More on DAC stepping

[Paul Schreiber]

Most modern DACs "multiply" a reference voltage by a fraction to get the
output. The
fraction is:

input digital word / # of possible words

for example, a 12 bit DAC with 4096 steps, when used with a voltage
reference that is 4.096V,
has 1mv/step output. This is very common in industrial process controls.
Why? it's *easy* to
remember! Want 2.554V out? send 2,554 to the DAC!!

What about a 1V/Oct system that wants 83.3mv/note? (not counting gliding
in-between!) Why not just
step in increments of 83.3mv?

Answer: the DAC isn't *accurate* enough to do that. For VCOs, we need 0.1%
error to be "on perfect pitch".
0.1% of 83.3mv is 83uV. If the LSB is 83.3mv (1 bit count = 1 step) the
linearity needs to be 0.001LSB. Nada.

Case #1: DAC swings all the output

If we don't range-switch (see case #2) and we want 10 octave (common) then
we need to resolve 10V/83uV or
120K steps in our DAC! That's a 17-bit DAC.

So, the best solution are 16-bit DACs (Maxim makes some with serial I/O)
which can span 65,536 * 83uV or
about 5.45V. Then with a *16-bit accurate range switch* span wider. In this
case just an accurate *inverter*!!

Case #2: DAC swings some, external ranging

Let's assume we only want the DAC to swing over 1 volt. then, 1/83uV =
12,000 steps or a 14-bit DAC with
some lesser error. The error is 1/16384 = 61uV per step. Then, we save $$$:
buy a 14-bit, 1LSB part!

What about designs using an 8-bit DAC? If we assume a "pretty good" 1/4LSB
linearity, the DAC's 'perfect'
resolution over 1 volt is:

1/256 = 3.9mv per step. but the DAC will in reality be between:

low side: 3.9 - .975 = 2.925mv
high side: 3.9 + .975 = 4.875mv

The pitch error on the high side is 4.875/83.3 = 5.8% which is way off. Even
the low-side error of 3.5% is well audible.

Of course, the DAC may be much better by *chance*, but not by *design*.

Even if we say "my [non-MOTM] VCOs can't track to 0.1% anyway!" OK, fair
enough. Let's say 0.4% (old Minimoog).

You still need 11 bits, at 1/4LSB over 1 volt span.

So, with modern 16-bit DACs for <$20, the need for complicated range
switching is unnecessary.

Lastly: You need *very low offset drift* op amps in a 16-bit DAC solution.
Look at OP-97s from
Analog Devices.

Paul Schreiber
Synthesis Technology