So this post is about a two subsets of multibit D/A converters. The first would be those (like Schiit) who utilize integrated circuit DAC chips, and the second would be discrete DACs made from discrete resistors, switches, and logic audio data interfaces. All too frequently in audio circles there are polarizing opinions stated (electrostatic headphones suck, solid state amps sound like ass, etc, etc) which represent single viewpoints over complex subjects. The fact is that there is no overreaching engineering argument in favor of either which multibit DAC type one uses. He who implements his preferred solution best wins. Notice I restrict this choice to multibit designs which I prefer for their sound. My position of delta sigma has not changed; they are inexpensive and preferable and competitive for lower cost designs. If one’s goal is to reproduce music in a manner where realism can thrill the listener, well, hey, multibit is the only choice - hands down.
I begin by mentioning that this is not intended to be a grad school discussion of digital signal processing applied math. I seek more to make this essentially accurate to the point that no one will fall asleep. On the topic of math let me get that over with first, so here we go: Digital audio is a series of regular interval (sample rate – like 44.1K samples per second) numerical representation of audio information. A snapsot, if you will. Now acoustical information tends to be positive and negative in nature. Meaning it deviates from a center. This center tends to be important because the music spends much of its time traveling through zero, either from positive to negative, or the other way around. These are referred to as zero crossings. Since music at its lowest level is closest to the zero, a small error here can have an ever larger bad impact on reproduced music as it reduces in volume. That said, there are several ways to format the numbers used in D/A converters. The most popular is two’s compliment which is almost universally used in digital audio. Two’s compliment has a number which represents all the minus and all the plus, and zero. The ubiquity of two’s compliment is because through zero (audio silence) it climbs from -2 to -1 to zero to +1 to +2, with the point being that there is only one value for zero (and vice versa). Now this is as expected that counting naturally should be. The disadvantage of two’s compliment is that the numbers for +1 and -1 are distant numerically, making the DAC chip naturally wanting to glitch as it crosses zero, which it does a lot. That was the biggest design problem (solved) with the Yggy and it was a head-scratcher.
With one’s compliment aka sign magnitude (the audio minority) you take one bit of your 16 or 24 and call it a sign bit setting it one way for plus and the other for minus. This means that if you count as above, you get -2, -1, - zero, + zero, +1, +2. This counter-intuitive; sorta unnatural like trying to cohabit in happy harmony with chickens. The workaround is you have to do math on every sample to add or subtract one to each minus or plus sample. The other problem is that you need a bit to set the plus or minus sign; your 16 bit DAC just became a 15 bit; or your 20 bit a 19 bit. Now those who implement sign magnitude design DACs are generally mathematically sophisticated so they can do the math (which does have quite a bit of overhead). Quite essential, though, to get the chicken schiit out of the house in the happy harmony above. Now, in all fairness, sign-magnitude adherents can laugh at all of us two’s compliment for all of our effort to get rid of zero crossing problems.
Now I shall address the discrete vs. monolithic (integrated circuit) DAC. Why do I use monolithics? Quite simple; it is because I can provide a much higher value scalable multibit solution than I can with discrete DACs. Now DACs have two critical sections – the digital section which routes the proper bits to the proper switches – the switches which switch the appropriate resistor in the network. There is also an electronic section which interfaces the switched resistor to the outside world which has little effect on the accuracy of the DAC if properly designed for the network. The tolerance of the resistor and its value shift with temperature are critical to the parts per million in a 20 bit system. Here are some advantages of monolithic DACs. The ladder/R2R resistors are properly designed/trimmed for their bit width, providing greater accuracy than some random purchase of resistors and switches in discrete DACs. Only in a monolith are all resistors are on the same die so their temperature variations track, resistor to resistor. This all contributes to the value metric favoring monolithic DACs mentioned above.
Does this say it is difficult/impossible to build a proper discrete DAC? No, it is more like making sure all of your 20 bit DACs in production are just that; in Singapore, Alaska in winter, or Key West. There could be nothing worse than making production quantity 20 bit DACs until you realize some are 12,15, or 21. It is more like building a highly tolerance precise, labor intensive, parts matching, temperature controlled DAC which would be difficult to exactly duplicate, sample to sample. Am I ever going to build it? Who knows? I have thought about it since the 1980s. If I were to do so, I would not use either one’s (sign magnitude) or two’s compliment. I would use an old coding designed to be used on polar co-ordinates which I feel would be the absolute best to decode music. I would put it in a temperature controlled oven and agonize over how to solve the switch variation problem. It is a bucket list item for me. I know I could make two the same. But two thousand? Probably not. Maybe I could learn.
