# Differential TDR

How can I use a single-ended TDR (time-domain-reflectometry) instrument to measure differential trace impedance? I tried using the signal ground of the probe on one trace and the center conductor of the probe on the other trace of the test pair, but when the test was run, the impedance varied when lifting or moving the board.

You make a measurement of differential impedance with antipodal (equal and opposite) signals on the two traces. To achieve this measurement, a differential TDR instrument provides two outputs, x and –x, which you connect to the traces under test. Assuming that the traces bear a symmetrical relationship to the pc-board reference plane, the voltage that one trace induces exactly cancels the equal but opposite voltage that the other trace induces, so that the reference-plane potential remains constant at all times and equal to the TDR frame potential. A connection between the pc-board reference plane and the TDR frame is customary but unnecessary to accomplish the measurement. (What does count is that the grounds of the two TDR test probes are well-connected to each other.)

Your experiment drove one trace with the TDR output x while grounding the other to the TDR frame. If the pc-board reference plane had had no connections to any other object, the voltage on the pc-board reference plane, which the signals on your two traces equally affects, would have arrived at a voltage precisely halfway between the two. Under this condition, the difference from the driven trace to the reference would be...

x – ½x = +½x

...and the difference from the grounded trace to the reference would be...

0 – ½x = –½x

...creating conditions virtually indistinguishable from a true differential measurement.

Unfortunately, you found that it was impossible to disconnect the pc-board reference plane from its capacitive connection to the rest of the earth. The voltage on the reference plane therefore never attained a potential exactly halfway between the driven trace and the grounded trace. Immediately after your TDR step, the reference plane probably was hovering at some voltage less than ½x, indicating the relative influences of the driven trace, the grounded trace, and other surrounding grounded objects. Your experiment did not meet the conditions for differential measurement, and your measured differential impedance was incorrect.

What's more, the impedance number you measured changed depending on the relative strength of the coupling of the pc-board reference to earth. In other words, your measurement changed depending on how and where you touched the board and how close you held it to other metallic objects.

Try using your single-ended TDR to make any two of the following measurements. From any combination of two of these measurements, you can work out the true differential impedance:

• The impedance of one trace while the other is reasonably well-terminated at both ends.
• The impedance when both traces are ganged together in parallel.
• The near-end crossstalk induced on the second trace when the first is driven.

The necessary equations are pretty hairy, but you don't have to know them. Just set up a simulator to represent your test cases and tweak the trace separation and width until you get results that match your measurements. Then read out from the simulator the true differential impedance.