No missing codes is a huge no-no for weapons technology. The missile must hit the weapons dump as opposed to the nunnery. The the makers of AD5791BRUZ and AD5781BRUZ D/A chips of which we use one per phase on our two top converters provide an evaluation board which is designed to be used with a pc and precise voltage measuring system to input all 20 bits and 18 bits worth of code, respectively. This no missing codes problem is due in part to the fact that all of the original samples are discarded and then later successively approximated in the filters inherent to SD and DS technology. Thus my extreme mistrust of SD and DS tech.
Well it's certainly true that ΔΣ technology is based on transforming a PCM input signal into a different domain as PDM. But I can't see why this would be a crucial problem. There are plenty of R2R-PCM DAC chips that also transform their input signals in order to leverage circuit designs that allow greater linearity. The venerable PCM63, for instance, was based on a colinear design composed of two DACs sharing an R2R ladder so they could convert the twos-complement input into unsigned values. It was also, of course, designed to be fed by an 8x oversampling filter which grossly transformed the 16bit inputs from CD. The AD5791 you mention handles the upper 6 MSBs through 63 dedicated resistor switches and the rest of the signal by an R2R ladder, a transformation that underlines the fact that some bits are more equal than others and reflects a logical allocation of resources.
Now, it's certainly true that it's
simpler to trace the transformation in the last two cases, and it's easy to see the correspondence between input and output, even though it's not precisely 1-to-1. Any oversampling of the input will introduce integration, but it's still fairly easy to understand. ΔΣ transforms, on the other hand, are a lot more complex, consist of multiple stages, have multiple possible topologies, and if you really want to understand them you need to consult some
textbooks. But they're still fundamentally deterministic. The output reflects the input without any 'approximation' taking place beyond the constraints imposed by the noise inherent in all physical instantiations of circuitry, and ΔΣ designs are centered around pushing that noise out to places where it doesn't matter and can be removed with ease.
I'm not quite sure why you're so concerned about the 'no missing codes' criterion, since that applies to ADCs and not DACs: it basically refers to an ADC's ability to sweep through the entire range of output values without missing any as the input sweeps through its full range. It's certainly desireable, but any decent modern
ΔΣ ADC can fulfill that requirement.
And that's really the take-home message, isn't it? Let's not beat about the bush, a modern high-precision PCM DAC like the AD5791 is
obscenely expensive, almost ten times the price of a ΔΣ DAC of comparable quality. Since this is BOM cost, it gets transmitted and multiplied all the way up the chain and the cost to the consumer balloons.
Now, I can't blame Analog Devices for selling expensive chips, or manufacturers like Schiit for implementing them: if people want this stuff and they're willing to pay for it, then you'd be stupid not to provide products to tap that section of the market. The home audio market has a significant carriage trade component, and only a fool would turn down the margins provided by luxury goods.
But this is a consumer forum, and we're trying to be rational here: if we see one product that costs ten times as much as another we need to ask why we would possibly consider it. You can make perfectly good DACs using ΔΣ technology, and you can make equally good DACs using PCM technology, but the latter will cost considerably more for comparable performance. I can't see any reason to choose the straight PCM option apart from the false equivalence of cost = value.
