[sdiy] Deciphering the Buchla 259's expo converter

[Aaron Lanterman]

Greetings! This is Aaron Lanterman, the GaTech professor that taught a  
class called "Theory and Design of Music Synthesizers" a couple of  
times a couple of times during 2006.

I'm running the class again, somewhat modified, this semester, under  
the name "Electronics for Music Synthesis." Alas, I don't have the  
website for the class really set up yet. I will post here when I've  
done so. In the meantime, I've been recording the lectures with a  
cheap camcorder and posting them on blip.tv under the username  
"abovenyquist." Stop by and enjoy. (It's blip.tv, not blip.tv.com - I  
think you can get it from abovenyquist.blip.tv, or go to blip.tv and  
search on the username abovenyquist.) You can also find lectures from  
my Fall 2007 class, "Multicore and GPU Programming for Video Games,"  
if your interested in that sort of thing - I've been spending many  
months knee deep in things like shader programming and the Cell  
processor, which is why I'd dropped out of looking at synths for a  
while.

Anyway, last time I did the class, I analyzed the core of the Buchla  
259 in lecture as an example of a triangle-core VCO. I talked about  
the discrete OTA, the comparitor, the integrator, etc., and then  
handwaved and said "look, here's the expo generator."

This time I'd like to actually do the expo generator. I'm pretty well  
versed in Buchlaese by this point (and I teach Buchlaese, i.e. how to  
read his schematics, to my students), but this one has me confused.

I'm looking here:

http://rubidium.dyndns.org/~magnus/synths/companies/buchla/Buchla_2590_2_200.jpg

So, I'm looking at R122, R123 and R123A. R122 is a 1K tempo, R123  
appears to be 68K but it's hard to read from the schematic, and R123A  
is 121K. R122 and R123 form a typical divide down ladder before the  
base of an expo-converting differential pair. R123A is tied up to +15  
for reasons that befuddle me - I'm not sure why you'd mix in something  
here instead of mixing it in at the inverting op amp.

Anyway, I'm guessing that 121K in parallel with 1K is sufficiently  
close to 1K (i.e. it's 0.99K) that I could interpret the divide down  
ladder as consisting of 1K and 68K, which gives me, if I want to find  
the volts per octave,

exp(-v*(1/69)/vt) = 2

and assuming a vt of 26 mv, I get
-v*(1/69) = 0.026*log(2)
v = -1.2435

The divide down ladder is fed by an inverting op amp, so I could  
interpret this as being 1.2435 volts per octave. This, I suppose, is  
pretty close to the 1.2 volts/octave I've heard that Buchla uses.

But then the inverting op amp is confusing me. I see an octave input -  
OK, I imagine thats from some kind of rotary switch, maybe - that  
comes in through a 56K input resistor, and a "freq cv" input that  
comes in through a 150K resistor. In any case, the feedback resistor  
is 100K - so it doesn't seem there's any way I could interpret either  
input voltage as giving 1.2 volts per octave. If I saw something with  
a 100K input resistor that would make more sense to me.

Can someone help me with my confusion?  If I can't figure it out, I'm  
going to handwave when I get to the expo converter part. (Last week I  
showed how how expos work in a typical 1 volt/octave style converter,  
as discussed on Rene Schmitz's website, but I wanted to do another  
example of one since I didn't explain it very clearly. I off my game  
that day.)

- Aaron