[sdiy] Deciphering the Buchla 259's expo converter

[Tim Stinchcombe]

Hi Aaron,
	I did a few quick calculations and arrived at pretty much the same
figures that you give. In taking the expo converter slightly out of context
(I'm assuming you don't know exactly what is at '17' and '21' - at least I
couldn't find them skimmng the other 3 schemos), it is obviously difficult
to be 100% sure just what 'x/octave' the law is, but I don't see that as a
reason not to present the maths to your class - it will serve as an example
to be wary when you haven't got the complete picture! (?).

Tim
__________________________________________________________
Tim Stinchcombe 

Cheltenham, Glos, UK
email: tim102 at tstinchcombe.freeserve.co.uk


> -----Original Message-----
> From: synth-diy-bounces at dropmix.xs4all.nl 
> [mailto:synth-diy-bounces at dropmix.xs4all.nl] On Behalf Of 
> Aaron Lanterman
> Sent: 05 February 2008 07:04
> To: SDIY
> Subject: [sdiy] Deciphering the Buchla 259's expo converter
> 
> 
> 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/Buc
> hla_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 
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