Bit depth, how low can you go

[Vincent Kars]

Some more simple calculations

If we have a 16 bits recording, there are 2^16=65536 steps.
If we have a 24 bits recording, there are 2^24=16777216 steps.

If the maximum output of our DAC is 2 V, the output will fluctuate between +2 and -2 so a range of 4 V
At the analog site of the DAC we have a step size of
4/2^16=0.0000610351562500000000000 V
4/2^24=0.0000002384185791015620000 V

Any DAC able to resolve 0.000000238418579101562 V exactly?
No, this is such an extremely low value that it is at the present not possible to resolve this correctly.
Even if this was the case, it will be drown in the noise floor of your gear.

1 Bit is 6 dB (6N+1.8 dB to be exact but let’s forget this 1.8)
Bit dBFS
16 -96
17 -102
18 -108
19 -114
20 -120
21 -126
22 -132
23 -138
24 -144
25 -150
26 -156
27 -162
28 -168
29 -174
30 -180
31 -186
32 -192


If the noise floor of your DAC is at -96 dBFS, you just can resolve CD quality.
If you have a DAC with whisper quiet circuits at -132 dBFS you can resolve 22 bits.
The Resonessence Labs Invicta is the only DAC known to me able to do this.
No DAC at the present is able to resolve 24 bits as none have a noise floor of -144 dBFS.

 

[garylkoh]

Hi Vincent,
Would you please extend that table to 32 bits - I need it to support my case when I tell people that 24 bits is far, far more than needed, and 32 bits is ridiculous.

 

[Vincent Kars]

Would be nice if the forum software would support the HTML table format

 

[DonH50]

Note the 6N+1.8 formula is for SNR from quantization noise, which uses the integrated noise at the output; the noise floor (spurious-free dynamic range) goes as roughly 9N. The actual noise floor is set by a combination of quantization noise and circuit noise (thermal noise, shot noise, etc.)

Achieving even 16-bit linearity and noise is tough, let alone 24 or 32. The only DACs I know with that sort of real-world performance have very low bandwidth (few Hz or less) and are used in precision measurement systems. On a bench, getting 100+ dB of dynamic range is tough even in a screen room (shielded from outside interference).

 

[garylkoh]

I've seen specs where the manufacturer "cheats" by specifying noise without specifying a frequency they measure it, and measure at 1kHz or 500Hz. If you look at the PSRR of opamps used by most DAC output stages and the noise in the power supply at 10kHz, SNR could be at low as -20dB gated.

 

[Bruce B]

Every DAC I've used puts out between 7v and 15v. I know that doesn't change the figures for bit-depth, but there are several that have a noise floor > -120dB

 

[DonH50]

32-bit SNR = 6*32+1.8 = 194 dB; SFDR ~ 9*32 = 288 dB. Good luck with that.

Opamps depend upon good supply regulation and filtering to supplement falling PSRR (and CMRR) at high frequencies.

I do not know any DAC chip itself that puts out that much signal; the amplifier after it does. I bring this up not to be anal (well, maybe a little), but to highlight the fact there are other things in the signal path that add noise and distortion.

 

[Vincent Kars]

I do not know any DAC chip itself that puts out that much signal; the amplifier after it does.

Any idea of the level a DAC (chip) produces?
If that is much lower than 4 V than the numbers are even more stunning.

 

[fas42]

The sweet spot, or range, in all this, audio that is, is 60 - 80dB. 60dB is just enough, and 80dB means you're safe. And guess what, all those admirable R2R units work in that range. As Don says, trying to get to a genuine 100dB is hard work, and from the point of view of listening in a normal room, pointless. Try listening to a recording that's been attenuated 60dB without altering the volume, and you'll have trouble picking that something's happening.

Frank

 

[garylkoh]

Some of us are happy with the 30dB signal to noise on a noisy LP as long as the music is very good

 

[DonH50]

Any idea of the level a DAC (chip) produces?
If that is much lower than 4 V than the numbers are even more stunning.

Just checked the TI site; they list a bunch of 24-bit DACs with SNR from 105 to 127 dB. Most output current, not voltage, so drive a buffer amplifier or resistor and the actual output swing at the chip is ideally 0 V. The hottest (highest-performance) TI part specifies 4.5 Vrms max, but that is after an external amplifier. I checked the ADI site, and they have a 24-bit, 120 dB DAC, but again it is current output. So, based on a very brief look, the actual DACs are mostly designed to drive current into a virtual ground (0 V swing), with voltage output provided by an external amplifier (op-amp, or combination of op-amps). However, specs are often after the specified amp (e.g. specifies SNR and THD after their reference amplifier circuit), so your numbers are valid in the real world.

