[SI-LIST] Re: lumped model vs distributed model
- From: "Abe Riazi" <ARIAZI@xxxxxxxxxxx>
- To: <si-list@xxxxxxxxxxxxx>
- Date: Mon, 3 Dec 2001 21:42:16 -0800
Steve:
Indeed, theoretical transmission line derivations and modeling frequently
employ transverse electromagnetic (TEM) assumption. Fortunately, TEM
mode is regarded sufficient estimate for transmission line propagation
up to high frequencies.
I find it difficult to accept that a transmission line model consisting of
a large number of cascaded RLCG segments can be a good representation
only at low frequencies. The following relationship adapted from
S. H. Hall, et al., Page 16 and discussed in my previous post leads to
different conclusions :
Segments >= 10 * x / (Tr * v)
The required number of RLCG segments varies directly with transmission line
length and inversely with Tr . Therefore, modeling a long fast edge rate
(wide
bandwidth) line can demand multiple RLCG stages; whereas, a single RLCG
lump model appears suitable only for a line exhibiting short electrical
length.
A question:
Do you think above conclusions are valid for low frequency lossless (ideal)
case, and break down for high frequency lossy (real) lines?
Thank you.
Abe
----- Original Message -----
From: "Steve Corey" <steve@xxxxxxxxxxxxxx>
To: <si-list@xxxxxxxxxxxxx>
Sent: Sunday, December 02, 2001 8:11 PM
Subject: [SI-LIST] Re: lumped model vs distributed model
>
> 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
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