[...] Because constant phase noise accumulates as a time jitter over time [...]
Wouldn't the noise introduce both positive and negative jitter, so it nets out to zero in the long run?
Wouldn't the noise introduce both positive and negative jitter, so it nets out to zero in the long run?
Yes, both negative and positive, and zero in average, yet it accumulates as larger and larger time jitter. At the first I was intrigued by the same question until it was kindly explained in another forum by somebody named "cirip". In fact, I re-"discovered" that myself, by accident, while trying to measure something else.
The intuitive explanation (as in rough and no math) is like this:
- phase noise can be seen as a frequency modulation (an ideal oscillator is FM modulate by some noise)
- frequency modulation can be seen as a "lenght" modulation (the length between two consecutive zero crossings)
- the noise has both + and - variations, averaging on zero
- let's make an analogy with a (foot) walking down an alley, where each wavelenght of the oscillator is a step made in the same direction, and the phase will be a small error, let's say randomly distributed in the range of +/- 0.1 steps
- we make one step, we arrive at the distance 1 +/- 0.1 steps
- if we walk 100 steps, we arrive in average at a distance of 100 steps, correct, but what will be the range of the final error?
The real question here is what is the worst possible error? That would be if by chance all the errors (at each step) will be +0.1 (or -0.1). In conclusion:
- walk 1 step and arrive at the distance 1 step +/- 0.1, so the end point is at [1 step +/-0.1] steps
- walk 10 steps and arrive at the distance 10 steps +/-0.1*10, so the end point is at [10 steps +/-1] steps
- ...
- walk 999 steps and arrive at the distance 999 steps +/-0.1*999, so the end point is at [999 steps +/-99.9] steps
- the more we walk, the bigger the range of the final error.
The +/- n steps is the error after walking n steps (caused by the noise), and this length error is what we perceive as time jitter on the oscilloscope.
are we in effect depending on the low frequency components of the phase noise to "stack up" and cause enough jitter to become visible?
are we in effect depending on the low frequency components of the phase noise to "stack up" and cause enough jitter to become visible?
This is the next very good question, after the previous one. Kind of yes, but there is yet another very tricky thing here.
Our (wrong) intuition would say:
- OK, so if I look n edges later from the triggering point (let's assume it's a square wave instead of sinus) I would see all the n'th falling edges uniformly distributed in the range of the final +/- error, around the average point, but this is not what we see!
Most of the edges are right near the expected average, even if the error came from a white noise. So, initially all the values in the range were equally possible in the +/- error range, yet after many steps we see most of the errors will like to "cluster" around the average, only a very few fall farther away from the expected average. The final errors distribution after many, many steps has a Gaussian shape.
This is because of something very fundamental to statistics, called Central Limit Theorem. For our case it means that if we "accumulate" many errors equally distributed (white noise) we will end up with errors that are not equally distributed, the final errors will have a Gaussian distribution (Gaussian noise).
The resulting Gaussian shape is very convenient for us, because we know that standard deviation \$\sigma\$ directly relates with the RMS power of the noise, while the mean value \$\mu\$ directly relates with the DC component of the noise.
That Gaussian shape happens no matter what when "adding randomness", and is sometimes called Normal Distribution.
https://en.wikipedia.org/wiki/Normal_distribution
Here's an interactive model of a Gaussian shape (in general), and how it changes with its standard deviation and its mean values \$\sigma\$ and \$\mu\$. (drag the sliders)
https://www.geogebra.org/classic/ehkwndma
How much are you willing to spend? What carrier frequencies are we talking about?
There are many ways to measure and characterize the phase noise. Would be nice to link or name the documents you were talking about.
There are many ways to measure and characterize the phase noise. Would be nice to link or name the documents you were talking about.
My colleague supplied the IEEE MACOM Paper. See my edited post earlier.
Best
Thanks, but correct me if I am wrong, but it looks like they are using the term "injection" for phase (e.g. injection locking v. phase locking) and if so, this is the procedure I'm currently evaluating.
I've been communicating via email with Andrew Holme and plan to build his system. I'll post as i progress thru his FPGA based system and my analog version.
Thanks for all the comments.
Jerry
So, now I have an extension to the project. I've written a lot of DSP code but not on FGA but this shouldn't be all the complicated to implement. I would love to have help on this aspect of the project.