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This is my RC integrator:

rc integrator

From my two different analysises:

$$ V_{out}(s) = V_{in}\dfrac1{sRC} $$

and

$$ V_{out}(t) = \dfrac1{RC}\int V_{in} dt $$

These are of course different as one is in the frequency domain and one in the time domain.

If I understand correctly, \$ \mathcal{L}\{V_{out}(t)\} = V_{out}(s) \$

However, Wolfram Alpha tells me \$ \mathcal{L}\{V_{out}(t)\} = V_{in}\dfrac1{s^2RC} \neq V_{out}(s) \$

What am I doing wrong?

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Your equations are correct, assuming initial conditions are zero, but your Vi should be Vi(s) in the first equation. I would guess that the Vin in Wolfram is a step of magnitude Vi, with Laplace transform Vi/s, which gives the Laplace output, Vout(s), in your final equation.

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  • \$\begingroup\$ ah of course it should be Vi(s). Looking it up somewhere else it gives me the right answer, so I guess Wolfram is just interpretting my input wrong. thanks \$\endgroup\$ – ACarter Apr 19 '15 at 17:29
  • \$\begingroup\$ Easy slip to make. Always wise to double check the results obtained from packages like Wolfram. \$\endgroup\$ – Chu Apr 19 '15 at 20:26
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It looks to me as it's interpreting Vin(t) as a constant Vin which has a transform of Vin/s.

The answer should include the Laplace transform of Vin(t).

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