Q: What are the effects of dividing the VCO output by 2 on output jitter?
A: It depends on your assumptions although in general it doesn't make much
difference.
Analysis:
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When comparing the effects of dividing the VCO by 1 or 2
on clock jitter, to first-order we can ignore the PLL's feedback
loop. Why? VCO jitter is primarily determined by high-frequency
power-supply noise and other forces that act on the VCO much faster
than the feedback loop can respond.
There are four scenaria to consider:
Cases #1 and #2 are more realistic in that VCO jitter tends to decrease with
increasing VCO frequency. To first order, you can assume that VCO jitter
remains a constant percentage of the VCO period. This is the assumption
used in the first two scenaria.
1) If VCO jitter is a constant percentage of period (smaller absolute
jitter at high frequencies) and random, then jit(div2) = sqrt(2)/2 * jit(div1).
Dividing by 2 is better by 30%.
Note that the sqrt(2) function accounts for how we add two statistically independent error functions.
2) If VCO jitter is a constant percentage of period and deterministic,
then jit(div2) = jit(div1). Div-by-2 is the same as div-by-1.
The assumption is that the worst-case noise pattern persists for at least
2 VCO cycles, and so both phases of the divided clock "see" the noise.
3) If VCO jitter magnitude is constant with changing frequency and Gaussian
(think thermal noise and/or random VDD noise), then jit(div2) = sqrt(2) * jit(div1).
In this case, dividing by 2 is 40% worse.
4) If VCO jitter is constant and deterministic (think pattern-dependent VDD noise),
then jit(div2) = 2 * jit(div1). In this case, dividing by 2 is 100% worse.
In the end, the decision whether or not to divide the VCO by 2 is going to be driven
by duty cycle requirements, VCO min/max speed, VCO frequency range over which
power-supply noise is acceptable, PVT-related variations, divider logic
complexity, availability of power-supply filter, etc. The "academic" exercise
above shows merely that there is NOT a strong "a priori" argument to dividing
the the VCO clock by 2. Sometimes it helps, sometimes it hurts.