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Quick question regarding some algebra?

  1. Jan 29, 2013 #1
    The gain of an internally compensated op amp may be expressed by

    Equation 1) A(s) = A0 / ( 1 + s/[itex]\omega[/itex]b) where [itex]\omega[/itex]b is the 3dB frequency or "break frequency" and A0 is the dc gain.

    Plugging in s=j[itex]\omega[/itex] and [itex]\omega[/itex] = 2*pi*f gives

    Equation 2) A= A0 / (1 + j*f / fb) where fb is still the "break frequency"

    I understand how all of that works.

    What I don't understand is how you can go from Equation 2 to this:

    Equation 3) A = A0 / sqrt( 1 + (f/fb)^2).

    I hope all of this makes sense and someone can help me. Thank you.
  2. jcsd
  3. Jan 29, 2013 #2


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    Staff: Mentor

    That's the magnitude of the complex gain... See Equation #9 here for example:

    http://cheme.eng.wayne.edu/neuron/auth/ece3310/experiment_12.htm [Broken]

    Last edited by a moderator: May 6, 2017
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