[SI-LIST] Re: frquency limit of a channel
- From: "Brad Brim" <bradb@xxxxxxxxxxx>
- To: "'Lakshmi N. Sundararajan - PTU'" <lakshmi.s@xxxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Sat, 6 Mar 2010 17:47:52 -0800
hello Lakshmi,
As Patrick pointed out, you are probably not going to support a 6Gbps signal
with 150pS rise time! It's also safe to say you probably won't model your
channel successfully with 3GHz bandwidth models.
As both Patrick and Hany discussed, there are various arguments for how to
determine the bandwidth required of your models to successfully characterize
a channel of given datarate. Hany points out a precise method but suspect
you're looking for initial high-level guidance with your inquiry.
The factors upon which the bandwidth requirement depends are: datarate, rise
time, coding scheme, possible high frequency high-Q channel behavior (e.g.
resonances), etc. Datarate is obvious. Rise time should not be too slow or,
as for your case, you won't be able to support the datarate. Rise time
should not be too fast or you're pumping unnecessary high frequency content
into your system where it is likely to only attenuate and serve no purpose
or it could couple into higher frequency resonances and distribute high
frequency noise throughout the system. The generally accepted rule of thumb
is to use model bandwidth of 0.35/Tr to 0.5/Tr. This is based on the signal
energy CDF (cumulative distribution function - integrated probability
density function). In other words, a large percentage (e.g. >90%) of the
energy is expected below this frequency. You can try some typical numbers
for rise times, but if you examine plausible rise times as a percentage of
the symbol width you come up with bandwidth requirements of 2X to 3X the
datarate. In your case, 12GHz to 18GHz. Coding scheme will serve to push the
power spectrum to a lower value so don't be too aggressive with too high
bandwidth.
A completely different high-level argument is to examine your signal as a
smoothed square wave when you consider the 0-1-0-1 pattern repeated. This
smoothed square wave has a fundamental at half the datarate (3GHz in your
case). The question then becomes - how many harmonics do I need to represent
the smoothed square wave. A reasonable answer seems to be about 5X the
fundamental frequency. It is even more logical when you recall a square wave
only has odd fourier components so a for this high level analysis and
personal experience with high speed system modeling, 2.5X datarate will
probably be closer to the actual required bandwidth than will either 1.5X or
3.5X datarate.
cheers,
-Brad
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx
> [mailto:si-list-bounce@xxxxxxxxxxxxx] On Behalf Of Lakshmi N.
> Sundararajan - PTU
> Sent: Saturday, March 06, 2010 1:00 PM
> To: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] frquency limit of a channel
>
> Hi Gurus,
> Suppose assume I have a high speed serial link at 6Gbps. The
> nominal rise time of the signals on this channel is 150ps.
>
> Given this rise time, the bandwidth required to transmit this
> signal is 0.35/tr = 2.33Ghz.
>
>
>
> So, to study this channel behavior, is it correct to only
> look at s-param frequency output till say 3Ghz.
> Can any higher frequency data points on this s-param be
> ignored and still correctly model the channel behavior?
>
>
>
> I also looked up BW * tr = 0.35. This equation is derived
> from a simple RC integrator circuit.
>
> How true can this model any channel, since we seem to be
> using this equation for all our studies.
>
> Please clarify.
>
>
> Thanks,
>
> -LN
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