So this gets me thinking about the closed form digital filter for the upcoming Yggy? So again, I'm thinking... why? That's nuts. Why make your lives so difficult? Why the crazy emphasis on accuracy? (The "accuracy" aspect from the guys at Schiit is subtle, but its very much there if you've been reading carefully.) And then we when go back in time, with Theta, and their DSP filters, reading old Stereophiles, product information, marketing materials, interviews, you realize that Mike Moffat has a thing for accuracy.

So now I'm wondering... Maybe there's something to it other than just fancy technology that can be marketed. That these guys might know something. Like maybe more accuracy = better sound quality.

I'll leave this up for you guys to discuss. Just some thoughts. I did own a Theta DAC back in the day.

For me, what Schiit is doing with the Ygg is much more impressive than the Rag. The Rag may very well be super king big nuts of SS headphone amps, but I know from first hand listening that there are a lot of ways, A LOT, to make a great sounding SS amp, from Valvet's ultra simple floating bias pure Class A design with a single bipolar output transistor to Accuphase's awesome Class A amps to the absolutely incredible stuff from Vitus and BALabo. All great, all very different design ideas.

What I'm saying is, the Rag destroying its competition in the headphone arena I think says more about the state of the competition than it does about the Rag.

There isn't the same separation when it comes to DACs. A DAC is a DAC, you don't have headphone DACs and speaker DACs. It would've been the easiest thing in the world for Schiit to slap some TI chips on a board and call it a day, or to make yet another Sabre DAC. Just about everybody else is doing it at anywhere near the Ygg's price level. You even have Charlie Hansen from Ayre calling out DSD as a bunch of dumb BS, and then making the QB9 DSD with a Sabre DAC because that's what the market wants.

The Ygg seems to me to be about as far in the other direction from that as you can go, and it's definitely the hard road to take. Considering how ambitious of a product it is, it should probably be priced like an Empirical Overdrive. The fact that it's going to be about a third of that is crazy.

I'll take a shot at responding on the amp side. I suspect Mike will weigh in on the DAC side, sooner or later...maybe later, since I know he and Dave are doing some tweaking on the Yggdrasil tonight, and are in full "make sure it's fully ready for the show mode" right now.

First, a disambiguation of Ragnarok and Mjolnir topologies. They're actually quite different, though both are circlotron-output amps. Simply scaling up a Mjolnir wouldn't work for Ragnarok, mainly because the output stage has to have a low enough impedance to control complex speaker loads. The key differences are:

Mjolnir: ALPS 4-gang volume pot, single JFET gain stage, JFET-buffered and capacitively coupled to the MOSFET circlotron output, with MOSFET bias via a differential DC servo.

Ragnarok: Relay-switched resistor ladder attenuator, JFET input differential stage, plus BJT VAS and driver stage DC-coupled to the MOSFET circlotron output stage, with bias set by microprocessor. The MOSFET outputs in this case are MUCH bigger than Mjolnir, and require drivers. There is feedback that combobulates the VAS and output stage into their own "output local" loop. There's no overall feedback, and feedback switching at different levels uses differential localized feedback, rather than changing the output local loop.

So why does this sound good? Well, let me get back to that. Because we're entering into the "IMO" realm here, and lot of people won't agree with what I'm going to say right now, as their belief system lies along the "well, if it's got PPM (parts per million, or 0.000X% levels) distortion at 20kHz, it's the most accurate it can possibly be."

And designing an amp purely for super-low distortion is no easy task—but, surprisingly enough, it's not due to the topology, it's due to the actual physical layout of the boards. Topology-wise, designing a PPM-level amp is well-known. It just takes a bunch of gain and a lot of feedback, with attention paid to minimizing commonly known distortion mechanisms in the open-loop design. This will mean lots of parts. However, once things get on the board, a trace run the wrong way can increase distortion by orders of magnitude. In addition, most of the distortion will come from the output stage, and how it interfaces with the speaker load. This can cause all sorts of unpredictable behavior with complex loads (which are not typically measured.) So, a couple of board errors, and a reactive load...and you gotta wonder if designs that deliver low THD in simulation are really the be-all-end-all.

We don't design for PPM distortion, though low overall distortion is one criterion. So why does Ragnarok have a good chance of sounding good, in our opinion?

I think it comes down to really one thing: avoiding overall loops, of any kind, that feed stuff that isn't the signal back to the front end of the amp.

Huh?

Well, traditional feedback takes the output of the amp (at the speaker taps) and feeds it back all the way to the front end of the amp. This scaled signal sets the gain of the amp...and it also brings back any distortion generated by the interaction of the output stage and the speaker reactive load to correct the distortion of the overall system. The more feedback, the lower the distortion.

Also, most DC servos do the same thing--sample the output, bring the DC correction signal back to the input. Of course, this also means you have a phase-shifted, frequency-dependent part of the output coming back as well, because a DC servo doesn't just amplify DC.

But--and here's where I'm way out in la-la land, where the "THD is all" crowd will crucify me--you're also feeding back stuff that was never in the input signal in the first place...nonlinear distortion from the output stage, plus frequency-limited and clipped garbage from the servo. And this stuff goes through the full gain stage of the amp.

The best amps I've heard (and designed) in the past did two things:

1. Kept the output stage as its own loop (via Hawksford error correction) with no feedback back to the gain stage. (Hawksford is a neat way to get low output impedance and very linear output stages, without having to do overall loop feedback.) So, in effect, it "decoupled" the output from what the rest of the amp was doing.

