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Can you determine the accuracy (ie. how many bits) the actual DAC inside delta-sigma DAC is?

mike7877

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I've been wondering!

I've noticed, after looking at numerous datasheets, that usually, the oversampling is done 128 or 256x, sometimes 512x, when rendering 44.1/48.0kHz. Obviously when you increase to 88.2/96, you half the amount of oversampling, because the DAC runs at the same rate all the time, usually the equivalent to DSD512 - octuple-rate DSD, or, in MHz, 22.5792/24.5760 (44.1/48.0).

I noticed!

I noticed that, when DAC maker AKM released the updated version of their flagship 4499 (AK4499), now called the AK4499EXEQ, and they separated the entire SOC into two parts, analog and digital, because seven pins were used to drive the DAC, AKM had no choice but to tell us that the design of their excellent resistor DAC was 7 bit!

2^7 = 128

Is it a coincidence?

With a 7 bit DAC, we have 128 different voltages represented. They say when you oversample 4x, you gain 1 bit of resolution. I guess this is because if, say you want a voltage half way between the voltage represented by 127 and 128. Pretend 127 is +63V, and 128 is +64V - what do you do to make 63.5V (this DAC is linear like that lol - also, the sample rate of the signal is one sample per second. What you do is, you send 127, then 128, then 127 again, and finally 128. This is 63, then 64, then 63, then 64V. Because this is oversampled 4x, each of these voltages is maintained for only 1/4 second. Averaged out, (ie. properly lowpass-filtered) you get the average of bits 127 and 128 (bit 127.5): 63.5V!

So every two bits of oversampling added (4 samples), you gain 1 bit of accuracy - you double the accuracy.

The datasheet of the AK4499EXEQ in my second-favourite personally-owned DAC (Topping E70 Velvet), states that for best measurements, 128x oversampling is used, and for best sound quality, 256x oversampling is used. This is said in a roundabout way (there's a spot in the low level configuration where the OEM selects 0 or 1, 0=best measurements 1=best sound quality, and 0 is 128x, 1 is 256x, and all the measurements in the datasheet are at the 128x rate except for the one at 256, which IIRC is 7 or 8dB higher THD+n)

The digital chip of the AK4499EXEQ chipset (technically called AK4191EQ) can be used to drive chips other than the standalone 7 bit resistor DAC AK4499EX - it says as much somewhere in its datasheet. Since 7 is more than the usual number of bits available, it delta-sigma section can be configured to drive lower bit DACs, specifically 5 and 6. You have a 4 bit DAC? Too bad for you! Lol. So from this, I gather that most audio DACs (save for true one bit DSD DACs) are 5, 6, or 7 bit.

Can we use the amount of times oversampled and approximate performance to estimate how many bit the DAC being used in a chip is? Or is that a stretch?
 
So from this, I gather that most audio DACs (save for true one bit DSD DACs) are 5, 6, or 7 bit.
I think that's basically all we can say. And I don't think it has any special importance. It's just a technological implementation detail and I wouldn't draw any general conclusions from that.
 
For decades now the vast majority of delta-sigma DACs have used multibit internal stages, often several in cascade, to improve the performance without requiring extremely high sample rates.

You gain 0.5 bit for each doubling of the sampling rate without noise shaping; noise shaping typically adds about N.5 bits for each doubling of the sampling rate for an Nth-order modulator. Multibit internal DACs add about 1 bit for each additional bit, e.g. a 7-bit internal stage adds about (7-1)*6 = 36 dB ( bits) -- ideally.

Delta-sigma overview:

If you want to try to find out the number of internal bits, certain tests can help find signatures (patterns) in the output, but in general and for a proper design it is virtually impossible to tell externally by listening or casual testing.
 
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