[sdiy] Basic 4th order LP butterworth filter papers

[ASSI]

On Friday 05 February 2010, Karl Ekdahl wrote:
> I'm looking for info on the basic building blocks of an *active*
> 4th order butterworth LP filter, so far the internet has given me
> nothing. If anyone have any pointers i'd sure appreciate it!

Don Lancaster and most other sources would suggest two cascaded second 
order sections.  For Butterworth response the cutoff frequency in each 
section is identical, while the gain/damping is not.  The required 
filter response for two second order sections can be gleaned from: 

http://en.wikipedia.org/wiki/Butterworth_filter

If you absolutely need a true fourth order section you'll probably 
start with a ladder filter prototye (now known as Cauer, but 
originally introduced by Campbell) and then either use actual L and C 
or synthesize the L with an impedance converter.  At the end of the 
page above you'll find a link to Butterworth's original paper which 
deals with exactly this situation.  Note that Butterworth talks about 
the magnitude of the transfer function and hence all exponents are 
scaled by two (fourth order => x^8).  The L/C values are also given 
explicitly here:

http://www.rfcafe.com/references/electrical/butter-proto-values.htm

Some online Design & Simulation resources:

http://www.bessernet.com/articles/lowpfilt/bwfiltstep00.html
http://astro.u-strasbg.fr/~koppen/radio/Activee.html
http://www-users.cs.york.ac.uk/~fisher/lcfilter/


Achim.
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