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Homework Help (Signal Processing)

  1. Feb 1, 2008 #1
    Hello All, I am currently taking Signal Processing & Linear Systems. Ive come across my last problem for homework but cant find a way to do it. If someone can show me in the right direction it will be very helpful.

    Thanks

    The Problem:
    The voltage f(t) = 2u(t) is applied to the circuit shown in the figure below. The
    initial inductor current is i(0) = 2mA.

    250mH
    |-----mmm------| +
    f(t) ( ~ ) i(t)--> Z 500 Ohms y(t)
    |______________| _

    a) Find the zero-input response yzi(t) of the system.
    b) Find the zero-state response yzs(t) of the system.
    c) What is the total response y(t) of the system?

    so far all i can get is the differential needed, but im not even sure if its right:
    f(t) = 250mH*Ldi/dt + 500*i(t) --> 250mH D + 500y(t)

    any help trying to finish this problem would be great thanks again!

    Ajay
     
    Last edited by a moderator: Feb 1, 2008
  2. jcsd
  3. Feb 1, 2008 #2

    CEL

    User Avatar

    The value of the inductor L is 250mH = 0.25H, so your first term is redundant. You should have:
    [tex]0.25\frac{di}{dt}+500i=f(t)[/tex]
    with the initial condition [tex]i(0)=2\times10^{-3}[/tex]
    To find the zero input response you solve the homogeneous equation (f(t)=0) and replace the initial condition [tex]i(0)=2\times10^{-3}[/tex] in order to eliminate the integration constant.
    To find the zero state response you solve the non-homogeneous equation (f(t)=2u(t)) and replace the initial condition [tex]i(0)=0[/tex] in order to eliminate the integration constant.
    The total response is the sum of yzi and yzs.
     
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