Dear Ken:

I've recently read your paper about predicting the phase noise and jitter in PLL based Freq synthesizers. That's was indeed a great work, and I've learned a lot about phase&jitter in PLL's in a good depth. In this paper(phase+jitter), I still have encountered some problems. Maybe these problems are quite fundamental, I hope you can explain for me  in order to be sure that I didn't mistake or miss something.

First of all, when the effective gain of the PFD/CP, Kdet, was mentioned. It was said that I should scale this gain so that it has the units of A/sec. While eq(54) wrote:
Jee,pfd/cp=(T/2*pi*Kdet)*sqrt(var(n)/2)
I believed that the factor of "1/2" in "sqrt(var(n)/2)" counts for the two transition of a single cycle, "Jee" and "T" has the units of sec., and the "sqrt(var(n)/2)" has A.. So I thought "Kdet" should has the units of "A" instead of "A/sec". Have I mistaken something?

Secondly, In the extraction of jitter in either PFD/CP or dividers, it was recommended that I could set the "T" smaller in order to reduce the number of sideband needed. What I need to ask is that when "T" varies, doesn't the output noise change? IF the reason is that the changes could be negligible, how should I judge the side effect of smaller "T" which may away from the its operation range in a PLL. For instance, a certain divider in my PLL has an input range near 1GHz. Should I drive it at 2GHz or even higher freq. , of course not exceed its capability, in the jitter extraction process?

And the last question, all the derivation of jitter in this paper is based on the exception of 1/f noise. If I want to count for the effect of flicker noise, How should I modify the process of tranfer phase noise to jitter?

After all, I stiil want to thank you to offer such a good work in dealing with phase/jitter in PLL's. That was really a good paper.

Dear Ken:

Thanks a lot for your immediate response, and that's was indeed helpful for me. I am a new comer to Spectre, so I hope my questions didn't bother you if their answers are quite obvious!


-Aigneryu

Aigneryu,
   Here is the final installment.
-Ken
Quote:

The first thing you have to know is that most of the jitter metrics are unbounded in the presence of flicker noise (the one exception is cycle-to-cycle jitter because it ignores low frequency jitter). If you were to try to measure any of these metrics you would find the result would be finite, but would vary depending on how long you observed the jitter when making the measurement. The longer you observe the jitter, the greater the measured jitter.

Second, building a model that exhibits flicker noise is not easy. The only way I know to generate flicker noise in a time-domain simulator is to generate a white noise sequence, and then pass it through a half-pole integrator. So then the question becomes, how does one generate a half-pole integrator? The basic approach is to build a high-order filter where the poles and zeros alternate on the real frequency axis and are equally spaced in a logarithmic sense (this is discussed in The FracPole Suite in www.designers-guide.com/Modeling).

These problems with flicker noise are one of the reasons why I presented the phase domain models. They are well defined in the presence of flicker noise. In addition, I have yet to encounter an application in which flicker noise was important that wasn’t better handled in terms of phase noise. So, I haven't spent much time thinking about how to extract the jitter of systems that exhibit flicker noise. And other than identifying some of the problems, I don’t really have much to suggest.

Aigneryu,
   I was following until I got to "the final answer is", and then things stopped making sense to me.  Allow me to derive J_cc from J_ee.

Consider synchronous jitter and let T_i = T + dT_i where dT is a random process with
J_ee² = var(dT_i)
for all i. Then
J_cc² = var(T_i+1 - T_i)
J_cc² = var(T + dT_i+1 - (T + dT_i))
J_cc² = var(dT_i+1 - dT_i)
If dT_i+1 and dT_i are uncorrelated, then
J_cc² = var(dT_i+1) + var(dT_i)
J_cc² = 2J_ee²
J_cc = sqrt(2)J_ee

With flicker noise J_ee is unbounded. And so if dT_i+1 and dT_i were uncorrelated, then J_cc would also be unbounded. However, with flicker noise dT_i+1 and dT_i will be strongly correlated because flicker noise is a slowly varying process. In effect, the cycle-to-cycle jitter measures how much the flicker noise varies over the length of one cycle (which is bounded) whereas the edge-to-edge jitter measures how much the flicker noise varies over all time, and since flicker noise goes to infinity as frequency goes to zero, J_ee is unbounded.

-Ken

I have one comment regarding flicker noise in PLLs. If it only affects the really close in PLL phase noise it may be irrelevant. The system using the data riding on the carrier probably has a tracking loop capable of following the close in phase noise. If it were me, I'd check the receiving end for a phase tracking loop and if one existed, I'd check the bandwidth, before building any detailed models of close in phase noise.