SYNTHESIS TECHNOLOGY
PAGE 15
MOTM-510 ASSEMBLY 7/11/04
WWW.SYNTHTECH.COM
What you do is find, in the table (let’s not go into how we
got
the table, OK?), the logarithms
(in this case, these are called the natural logarithms and are abbreviated ln(x), like ln(2). You
may have seen log(x), which are DIFFERENT logarithms and that’s for another day).
So, we find: ln(2) = .6931 and ln(3) = 1.0986. Adding these together, we get 1.7917…Errr…now
what? Well, we perform the
inverse logarithm
, meaning we look in the table for the ‘answer’ of
1.7917 and see what number has
this
for it’s logarithm (the choice of the term ‘inverse’ is
sometimes called ‘anti-log’ so that you don’t get confused with the ‘inverse of a number’ which
is 1 divided by that number). Scanning the table, we see that there IS in fact an entry for this
number (1.7917) and by some miracle, that number is 6! So, 2 x 3 = 6. The way inverse
logarithm is written is like this: ln
-1
.
Now, I’m sure by this point many of you are questioning my sanity why this is even relevant to
the ‘510. The point is: if you want to make an analog multiplier function, then what you can
possibly do is:
a) somehow take the logarithm of the inputs (not obvious)
b) add them together (EASY!!)
c) somehow perform the anti-log and BINGO! (still not obvious)
The solution: the circuitry inside the AD538 does this for us (if you
really
want to understand
exactly how circuits can perform log/antilog functions, get a copy of the Non-Linear Handbook
from Analog Devices (1-800-262-5643, select option 3). In a manner of speaking, the AD538 IC
calculates, in real time, both log and anti-log functions of input signals. The data sheet for the
AD538 also has more theory, and is contained as a PDF file on the CD-ROM (and also on the
Analog Devices website).
If all the AD538 did was to act as a multiplier, that would be fine but not that exciting (there
are many other analog multiplier ICs out there that don’t cost $55). We already use multipliers
in our synths: these are called ‘Ring Modulators” and “VCAs”. So what’s the big deal with the
AD538 and the WaveWarper?
Well, 2 things. First, the AD538 can also
divide.
Hmmm…haven’t seen
that
before in a synth
module! The AD538 does this by another ‘trick’ using logarithms:
ln(X/Y) = ln(X)-ln(Y)
Meaning, that if we
subtract the logarithms
instead of
adding
them, we divide! Awesome,
dude! (and people think math is boring). In analog circuits, this is trivial (simple op amp
inverting summer). All of a sudden, the AD538 is looking quite interesting.
But there is one more surprise, and it’s a biggie: using logarithms, it’s also easy to calculate
roots and powers
of numbers, too!
This is calculated by using the well-know relationship:
ln(X
y
) = y * ln(X)
For example, to calculate 4
3
:
Summary of Contents for MOTM-510 The WaveWarper
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