how to derive transfer functon from bode plot?

Discussion in 'Homework Help' started by muhibraza, Dec 7, 2010.

  1. muhibraza

    Thread Starter New Member

    Dec 7, 2010
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    I have to find out the transfer function of an op amp based active filter using only its bode plot....how can i do this?
     
  2. tyblu

    Member

    Nov 29, 2010
    199
    16
    Hopefully you can assume the tf is of the form:

    Y = A*(s-z0)^a0*(s-z1)^a1 ... (s-zm)^am/( (s-p0)^b0*(s-p1)^b1 ... (s-pn)^bn )

    This is a generalized pole-zero statement. It denotes poles at all [p0, p1, ..., pn] and zeroes at all [z0, z1, ..., zm].

    From the magnitude plot you can pick out the critical frequencies -- those where the slop changes. Poles introduce a bi*(-20dB/dec) slope; simple zeros introduce ai*(+20dB/dec); where bi or ai are the order of that pole (a0, a1, ..., am, b0, b1, ..., bn).

    A Bode plot starts at s = jw = 0 (DC). This gives:
    Y = A*(z0)^a0*(z1)^a1 ... (zm)^am/( (p0)^b0*(p1)^b1 ... (pn)^bn ), a constant.
    The only unknown is A.
     
  3. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    tyblu likes this.
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