Pulse Response Homework Help

Discussion in 'Homework Help' started by testing12, Mar 19, 2011.

  1. testing12

    Thread Starter Member

    Jan 30, 2011
    Hello everyone,
    I have yet another question reguarding pulse response:

    I need some help determining i(infinity). I have tried mesh analysis for il and tried using VL = L di/dt but i got an answer as a function of the derrivative of u(t).
    I have 2 problems with the solution:

    1) why can we assume u(t) is 0 at t=0, its an unknown function.

    2) how do they get i(infinity)
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    u(t) is often referred to a s the Heavyside function which is defined as

    u(t)=0 for t<0 and u(t)=1 for t>=0

    For i(∞) simply consider the inductor as a short and solve the circuit as if it were a purely DC circuit.

    The problem you posted doesn't appear to explicitly state the value of Vs. Was this given in the problem somewhere?
  3. testing12

    Thread Starter Member

    Jan 30, 2011
    ok i got it, but i have some problems with it:

    How can they assume that as iL(0) =0 and Vs(infinity) = 9 volts.
    when u(t) is there, its like it was completly ignored, then added in the final answer.
  4. testing12

    Thread Starter Member

    Jan 30, 2011
    quick reply t n k, i posted at the same time as you :)

    thank you sir!

    NOTE: yes Vs was given in the problem to be 9u(t) volts and i was asked to solve Vo (t).

    Thanks for the information reguarding u(t), i had no idea what that was!! I will think of it as the on/off switch at t=0.
    note for student reading this: http://en.wikipedia.org/wiki/Heaviside_step_function
    Very interesting!

    final note: i should also mention the solution manual is slightly older then the edition of my text and my text has the solution as
    vo(t) = 3e^(-4t) u(t) volts, which is what i got when i solved.
    Last edited: Mar 19, 2011