RE: Estimating the magnitude of PMD
Vipul,
Regarding your request for feedback on your back-of-the-envelope
calculation of PMD and where to go from here:
1. Your calculation is not exactly correct. Strictly speaking, it's
illegal to equate a probability density (the Maxwellian expression) to
a probability (the 10^-12). The correct physical condition on the
separation time you are trying to calculate is that the probability of
the actual separation time being equal to or greater than that time is
no greater than 10^-12. Therefore you have to integrate the probability
density from that time (which is unknown when you start) to infinity,
and set that integral equal to 10^-12. Evaluating the integral results
in an equation for the time you seek, whkch can easily be solved
numerically. Interestingly enough, the answer is not far from what you
calculated. Using this procedure, I obtained a separation time of ~ 4.81
times the mean, which is pretty close to the factor fo 5 that you got.
NOTE: I haven't given any thought to the relative amount of energy in
the two polarizations, but simply assumed that each carried half of
the energy. While this is probably what happens on average, there is
probably a probability distribution of relative amplitudes as well as
delay times, and this should probably be taken into account.
2. As regards the question of how this affects the 1550 PMD, there
are two issues (there may be more):
a. Vertical eye closure - The PMD will contribute something to the
ISI penalty. The "impulse response" of the PMD is two delta functions
separated in time by the PMD separation time calculated above. While
this can be dealt with as is, it's mathematically much easier if this
impulse response is approximated by an "effective" gaussian impulse
response, defined so that it has the same mean and variance as the
delta function impulse response. While this seems like a bad approx-
imation, it isn't really, especially when you consider that either
will be convolved with the response of the rest of the system and result
in an overall gaussian system response. In fact, it's not hard to
show that a gaussian PMD impulse response results in a total ISI penalty
which agrees with that calculated using the delta function response to
a few 10ths of a dB or better, even when the PMD separation time is as
large as one half the baud period. A fiber polarization modal bandwidth
(analagous to the MMF modal bandwidth in multimode systems) can then be
calculated using the familiar relationship between a gaussian impulse
response and its corresponding frequency response. The PMD would then
enter into the model and the ISI calculation in an analagous way to the
current modal bandwidth for MMF, with the difference that it scales as
the square root of the link length rather than the length itself. I've
done the math on all this, and I would be happy to share it if people
are interested.
b. Horizontal eye closure/jitter - Here the situation is a little more
ambiguous, given that we really don't have a good way of incorporating
these effects into the model at present. The method of dealing with
the bimodal impulse response resulting from DMD in multimode fiber was
to reduce the effective baud time by some fraction - the duty cycle
distortion_deterministic jitter factor. The same approach could be
used here, although we need to give some serious thought to exactly
how much the period should be reduced, given the non-determinsitic
nature of PMD.
Dave Dolfi
Agilent Technologies
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> From: Jonathan Thatcher <Jonathan.Thatcher@xxxxxxxxxxxxxxxxxxxx>
> To: vipul.bhatt@xxxxxxxxxxx,
Equalization Ad-Hoc Reflector <stds-802-3-hssg-equal@xxxxxxxx>
> Cc: Mike Hackert <HACKERTMJ@xxxxxxxxxxx>,
Steven E Swanson <SwansonSE@xxxxxxxxxxx>
> Subject: RE: Estimating the magnitude of PMD
> Date: Wed, 27 Sep 2000 06:44:46 -0700
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>
> Vipul,
>
> Point: don't wait too long before you include the clause 52 folk. We spent
> some time talking about this on a teleconference today. We do be worried. To
> the first order, I would assume that we would PMD directly to the DCD. This
> would affect both the jitter budget and the power budget. In "z" we
> discovered that 65 ps of DCD out of 800 made a huge difference. Imagine what
> an additional 7 (or worse, 17) might do to "ae."
>
> Question: why did you pick 10e-12 for your calculation? Because of the
> assumption that PMD will add linearly to the jitter?
> Something bothers me here, but I can't put my finger on it. I think you
> might be mixing metaphors. Let me ask the question in a different way (no, I
> do not know if this is the correct way to think about the problem):
> statistically, what would the maximum PMD be for 99.99% of the population of
> fibers (meeting some reference specification)?
>
> jonathan
>
> > -----Original Message-----
> > From: Vipul Bhatt [mailto:vipul.bhatt@xxxxxxxxxxx]
> > Sent: Tuesday, September 26, 2000 2:06 PM
> > To: Equalization Ad-Hoc Reflector
> > Cc: Mike Hackert; Steven E Swanson
> > Subject: 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
> >