RC Circuit Pulse Excitation

Discussion in 'Homework Help' started by blah2222, Jan 23, 2011.

  1. blah2222

    Thread Starter Well-Known Member

    May 3, 2010
    554
    33
    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
     
  2. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    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).
     
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