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Factoring transfer funtions

  1. May 6, 2012 #1
    Hi all. I'm trying to relearn S-plane analysis and filter transfer functions. What I'm having problems with is simple algebra i think, because it's been a while. Right now I've been reading http://www.ee.up.ac.za/main/_media/en/undergrad/subjects/eli220/polezero.pdf. What I'm confused about, among other things, is factoring the transfer function H(s).
    In their example:

    H(s) = [itex]\frac{2s + 1}{(s^2 + 5S + 6)}[/itex]


    H(s) = [itex]\frac{1}{2}[/itex] [itex]\frac{s+1/2}{(s+3)(s+2)}[/itex]

    I don't understand how they get that. The way I see it, because:
    2s+1 = 2(s+1/2)
    [itex]s^{2}[/itex]+5s+6 = (s+3)(s+2)

    H(s) = [itex]\frac{2s + 1}{(s^2 + 5S + 6)}[/itex] = [itex]\frac{2}{1}[/itex] [itex]\frac{s+1/2}{(s+3)(s+2)}[/itex]

    Also It seems that:

    [itex]\frac{2s + 1}{(s^2 + 5S + 6)}[/itex] ≠ [itex]\frac{1}{2}[/itex] [itex]\frac{s+1/2}{(s+3)(s+2)}[/itex]

    So I guess what I don't understand is why it seems that instead of factoring out 2 from the numerator, we are dividing the numerator by 2 and multiplying the denominator by 2.

    Can someone please set me straight. I know I did this a few years ago and it seemed to make more sense then, than it does now.

    Thanks a lot.
  2. jcsd
  3. May 6, 2012 #2


    User Avatar

    Staff: Mentor

    Hi FrankJ777. The explanation is quite simple: you are right and they are wrong. :smile:
  4. May 7, 2012 #3
    Really? I hope that's the case. Too bad I wasted several study hours trying to get it.

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