# Butterworth

Discussion in 'Homework Help' started by Cerkit, Apr 16, 2009.

1. ### Cerkit Thread Starter Active Member

Jan 4, 2009
275
3
Hi. I have to derive the transfer function of a third order Butterworth low-pass filter with cutoff frequency 200 Hz. is the following correct?

(|H(jω)|^2)= 1/(1+ω^2n)

let ω=s/j

H(s).H(-s)=1/(1+(s/j)^2n)=1/(1+((-j)^2n).(s^2n))
:
:
:
:
H(s)=1/(1+s^6)

if this is correct how does the extraction of the H(s) bit occur from the H(s).H(-s). Please can someone explain to me. Thanks

Feb 10, 2009
262
11
3. ### thatoneguy AAC Fanatic!

Feb 19, 2009
6,357
718
Chapter 2 of this book covers some equation derivations.

4. ### Cerkit Thread Starter Active Member

Jan 4, 2009
275
3
It is a lot of information but there has been no direct feedback to what I put up...

5. ### thatoneguy AAC Fanatic!

Feb 19, 2009
6,357
718
What are your handwavium steps denoted by ":"?

6. ### Cerkit Thread Starter Active Member

Jan 4, 2009
275
3
Intermediate steps

7. ### thatoneguy AAC Fanatic!

Feb 19, 2009
6,357
718
Can you post the intermediate steps?

Or do you have the question, and answer, but not the middle part?

The intermediate steps imply you worked through the formula to get to that answer.

8. ### Cerkit Thread Starter Active Member

Jan 4, 2009
275
3
The question is "Derive the transfer function of a third order Butterworth low-pass filter having a cutoff frequency equal to 200 Hz".
What I have put is as far as I get through reading notes on filters. I don't know if it is correct. The intermediate steps are large jumps i have made which are jumps in calculations also in my notes.
Therefore not sure if my answer is right and if it is what the exact steps are...??

9. ### hgmjr Moderator

Jan 28, 2005
9,030
214
Can you post a schematic of the third-order Butterworth low-pass filter circuit?

hgmjr