why does digital volume control cause loss in info

Mapman has the right idea. I would slightly reword his statement as follows:

"If all bits in each sample are required to represent a signal at the maximum possible volume, fewer bits will be available to represent each sample at lower volumes."

The higher order (most significant) bits will be fixed in a single state (e.g., 0, as opposed to being able to change between 0 and 1), in order to represent the fact that the signal does not extend above a certain volume.

It should be kept in mind, though, that in concept the loss of resolution with a digital volume control at lower volumes is no different than what occurs with an analog volume control, although there will certainly be differences in degree.

In both cases, the signal level is being reduced relative to the noise "floor" of the parts of the system that are at and "after" the volume control. Simplifying slightly, in the case of a digital volume control the noise floor (referred to as "quantization noise") corresponds to the resolution that is provided by the least significant bit. In the case of an analog volume control the noise floor corresponds to any analog noise that is introduced into the signal path by the circuitry at or after the volume control (noise that is introduced "before" the volume control will be attenuated by the volume control by the same amount as the signal is attenuated, and so the ratio of signal to noise will not change).

In practice, though, noise introduced in the analog signal path following the volume control is usually pretty minimal in a quality system, and the spectral characteristics of analog noise are usually such that the ear can discriminate between the noise and signal levels that are significantly below the noise level. While the 16 bits of the redbook cd standard are significantly less than ideal to begin with, especially considering that two or three of those bits may be thrown away in the recording process to prevent the possibility of clipping the recorder.

Regards,
-- Al

Shadorne: Thanks. Not sure, though, that it's fair to say that properly applied dither will necessarily make a digital volume control "as good as analog." It will certainly reduce the subjective objectionability of quantization noise. But I suspect that it could not adequately compensate for the loss of say 4 or 5 bits, corresponding to a volume control setting that is 24 or 30 db below maximum.

Also, it would seem expectable that in a standalone audio component, that most likely does not have the computing horsepower of a general purpose computer, and that has to calculate and apply the digital volume control function and the corresponding dither on-the-fly, in real time, for any arbitrary volume setting, that optimal dithering and noise shaping is not necessarily going to happen.

ElDartford: If an analog output is being produced there is no reason to use another implementation.

Cost, perhaps? In other words, reducing cost by eliminating that chip altogether, and incorporating the digital volume control function within a gate array or other custom digital chip that is required for other purposes.

Regards,
-- Al

I took a quick look through the CS3310 datasheet. It looks like a pretty nice device, although I'd expect that designing with it, and achieving good results, would be a non-trivial challenge because of the presence of both digital and analog signals and power on the same device. And I note that its datasheet was initially released in 1991, so there may be newer and better comparable devices available now.

Digikey charges $6.57 for it in quantities of 1000. I believe that a generally accepted rough rule of thumb for equating parts cost with final assembly selling price is to apply a factor of 5. So it would have about a $33 impact on the selling price of an audio component, or perhaps say $50 to $100 factoring in possible requirements for additional surrounding circuitry to interface to it, and additional circuit board real estate that may be required. Not a huge cost, but certainly significant.

A purely digital volume control, on the other hand, could perhaps be implemented within a custom digital chip that is required in the design for other purposes, resulting in negligible impact on recurring cost.

Thanks for pointing out this device, ElDartford and Shadorne.

Regards,
-- Al

Excellent comments, Kirk. Thanks.

Re your first point, to make sure its clear to others who may read this I'll add that the fundamental purpose of dither is to convert quantization distortion into low level analog-like broadband noise. Or even better, into "shaped" noise, that predominantly occupies parts of the spectrum to which the ear is relatively insensitive.

Re your second point, which I hadn't thought of when I wrote my earlier posts, that would say that the bad rap digital volume controls justifiably got a decade or two ago would seem to be much less applicable, and in some cases completely inapplicable, to today's designs.

Best regards,
-- Al