Estimating the magnitude of PMD
Dear colleagues,
The purpose of this note is to start a discussion: how significant is
this PMD issue for us? (Yes, DMD for multimode is also on our agenda;
it's next on my list.) We need to estimate its impact on equalization for
singlemode 1550 nm link, and on the performance of an unequalized link.
We need to start by quantifying the magnitude of PMD for the 1550 nm link
under consideration by P802.3ae.
I have done some back-of-the-envelope calculations, which I will describe
here, then I will point you to a more rigorous document. To start, I
needed to know what are the mean and variance of DGD (Differential Group
Delay) PDF (Probability Density Function). I sent a note to TIA FO 2.2
members, some of them responded, and subsequently I conducted an offline
conversation with some of them. (PMD value is defined as DGD value
averaged over all wavelengths present in a signal.)
I learned that this PMD subject is still evolving, and many measurement
methods are still being debated. But I needed to start somewhere, so I
started with the following assumptions:
- We can consider the PMD effect of our 1550 nm link as stochastic,
dominated by cable. We can ignore PMD contribution of all other
components, deterministic or random.
- For such a link, assuming the wavelength averaging doesn't change the
picture much, we can take the PMD value specified in a manufacturer's
data sheet as the mean of the DGD PDF, which is Maxwell type.
- In the PDF, parameter alpha can be assumed to be 1.
- With a Maxwell PDF assumption, we can derive variance from the given
value of mean.
- With a desired upper limit on probability of catastrophe, we can derive
the acceptable worst case value of DGD in picoseconds.
Next, I confirmed that the worst case value of x (for which the
normalized Maxwell_Probability reaches a value of 10^-12), is about 5
times mean.
%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all;
alpha = 1;
mean = alpha*sqrt(8/pi)
sigma = alpha*sqrt(3 - (8/pi))
x = mean + 9.42*sigma
Maxwell_Probability = sqrt(2/pi)*(x^2/alpha^3)*exp(-x^2/(2*alpha^2))
%result: Maxwell_Probability = 10^-12
%%%%%%%%%%%%%%%%%%%%%%%%%%
The worst case value of x is 9.42 sigma away from the mean, or about 5
times mean. So if our value of mean is 0.5 ps/sqrt(km), which is the
value proposed by IEC E61282-3 draft, the DGD can reach 2.5 ps/sqrt(km)
in the worst case. For a 49 kilometer link, DGD can be 2.5*sqrt(49) =
17.5 ps. If I assume that DGD is approximately equal to pulse broadening,
we conclude that the 10G pulse will broaden by 17.5 ps worst case.
If I pick a link composite PMD value of 0.2 ps/sqrt(km) as given in some
fiber data sheets, the pulse broadening will be 7 ps.
My questions for the group:
1. Steve Swanson (Corning) has kindly given me a copy of the IEC E61282-3
draft (Guidelines for the calculation of polarization mode dispersion in
fiber optic systems). I have placed it on our website:
http://www.ieee802.org/3/ae/public/adhoc/equal/
If you feel up to the challenge, please wade through it, and tell me how
far off my simple minded calculation is from the more accurate methods
described in that document.
2. Once we agree on a number (pulse broadening in picoseconds), we need
to decide if it is significant enough that we should alert our friends in
802.3ae who are working on defining the link specs for Clause 52,
10GBASE-E. And what do we recommend to them? Add this worst case value to
horizontal eye closure (due to jitter, ISI, etc.)? How bad is the
approximation that PMD horizontal eye closure will add linearly to that
caused by chromatic dispersion?
3. The PMD value of 0.2 ps/sqrt(km) is from a recent data sheet. It has
been suggested that fiber made prior to 1992 has higher values of PMD. We
may have the option of dismissing this concern if we know that it is a
negligible portion of the total fiber in the ground. Mike, can we request
you to investigate that, and email that info to us?
Thanks,
Vipul
vipul.bhatt@xxxxxxxxxxx
(408)542-4113