Dear Rob
Hope all is well with you.
If I may ask, why are resistors impossible to match in R2R Dacs?
Im enjoying my Hugo and Mojo every single day.
I played this Sade Album (love Deluxe) on my entry level turntable and then on Hugo
It isn't even funny anymore, the turntable needs to be retired/sold, the Hugo is so superior sonically and musically
Anyone who heard the difference would have had a "jaw dropping" moment when I played it in Hugo.
I cannot imagine how good the Dave is given it has 166,000+ taps and Hugo 26,000+...
Thanks
I will defer to Rob as always but I have my own contribution to make as I used to own a very good R2R DAC, the TotalDac d1-monobloc. This DAC incorporates 400 Vishay Foil resistors and Vincent Brient, its creator, went out of his way to use the more expensive variety with a very fine tolerance of 0.01%. Bought in bulk, these resistors sell for about $20 a piece and so for this DAC, the resistors alone cost about $8,000 (a reason why R2R DACs are so expensive). Obviously, he felt it was important to pay this premium from a SQ standpoint because the Vishay Foil resistors with a lesser tolerance of 0.05% cost 25% less. He could have gone for the best (0.005% tolerance) but that would have more than doubled the cost to $50 per resistor. Even at that, this suggests no 2 resistors will be 100% the same.
Just to give you an idea of the scale of the problem - imagine that we wanted a R2R DAC that could resolve to an accuracy of -350 dB - the performance that I get with Dave's noise shapers, and the spec for which was based on listening tests of depth - then if we want to guarantee -350 dB accuracy then that implies a resistor accuracy of 0.000000000000003%. That's why the idea that you need noise shapers to be that accurate is so crazy - and the implication that the brain can detect this level is also crazy. Indeed, I was actually reluctant to talk about this issue, as the numbers are so tiny. But at the end of the day, I stand by my listening tests, and I have been pleased that other listeners has discovered the same thing about Dave in that it portrays depth very unusually.
But you may argue that there is something odd about noise shaping that does not apply to R2R DAC's in regards to depth - I think not, as I have had un-measurable small signal errors that degrade depth, and all R2R DAC's suffer with measurable small signal distortion - but there is another way of looking at the problem. One of the interesting things I got out of the Dave project was reducing high order distortion products and finding out how very audible they were. To match Dave's THD performance you would need resistors of 0.000003% tolerance.
Now whether you need 0.000000000000003% or 0.000003% they are both not possible to achieve. Even if you could match those levels, by hand selection, you could never guarantee matching, as resistors naturally drift, and will always have temperature differences, thus changing the value too. Even the PCB tracks would present a problem - 0.000003% for a 1k ohm resistor is 30 thousandth of an ohm - you can't even etch copper to that accuracy! This of course ignores the switching components which is impossible to match at this kind of level, let alone the problems of getting the timing to be accurate enough. For 0.000003% accuracy, with a 16FS R2R DAC, you would need a timing accuracy of 40 femto S applied to the clock, clock tree, and all of the switching components together. To give you a scale of the problem, the best silicon device I worked on had 4,000 fS accuracy from switching element to switching element, and this used FETs that were very much faster than the FET that has a low enough RDS on for a R2R DAC. Indeed, you would need to place all components to a 6 micron accuracy so they all had the same delay. This of course ignores the fact that 16FS from a timing of transients accuracy is not good enough either.
This gives you a tiny flavor of the challenges that one has in designing R2R DAC's, and why it would be impossible to match Dave's performance with them.
Rob