 

[Vincent Kars]

Thanks Don

 

[fas42]

Some of us are happy with the 30dB signal to noise on a noisy LP as long as the music is very good

Actually, it's fascinating that one can listen to performances with atrocious signal to noise ratios, probably 20dB of worse, and if the system is doing enough things right, the magic and emotion of the musical event still comes through, it's not a disturbing or fatiguing experience ...

Frank

 

[JackD201]

These are the D/A Conversion specs of my main player. It's all greek to me. All I know is it replaced some very respected sources. Can someone please translate what these numbers mean?

Theorical Resolution : 24 Bits > 192 KHz samples Rates
Resampling Rate : 384 Fs
D.A.C Architecture : Delta-Sigma Modulation
Power Bandwidth : 5 Hz to 24 KHz +/- 0,0015 dB
Channel Isolation : - 125 dB
Channel-to-channel phase error : N measurable
Noise/Signal Ratio : - 130 dB
A weighted noise/signal Ratio : - 160 dB
Phase linearity : +/- 0.19°
Unbalanced Analog Output Voltage : 3,30 V

 

[fas42]

What it means, Jack, if it's all true, right up to the output sockets, is that the performance is so superior, firstly to vinyl, and secondly to the very best reel to reel, that it should blow them into the weeds. If it doesn't, then someone's not telling the truth, or some other performance parameters which are never or rarely mentioned are just as, or more important, than those ...

Frank

 

[JackD201]

Since I own this player, I wish that were true. I still however prefer a clean first pressing, with a great cart mounted fanatically on a great arm on a stable and quiet table. Same goes for tape on a well maintained machine. Remember I'll always try and get good sound wherever I can get it. Having said that, I could very well live with the sound of this player if I didn't have good LP that I can AB it with easily.

So based on the numbers, what's this player doing that allows it to resolve spatial information and timbre that all my other players and DACs could never do (but my analog has always been able to do)? Is it the noise floor? The chip itself isn't exotic. It has separate transformer based power supplies that are analog filtered. That isn't new either. I've been playing with three models from the same manufacturer. Everything is identical (chips and even the chassis) except that the noise floor drops and the output voltage goes up as the manufacturer adds output devices per side along with their own dedicated supplies. This is why this thread is of interest to me. Vincent is definitely on to something here.

 

[DonH50]

Jack, the Noise/Signal Ratio and Channel isolation in particular are superb, pointing to a very excellent design realization. The output provides enough drive for most power amps with headroom to spare, and the noise floor supports an output that is probably a fraction of that 3.3 V in normal playback. Frankly, the DAC chips have gotten so good that the real magic is in the power supply, output amplifier and other circuits around the DAC. That includes the digital input and clock circuits. Basic measurements found on the usual data sheet only hint at real-world performance. Be happy. - Don

 

[fas42]

So based on the numbers, what's this player doing that allows it to resolve spatial information and timbre that all my other players and DACs could never do (but my analog has always been able to do)? Is it the noise floor? The chip itself isn't exotic. It has separate transformer based power supplies that are analog filtered. That isn't new either. I've been playing with three models from the same manufacturer. Everything is identical (chips and even the chassis) except that the noise floor drops and the output voltage goes up as the manufacturer adds output devices per side along with their own dedicated supplies. This is why this thread is of interest to me. Vincent is definitely on to something here.

The numbers you quoted say nothing of value about SQ, except that the designer has been very careful in getting the circuitry to work correctly, which should reflect in good "craftmenship" elsewhere in the machine, where being that way makes a great deal of difference. The effort with the power supplies is important because digital is fragile, or rather, the D to A process is extremely susceptible to interference. That it improves, I presume, with extra output devices, I assume you mean DAC chips, is because he's added extra power supplies -- in engineering lingo the supplies overall will be effectively stiffer, less prone to nasty transient spikes on the voltage lines being manifest, because the outputs will add, reducing the impact that noise on a single voltage source has.

So, yes, in an indirect way, the very low noise figure is telling you something good about the player, but the figure itself is so ridiculously low it means nothing as a figure in itself -- the very best R2R struggle to get anywhere near -80dB S/N.

Frank

 

[JackD201]

Thanks Don.

Frankie, I meant analog output devices. Although this player uses two chips, one for each channel. They have separate supplies too. The chassis and component sections are also shielded to some extent. I still think Vincent is on to something here. In conjunction with a question I asked Bernice of Spectral in another thread about DAC steps, I hope I'm finally beginning to understand the importance of bit depth not so much in terms of maximum dynamic headroom but in the actual usable voltage changes the increased number of steps allow to be represented.

 

[fas42]

Sorry, Jack, I thought it might have had some configuration like the Calyx, which uses a Sabre chip to give effectively 8 DAC's (4 x2 ) in parallel to improve performance. Playing with numbers again, that claims 32 bit performance, where will it all stop??!

Frank