Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. It only takes a minute to sign up.
Sign up to join this community
This is my 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?
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.
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).
