[SI-LIST] Re: impedance relation with frequency...
- From: andrew.c.byers@xxxxxxxxxxxxxx
- To: jeff.loyer@xxxxxxxxx
- Date: Wed, 24 Sep 2003 15:00:23 -0700
Hi Jeff,
In my reply, which is included below, I mention the following:
-------------------
"On boards, typically the frequency-dependent impedance change
starts leveling out at much lower frequencies. Essentially you are
approaching the sqrt(L/C) impedance, because your omega*L overwhelms your R.
*Usually* by 1MHz your Zo curve is flat."
--------------------
So, in your case where the 400ps risetime has a frequency content of 875MHz,
you are still well above the place where the Zo is changing. Essentially
what I was trying to say with that reply was that it is important to
remember that Zo is not always constant - not in theory or practice. You can
look at the equation to see the frequency dependence:
Zo = sqrt[(R+jwL)/(G+jwC)]
This is straightforward. Then a practical aside is that for PCBs you have to
go much lower in frequency to see the changing Zo, but for lines on
chip-like dimensions (say 2um by 10um cross section), the Zo curve is
shifted up in frequency. Dr. Johnson's book describes this topic very well.
I just now read Scott's email: it is a great reference on all this. His
point about how the TDR continues to rise due to resistive loss is one way
to see this effect. If you were to TDR a very resistive, long chip line,
your high frequencies (short times) would jump up to the sqrt(L/C) Zo level,
then after that your TDR signal would slowly rise until it reaches the time
(lower frequencies ) when the DC resistance of the line is reached, when you
would then level off. This is way easier to describe with pictures - I hope
I got the words correct...
This lead to another interesting topic that Scott hinted at: causality in
transmission line models. Frequency-dependent R and L are inherently linked.
If they are not, they you risk generating a non-causal model. ALSO, Zo does
not increase to infinity at DC. But I think that the widely-used W-element
model does not verify these two requirements, and therefore is non-causal.
Does anyone have experience showing this in experiment? Or any confirmation
of this?
thanks,
Andy
-----Original Message-----
From: Loyer, Jeff [mailto:jeff.loyer@xxxxxxxxx]
Sent: Wednesday, September 24, 2003 12:40 PM
To: Byers, Andrew C
Cc: si-list@xxxxxxxxxxxxx
Subject: RE: [SI-LIST] Re: impedance relation with frequency...
Hi Andrew,
I would like some help understanding the difference between board traces and
"chip lines". My experience has been that I can TDR a trace using a 35ps
risetime, or through 100 and 400ps filters, and measure the same Z0 for that
trace. This would seem to be backed up by the fact that there is no
compensation made when measuring traces with different TDRs, regardless of
their risetime.
I just confirmed that again, measuring the same 3" microstrip trace with no
filter, and 100ps and 400ps filters, and finding the TDR and TDT waveforms
stabilize at the same level, regardless of the risetime. Of course, there's
significant impact to the risetime of the TDT, but the Z0 of the trace (as
indicated by the DC level of the TDR trace) remains constant.
This implies to me that the Z0 of the trace is constant for 10GHz , 3.5GHz,
or 875MHz (35ps, 100ps, 400ps risetimes, respectively).
My experience with VNA seems to substantiate this - S11 typically remains
fairly constant (other than resonances at lambda/4, etc.) while S21 varies
with frequency due to loss effects.
Is there something else I'm missing?
Jeff Loyer
-----Original Message-----
From: andrew.c.byers@xxxxxxxxxxxxxx
[mailto:andrew.c.byers@xxxxxxxxxxxxxx]
Sent: Wednesday, September 17, 2003 12:05 PM
To: jonpowell@xxxxxxxxxxxx; kbagga31@xxxxxxxxx; si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: impedance relation with frequency...
Concerning Zo relation with frequency:
Once again, depends where you live. On boards, typically the
frequency-dependent impedance change starts leveling out at much lower
frequencies. Essentially you are approaching the sqrt(L/C) impedance,
because your omega*L overwhelms your R. *Usually* by 1MHz your Zo curve is
flat. But if you are modeling chip lines, your R value for the line might be
comparable (or greater) than omega*L up to a couple GHz or so. Then you
cannot ignore this frequency dependent behavior. I have seen a typical line
on chip go from about Zo=100ohms @100MHz, to Zo=63ohms @1GHz, to Zo=55ohms
@10GHz. Measurement, simulation, theory, literature, and gut feel all back
this up.
So the bottom line (as it always is in the world of interconnect modeling)
is it depends on how high you go in frequency, the dimensions of line you
are using, and if you are designing in a narrow band or a wide band.
HOWEVER, as Jon pointed out, you can often see greater variations due to
coupling from nearby traces. Plus you have to remember that impedance
control is an issue too - usually +/- 10% is as good as it gets for
run-of-the-mill PCBs out there (but money talks).
To get a feel for the numbers I got above, you can use a 2D field solver
that handles the frequency dependent behavior of R and L (ansoft spicelink
or some other flavor). Or you can dig up equations and plug them into a
matlab or mathcad. Calculate your R and L and C (usually G is non-existant
or insignificant...) and crunch away.
salud,
Andy Byers
-----Original Message-----
From: Jon Powell [mailto:jonpowell@xxxxxxxxxxxx]
Sent: Wednesday, September 17, 2003 9:09 AM
To: kbagga31@xxxxxxxxx; si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: impedance relation with frequency...
Karen,
It is my feeling that the frequency related impedance changes on a signal
will be second order considerations compared to the impedance changes caused
by crosstalk from neighboring wires. These effects can be shown with most
good SI engines. Intel has often recommended (for instance) calculating the
effective impedance when the coupled wires on either side of the target wire
switch simultaneously with the target wire in both the same direction (all
going high and low) and opposite (target going high and low and coupled
going low and high).
hope this helps (and if I am wrong, I am sure someone will scream at me so
wait a couple of minutes).
regards,
jon
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx
[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of karan bagga
Sent: Wednesday, September 17, 2003 2:24 AM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] impedance relation with frequency...
Hi
From the telegraphic equations on Transmision lines it seems the impedance
of the Trace varies with frequency.
In my design specifications it is specified that my trace should be on (25
+/- 10%) Ohms.
How will I do it ? How will I do these kind of analysis?
The frequency of the signal is high and also the rise time is significantly
low.
Will FFT be of some help here ?
Regards
Karan.
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