# [SI-LIST] Using standard scope and single ended pulse to estimate differential impedance

• From: "alfred1520list" <alfred1520list@xxxxxxxxx>
• To: <si-list@xxxxxxxxxxxxx>
• Date: Fri, 5 Mar 2010 14:34:15 -0800

```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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