[SI-LIST] Re: 2.5Gbps
- From: "Zabinski, Patrick J." <zabinski.patrick@xxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Mon, 21 Jul 2003 12:12:19 -0500
Hi Patrick,
Thanks for you reply. Can we go through an example?
1) We have BER=10e-6; thus,
Poe=0.5*(1-erf)*sqrt(Eb/No)
I need to take a value for erf, error function, to get Eb/No => erf=?
Eb= energy in one bit
No= noise power density
=> Eb/No
Yes, but not quite. The Eb/No ratio comes from basic communcations theory,
and it
assumes that the receiver is able to integrate the energy over an entire bit
period
before sampling. In the majority of digital serial links, the receivers do
not integrate
the incoming signal, so you need to compensate for it by adding a
fudge-factor
of sorts. For digital circuits with common detection circuits, the simple
signal
to noise level is sufficiently-equivalent to the Eb/No, and works well in
this
analysis. Note: Signal is the distance from the signal level to the
threshold
level, and noise is the RMS noise level, both given in voltage.
Also, I think the Poe formula is slightly incorrect. I believe it should be
Poe = 0.5 * {1 - erf[SNR/Sqrt(2)]}
I believe this equation is probably what's leading you astray.
"erf" is a version of a cumlative distribution function based on the normal
distribution
function (i.e., Guassian distributions). It is simply scaled in value and
parameters from BER,
and I believe it is not what you are looking for. Essentially, BER = 0.5 *
(1 - erf), so
for BER = 10^-6, erf = 1 - 0.000002 = 0.999998.
From this, for a BER = 10^-6, you should end up with an SNR requirement of
4.7-4.8.
2) S/N=(Eb/No)*R/W
N=0.05V
S= wanted unknown
R=2.5Gb/s
W= signal energy sent into the line; suppose W=20mW
=> S
Again, the data rate analysis is based on optimal receivers which integrate
the
incoming signal over a bit's period. I don't believe this set of info is
directly
relevant (at least to the first order) in most common digital links.
3) S=0.1+Smargin
0.1V is the signal threshold
=> Smargin which is the requested value
With SNR target of 4.8, you have a basic starting point to work from.
However,
you probably don't know the noise level quite yet, so it will be difficult
to get a
signal margin requirement. One way to look at it is to set your signal
level
(say, the 200 mV you originaly suggested) and extract the max noise
(200 / 4.8 = 42 mV).
The key to keep in mind is that BER is directly dependent upon signal
strength
and noise levels. You cannot determine BER without both of these (or at
least
their ratio). Accordingly, if you are given a BER requirement, you are then
left
with one equation (the SNR ratio) and two unknowns (signal and noise
levels).
Is it correct? How do I determine erf?
A gain, I believe the first formula has led you astray. "erf" is the formula
you use
to determine BER; it is not a parameter per say.
Best regards,
Dorin
Hope this helps a little bit, and good luck.
Pat
------------------------------------------------------------------
To unsubscribe from si-list:
si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field
or to administer your membership from a web page, go to:
//www.freelists.org/webpage/si-list
For help:
si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field
List archives are viewable at:
//www.freelists.org/archives/si-list
or at our remote archives:
http://groups.yahoo.com/group/si-list/messages
Old (prior to June 6, 2001) list archives are viewable at:
http://www.qsl.net/wb6tpu
Other related posts:
