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Stability and resonance

  1. Nov 4, 2005 #1
    Can a circuit that has transfer function with poles in right-hand side part of the imaginary-real plane (unstable system) have resonant frequency?
     
  2. jcsd
  3. Nov 6, 2005 #2

    berkeman

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    Staff: Mentor

    Sure. Several of my circuit designs had a resonant frequency that they kept wanting to find.... :-)
     
  4. Nov 7, 2005 #3

    SGT

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    No passive circuit can have poles in the RHP. An active circuit can have them and the output (assuming second order behavior) will be:
    [tex]ke^{\alpha t}cos(\omega_g t + \phi)[/tex], where [tex] \omega_g[\tex] is the resonant frequency.
    Theoretically this circuit will produce oscillations in the frequency [tex] \omega_g[\tex] with amplitude growing to infinity.
    In a real circuit, when the amplitude grows, non linearities arise and the circuit will oscillate with fixed amplitude. Only we would not have a sinusoid anymore, but a distorted waveform, whose fundamental frequency is [tex] \omega_g[\tex] .

    I donĀ“t understand why LaTex has not generated the correct image.
     
    Last edited by a moderator: Nov 7, 2005
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