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

 

This any help?

 

Chapter 2 of this book covers some equation derivations.

 

It is a lot of information but there has been no direct feedback to what I put up...

 

What are your handwavium steps denoted by ":"?

 

Intermediate steps

 

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.

 

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...??

 

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

Can you post a schematic of the third-order Butterworth low-pass filter circuit?

hgmjr