Nice work. Now we need to expand the argument. So far, we talked about a full scale 1KHz sine wave, and what happens when you effectively truncate it. You decrease the signal to noise and generate some distortions. It still "looks like" a sine wave with little alterations.
But take a real instrument, where the character of the sound is defined by harmonics. Low level harmonics (with small amplitude) require lower order bits. If digital “push down” some lower bits signals under the noise floor, it may eliminate the fine details that define the instrument sound.
For volume control, I chose analog attenuation. The main reason (if I recall) was the noise issue. Say feeding an 18dBu signal directly to a 4dBu line level requires 14dB attenuation. With digital attenuation, the noise of the DA (even with no digital signal) is fed directly to the power amplifier input. With analog attenuation the noise is reduced by 14dB.
Can anyone hear 14dB more noise, some added distortions and some loss of details (harmonics)? It depends on the music, the setup and of course the listener. Driving consumer level is 26dB more noise. My view as a designer is to avoid degradation if it can be avoided (and be ready for worse case scenario). It calls for providing some MARGIN for the best ears under the most critical conditions (say a great mastering room).
Analog attenuation is nearly perfect. Digital attenuation causes some alteration of the data. Doing it in digital would be much cheaper and easier, and it is “not noticeable” to almost all the customers. I still want to avoid all possible issues with large margins, beyond human hearing capabilities.
Leaving sound and audibility aside for a moment, there are other factors in choosing digital or analog attenuation.But isin't it the case that in a 24 bit or higher dac, the 16 bit data is padded out to 24bits before passing to the actual DAC function. As long as digital volume control is done after padding then we are dealing with a 24 bit noise floor. In fact the 16 bit noise floor is part of the padded signal, and being 48dB above the 24bit digital noise floor, is itself turned down without SNR loss for that first 48dB.
Yes - if digital volume is carried out at the 16 bit domain perhaps there is an issue - but I don't think it is in typical DAC with preamp function, even when the source is 16 bits.
Edited to add:
I fully agree that if one is only looking at the numbers/measurements, and ignoring audibility - then analogue attenuation is going to beat digital for most metrics - possibly excluding channel matching depending on the analogue implementation.
A DA for professional use output level is often 24dBu/18dBu balanced, or 18dBu/12dBu unbalanced. Some studios required a front panel 0.1dB fine adjustment (+/-0.7dB). High signal level (and balanced) offers some advantages.
But most power amplifiers and other gear with analog input requires less signal. Listening in real time to professional signal can be done with two DAs. One DA for professional level, the other DA receives different data. That approach is "complicated".
I used the analog attenuator to ELIMINATE the need for a second DA.
There is a MAIN output (L/R XLR’s) for the DA. But there is a secondary MONITOR output (L/R XLR’s). The monitor input simply taps the MAIN output signal through analog resistor dividers. If set to 0dB attenuation the MAIN and MONITOR are the same, it is the same DA signal.
I could have done it digitally inside the Quintessence DA. Intercept the data, digital attenuation, second DA and associated circuitry for the MONITOR output. Add that to all we talked about earlier…
I am not saying that doing a clean analog is easy. I think it was worth it to remove the need for a second DA in many situations. Also, the MONITOR output sound is as close to activity on the MAIN.