[sdiy] Figureing out Buchla timbre waveshaper

[Aaron Lanterman]

On Tue, 15 Nov 2005, Barry Klein wrote:

> How about someone put a soundfile up somewhere showing why this circuit is
> so special.  What characteristics of the sound make it a "gotta have"?  How
> is it generally used in a modular patch etc.

That would be very cool, to have an example of what it sounds like as the 
symmetry and timbre parameters are swept.

Buchla soundfiles seem rare - the best example of an Easel in full glory 
is Charles Cohen's stuff - but there aren't many (any?) examples of the 
various bits in isolate.

For that matter, I've been dying to hear examples of the 200e.

> We focus our discussions so much on circuitry but little on the resultant
> sounds that result and what people like about them.

I'm hoping to make progress figuring out the circuit so I can make a 
software simulation of it that everyone can play with. ;)

There appear to be several versions of the Buchla waveshaper. I've come 
across two different schematics claiming to be 259's (both in 
Buchlascript). One is more complex that the other - one seems to have 
various electronic switches not in the other. In any case, the waveshaper 
circuitry in both looks to be the same at first glance - it's the version 
with separate symmetry (offset going into shaper) and timbre (gain going 
into shaper) controls. The Music Easle (208) has another version of thee 
circuit, which only has timbre, not symmetry (so it has one fet instead of 
two.

The basic structure of waveshaping and summing sections of the two 
versions is the same, but the Easel and 259 versions have different 
resistor choices. It appears the Easel version is supposed to spit out .8v 
pp, and the 259 version spits out 2.2 v pp.

The 259 version has an odd bit at the bottom of the waveshaper, where it 
has a 10K resistor and a 100 pf capacitor that goes to - a picture of a 
sine wave??? This makes no sense, as the sine wave clearly goes into the 
waveshaper in the upper left part of the diagram. There's no similar 
notation on the Easel version. Not sure what that is.

The Easel version is interesting since some of the "resistors" in the 
summing amps at the end appear to be made of big and small resistors in 
parallel. It makes me think Buchla started with a basic design, and 
started throwing in other resistors to tweak the values until he got 
something he liked.

Oh... here's another interesting difference. The 259s use this CA3160 
single op amp with p/m 6 volt supplies. Several people have noticed is 
interesting due to its use of MOSFET inputs and CMOS outputs:

http://www.intersil.com/data/fn/fn976.pdf

But, the Easel version uses a quad op amp RC4136, which appears to be a 
garden variety bipolar op amp:

http://wwww.ges.cz/sheet/r/rc4136.pdf

Curiouser and curiouser... Even more curious is the fact that the Easel 
schematics give no clue what the supply voltages on the RC4136s should 
be!!!!! So if one of the tricks here is running the op amps with low 
supplies to form clipping, this one would be hard to figure out...

When Buchla drew the schematics, I wonder if he knew a young ECE prof in 
Atlanta would be trying to figure them out one day, and as he drew them he 
cackled with glee...

---------------------------------------------------------------------------

Anyway, here's my analysis so far:

There's five shaping op amps, but at the bottom there's a sixth length, 
which is the sine wave just passing through. If I were to number the 
op amps from bottom to top and represent their nonlinearities as f1, f2, 
f3, f4, and f5, I think we're computing this:

a0 x + a1 f1(x) + a2 f2(x) - a3 f3(x) - a4 f4(x) - a5 f5(x).

The original signal and the f1 and f2 are premixed in an inverting
mixer, and then that gets mixed with f3 f4 and f5 in an inverting mixer.

I can figure out the a's from the resistor values.

What I'm still scratching my head on a bit is the nonlinearities, which 
have a structure like:

in----R1--+------------------+--- out
           |                  |
           |   \              |
           |   |\             |
           +---|+\            |
               |  \           |
               |   \          |
               |    |---R2----+
               |   /
               |  /
  gnd-resistor-|-/
               |/
               /

What I was expected to see where was R2 along the top, so it would be a 
standard inverting amp with R2 and R1 setting the gain deliberately to hit 
the +/- 6 volt rails (or whatever they are in the Easel), making a 
saturating circuit. I could see how adding those up in the right way would 
make a zig-zag transfer function.

However, with R2 where it is, if I apply my usual op amp rules, that puts 
the output at ground, which makes no sense. So this must be a case where I 
can't apply my usual op amp rules so I'm outside my comfort zone.

Nontheless, I soldier on. I assume it's a nonideal op amp with a 
noninfinite gain of A. Analyzing the above circuit, I come up with

vout = vin R2 / (R2 - R1(A+1))   (Eq. 1)

As a sanity check, I see as a -> infinity, vout approaches zero which is 
as I would expect using my usual gain rules.

Let's see what the gain of the CA3160 is. It appears to be... 320 kV/V
"typical," and 50 kV/V, min, but still, that makes by A = 50,000 to 
320,000, which makes by coefficient in (Eq. 1) really ___small___.

The RC4136 is listed as having gains of 20,000 (min) and 300,000 (max).
I'm afraid I may be going in the wrong direction...

One SDIYer wrote me noting that "the output stays near the virtual earth, 
until the output reaches the rails and it's not at virtual earth anymore." 
I believe there is insight there but I don't see it yet.

Anyway, I'm going to put it to bed for the moment lest my analysis take me 
in a wrong direction.

As usual, any insights appreciated!

- Aaron

-----------------------------------------------------------------------------

Dr. Aaron Lanterman, Asst. Prof.       Voice:  404-385-2548
School of Electrical and Comp. Eng.    Fax:    404-894-8363
Georgia Institute of Technology        E-mail: lanterma at ece.gatech.edu
Mail Code 0250                         Web:    users.ece.gatech.edu/~lanterma
Atlanta, GA 30332                      Office: GCATT 334B