[SI-LIST] Re: Doug Brooks's Question
- From: Sainath Nimmagadda <intrinsi@xxxxxxxxx>
- To: Si-List <si-list@xxxxxxxxxxxxx>
- Date: Mon, 17 Nov 2003 09:15:19 -0800 (PST)
Eric,
You are a great guy I find on this list. You have covered possible scenarios
(though my question was kind of open-ended) and made sure I understood the
issues. First, I hesitated to revive a closed thread but good thing I did, I
learnt a great deal.
When transmission lines are introduced, they talk about electric and magnetic
fields and develop the RLCG model. And then ideal lines... and then Zo=
sqrt(L/C). And then forget about those fields (non-SI folks, I mean).
L and C are parameters related to fileds. Is it possible to explain above
equation in terms of fields?
Thanks,
Sainath
Eric Bogatin <eric@xxxxxxxxxxxx> wrote:
Sainath-
I did not get Tom's posting, but in general, I think the easy "physics" to
understand is in the Q, rather than matching time constants. For the case of a
Q = 1 at the resonant frequency, it happens that the condition for the time
constants being equal is also the condition for Q = 1. For L/R = CR, we find
after a little algebra, R^2 = L/C, or R = sqrt(L/C).
The R needed to get critical damping is just R = sqrt (L per length/ C per
length), which is the same as the characteristic impedance of the line.
I'm not sure there is any physics as the basis for understanding reflections
from the time constants. This is not the mechanism that causes the reflections.
If you want to understand the nature of reflections in terms of the LC
n-section model, for the case other than matched termination, I think the only
way to see this is, as was pointed out earlier, by matching the voltage and
current boundary conditions. If you are going to go through this effort, it is
much easier to do it in terms of general impedances, from which you can also
get insight into the reflections for any termination, not just an ideal
resistive load.
Using the approximation that the line is an n-section LC network is a perfectly
good approximation, as long as you have enough sections given the time delay of
the line and the required bandwidth of the model. I wrote about this in my June
2002 PCD&M column. Here is a link:
http://www.ericbogatin.com/SignalIntegrityColumns/pdfFiles/0206NMA.pdf
If you think about the ringing of a transmission line as an issue related to
the LC nature of the line and the termination at the end, be careful. This
model is only an accurate model up to a limited bandwidth. The number of
sections you need is n = BW x 10 x 1/TD.
If you have a rise time that is RT, and want to understand how this fast rising
signal interacts with a real transmission line, approximated as an n-section LC
lumped circuit model, this is only accurate if you have at least n sections,
where n > 0.35/RT x 10 x TD = 3.5 x TD/RT.
If you are trying to calibrate your intuition about transmission lines based on
thinking about it as a single LC section, this will be OK, as long as: RT > 3.5
x TD. If the line is 6 inches long, its TD ~ 1 nsec and the shortest rise time
signal you can use with this approximation is 3.5 nsec, roughly. If you apply a
3.5 nsec signal to a transmission line that is 1 nsec long, the ringing will
look like an RLC circuit- don;t forget to include the R from the source
impedance of the driver.
In my professional opinion as an educator, the effort folks might want to
invest in trying to understand transmission lines as LC networks is much better
spent trying to develop a little intuition about the distributed nature of
transmission lines. There is far more "bang for the buck" in using distributed
or "T element" models to give you an intuitive sense of the nature of signals
interacting with the instantaneous impedance they see on a transmission line
and how this accounts for reflections, not just from terminations at the end,
but also from discontinuities along the way.
While an LC sectional model is not wrong, it is just not as simple nor as high
a bandwidth as a T element model. Other than a single LC section model, I find
it difficult to apply my intuition to lots of circuit elements.
Those of you who have taken my class, or read my book (chapter 7) and
understand the instantaneous impedance of a transmission line, please feel free
to chime in about which model helps you to more quickly solve real world
problems.
