# [SI-LIST] Re: lumped model vs distributed model

• From: "Abe Riazi" <ARIAZI@xxxxxxxxxxx>
• To: <si-list@xxxxxxxxxxxxx>
• Date: Sun, 2 Dec 2001 09:22:34 -0800

```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...
>
> 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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