Transfer Function Mid-band Gain & Open Circuit/Short Circuit Time Constant Method

  1. Hey guys,

    I recently had a quiz on


    Circuit is attached in photo below.

    T(s) = (A)(s/s+20)*(s/s+200)

    **All values of R in the circuit attached are 2000 ohms.
    and C1>C2


    a. find the mid-band gain A.

    I do not know how to start this question... Can anyone give me an idea of where to start.



    b. find values of C1 and C2

    For this problem I got a little confused when applying OCTC and SCTC

    Firstly, would 200 be my upper corner frequency? If so,

    200 = 1/(Rth*Ci)

    Where Rth= thevenin resistance, and Ci = the capacitor we wish to analyze the effect of the pole.

    So basically, I open circuit C2 and I short circuit C1 and find the thevenin resistance from C1.

    Can anyone confirm if this is correct?
     

    Attached Files:

  2. jcsd
  3. rude man

    rude man 5,755
    Homework Helper
    Gold Member

    a: s = jw, then remember how to get the max of a function from your elementary calculus.

    Actually, since the corner frequencies in this xfer fn are so far apart (10:1) you can get a close approximation of the mid-band gain by drawing the asymptotes on a Bode plot. Have you had Bode (frequency & phase) plots yet?


    b: without thinking about it more, I see no other way than to actually compute the transfer function of the network, then equate the constants in the given transfer function (i.e. 20 and 200) with the corresponding terms in the computed transfer fuction & solving some simultaneous equations. Perhaps your teach showed you a neater way.

    In practice one would look up the network in the appropriate tables!
     
    Last edited: Oct 8, 2011
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