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Digital Drive Upsamplers, DACs, jitter, shakes and analogue withdrawals, this is it. |
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Digital Drive Upsamplers, DACs, jitter, shakes and analogue withdrawals, this is it. |
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In Reply to: Re: Technical merits behind multiple DACs posted by Kal Rubinson on January 17, 2004 at 15:26:28:
I've been asking myself the same question, and now you pushed me into geek-mode so I had to dust of the old math :-)OK, let's say that the DAC outputs a sine wave sin(t), now we take two DACs in parallel, they both output the same sinewave in phase, to the total output is sin(t)+sin(t). So the signal is doubled.
If we imagine that DAC errors, noise etc. can also be described as sinewaves, we can do the same for the noise. Only this time, the signals are not correlated, so they are randomly out of phase. Some might be completely out of phase and cancel out to zero (t offset by PI), some are in phase and add up to 2*sin(t) as before, but on the average, the noise waves must be halfway in between, ie. offset by PI/2.
So the noise output is f(t) = sin(t) + sin(t+PI/2). This function has it's maximum where cos(t)+cos(t+PI/2) = 0. Solving this leads to t=PI/4, and if we insert in the output function and use a couple of trigonometric identities, we get sin(PI/4)+sin(3PI/4) = 2*cos(PI/4) = 2*sqrt( (1+cos(PI/2)/2 ) = 2*sqrt(1/2) = sqrt(2).
So while the amplitude of the original signal doubles, the noise is only increased by a factor of sqrt(2)=1.41 when you run two DACs in parallel.
I think this is the general idea about running multiple DACs in parallel, but maybe my calculations are too simplistic (?)
Accuphase do it like this, but others might do things slightly different. Wadia 861 for example offsets the clock-signal with half a period between the DACs to effectively double the samplerate, but that shouldn't change anything with the noise-calculation I think.
And please correct me if I made any mistakes.
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Follow Ups
- Re: Technical merits behind multiple DACs - S 18:29:58 01/17/04 (3)
- Exactly. - Kal Rubinson 08:55:08 01/18/04 (2)
- Output Voltages would not double I think. - sbrians 04:28:54 01/23/04 (1)
- Re: Output Voltages would not double I think. - Kal Rubinson 09:01:01 01/23/04 (0)
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