[SI-LIST] Re: frquency limit of a channel
- From: "Lakshmi N. Sundararajan - PTU" <lakshmi.s@xxxxxxxxxxx>
- To: "Joshua Kim" <joshuakh@xxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Sat, 6 Mar 2010 13:08:43 -0800
Hi Joshua,
Here is one derivation from searching the internet...
====================================================================
This is how it works: the circuit is assumed or approximated to behave like a
simple RC integrator.
The time constant will then be: τ=RC
The bandwidth is then BW=1/(2*π*RC)=1/(2*π*τ)
On the other hand, the rise time for this simple RC circuit is calculated
starting from the equation of the voltage across the cap when a step impulse is
applied at the input:
u(t)=U*(1-exp(-t/τ))
For u(t)=0.1U you get 0.1U=U*(1-exp(-t10/τ)), where t10 is the time when the
voltage reaches 10% of the final value.
After simplification
0.9=exp(-t10/τ)
Applying the natural log to the equation you get:
ln0.9=-t10/τ or t10=-τ*ln0.9
Similarly, for u(t)=0.9U, we have t90=-τ*ln0.1
The rise time is then:
tr=t90-t10=τ*(ln0.9-ln0.1)≈2.2*τ or τ=tr/2.2
Substitute this value of τ into the expression for bandwidth:
BW=1/(2*π*tr/(2.2))=2.2/(2*π*tr)≈0.35/tr
or
BW*tr≈0.35
====================================================================
Is the above not true?
Thanks,
-LN
-----Original Message-----
From: Joshua Kim [mailto:joshuakh@xxxxxxxxx]
Sent: Saturday, March 06, 2010 1:06 PM
To: Lakshmi N. Sundararajan - PTU; si-list@xxxxxxxxxxxxx
Subject: RE: [SI-LIST] frquency limit of a channel
The equation is not from RC circuit. I know there will be many to explain this.
But if not try to contact me.
-----Original Message-----
From: Lakshmi N. Sundararajan - PTU <lakshmi.s@xxxxxxxxxxx>
Sent: March 6, 2010 3:59 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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