[time-nuts] from Sputnik to CD

[Bill Hawkins]

Bruce,

You have been more precise than this in other posts. Can you put
some numbers behind the sigma delta DAC's sensitivity to jitter?

Twenty years ago, the process control community got all jittery
about the jitter in the execution period of function blocks. The
fears have disappeared into the pages of history, because the
final control element was so much slower than the jitter.

Any time that someone is uncertain about the effect of some
measurable quantity (or not, think of N-rays) then they become
prey to anyone with the voice of power who claims a certain
effect with great certainty. For example, fundamentalist preachers
and certain audiophiles. This is human nature, part of what enabled
a prehistoric leader to gather a group of true believers and lead
them into battle.

But I really like the Great Dane's reply.

Bill Hawkins


-----Original Message-----
From: time-nuts-bounces at febo.com [mailto:time-nuts-bounces at febo.com] On
Behalf Of Bruce Griffiths
Sent: Monday, October 08, 2007 4:10 PM
To: Tom Van Baak; Discussion of precise time and frequency measurement
Subject: Re: [time-nuts] from Sputnik to CD

); SAEximRunCond expanded to false
Errors-To: time-nuts-bounces+bill=iaxs.net at febo.com RETRY

Tom Van Baak wrote:
>> As one who has worked in the pro digital audio field for years, I can

>> tell you that sub-100 ps jitter very definitely can be heard, 
>> depending on its spectrum.  Modern sigma-delta ADCs and DACs use 
>> oversampling clocks of 12 to 50 MHz for sample rates of 44.1 kHz to
>> 192 kHz at 24-bit resolution and achieve SNR and DNR of 120 dB or 
>> better, integrated over the audio range.  The noise floor can be -144

>> dB or better and a 1-bit signal can be discerned.  Higher-end 
>> consumer gear do use these as well as pro equipment.
>>     
>
> Can you show us the math behind this?
>
> If I calculate 1 / 192 kHz / 2^24 = 0.3 ps, my crude intuition says 
> that at 192 kHz (~ 5 us) one ps of time jitter is roughly equivalent 
> to about 2 bits of noise on a 24-bit DAC, yes?
>
> Similarly for a vintage 16-bit DAC at a modest 44.1 kHz, one bit of 
> DAC noise is equivalent to ~300 ps of time jitter (using a calculation

> of 1 / 44.1kHz / 2^16 = 346 ps).
>
> Is this the right way to do the math? Am I even close?
>
> It seems to me that all short-term imperfections in timebase stability

> have the identical effect as short-term imperfections in DAC stability

> and is also related to the number of bits of resolution in each 
> sample.
>
> So debates about signal fidelity, which are often framed in terms of 
> sample rate (e.g., 44.1 vs. 192 kHz) or sample width (e.g., 16 bits 
> vs. 24 bits), should equally discuss clock jitter parameters, no? 
> Only, I rarely see much about the role of clock jitter in digital 
> audio, or if I do, it's handwaving instead of real data.
>
> I don't want to get that far off time-nuts topics, but this does seem 
> to be an interesting real-world application of precise time and I've 
> not run across a scientific treatment of it, one that includes real 
> performance measurements of various digital audio recording and 
> playing devices, etc.
>
> It's also interesting when two list members disagree by so many tens 
> of dB, so I'm hoping David and PHK can settle this for us.
>
> /tvb
>
>   
Tom

Your analysis applies to a conventional non sigma delta DAC.
Sigma delta DACs can be rather sensitive to clock jitter.
Multibit sigma delta DACs are less sensitive to clock jitter than single
bit DACs.
Capacitive charge dispenser sigma delta DACs can be less sensitive than
switched resistor or switched current source sigma delta DACs.

Bruce

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