[sdiy] Passive filters and impedances

[Russell McClellan]

Hi Tom -

As Donald mentioned, these unbuffered filters are incredibly common in
synthesizers and music electronics in general, so it's a great thing
to be able to analyze painlessly.  For me, this is the perfect
application of a computer algebra package - these are simple equations
to solve for a computer, and as people have mentioned they are
error-prone to calculate by hand.  I have done a lot of these by hand,
and to be blunt, it's not a very enlightening activity.  Let the
computer do the drudgery.  I usually use SymPy, because, while a bit
limited, it's built into the python language so it fits into my
workflow, and it can be combined with numpy and matplotlib to make
pretty graphs.  A lot of people in the synth diy community use maxima
to great success, although I don't have much personal experience with
it.

For an example of how a computer algebra package helps with analyzing
these unbuffered filters, check out some work I did deriving transfer
functions for diode filters here (these are in "note to self" form -
please let me know if you have any questions about them - I hope to
expand them into a technical blog post in the near future)

https://gist.github.com/russellmcc/a6576721f2a394364bf2 - the
"plot_diode.py" file contains the approach you were starting down,
while "alternate_derivation.py" uses the kirkhoff's law approach.  It
turns out it's fewer lines of code to tell the computer to solve
kirkhoff's laws, but for me the impedance model is conceptually
similar.

Thanks,
-Russell

On Sat, Oct 31, 2015 at 7:24 PM, Donald Tillman <don at till.com> wrote:
>
>> On Oct 31, 2015, at 10:07 AM, Richie Burnett <rburnett at richieburnett.co.uk> wrote:
>>
>> In general we don't usually build filters like this because the lack of buffering causes loading effects that move the filter poles.
>
> That's how the Roland Diode Ladder filter works.
>
> And slight variations of simple RC ladders are used all over guitar amplifiers.  Like the "slope" control on the Marshall JCM 800 bass amp.  Or the weird tone controls in the Sound City amps.  The Gibson GA-40.  There are several other examples I'm not thinking of right now.
>
>   -- Don
>
> --
> Don Tillman
> Palo Alto, California
> don at till.com
> http://www.till.com
>
>
>
>
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