[SI-LIST] Re: Using standard scope and single ended pulse to estimate differential impedance
- From: wolfgang.maichen@xxxxxxxxxxxx
- To: "alfred1520list" <alfred1520list@xxxxxxxxx>
- Date: Fri, 5 Mar 2010 17:09:48 -0800
Hello Alfred,
another way to look at a coupled differential pair is as two single ended
lines with crosstalk. The physics will not change regardless of the
picture - one line's electric and magnetic field affecting the other, and
vice versa. So you are free to choose whichever picture is more suitable,
and you can translate the results between them.
(1) How does one measure characteristic impedance? You need a signal with
a rise time faster than the round trip delay of the line. Then you look at
the signal level at the source side when the step source drives the step.
This signal at any point in time is the sum of the incident signal and the
reflection arriving at that instant. The reflection coefficient is then
rho = (Zo - Zref) / (Zo + Zref) (formula A)
with Zo being the line's characteristic impedance, and Zref being the
reference (driver) impedance. You can use this relationship - with known
Zref, and measured rho - to deduce the (single ended) line impedance.
Zo = Zref * (rho + 1) / (rho - 1) (formula B)
(2) Second experiment - you keep the first line quiet, but still monitor
the signal coming out of it. Now stimulate the nearby second line of the
pair (the "agressor" in the crosstalk picture). You will see near-end
crosstalk (NEXT) appear on the first line (the victim). Next increases
for one signal rise time and then plateaus. The NEXT coefficient is always
positive, so a positive going aggressor step produces positive NEXT, a
negative step produces negative NEXT on the victim. The level will not
change for one round trip delay (or never if all ports are terminated with
the line's characterisitic impedance).
(3) What changes with a coupled differential pair? You will see the sum of
two responses, namely (1) (single ended TDR response) and (2) (NEXT).
Since the second line's step has opposite polarity to the first, the NEXT
signal will also be opposite (negative) and thus partially cancel the TDR
signal. The total response level on the victim will thus be smaller than
for single ended stimulus. With formula B you can describe this as a
reduced impedance - and indeed, the odd mode impedance for a coupled pair
is less than the single ended impedance. Heureka!
(4) do the same, but with common stimulus. Now the NEXT will increase the
total response, and this can be described as an increased line impedance.
Again in nice agreement with the differential line picture, where the even
mode impedance of a coupled pair is larger than the single ended
impedance.
So in summary, it is perfectly legal to measure single ended TDR and then
NEXT separately, subtract them (for Zodd) or add those two up (for Zeven)
and that way calculate odd mode impedance (Zodd) and even mode impedance
(Zeven). The differential impedance is then simply Zdiff = 2 * Zodd. (of
course this assumes a linear, time-invariant system, but a cable or
printed circuit board trace is an almost perfect example for such a
system).
Wolfgang
"alfred1520list" <alfred1520list@xxxxxxxxx>
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03/05/2010 02:34 PM
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Subject
[SI-LIST] Using standard scope and single ended pulse to estimate
differential impedance
Dear List members,
I have done some experiments and have gotten what seems to
be reasonable results. I seek the list's wisdom to comment on
whether the technique is valid or it was just a coincident that
the results looked right but can't be trusted.
My application is very limited. We are making board assemblies
with HDMI receivers. One of the HDMI compliance requirements
is that the differential impedance must be between 85 and 115 ohm.
We do not own a differential TDR scope, but we do have a high
performance DSA70804 with a 300 psec risetime FAST EDGE
output from the scope and ~100 psec risetime probe+front end.
I thought I could press it into giving a reasonable estimate if
the line length is more than a couple of inches.
Starting from the 2x2 impedance matrix and the relationship
between the two voltages and the two currents as shown on
page 14 of this very nice article by Daniel Wu:
http://www.ansoft.com/hfworkshop02/Danile_Wu.pdf
It seems that even if the -phase is not driven, we should be able
to observe the induced voltage and thus infer the differential
impedance.
Assuming symmetry and rewriting the equations:
V1 = i1 * Z11 + i2 * Z12
V2 = i2 * Z11 + i1 * Z12
Rearranging and combining:
Z11 = (V1 - i2/i1 * V2) * (i1) / (i1^2 - i2^2)
Z12 = (V1 - i1/i2 * V2) * (i2) / (i2^2 - i1^2)
V1 and V2 are the instantaneous voltages and
i1 = (V1open - V1) / 50ohm
i2 = (V2open - V2) / 50ohm
Since all unknown variables can be measured, we
can compute Z11 and Z12. Then:
Zdiff = 2 * (Z11 - Z12);
Zcm = (Z11 + Z12) / 2;
I have made some measurements and plotted some results here:
http://alfred1520.wiki.zoho.com/HomebrewTdrMeasurements.html
The first graph is the V1, V2, and the computed Zdiff and Zcm
of stuffed board.
The second graph is the Zdiff of 12 measurements. They all seem
to give believable results.
I'll be more than happy to share more details about the procedure
here or else where if this is really a valid technique.
Best Regards,
Alfred Lee
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