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Calculate the Laplace for the Ramp

  1. Nov 7, 2014 #1
    Hi, i am new to Laplace transforms/Algebra. I have been given a worked example by lecture to calculate the Laplace transform for a ramped input into a single pole RC high pass filter.

    i have managed to calculate the Laplace for the Ramp and the Laplace for the Filter. however i cant figure out how to get to the final answer. any help would be great.

    Dave

    a ramped voltage of 5000s/V is inputted into the filter. R = 10K and c= 1u.

    hi_pass_rc_sch.gif



    [itex] τ = RC = 0.01[/itex]

    [tex]\ T(L)= \frac{R}{R +\frac{1}{Jωc}} = \frac{JωRC}{JωRC +1} = \frac{Sτ}{Sτ+1} [/tex]

    [tex]\ Fin(L)= \frac{5000}{S^2}[/tex]

    [tex]\ Fout(L)= \frac{5000}{S^2} . \frac{Sτ}{Sτ+1}[/tex]

    The answer on the worked example is

    [tex]\ Fout(L)= \frac{5}{τ} . \frac{1}{S(\frac{1}{τ}+S)}[/tex]


    Any help on the steps to get to the final answer would be great :)

    Dave
     
  2. jcsd
  3. Nov 7, 2014 #2

    vela

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    The constant factor of 5 or 5000 probably has to do with the units you're working in. The rest is just basic algebra. Surely, you've made some attempt. Show what you did.
     
  4. Nov 8, 2014 #3

    rude man

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    Meaning 5000V/s I presume.
    What you did was correct. The given answer is wrong. The final answer, in any consistent units, must be of the form
    Vout(s) = k/s(s + 1/T).
    k being the ramp input rate, V/s
    T = RC
    BTW make your "s" lower case, not upper.
     
    Last edited by a moderator: Nov 12, 2014
  5. Nov 9, 2014 #4
    Thanks for the two replies, i will speak to the lecturer on Thursday to see why he gave the answer he did.

    I would still like to understand how he ended up with the final answerr, just so i can improve my basic algebra. I have had an attempt but quite quickly get stuck

    [tex]\ Fout(L)= \frac{5000}{s^2} . \frac{sτ}{sτ+1}[/tex]

    [tex]\ Fout(L)= \frac{5000}{s^2} . \frac{sτ}{τ(\frac{1}{τ}+s)}[/tex]

    do both the τ cancel out ? leaving


    [tex]\ Fout(L)= \frac{5000}{s^2} . \frac{s}{(\frac{1}{τ}+s)}[/tex]
     
  6. Nov 9, 2014 #5

    NascentOxygen

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    Now cancel that numerator s with one in the denominator.
     
  7. Nov 9, 2014 #6
    so now i have

    [tex]\ Fout(L)= \frac{5000}{s} . \frac{1}{(\frac{1}{τ}+s)}[/tex]

    but how do i get the s to the denominator on the other side and where does the denominator τ come from ?
     
  8. Nov 9, 2014 #7

    rude man

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    You don't. It's still wrong.
     
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