( + C2) s
------------------------------------------------------------------------------
( + C2 + C3 + C4) s
( + C2 C1 R1 + C3 C1 R1 + C4 C1 R1 + C3 C2 R1 + C4 C2 R2 + C4 C2 R1 + C4 C3 R2) s^2
( + C4 C2 C1 R1 R2 + C4 C3 C1 R1 R2 + C4 C3 C2 R1 R2) s^3
Here is what you did wrong.I plugged in some typical values for the caps and resistors into the transfer function and calculated the coefficients for the Laplace terms. I came up with this:
View attachment 142012
I then plugged that into an inverse Laplace engine at www.symbolab.com and got this:
View attachment 142014
In case that's not readable, the equation is 4406849 * e(-18933377 * t)* sin(6322814 * t). If I'm using this correctly, then Vout(t) = Vin * 4406849 * e(-18933377 * t)* sin(6322814 * t).
The inverse laplace transform is the system response to a dirac pulse, but you are asking for the step response.I'm not sure what you mean by "calculate the impulse instead of the step response"
Depends on what you consider steady state. It reaches 0.999 of final value in about 0.5 us. Everything under the ideal assumption of infinite output load resistance.So the circuit reaches steady state in about 0.15 us.
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