[SI-LIST] Re: bandwidth: based on edge rate or data rate?
- From: Peter.Pupalaikis@xxxxxxxxxx
- To: si-list@xxxxxxxxxxxxx, si-list-bounce@xxxxxxxxxxxxx, "Zabinski, Patrick" <zabinski.patrick@xxxxxxxx>
- Date: Tue, 9 Mar 2010 01:10:40 -0500
The 0.35 BW*RT multiplier is derived from a single pole system, which is
the same as saying a system with a single
time constant, or as others have stated, an RC filter.
simply solve 1-exp(-t/tau) for 0.1 and 0.9, subtract the two to generate
the risetime (10-90) and correspond this with the
bandwidth of a filter (1/tau)/(s+1/tau).
It is a common multiplier used for connecting oscilloscope bandwidth with
risetime (although no high-end real-time
oscilloscope has a single-pole roll-off - most are nearly brick-wall in
response).
This number does not imply anything about data rates. Again, it simply
says that if you have a channel with a given
bandwidth, where the bandwidth refers to the -3 dB point of a single-pole
filter, then you will observe a risetime of
0.35/BW if the channel is stimulated with an infinitely fast step.
Most high-end scopes have a multiplier more like 0.45.
There are some reasonable rules-of thumb regarding bandwidths of
oscilloscopes needed for serial data measurement
which are roughly correlated with bandwidths of channels needed for serial
data transmission - but these numbers are
overly pessimistic, because they are used to determine how much scope
bandwidth is required to get a good looking
eye - we know that many much, much worse channels are used for serial data
transmission than a scope front-end and
that many of the eyes at the receiver are in fact not good looking.
These rules of thumb are:
BW = 2 X bitrate for risetimes that are slower than 30% of the unit
interval (UI), and 3 X bitrate for faster.
If you meet this criteria, you will have absolutely no trouble in
transmission. Here BW does not mean the -3 dB point, but
rather the point at which no further frequencies are transmitted (i.e. is
a brick-wall BW).
Some other reasonable rules of thumb are:
-10 dB at bitrate will transmit serial data without equalization.
-20 dB at bitrate will transmit serial data with some equalization.
These are rules of thumb and imply relatively smooth channel roll-offs
without weird things. The dB values correspond
to SDD21 for differential lines.
it is possible to transmit serial data with -60 dB at bitrate with extreme
equalization (or maybe worse - I don't know).
There are various references that talk about all of these multipliers,
risetime and bandwidth. Some I agree with mostly:
Relating wideband DSO risetime to bandwidth: Lose the 0.35! - Dennis
Weller, Agilent Technologies: http://www.edn.com/article/CA263113.html
The Fifth Harmonic: Tradeoffs between sampling and real-time
oscilloscopes: - Brig Assay - Agilent Technologies
http://electronicdesign.com/content.aspx?topic=the-fifth-harmonic-tradeoffs-between-sampling-and-&page=2&catpath=test-and-measurement
Eye Patterns in Scopes - Pete Pupalaikis - LeCroy
http://www.lecroy.com/tm/Library/WhitePapers/PDF/Eye_Patterns_in_Scopes-designcon_2005.pdf
While these are all oscilloscope based articles, the information
corresponds well with serial data channels, at least unequalized.
For equalized channels, things are a more complicated.
The last article in the list tries to show the relationship of bitrate and
risetime by using a square-wave (infinitely fast) and triangle-wave
(as slow as possible) analogy along with power spectral densities of random
sequences.
Pete
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