[sdiy] Consider this DAC

[Magnus Danielson]

ASSI wrote:
> On Saturday 13 March 2010, Antti Huovilainen wrote:
>> Please correct me if I'm wrong, but a TL072 for example has 18
>> nV/sqrt(Hz) voltage noise. For 20 kHz bandwidth (RC lowpass at
>> 10kHz meaning settling time of less than 0.2 msec) the resulting
>> RMS noise is 2.5 uV. That's quite a lot less than 1mV.
> 
> Look up the graph of noise vs. frequency to see that you've missed to 
> integrate a substantial amount of noise.  The flicker noise corner is 
> at around 400Hz for the TL072 and the noise figure on the first page 
> is for 1kHz and a source impedance of 50Ohm (guess what?).  There's 
> also this pesky little thing called offset and offset drift (with both 
> temperature and common mode voltage) that will need attention.  But 
> maybe I'm still missing your point.
> 
> My definition of 1mV _precision_ is that there is at most +-0.5mV 
> deviation from the ideal CV across all operating points.

That is actually a very weak definition in the sense that you have not 
quantified the PDF and when assuming that most of the random sources has 
a gaussian distribution, which is not limited in extent, you run into a 
situation where the definition forces you into over-specifying the 
system requirements. It would be much more useful to apply a k-value or 
probability within those limits. I propose that good engineering 3-sigma 
values should be used meaning that 99,73% it would be within the limits, 
so we have a Type B specification at least. The RMS error allowed would 
be 1/3 mV.

>  For a 10Vpp 
> signal range that results in about 14bit precision across the whole 
> system (in voltmeter speak: 4½ digits) - which is doable, but not as 
> easily or cheaply as you seem to believe.

It should be noted that 14 bit precision does not imply a 14 bit 
resolution DAC, it is a separate spec.

> Getting back to the CV->VCO example: "merely 1mV precision" across the 
> whole system (just having this for the CV is not going to cut it) 
> would allow you to set up two VCO five octaves apart (say 220Hz / 
> 7040Hz, after calibrating the beats out with both VCO at the same 
> frequency) and have them beating at less than 2.5Hz.

Assuming of course that you have that level of repeatability in your 
adjustment of the oscillator tracking.

>  Not only that, 
> if you reverse which VCO plays the lower and the higher frequency, you 
> still get less than 2.5Hz beats.

Again assuming that repeatability.

>  Modulating both VCO with the same 
> voltage never produces any faster beats than said 2.5Hz and 
> transposing the patch four octaves lower (13.75Hz / 440Hz) produces 
> less than 0.2Hz beat frequency of the 32nd harmonic of VCO1 vs. the 
> fundamental of VCO2.  Lastly, if you switch that hypothetical synth 
> off, let it sit for a year and switch it back on, you would get the 
> same results (not exactly the same beat frequencies, mind you, but in 
> the same range, perhaps after warm up).  Ian Fritz might have such 
> wonderfully precisely calibrated VCO, but there surely are a lot of 
> systems that would fail this test.  In other words their precision is 
> worse than 14bit/1mV and yet they are still perfectly useable.

I think precision is a word to be used carefully, so is the other very 
hard word accuracy. The way one should specify the achieved level of 
precision and accuracy is also difficult. I think for most uses 
resolution is of greater importance than actual precision. Also, for the 
case of beating oscillator, the absolute precision requirement is still 
not very high but the relative precision requirement (beating rate 
precision) is. This is true for most guitar-players... the relative 
tuning between the strings is more important than the tuning of their 
base string.

If we want absolute precision for the beating, then maybe our wide-range 
analogue oscillators should be locked to precision DDS oscillators with 
traceable frequency standard input?

No, that would be plain ridiculous.

Cheers,
Magnus