[sdiy] Cataloging and understanding expo V-to-I converters

[René Schmitz]

Hi Aaron and all,

> Quick question, before going onto the big question - there's a cap in 
> both designs around the op amp that's used to hold one end of the 
> reference resistor at ground that's not shown in Rene's diagram. What is 
> the purpose of that cap?

Its for preventing oscillations. I left it out of the diagrams since my 
treatment doesn't go into these side details and focuses on DC only.

> OK now on to the heavier question.
> 
> I lectured on that last semester, and I'm going to be lecturing on it 
> again tomorrow (alas, my lectures are not being videoed this time around).
> 
> Anyway, I'd like to try to give my students a better understanding of a 
> wider variety of expo V-to-I circuits they may encounter, but of course, 
> to do that, I need to understand them myself first, and hence as usual, 
> I turn to this list (and try to in lecture give credit to where it's due.)
> 
> For instance... the expo converter used in the Polyfusion VCA
> 
> http://www.synthfool.com/schematics/polyvca.jpg
> 
> Is that a good circuit to explain? And if so, how do I explain it?

I'm afraid thats not exponential at all. To me it looks like a linear 
source. (The absense of a 1V->17mV divider is a giveaway...) The PNP 
close to the 3080 is a base grounded stage which is used with current 
drive. (Via the resistor, the emitter acting as a summation node held 
~600mV above GND. The follower preceding this stage does compensate for 
that by adding a ~600mV offset.)
The important thing to remember about base grounded amplifiers is that 
Ic ~= Ie.

> Are there other common expo conversion schemes I should make sure they 
> understand?
> 
> Should I try to explain how PNP/NPN style converters work - or should I 
> just tell them that they should stick with dual NPN or dual PNP 
> (depending if they need a source or a sink) in their designs since the 
> matched pairs are (relatively) easier to come by nowadays?

Well, the way I reason about them, they are all same. :-)

Note that they're all comprised out of an emitter follower, which takes 
care to adding a temperature dependant offset (the Vbe) to the input 
(1V/17mV divided control) and a base grounded circuit, which gets this 
shifted signal. In contrast to the polyfusion circuit above, this has 
low impedance to drive the base grounded circuit, i.e. voltage drive.

If you have two PNPs or two NPNs its a classic (long tailed) diff pair 
(which is nothing but an emitter follower followed by a base grounded 
stage...), and if you use mixed PNPs and NPNs the same reasoning still 
applies. This also catches the simple ARP-style expo as well as the 
opamp servoed varieties. (In which the servo does nothing else but to 
stabilize the current through that emitter follower.)

Hence the maths is the same. While in practice the assumptions for the 
math might not be exactly met. Like keeping the current constant through 
the first transistor.

Cheers,
  René

-- 
uzs159 at uni-bonn.de
http://www.uni-bonn.de/~uzs159