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Bode plot of type 1 system?

  1. May 9, 2012 #1
    For a transfer function of G(s) = 100 / (s(s+5)), I'm having trouble finding the initial magnitude in dB. It's a type 1 system. If it was a type 0 system with only (s+5) in the denominator, the initial magnitude would be 20log(nominator/denominator) where s is an element of 0, and would decrease by 20 dB per decade. For the system 1, the magnitude should decrease by 40 dB each decade. However, most transfer functions which I've bode plotted in wolfram alpha, appear to have a slightly damped slope until it reaches 0 db, before decreasing at a steady rate of 40dB.

    Care to explain how I find the initial magnitude?

    [This is NOT homework, but research of (art of) bode plotting transfer functions with denominator of higher order]
  2. jcsd
  3. May 17, 2012 #2


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    Staff: Mentor

    G(s) = 100/(s² + 5s)
    Let s ← jѠ

    G(s) = 100/(-Ѡ² + j5Ѡ)

    amplitude = 100/ √(25Ѡ² + Ѡ⁴)
          = 100/(5Ѡ √(1 + Ѡ²/25)) 

    At low frequencies where Ѡ « 5, amplitude ≈ [PLAIN]https://www.physicsforums.com/images/icons/icon5.gif [Broken] [Broken][PLAIN]https://www.physicsforums.com/images/icons/icon5.gif [Broken] [Broken]

    How many dB/decade will the slope of this be in the region Ѡ « 5?
    Last edited by a moderator: May 6, 2017
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