[sdiy] Expo converters, lin log etc.

[Magnus Danielson]

From: Karl Ekdahl <elektrodwarf at yahoo.se>
Subject: [sdiy] Expo converters, lin log etc.
Date: Wed, 31 Jan 2007 21:05:45 +0100 (CET)
Message-ID: <210853.71062.qm at web26205.mail.ukl.yahoo.com>

> Hi list,
> 
> i'm a little confused as to the whole lin/log expo
> stuff and i need some clarification.
> 
> Basically, the response of a "normal" vco (for
> example) is logarithmic, therefore an exponential
> converter is needed to linearize the final response -
> right?

Not really. A "normal" VCO is exponential and therefore an exponential function
is needed. A freq-to-CV converter is logarithmic in its frequency to CV
conversion for a "normal" VCO.

For some reason the terms is widely missused.

> Would any exponential/anti-log converter work? What is
> the base or the mathematical formula used to get this?

       U
f = f 2
     0

where U is the input frequence. The base 2 is natural since you want to double
the frequency for the rise in voltage of 1 V. f0 is the frequency of the
oscillator with the net sum of 0 V.

> I'm not a math-head but perhaps there's a simple (and
> probably inefficient) way to explain this even to me
> :)

I hope the above was simple enought.

> For me to fully understand this it'd be intersting to
> create a fully "mathematical" circuit that performs
> expo-conversion using purely mathematical building
> blocks, i.e. something that does not rely on
> transistor parameters i don't understand etc. Is this
> possible?

The transistor has the "right" properties, i.e. the exponential function but
with incorrect values. For most practical matters it is:
         qV
        (--)
I = Is e kT

where Is is a very small current due to material aspects
e is the natural base (about 2.718281828... )
q is the elementary charge (a constant)
k is the Boltzman constant
T is the NP-junction temperature in Kelvins
V is the NP-junction voltage

Assuming a stable (or compensated) temperature (this is a big issue to us),
the input voltage will be exponentially converted into a current. This current
we use to feed into a CCO core (Current Controlled Oscillator). We scale our
voltage down to about 1/57 V per octave, compensate for the scaling error and
the frequency offset error.

It is not too hard to have those strange transistor to have some 15-20 octaves
of nice exponential response. It is still a valid method even if it may feel
strange. Infact, I'm not fully sure that I understand all that happends in
there, but for all practical reasons it does the right thing and that is what
matters in the end.

Cheers,
Magnus