2. Paid careful attention to making sure the DC servo was as close to DC as possible. This was done, in the past, with heroic multi-pole filtering, and careful choice of time constants. But still, if you amplified the output of a DC servo, you could hear the original signal, even after this kind of filtering, so it wasn't perfect.

So, Ragnarok is an extension of this. We aren't doing Hawksford error correction, but instead relying on a close-coupled local output feedback loop between the VAS and the output stage. Similar results overall (but slightly higher distortion). None of this is taken back to the input of the amp. In addition, we simply threw out the DC servo, because microprocessor-controlled bias means it isn't necessary (at least after we got the Ragnaroks to stop blowing up.)

Are there other topologies that could express this exact design goal (output isolation, limited feedback, no servo)? Sure. A neat topology for a single-ended amp would be a very linear front-end stage with local feedback from the drivers, coupled with a Hawksford-linearized output stage with bias set by microprocessor and a voltage controlled voltage source. It would work for a balanced amp too, but a SE amp in this configuration would be very affordable to make.

(And, the usual disclaimer--this is blue-sky stuff, not necessarily hints at future products.)

Annnndddd...who knows, I could be completely full of it, or barking up the wrong tree. It could be possible that my conclusions are entirely wrong (look at Vali, capacitively-coupled and relatively high THD...and it sounds good.) However, the output stage does not have any overall feedback to the front end...and nor is there a DC servo...

Hope this helps a bit!

For example, not sure what it's meant by closed-from digital filter... Best guess is that they mean they don't approximate some types of filters with a finite number of IIR or FIR coefficients and do some other strange stuff?

I could be full of it or completely wrong... Maybe it works by hanging on to the original samples where an initial output from the digital filter is compared to originals. Error is calculated. Output function is tweaked to minimize or effectively zero out error. Then that output is used. Sort of like closed loop operation on an engine - where the computer measures emissions and tries to maintain a certain AF ratio for fuel economy.

Lots of variations of how this can be done.

With the talk of quantization (rounding) error in the chatbox, I can understand why the DSD thing is an anathema to the Schiit guys. The DSD noise shaping thing to push the 1-bit crap up to higher frequencies. Of course "noise shaping " is another word for adding adding RNG noise to the original signal. Dynamic range is expanded in the audible region, but total error is going to increase.

Sort of goes against Mike Moffat always talking about the accuracy requirements of cruise missiles and medical equipment.

When dealing with DACs, the stored sample is already digitized (amplitude quantization) and sampled (time quantization).

Suppose we have the luxury of infinite precision. Then we would still be missing the data in between samples due to sampling, and would have to do our best effort in guessing what was going on there. The relevance of what Nyquist said about this problem was that there is a unique solution for all the missing data points between samples if the signal minimum period is constrained to be at least two times more than the time distance between samples. It's a pretty powerful theorem, but it does have it's real world implementation problems (like pretty much everything).

As far as amplitude quantization, AFAIK not much we can do about that if things were already digitized to 16 bits. Usually there is no original signal to compare with. One could encode an error (or residual) signal channel, and do some sort of interesting stuff like it seems DTS-HD does. But if music was encoded 16-bits and that's all there is left, then don't know how one can beat up 24-bits of resolution out of it. Damage is done.

A hi-res file could be done at 96 kHz and with 24 bits of precision and then it may be up to the equipment to handle the file gracefully. Still, at some point going for 125412588 bits will likely result in doing an awesome job at capturing every single background and thermal noise nuisance of the recording equipment. I guess one could check where noise floor usually lies on recording equipment and derive requirements from there.

The job of most digital and analog filters in the DAC signal path (AFAIK) is to do as best of a job as possible in guessing missing signal between samples (time quantization). Not much it can do about number of bits except to not further reduce precision. It's not  much different from what an analog filter needs to do, except a digital filter doesn't have to deal with component tolerances which can render a high order analog filter unstable or weird, and certain component non-linear behavior. Dealing with loss of precision is not an easy task though. Specially when dealing with very long digital filters. The good news is that simulation in the digital world yields sort of predictable results. Analog ICs (and board layout) are much more unpredictable.

As far as boards and amps I get a lot of what Jason is saying (not an expert in those areas though). I appreciate the fact that Rggy has to deal with less than 8 ohm loads and things will have to be different. I also get the feedback discussion, and optimal setting of operating points. There is a lot I still don't understand about interaction between amp and non-linear loads though. While I do get how feedback can correct for transistor turn on stuff due to class B or A/B operation, I don't see how it can correct for non-linear load issues.

As far as 1 bit stuff, I can say that GPS is QPSK modulation which is 1 bit per quadrature. It is also spread spectrum. Lots of military equipment use FSK, BPSK and QPSK. Usually no need for 88939 bit DACs (or even ADCs) there. Some applications are PAR constrained.

...

As far as delta sigma, that's a different problem than 20/48 or 1582/52581. 1-bit delta sigmas can suffer from limit cycles and other issues, but n-bit delta sigmas can deal with some of those problems (ala AKM). And they can be very accurate.

This is going to sound over the top, but for digital and analog communications EEs one important concept is the one about channel capacity (the Shannon Limit). It is given by BW*log2(1+SNR) where I guess BW is related to oversampling and SNR is related to n-bits. When given the choice between BW or SNR, one should increase BW (though one should really increase both if sky is the limit). Delta Sigmas, Spread Spectrum, Error Correction and other crap work and correlate highly to the channel capacity idea.