🚀 go-pugleaf

In article <25423@amdcad.AMD.COM> rpw3@amdcad.UUCP (Rob Warnock) writes:
>josh@klaatu.rutgers.edu (J Storrs Hall) writes:
>+---------------
>| One commonly reads in articles about arbiter circuits that
>| it has been proven that the problem of metastability cannot
>| be completely avoided.  Is there an actual proof anywhere?
>| --JoSH
>+---------------
>
>The real trick to making a good (not perfect) synchronizer is getting
>a latch stage with a very high gain-bandwidth product "around the loop".

The GBP also depends heavily on the capacitive loading at the output of
the loop.  If the synchronizer is designed on chip, I'll try to minimize
the caps (diffusion, interconnects, fanout) by using a small output
driver, and not let anything else to touch the cross-coupled nodes.

>You can also make a two-stage synchronizer, where the second stage can
>fail only if the first stage comes out of metastable just as the second
>stage clocks. [You have to bias the output of the first stage so a first-
>stage metastable looks like a clean one or zero to the second stage.]
>Depending on your environment, this is sometimes better than clocking
>a single-stage synchronizer at 1/2 the rate.
>
My feeling is that the propagation delay of the second stage
significantly reduce the available time for synchronization.  So
instead of having a probability fo failure (with respect to the
available time) Pr(T-Tprop), the two-stage synchronizer has a
probability approximately Pr(T/2 - Tprop)**2.  But Pr(t) is exponential
      
             -t/tau
   Pr(t) = Ke            (tau = sqrt(1/GB))
                                      +T/2tau
   Pr(T/2 - Tprop) = Pr(T - Tprop) * e
                     2
So, (Pr(T/2 - Tprop))      Tprop/tau
    ------------------ = Ke
      Pr(T - Tprop)

Typically, Tprop >> tau and K is O(1).
Just my opinion, Rob.
>
>Rob Warnock
>Systems Architecture Consultant
>
>UUCP:	  {amdcad,fortune,sun}!redwood!rpw3
>DDD:	  (415)572-2607
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>

A paper by L. Marino (IEEE Trans. on Comp., Feb.81) and another
by Lindsay Kleeman & A. Cantoni (same, Jan. 87) has proofs on
metastable problems.

Several papers on metastability (all published in JSSC) deserve credits:

Veendrick, 4'80,
Flannagan, 8'85,
Sakurai,   8'88

Henry Choy
Advanced Micro Devices, Inc.
henry@amdcad.AMD.com