Since I heard my name invoked I'll offer a bit of insight here... but some of you may not find it especially inspiring.
Originally most standard analog Volume controls were potentiometers.
A potentiometer is literally a long resistor, with one connection at each end, and a contact that slides along, making contact wherever it is.
In a standard rotary knob potentiometer this is curved around into a horseshoe shape; they even make multi-turn potentiometers where it makes ten or twenty turns like a sort of corkscrew shaped ramp.
Things like Volume controls usually use a strip of plasticky resistor stuff... and big power ones often use a ceramic rod or donut with a spiral of nichrome or similar resistor wire wrapped around it.
These work OK... but for a Volume control you generally want an "audio taper"... which means that, rather than being linear, the resistance is "all bunched together - often logarithmically - towards one end".
The catch is that, at the bottom end, it's very difficult to get them perfectly consistent, so they tend to "not have good channel tracking at the bottom end".
This is why, with analog potentiometers, you tend to get "balance errors" near the bottom... which often get really bad close to the bottom.
You can pay a lot more for high quality ones that track better... but even the really expensive ones aren't great down near the bottom.
The next step up is a "stepped attenuator"...
This is simply a selector switch with resistors connected to all of the contacts.
Since they use separate resistors, you get to choose whatever values you like, and it's easy to use arrangements that allow really good tracking between channels, and whatever taper you prefer.
The catch with these is that you need a selector switch with a lot of contacts - one for each "step" - and one or two resistors for each step.
In the end, you need a huge selector switch, with a lot of contacts, and a lot of resistors, and there is still a practical limit on how many steps you can make.
You have a tradeoff between a mechanically huge and horrifically expensive one with lots of steps and a practical one with not as many steps as you would like.
(You rarely ever see these any more.)
What you do often see is a plain old potentiometer with a little "click thingy" that "makes it click like a real stepped attenuator".
NOW we move on to devices with digital displays and "digital controls"... which is what almost all of our gear uses (except the A2mini).
Basically, inside, the Volume is being controlled by an electronic circuit, which is in turn controlled by "a computer".
This can be a "pure digital Volume control" which "changes the Volume by changing numbers"...
But the type we usually prefer is, and use in most of our gear, is "a digitally controlled analog ladder network".
This is basically one of those stepped attenuators... with a whole bunch of resistors... and a selector switch with a whole bunch of contacts... for each channel.
However, in this case, all of the resistors, and all of the switches, are in a chip (or several chips)... and the switches are controlled by a microprocessor.
The signal is still analog... and the resistors are still resistors... and the switches are still analog switches.
You can get up to 128 or 256 steps...
And the steps themselves are really precise (so the channels track really well)...
And you can get multiple channels in a single chip...
Something like an RMC-1 has 16 channels to control... and, since they're balanced, each of those requires two channel of controls...
But, from "the outside", all of this analog complexity is controlled digitally...
This allows the computer that controls the Volume to set the level of each channel exactly where we want it... to an accuracy of a fraction of a dB.
And, at this point, the "knob" is just attached to something called an encoder.
And, like the mouse on your computer, the knob is just a convenient way for you to interact with the computer that controls the Volume.
The encoder simply tells the computer that you've turned the knob, which direction, and how much, (and maybe how fast).
There are different sorts of rotary encoders but they all serve this same purpose...
And, with most, including ours, the "clicks" are mechanically generated... just to provide a nice feel when you turn the knob... and to provide the equivalent of "friction" for the knob.
And "how much the numbers move when you turn the knob a given amount" is just down to how the control computer is programmed.
(I don't have the exact "turns ratio" listed for our different products... and some even give you the option of using either "numbers 0-80" or "dB".)
However, because of the way it's done, the control itself is remarkably precise, and the channels track exactly, to within a small fraction of a dB.
