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
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    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
    5,448
    782
    You assume the circuit response has reached steady state.

    For the charging condition

    Vmax=Vmin+(5-Vmin)*(1-exp(-t/RC))

    For the discharging condition

    Vmin=Vmax*exp(-t/RC)

    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
    9
    0
    I got it. Thanks for your help. Your solution makes complete sense and I'm not sure how I missed that before.
    Thank you!
     
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