Absolute top tier DAC for standard res Redbook CD

It’s funny how the reviewer thought the total dac had more detail. I totally found the opposite. Not only more detail but also much more open and much bigger soundstage beyond the speakers for the Bricasti. When I told the total dac owner about not very open, he said, oh you have to try my new 20,000.00 dac seven. Oh my did I laugh to myself. 

The best explanation is the “measuring cup analogy” in Stereophile 1990. Nothing is “thrown away” - Delta-Sigma is just a different (more accurate measuring cup) method for conversion to analog. R2R methodology lost the technical battle about 20 years ago - R2R is too expensive and too inaccurate to be a leader in DAC technology. R2R relies on impossible accuracy in analog devices whilst Delta-Sigma elegantly uses mathematics to achieve superior performance in a simple robust way.

The latest hybrid ESS approach - massively parallel one-bit DACs all on the same DAC chip with random selection to reduce noise is some 30dB+ better in THD+N - massively outperforming R2R for a fraction of the cost. Technical progress is wonderful!

As far as I can see, the marketing of R2R is highly misleading - full of all kinds of false insinuations - “throwing away data” - simply not true, not bit-perfect (when delta-sigma is far more accurate), “facsimile” - ironically R2R is actually the poor quality analog facsimile, “guessing” - again ironic because R2R actually has built-in massive non-linearities that makes the accuracy no better than a guess where delta-sigma is many times more accurate.

Here is a basic description of the different approaches:

”The same reasoning underlies the development of bit-stream decoders. The problem with a conventional digital/analog converter (DAC) is that its operation involves mainly analog processes and is therefore approximate. A 16-bit DAC contains a precision current source and an array of 16 switches. Each switch is connected to a resistor, and the resistors are supposed to be scaled in exact 2:1 ratios so that each switch, when opened, will contribute exactly twice as much current to the output as the switch below it. The switches are controlled by the 16-bit codes from the CD; thus by opening and closing in various combinations, a total of 65,536 different output values can be generated.

But the topmost switch (the most-significant bit, or MSB) contributes 32,768 times as much current as the least-significant bit (LSB). If the MSB current is in error by as little as one part in 32,768, the effect of the LSB is swamped. In most CD players it is; few 16-bit DACs operate to better than 15-bit accuracy. The practical result is that most CD players are non-linear at very low signal levels, reproducing small signals at the wrong levels and with added distortion. Keep in mind that this problem arises not from the digital code itself but from small errors in an analog quantity—the current produced by the DAC for the several most-significant bits.

For comparison, imagine that you were assigned to fill a bucket with a known amount of water, using measuring cups varying in size from one ounce to 64 ounces. Even if you use care in filling the largest cup, it might contain 63.7 or 64.5 ounces instead of 64; you can’t be sure that it contains exactly 64 times as much water as the smallest cup. But there is a way to obtain an exact result: use only the one-ounce cup, and transfer its contents to the bucket 64 times. The capacity of the cup may not be exactly one ounce, but as long as you fill it the same way each time, the total amount transferred will be proportional to the number of refills—an exactly linear relationship. This is the idea behind 1-bit decoding. In place of a method whose result depended on slightly uncertain analog quantities (the currents in the DAC), we have adopted a simple counting scheme—a purely digital process.

Of course with a small cup you’ll have to work fast, but in modern digital electronics that’s not an obstacle.”


Read more at https://www.stereophile.com/content/pdm-pwm-delta-sigma-1-bit-dacs-peter-w-mitchell#44ZdP17jRzTtUGor...

Jeff,
The primary claim concerning R2R superiority is that it is more "analogue " like in its sonic character. You and I have heard a fair number of R2R DACs and haven’t found this to be the general consistent result although individually some succeed more than others.

What I found interesting is the Bricasti SE was more dynamically potent than the TotalDac but also  "more" analogue like and more organic. This went against the so called conventional  wisdom expectation. George and his 8 fellow listeners heard a different outcome.

This isn’t surprising given the undeniable subjective nature of audio, listening sessions and all the accompanying variables associated. Ironically this is what contributes to the joy and fascination of what is the High End audio experience we’re all enthusiastically immersed in.
Charles

@shadorne 

Thank you. I mean that sincerely because you do in fact present an abundance of technical data in support of delta-sigma. In my case, I suppose I'm fortunate to have components with both technologies, and have carefully listened to both. While I may not have a 30K divinci dac - which uses delta sigma - I'd have to imagine it sounds spectacular to say the least. All I can indicate with certainty, however, is that to my ears, I prefer the sound presentation of my multibit DAC to that of my delta-sigma. Not only because it sounds more analog, but because it sounds more "real" and authentic. And I get what Al is saying - that those qualities are a result of the implementation and not the technology. So be it. Anyway, who knows what tomorrow's technology will be. Enjoy the music while we can.

The writeup by Peter Mitchell which Shadorne provided (thanks!) is excellent. But to be precise, the architecture it describes for a "conventional" DAC, in which "the resistors are supposed to be scaled in exact 2:1 ratios," is not R2R. In an R2R ladder only two unique resistor values are required, rather than a different resistor value for each of the 16 (or however many) bits in each sample.  R2R architecture is explained pretty well in the Wikipedia writeup on "Resistor Ladders."

However Mr. Mitchell's basic points about the issues inherent in the "conventional" architecture he describes are nevertheless applicable to R2R as well, as can be seen in the Wikipedia writeup.

Regards,
-- Al