# 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
2
0
Hi, everybody,

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
5,451
1,070

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
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3. ### xinyancode Thread Starter New Member

Sep 22, 2015
2
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......

Oct 2, 2009
5,451
1,070
Not likely: