Thank you for the response. I have watched that video serval times.
I get that one edge is always canceled by just 1 other edge. I even understand how choosing the number of elements is related to the resolution of the PWM signal.
Where I lose the plot is when we look at each element individually.
Each element is essentially a single PWM signal of the whole music signal. In other words, If we could just play a single element out of the array and we would have music on the output. This is how you get matching across all the elements in the array.
But since each element is slightly delayed, each signal will arrive at the output at different times. How is it possible that 10 or 20 slightly different signals all sum up to 1 "correct" signal.
A different way of saying it is how does this function make sense?
((Signal1 + 0t) || (Signal2 + 1t) || (Signal3 + 2t) || (Signal4 + 3t) || (Signal5 + 4t) || (Signal6 + 5t) || (Signal7 + 6t) || (Signal8 + 7t) || (Signal9 + 8t) || (Signal10 + 9t)) = Signal1 + 0t
Where t is not equal to 0.
And again, why go through the trouble of time shifting everything? Wouldn't a differential signal cancel just once at every rising and falling edge without the need for time shifting? I'm not trying to be intentionally dense, but this has been bugging me for years. I saw Mr. Watts presentation a while back at cam jam and I have regretted not asking these questions.
The elements are not mathematical objects but physical switches so it’s impossible for the elements to be identical. That means signal1 is not perfectly equal to signal 2 and 3 and 4 and 5. Most DACs use some form of dynamic element matching so that if you just a signal level of 1 (out of 10) instead of always firing signal 1, you would sometimes fire signal 2 or 3 or 4 or 5. That way it evens out the errors amongst the elements.
As to why a differential signal approach is not equivalent to a constant switching approach, you can think of it this way.
Let’s imagine a signal of 000111
So in differential signal, you’ll actually have 000111 on one end and 000-1-1-1 on the other end which is basically still 000111
In a constant switching scheme, to get 000111
Flip up 111111
Flip down 111011
But in a differential scheme
Flip up 000100
Flip down 000000 for the positive end
Flip up 000000
Flip down 000100 for the negative end
So what you’re saying is that it’s the same thing because the differential scheme canceled each other.
Except when the elements are not flipping, they have a different energy level and less noise than when the elements are flipping. And flipping up and down also tend to have slightly different levels of energy. These slight differences would generate varying degrees of noise.
so far, we are dealing with a small signal change. If we are going from super quiet to super loud in a differential scheme then suddenly you’re going to have signal dependent noise because you only need to switch when the music is loud and you don’t switch much when the music is soft.
This is why constant switching schemes tend to have lower levels of jitter and noise floor modulation.
Like I said, I’m thinking about this like a layman so my explanations are very clumsy. But I hope this makes sense.