I promise, just one, last, blatant plug for my book- all these details, and
some intuitive understanding of what really is a transmission line is in my
book: http://vig.prenhall.com/catalog/academic/product/0,4096,0130669466,00.html
order it from Prentice Hall and get a 10% discount.
--eric
********************************************************************
Recently published by Prentice Hall, www.phptr.com
Signal Integrity-Simplified, by Eric Bogatin
Attend the GTL Signal Integrity University in Sunnyvale, CA - Nov 6-13
GTL 122 - Fundamental Principles of Signal Integrity
GTL 250 - High Speed Board Design
GTL 260 - Interconnect Models from Measurement
-------------------------------------------------------------------------------------
Dr. Eric Bogatin
CTO, GigaTest Labs
26235 w 110th Terr
Olathe, KS 66061
v: 913-393-1305, f: 913-393-1306
e: eric@xxxxxxxxxxxx
www.GigaTest.com
********************************************************************
-----Original Message-----
From: Sainath Nimmagadda [mailto:intrinsi@xxxxxxxxx]
Sent: Sunday, November 16, 2003 10:31 AM
To: Si-List
Cc: eric bogatin; Doug Brooks; weirsp@xxxxxxxxxx; tom@xxxxxxxxxxxxx;
intrinsi@xxxxxxxxx
Subject: Re: [SI-LIST] Doug Brooks's Question
Eric,
I am glad you joined the discussion. Looks like you have addressed Steve
Weir's LCR concerns. As you can see from yesterday postings, Tom Dagostino
asked this question: what insight do you get by using these L's or C's in the
equation RC=L/R? Also, would you please extend the discussion, in terms of time
constants, to cases where R>Zo and R<Zo.
Regards,
Sainath
Eric Bogatin <eric@xxxxxxxxxxxx> wrote:
Doug-
I'll take a stab at answering your question about understanding the
termination for a transmission line.
There are two different ways of thinking about it. First is the view
of matched boundary conditions. This will allow us to derive the
reflection coefficient as (Z2-Z1)/(Z2+Z1). I wrote a column on this
for the August 2003 issue of Printed Circuit Design and Manufacture
Magazine. You can download a pdf version of the paper from my personal
web site:
http://www.ericbogatin.com/SignalIntegrityColumns/pdfFiles/0308NMA.pdf
The second way is, as you are trying to do, approximating a uniform
transmission line as an LC approximation. Keep in mind, this is an
approximation. It is perfectly ok, and accurate to about 1% in
predicting the impedance of a line up to some bandwidth as long as the
number of segments > the band! width x 10 x 1/(time delay of the line).
(this derivation is in my book)
If you have an n-section LC network, and add a resistor at the far
end, the real question you want to ask is, what value of R across the
end will critically damp the LC network. This question applies to 1 LC
section, or 100 LC sections in the line. It is the last LC section
that will be damped.
Now, we have the question phrased as a circuit problem. If you have 1
LC section and add a resistor in series with the C-L-R, at the end of
the line, what is the Q of this circuit?
The Q is the ratio of the max energy stored in a cycle to the energy
dissipated in a cycle. It is also the ratio of the loss, the
resistance, to the reactance. Q = R/(2 x pi x f x L) = R x sqrt(C/L)
For any LC network, the last LC section will be a damped LC section.
The ideal R value will critically damp the circuit, with a Q of 1.
Note that for Q = 1, the value of R should be ! R = sqrt (L/C).
No matter how many sections we use to approximate our transmission
line, as long as the line is uniform, both L and C scale with the
length and we get the same ratio for sqrt (L/C). Of course, this is
also the characteristic impedance of the line.
The bottom line is, if you want to think about using an R to damp out
the oscillations of the last LC section in an n-section LC circuit,
you want to select an R that gives a Q of 1. This R is numerically the
same as the characteristic impedance of the line.
