Solve RC Transfer Function with R=C=1

[alexmath]

Homework Statement

R = C = 1;

Homework Equations

G(S) = 1/(s+1)

The Attempt at a Solution

Suppose R = C = 1 then the transfer function from the input voltage to the voltage across the capacitor is 1/ (s+1). So Vc(S) / V(S) = 1/(s+1). Getting back to time-domain: Vc(t) = V(t) * e^-t. What's wrong here? It should have been V(t) ( 1 - e^-t ). Thank you!

 

[Svein]

How you connect R and C, where do you connect the input and where is the output? As it stands, the question is impossible to answer.

 

[alexmath]

I connect them in series like this: V ------- R ------- C ------- gnd, where V is the input, and Vc is the output.
http://en.wikipedia.org/wiki/RC_circuit#Transfer_functions
What i want is to get back from s-domain to time-domain.

 

[gneill]

Suppose R = C = 1 then the transfer function from the input voltage to the voltage across the capacitor is 1/ (s+1). So Vc(S) / V(S) = 1/(s+1). Getting back to time-domain: Vc(t) = V(t) * e^-t. What's wrong here? It should have been V(t) ( 1 - e^-t ). Thank you!

What's your V(t)? Suppose that the transfer function is U(s) = 1/(s + 1). You need to deal with V(s)*U(s) if you expect to find the time domain response Vc(t) via Vc(s) = V(s)*U(s).

It looks like you were looking for the time domain response of the circuit to a step function: V(t) = V*u(t).

 

[alexmath]

Thank you!