Hi, I just have a quick question regarding a simple circuit with a resistor and capacitor both in series with a voltage source. The only trick to this question is that the voltage source is a pulse excitation where it can be anything.

The easy part is deriving the differential equation for the capacitor voltage:

\(\frac{dV(t)}{dt} + \frac{V(t)}{RC} = \frac{Vs(t)}{RC}\)

From this we use the integrating factor method to bring us to this:

\(V(t)*exp{\frac{t}{RC}} = \frac{1}{RC}\int{Vs(t)*exp{\frac{t}{RC}}dt}\)

Thing is, how do I use this if I'm given an input Vs(t) that is not a "normal" function of time.

Hope my question was clear, I'll try to post up an example of an input, soon.
JP

 

Integration doesn't need a continuous or smooth argument. For example this is valid: \(\int^{\inf}_{-inf} \delta (t-\tau) \cdot f(t) d t = f(\tau).\)