[time-nuts] Noise of digital frequency circuits (was: Programmable clock for BFO use....noise)

[ed breya]

Atilla wrote: "Yes. This effect has been known for a few decades at 
least. What kind of puzzles me is, that I have not seen a mathematically 
sound explanation of it, so far. People talk of aliasing and sampling, 
but do not describe where the sampling happens in the first place. After 
all, it's a time-continuous system and as such, there is no sampling. 
One could look at it as a (sub-harmonic) mixing system, but even that 
analogy falls short, as there is no second input. If someone knows of a 
description that goes beyond handwavy arguments, I would very much 
appreciate hearing of them."

I can only offer a handwavy suggestion, or food for thought, regarding 
digital dividers of all sorts.

Regardless of the type of divider or process used, the devices within 
have finite gain, so imperfect isolation between the output activity and 
input. Whatever is happening downstream in a divider chain can provide a 
delayed, topology- and pattern-dependent signal back to the input, 
containing the associated frequency content. The issue of course, is how 
big the effect may be.

I don't know if this sort of thing is trivial or has already been 
included somehow in the rigorous and theoretical studies, but I know 
it's there, having observed such anomalies over the years. I've never 
had a situation where the effect was big enough to prevent something 
from working right, just casual observations that made me think about 
what's going on.

You can probably observe it easily with enough dynamic range. Say, set 
up an ECL FF to divide by two, and AC couple everything for ground 
reference. Put in an RF clock signal - sine, square, doesn't matter - 
and look at this input signal with a spectrum analyzer (don't worry too 
much about impedance matching - just get the clock signal big enough to 
toggle). You should see the strong clock and its harmonics, as expected, 
and if you dig deep enough, should be able to see the one-half frequency 
that shouldn't exist with a perfect FF. Now, how it gets there may be 
due to a number of reasons like ground loops or power supply coupling, 
but some of it is going right through the device from out to in.

Ed