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Unit step response of RC high pass filter

  1. Oct 19, 2012 #1
    what is the unit step response of a high pass RC filter ?
    I want to calculate using transfer function approach.
    My solution :
    Y(s)/X(s) = RCs/(1+sRC)

    X(s)=1/s
    Y(s)=RC/(1+sRC)
    taking inverse laplace transform we should get
    y(t)=exp(-t/RC)


    But if we consider Y(s)=RC/(1+sRC)
    RCsY(s) + Y(s) = RC
    then this is a non homogeneous equation
    so the solution should contain a dc term also which is a complementary function.
    but the previous solution i have written above does not contain the dc term.
    Please clarify this........
     
  2. jcsd
  3. Oct 19, 2012 #2
    y(t)=exp(-t/RC)
     
  4. Oct 20, 2012 #3
    erece,

    The inverse Laplace of RCs/(1+sRC) is Dirac(t)-exp(-t/RC)/RC, not what you posted.

    Ratch
     
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