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


Nice explanation, except that I would argue that both
your "1 LC" lumped model and your "500 LC" model are
lumped models. The model with 500 lumps has a wider
bandwidth for the reasons you've stated, but is lumped never
the less. A down side on lumped models with lots of lumps is
that they are very expensive compute timewise.

An example of a couple of models that I'd classify as
"distributed" might be the Hspice T element and the W
element.

The "T" element is basically a couple of voltage controlled current
sources separated by a delay. This leaves out a lot of the 2nd and
3rd order transmission line effects (notably frequency dependence),
but does model the action of a transmission line pretty well,
especially at low frequencies. The "W" element is also distributed
in nature, but is a mathematical model based on indirect
numerical integration and difference approximations that are not
readily visualized with simple circuit elements.

A lumped element ladder realization can be made to incorporate frequency
dependent effects by the addition of additional reactive and 
dissapative elements, however it is still a realization and subject 
to the bandwidth limitations related to ratio of the signal rise time 
to the propagation delay of the LC sections.

If someone thinks I've butchered the explanation and have it
all wrong, by all means chime in.

-Ray Anderson


>
>
>Jason, 
>
>You'll probably get 10,000 replies to this one, but since it's late on a
>Friday and I haven't seen any of them yet I thought I might give you my
>version...
>
>You have to think about the speed your model is going to operate at and the
>lengh.  We need to pick some operating frequency so lets assume that you
>need 3.5GHz bandwidth.  If you were to use the "estimation" that the
>BW=.35/Trise and need a bandwidth of 3.5GHz that means your rise time would
>be about 100ps.  Now lets look at your lump model.  I'll exagerate the
>length to show the reasoning.  If you were to have a 1meter long piece of
>something that you modeled as a lump and try to put a 100ps edge into it
>what would happen?  
>
>The delay = (Length*Square root of the dielectric)/Speed of light (3e8m/s)
>= 6.23ns (assuming Er=3.5).  You usually assume in a transmission line that
>the time delay is no larger the 1/10 of the rise time.  Pretty far off using
>our 1meter long piece of something.  Now if we were to look again, but this
>time make our piece of something only 2mm in length...Delay = 12.47ps.  Now
>we are pretty close to 1/10 of the rise time.
>
>Ok...so what does this mean?  Well let's picture a ladder.  In a lumped
>model you would only have one rung in the ladder meaning that there would be
>one L and C to describe your whole 1 meter long piece of something.  If you
>were to break your 1meter long piece of something up into small 2mm sections
>(distributed) and cascade 500 of them together (500 rungs in the ladder) to
>make your 1m long piece of soemthing you would now have 500 L's and 500 C's
>that describe your piece of something. And, each rung of the ladder would
>have a delay of 12.47ps which would allow you to capture all of the
>discontinuities along the 1meter piece of something.  If you were to use the
>lumped model you wouldn't be able to see these discontinuities due to the
>time delay through the 1meter.
>
>The choice of lumped vs. distributed is based on the old cliche' that size
>does matter...and so does speed.  The relationship beteween the 2 is the
>deciding factor.  This is the reason that for high frequency you would use a
>distributed model.  High frequency meens BW is high and in the
>"approximation" BW=.35/Trise the .35 is fixed.  That means that if you
>increase BW you decrease the Trise.  This in turn means that you have to cut
>up your 1 meter of something proportionatly so that you don't exceed the
>1/10 "rule of thumb" due to the delay. 
>
>Regards, 
>
>Craig Clewell
>
>
>-----Original Message-----
>From: Jason D Leung [mailto:jleung@xxxxxxxxxxxxxxx]
>Sent: Friday, November 30, 2001 3:19 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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