#### george2525

- Jan 30, 2015

- 170

- Joined
- Jan 30, 2015

- Messages
- 170

Hello,

I have been having issues with the butterworth squared magnitude function for a while. I understand it enough to use it but its derivation is causing me a headache and realy bothers me. If anyone understands it mathematically it would be good to get some pointers.

here are the typical Butterworth formulas in mosts texts.

Then comes the step where we should find the poles in the S domain. The following relation is often used:

I understand this

But what causes me confusion is that this is only true if

Then the following is used to formulate the pole locations (on a circle)

Here is where I get lost. If we set

And if not, then why not? it is never written that way.

Also if we have already discarded the real parts of any poles by initially setting S = jw, then how do they magically re-appear in H(s)H(-S) to trace the classic butterworth pole circle?

Maybe I have missed a mathematical rule somewhere?

I hope this question makes sense. If you are willing to help and need further clarification, please ask. Thanks to anyone who can help.

I have been having issues with the butterworth squared magnitude function for a while. I understand it enough to use it but its derivation is causing me a headache and realy bothers me. If anyone understands it mathematically it would be good to get some pointers.

here are the typical Butterworth formulas in mosts texts.

Then comes the step where we should find the poles in the S domain. The following relation is often used:

I understand this

But what causes me confusion is that this is only true if

**s = jw.**IE we have discarded the real parts of any poles (which we need)Then the following is used to formulate the pole locations (on a circle)

Here is where I get lost. If we set

**w = S/j****then doesnt |H(jw)|^2 become |H(S)|^2 ?**

And if not, then why not? it is never written that way.

Also if we have already discarded the real parts of any poles by initially setting S = jw, then how do they magically re-appear in H(s)H(-S) to trace the classic butterworth pole circle?

Maybe I have missed a mathematical rule somewhere?

I hope this question makes sense. If you are willing to help and need further clarification, please ask. Thanks to anyone who can help.