[sdiy] Analysis of Buchla 259 amplitude modulation circuit

[Aaron Lanterman]

Because of an apparent masochistic streak, I'm currently trying to  
decipher the Buchla 259. Right now I'm checking out the amplitude  
modulation circuitry, which is essentially the last thing that gets  
applied. Gaze here:

http://rubidium.dyndns.org/~magnus/synths/companies/buchla/Buchla_2590_4_200.jpg

I'm looking primarily in the middle - there's a circuit with a dual  
vactrol, with a 0-5V CV from the modulation oscillator coming in,  
which I will call vi.

Denote the voltage at the junction of R272 and 273 as v*.

_If_ I assume "golden op amp rules" (this is iffy - see below), I get  
an equation from the currents summing at pin 5 of IC 34 (the +  
terminal of the op amp):

vi/49.9K + v*/20K = 15V/75K,

and for the v* node, I get

v*/(2K || R) = (15V - v*) / 30.1K, where R is the resistance of the  
vactrol.

After a veritable truckload of algebra, I get

R = 12Kohm * (10V - vi)/(5V + vi)

Fascinating! The vi determines the resistance R.

Let us define a "gain" from pin 1 of IC 33 to pin 7 of IC 3. This gain  
is given by

gain = -10K/115K + (1+10K/15K) * R / (R_trim+R),

where 10K < R_trim < 15K depending on how the pot is set.

Taking R_trim = 10K and plotting the gain in FreeMat (no, I didn't  
slog through more algebra), the result is remarkable - it looks like  
straight downward sloping lie going from 0.5 at vi = 0 volts to -0.04  
at vi = 5 volts. If I crank R_trim to 15K, I get something running  
from 0.36 to -0.19.

There's a second dual vactrol in the at the right, which controls how  
much of this AM signal gets mixed with an inverted version of the  
original signal, presumably to be able to crossfade from the original  
signal to a pure "ring mod" type sound if you get the original and  
inverted versions to cancel with at a high "index."

Two questions:

1) Let's talk about golden op amp rules. For those to hold, we need  
"negative feedback." First of all, the - terminal is grounded instead  
of the positive terminal, so that's suspicious - but then, this is  
clearly not being used like a comparator. Secondly, there's not any  
direct electrical connection from the output of the op amp back to the  
input.

Yet, the output of the op amp does effect the input through the LED/ 
resistor combination. I suspect the underlying feedback mechanism that  
I'm presuming is somehow inherentlly "negative," hence the need to  
back to the positive terminal.

The balanced modulator in the Music Easel has some similar kinds of  
craziness. And I've breadboarded that, and it works. (And some PCBs  
for it are on their way here from China now, but that's another story).

Am I on target? Anyone want to take a stab at making my handwaving  
more rigorous - rather than vigorous? ;)

2) Assuming all my analysis above works - and the results do make  
sense, it seems to do what it's supposed to - HOW THE HECK DID HE  
THINK OF THAT CIRCUIT?

- Aaron