why do I get a different transfer function of Butterworth filter

Discussion in 'General Electronics Chat' started by xinyancode, Sep 22, 2015.

  1. xinyancode

    Thread Starter New Member

    Sep 22, 2015
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    0
    Hi, everybody,

    upload_2015-9-23_7-32-13.png
    I have deduced several times for the transfer function of 3rd order Butterworth low pass filter, but the transfer function I got is
    vo(s)/vi(s) = 1/( 2S^3 + 4S^2 + 4S + 2 )

    while the transfer function of this filter in textbook and many document is
    vo(s)/vi(s) = 1/( S^3 + 2S^2 + 2S + 1 )

    I don't know what the problem is in my deduction, can anyone help me?
     
  2. MikeML

    AAC Fanatic!

    Oct 2, 2009
    5,450
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    117.gif
    V(out) = V(yours); V(b00k) is wrong.

    You can see that yours is more realistic. Think about what happens at low frequency; R1,R2 create a voltage divider of 1/2.
     
    Last edited: Sep 22, 2015
    xinyancode likes this.
  3. xinyancode

    Thread Starter New Member

    Sep 22, 2015
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    0
    Hi, MikeML,

    thank you so much for your help, I come to understand more about this problem. and your simulation is great, I will also learn to use LTSpice, it seems very powerful.

    yet, I am still a little confused on why there is the gap between the two transfer function. Is it possible that other people consider the transfer function based on voltage source with the 1 ohm internal resister, while I only consider the ideal voltage source.

    thank you again......
     
  4. MikeML

    AAC Fanatic!

    Oct 2, 2009
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    Not likely:

    117a.gif
     
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