Master of The Clocks

This is the heart-beat of any DAC. The importance of a master clock and it’s quality should not be taken lightly. There is plenty of information (and same amount of red herring)  about this topic online. I think it all boils down to this: if all other DAC system components are very well optimized, improvements from a better clock can always be easily recognized. However in a sub-pair system they are simply masked by other flaws. But what is a “good” clock? And how to recognize one? Is jitter bad? What about rubidium time standards? Couple things needs to be addressed here.

First of all, unlike in digital communications, we don’t care about the clock jitter specs in audio. Shocking, I know. But I’m just getting started. We also have none of the slightest interest in absolute frequency value and it’s long term stability. So forget about rubidium time standards and other “space clocks”. What we do care though is a spectrum of the jitter or a phase noise of the clock. Let me explain by example.

Above is a snippet from a well known NZ2520SDA oscillator datasheet. Jitter is spec’d at mind blowing 43 femto seconds, wow! Spectacular.  Can you imagine how good that looks on magazine covers and product brochures? Here is where all the femto-clocks and other marketing wonders are born. Unfortunately this is an absolutely meaningless number for audio. Just like THD. Why? Because it’s very far from the carrier frequency! And it is essentially a specification of a clock noise floor.  Again, very important in digital signaling/communications where it will mean channel bandwidth and transfer speed, but pointless for audio D/A conversion.

Yeah it might increase your noise floor, so what? I’m loving my vinyl with it’s miserable 70dB at best. At least NDK is being honest and specify the measurement bandwidth in their datasheets. This is a very rare case indeed. With some more luck, you can find actual phase noise measurements done like in this NDK Japanese datasheet. 

What is of the most importance in audio is the close-in phase noise of the clock. We can agree to disagree here and that’s fine, but I done my homework and my fair share of critical blind A/B listening to prove that to my self once and for all. How exactly this noise couples to a final audio signal and how much of it is tolerable will depend on the DAC type (R2R, PWM), oversampling and many other factors. But in a most general sense it does exactly what you think it will – modulates the audio signal. Just like a turntable with of-centered record in this example. When it comes to audibility of that modulation, it’s all about auditory masking. It’s quite an subjective thing as with all things in psychoacoustics, but generally problems start to appear as we get very close to a carrier. Tests with pure tones shows it’s most audible at ~3-4Hz and is perceived as “fluctuation”. This seems to be the most sensitive syllabic rate in speech perception so our ear is really fine tuned there. Above ~15Hz it starts to sound as “roughness” of the main tone hence detect-ability threshold drops down.

Or they have to be at a insanely high levels of -50dB and above which would translate to micro-second level jitter. Please take a note that we are talking here about static side-bands! Which are stable pure tones around the center frequency. When those tones start to wonder around – all bets are off. This happens in a case of data-induced jitter which has a pseudo-random frequency  distribution and is correlated to incoming data stream. This thing is nasty for a couple of reasons. First of all it sounds just dreadful to even an untrained ear. Then it’s really difficult to catch it in a frequency spectrum, because it’s energy is spread out around fundamental and is seen just as a “thick grass” with a lot of small spikes.

OK, but what about the vinyl then? Why it sounds so good having massive amount of this low frequency modulation? Well, mostly because it’s periodic. Unless it’s bearing noise or tonearm resonances, but that’s a whole different tangent to get into. And again, masking, masking and masking… I never said anything about vinyl being ultimate sound media. It’s very compromised in bandwidth, stereo separation and signal-to-noise ratio. Is it still fun and exciting representation of your favorite music? Sure! It’s masking everything that’s bad in that recording and your audio chain. When you eliminate all those dust pops and clicks, add three times of stereo separation and dynamic range, suddenly things that were invisible before start to dominate your attention. Now all those small and slow random inter-channel timing variations smears stereo image and spoils the dimensionality of an captured performance venue. Also it does some strange things to human voice too. It just sounds less natural and more like your Alexa or whatever is helping you out to spend more money on stuff you don’t need.

This is still well in agreement with papers on jitter audibility by Julian Dunn or this one from Dunn and Hawksford. Just none of them went below 20Hz in their evaluations and concentrated on audibility and masking of separate tones/beats. And I tend to fully agree with those findings. Here I show same modulation side-bands from a 100Hz DEM clock as close as 25Hz from 1kHz fundamental and it doesn’t present any problems sonically whatsoever.

Let’s get back to practical side of things. What can be done to lower the close-in noise of the clock oscillator? Well, I’m afraid not much if we can’t measure it in the first place. Last time I checked, cheapest piece of equipment capable of a really close-in phase noise measurement was 53100a phase noise analizer and will set you back some 20k$. Don’t even ask what a similar more “scientific lab orientated” systems from Rohde&Schwarz or Agilent costs. Arm and a leg will not cover that. There are some tricks and tradeoffs to be made here and I’m currently working on my own phase noise measurement solution. Until it’s up and running, couple things will definitely improve any clock performance. I have applied them in my reference DAC and you can read it here. We just have no way of verifying the results.