Results 1 to 3 of 3

Math Help - Inverse of this transfer function

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    92

    Inverse of this transfer function

    Hi,

    I have the transfer function for a particular configuration on an RLC circuit:

    H(s) = sRC/(LC*s^2 + sRC + 1)

    R, L, and C are constant. I want to transform it back to the time domain. Is there a standard transform pair I can match this to?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member yeKciM's Avatar
    Joined
    Jul 2010
    Posts
    456
    Quote Originally Posted by algorithm View Post
    Hi,

    I have the transfer function for a particular configuration on an RLC circuit:

    H(s) = sRC/(LC*s^2 + sRC + 1)



    R, L, and C are constant. I want to transform it back to the time domain. Is there a standard transform pair I can match this to?

    Thanks.
    as a matter a fact there is but it's based on your  s^2 LC + s RC +1 depends on which from 3 types will you use

    is it  B^2 < 4AC or  B^2 > 4AC or  B^2 = 4AC

    i had have it here on the desk but now... lol try google it, and soon as i find it i'll edit this post... (now i'm confused... like it has just disappeared )

    P.S. look for table of inverse Laplace transformations (there should be like 60 or so formulas for different types ... )
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member yeKciM's Avatar
    Joined
    Jul 2010
    Posts
    456
    okay this what i have

    for type :

     \displaystyle \frac {mS+n}{AS^2+BS+C}


    where those with S are just any numbers (this is type that is what you need just put n=0, and you will get that function in time domain)


    \displaystyle \frac {RCS}{LCS^2+RCS+1} \Rightarrow m=RC ; n=0 ; A=LC; B=RC; C=1


    now you have 3 different formulas depending on values of your A,B,C



    if  B^2>4AC than you will use :

    \displaystyle h(t)= e^{-at}(\frac {m}{A} \cosh {\omega_0 t} + \frac {n-am}{A\omega_0} \sinh{\omega_0 t})

    where \displaystyle a=\frac {B}{2A} and \displaystyle \omega_0 = \sqrt{a^2- \frac {C}{A}}





    if  B^2=4AC than you will use :

    \displaystyle h(t)= e^{-at}(\frac {m}{A} + \frac {n-am}{A}t)

    \displaystyle a=\frac {B}{2A}






    if  B^2<4AC than you will use :

    \displaystyle h(t)= e^{-at}(\frac {m}{A} \cos {\omega_0 t} + \frac {n-am}{A\omega_0} \sin{\omega_0 t})

    where \displaystyle a=\frac {B}{2A} and \displaystyle \omega_0 = \sqrt{\frac {C}{A} - a^2}



    there are "little" different formulas if you need to do this one for example :

     \displaystyle \frac {mS^2+nS+q}{S(AS^2+BS+C)}

    so if you need that or any another, just say
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Transfer Function Help
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: July 22nd 2011, 09:37 AM
  2. differential eq to transfer function
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: April 4th 2010, 05:25 AM
  3. transfer function
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: January 29th 2010, 01:07 AM
  4. ODE to transfer function
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: September 14th 2009, 06:05 AM
  5. Transfer Function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 12th 2008, 12:53 PM

Search Tags


/mathhelpforum @mathhelpforum