[SI-LIST] Re: lumped model vs distributed model
- From: Steve Corey <steve@xxxxxxxxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Sun, 02 Dec 2001 20:11:59 -0800
Abe -- In my opinion and experience, a model with an infinite number of
infinitesimal segments (implying infinite transmission bandwidth) is
only accurate at low frequencies, since real interconnects do not behave
this way. Such models are based on TEM assumptions and no skin effect,
and they also depend on a non-physical profile of loss tangent vs.
frequency that varies as 1/f.
As Ray Anderson mentioned in an earlier post, lumped element models can
be used to represent frequency-dependent losses such as dielectric and
skin-effect losses. Since a lossy lumped model itself needs to
attenuate high frequencies, it's not subject to such restrictive
constraints on segment length as those you have laid out for the
limiting, or frequency-independent case. However, determining how to
optimally segment such a model is still an area of active research.
-- Steve
-------------------------------------------
Steven D. Corey, Ph.D.
Time Domain Analysis Systems, Inc.
"The Interconnect Modeling Company."
http://www.tdasystems.com
email: steve@xxxxxxxxxxxxxx
phone: (503) 246-2272
fax: (503) 246-2282
-------------------------------------------
Abe Riazi wrote:
> Dear All:
>
> Ideally, an infinite (though impractical) number of cascaded RLCG segments
> are required to construct an accurate distributed transmission line model.
>
> Stephen H. Hall, et al., "High-Speed Digital System Design A handbook
> of Interconnect Theory and Design Practives", on page 16, describe a useful
> formula for determining the number of RLCG segments sufficient for
> distributed modeling :
>
> Segments >= 10 * x / (Tr * v)
>
> Where Tr, x, and v represent signal rise (fall) time, transmission line
> length, and velocity repectively.
>
> For example, when Tr = 500 ps, x = 6 Inch (= 15.24 cm) and
> v = c / SQRT(Er) = 3E10/2.06 = 1.456E10 cm/sec
> (a substrate dielectric constant of 4.25 being assumed)
>
> Then:
>
> Minimum number of segments = 10 * 15.24 cm / ( 500E-12 sec * 1.456E10
> cm/sec).
>
> Minimum number ~ 21 segments.
>
> When the cross sectional geomtery (and hence charateristic impednace Zo )
> of the stripline (or mictrostrip) transmission line are also known,
> then R, L, C and G for each segment can be ascertained by dividing the
> total value of each parameter by the number of segments.
> (Example: C_segment = C_total / number of segments). These calculations
> are of course simpler for the lossless case where R and G are negligible.
>
> Best Regards,
>
> Abe Riazi
> ServerWorks
>
>
>>Jason,
>>
>>I am sure you will get many good theoretical answers
>>to this question. However, I would suggest that in
>>order to get a better understanding, try it out yourself!
>>
>>If you have a spice simulator, build a network with a single
>>RLC lump, and compare it with say 10 of them in series, or
>>100 of them in series (don't forget to divide the individual
>>element values by the number of lumps, though). This is not
>>too hard if you know how to make a subcircuit... For the
>>"driver" you can just use a Thevenin circuit, with a Pulse
>>(or PWL) source where you can vary the edge rate from very
>>steep (1.0 ps) to less steep (10 ns). Then run the
>>simulations and put the waveforms on top of each other.
>>You should see pretty good differences...
>>
>>Arpad Muranyi
>>Intel Corporation
>>===========================================================
>>
>>-----Original Message-----
>>From: Jason D Leung [mailto:jleung@xxxxxxxxxxxxxxx]
>>Sent: Friday, November 30, 2001 12:19 PM
>>To: si-list@xxxxxxxxxxxxx
>>Subject: [SI-LIST] Re: lumped model vs distributed model
>>
>>
>>Hi everyone:
>>For transmission line we can always use a lumped R,L,C model to
>>represent a simple transmission line, or we can use a distributed model
>>.(I know that the distributed model is more accurate and for high freq
>>application we should use this model)
>>But my question is : what is the main difference between the lumped
>>model and distributed model?
>>If we are just using the lumped model for our SI simulation, what are we
>>going to miss ?
>>looking forward for your insight
>>thanks
>>Regards
>>Jason Leung
>>
>>
>>
>>
>
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