulty in using partial fraction expansion to derive this result.
  • Finally, one participant indicates they have resolved their issue without elaborating on the solution.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the method of using partial fraction expansion, as one participant expresses confusion while another claims to have solved the issue independently.

Contextual Notes

There are limitations in the clarity of the mathematical expressions presented, as well as potential misunderstandings regarding the application of partial fraction expansion. The discussion does not resolve these issues.

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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