Of course, more details on approximating T lines as LC networks and on
termination can be found in my book, Signal Integrity Simplified,
published by Prentice Hall.
Hope this helps.
--eric
********************************************************************
Recently published by Prentice Hall, www.phptr.com
Signal Integrity-Simplified, by Eric Bogatin
Attend the GTL Signal Integrity Universit! y in Sunnyvale, CA - Nov
6-13
GTL 122 - Fundamental Principles of Signal Integrity
GTL 250 - High Speed Board Design
GTL 260 - Interconnect Models from Measurement
----------------------------------------------------------------------
---------------
Dr. Eric Bogatin
CTO, GigaTest Labs
26235 w 110th Terr
Olathe, KS 66061
v: 913-393-1305, f: 913-393-1306
e: eric@xxxxxxxxxxxx
www.GigaTest.com
********************************************************************
Date: Sat, 15 Nov 2003 14:21:25 -0800
From: steve weir
Subject: [SI-LIST] Re: Doug Brooks's Question
Sainath, no, that is not the way that I see it. Unless I misread
Doug,
like you he noted that the LC at the end of the line, like all the
increments along the line has Zline. The problem is that a
transmission
line does not behave like a lumped LC. I don't personally see a way
to try
to replace the Tx line with a lum! ped LC, nor do I see a useful point.
If the idea is to think about the behavior intuitively, I personally
like
the parallels to conservation of momentum.
Jim Knighten's discussion of Kirchoff's Laws fits that nicely as well.
What doesn't seem to fit is a lumped LCR. The response doesn't
match. With a lumped LCR the ringing time constant is determined by
LC,
and L/R. With an underdamped transmission line, it is determined by
the
length of the line. All we get at the end of the line is L/C for
Zline. L
and C get scaled for convenience to solve the equations. The higher
the
frequency range we want to evaluate, the smaller both L and C become.
So,
the LCR time constant moves towards zero.
Regards,
Steve.
At 01:08 PM 11/15/2003 -0800, Sainath Nimmagadda wrote:
>Steve,
>
>I suppose Doug's track assumes that the line is matched with upstream
>networks and his concern is about the terminati! on- specifically,
about
>interpreting time constants when it is not matched to the line. The
end LC
>of the line also represents characeristic impedance of the line.
>
>Do you see it differently?
>
>Sainath
>
>
>
>steve weir wrote:
>Sainath, trying to combine just the end LC with the termination R
ignores
>the effects of the upstream networks and yields the wrong behavior.
>Regards,
>
>
>
>Steve.
>At 09:54 AM 11/15/2003 -0800, Sainath Nimmagadda wrote:
> >I understand the responses(using different tracks) to Doug's
> >question- but don't know why his track is wrong altogether.
Someone,
> >please explain why and where his approach doesn't work.
> >
> >Thanks,
> >Sainath
> >
> >[ from Archives]
> >==========================================================
> ! >From: Doug Brooks [mailto:doug@xxxxxxxxxx]
> >Sent: Wednesday, November 12, 2003 4:43 PM
> >To: si-list@xxxxxxxxxxxxx
> >Subject: [SI-LIST] Transmission line match
> >
> >I am trying to develop a *qualitative* (NOT quantitative)
explanation of
> >what happens at the terminating end of a transmission line. I think
I am on
> >the track with this model and discussion:
> >1. The transmission line model is a lumped model of a string of Ls
and Cs.
> >2. The termination value forms a time constant with these. That is,
if
> >R=Z=(L/C)^.5, then RC=L/R. That is, when correctly terminated, the
time
> >constants are matched.
> >3. If the terminating resistance is high, then the RC time constant
is
> >relatively longer. If it is low, then the L/R time constant is
relatively
> >longer.
> >
> >At this point I am having trouble getti! ng over the "so what?" and
> >completing the argument. What is the next step in this
argument..... or am
> >I on the wrong track altogether?
> >
> >Thanks
> >Doug Brooks
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