1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differential Eqn. of a 3rd order Filter

  1. Aug 2, 2012 #1
    Hi guys :) I'm going through some prep. work for my modules in Fall and I've come across a question I'm having some difficulty with.

    1. The problem statement, all variables and given/known data
    The question has a transfer function for which I need to find the differential equation relating the output voltage and the input voltage.


    2. Relevant equations
    Transfer function: H(s) = 15/(s3 + 6s2 + 15s + 15)


    3. The attempt at a solution
    I created the above circuit using a 3rd order sallen-key lowpass filter as in this website:http://sim.okawa-denshi.jp/en/Sallenkey3Lowkeisan.htm. I then split the circuit into 3 parts - A,B,C.

    I then deduced 3 voltage equations for the 3 nodes using kirchoffs circuit laws as follows;

    Va = (Va-Vin)/Z1 + (Va-Vb)/R2 + (Va-Vout)/Z2 = 0

    Vb = (Vb-Va)/R2 + (Vb-Vout)/Z2 + (Vb-Vc)/R3 = 0

    Vc = (Vc-Vb)/R3 + (Vc-0)/Z3 = 0

    where Vc = Vout.

    Are the above equations correct? I'm not very comfortable with 3rd order circuits as of yet, and am not sure if I got the equations right. I've gotten to this point, but after this I'm not sure what I need to do. If I simply the above equations I will get the transfer function, but that's not what I want to find, how do I proceed from here?
     
  2. jcsd
  3. Aug 2, 2012 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    If you're trying to derive the diff. eq. for the given transfer function, what are you doing with Sallen-Key filters???

    A transfer function is readily transposed to a diff. eq. since s → d/dt. Take it from there ....
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Differential Eqn. of a 3rd order Filter
Loading...