RC Circuit with Large Time Constant

Discussion in 'Homework Help' started by lvjudge1, Oct 15, 2009.

  1. lvjudge1

    Thread Starter New Member

    Jun 3, 2009
    I am working on a problem involving an RC circuit and I just cannot figure it out. The circuit consists of a voltage source, a 1k resistor and a 400nF capacitor connected in series. The source a 5V square wave source with on/off time of .5ms. Since the time constant of the circuit is .4ms, I know that the capacitor cannot fully charge/discharge before the input changes again.
    I have done a PSPICE simulation of the circuit, but I cannot figure out a mathematical equation to describe what is happening to the capacitor voltage. The graph of the capacitor voltage obtained from PSPICE is attached to this post.
    I have tried using the equations for vc charging(Vs*(1-e^(-t/RC))) and discharging (Vs*e^(-t/RC)), but they don't work because the relatively large time constant of the circuit does not allow the capacitor to charge up to 5V or discharge to 0V.
    How can I find the equation for capacitor voltage, both charging and discharging, when the RC time constant is greater than five times the on/off time of the source?
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    You assume the circuit response has reached steady state.

    For the charging condition


    For the discharging condition


    You then simultaneously solve for either Vmax or Vmin to satisfy the conditions at t=0.5ms and RC=0.4ms

    As a check you require that (Vmax+Vmin)/2=2.5V [the steady state average capacitor voltage]
  3. lvjudge1

    Thread Starter New Member

    Jun 3, 2009
    I got it. Thanks for your help. Your solution makes complete sense and I'm not sure how I missed that before.
    Thank you!