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Can the characteristic impedance value of a single-ended transmissions line be omitted when the two transmissions lines of a differential pair are routed differentially (not two isolated lines)?

I ask this because up to now when dealing with a diff pair, I've always first calculated the required width of the two traces from their Z0 value, to then use that width to calculate the required gap from the Zdiff value.

After recently watching some videos on the topic, I'm second guessing myself as the Z0 value is never used when calculating for diff pairs that are routed close together.

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No, it can't be ignored.

The following discussion assumes traces on a PCB. The situation is different for interfaces like twisted pairs.

For edge coupled (that is co-planar) traces, the differential impedance is mostly determined by the singled ended impedance of each individual trace.

An isolated trace has a ZO that depends primarily on it's width and distance from any ground or power planes (they're usually treated the same from a ZO standpoint).

When you use two widely separated traces to route a differential signal, the differential impedance will be 2*ZO.

When you bring those two traces close together their (in isolation) ZO is reduced because one trace starts to couple to the other by a small amount, assuming they are edge coupled. So each trace's impedance is reduced by some small amount, epsilon (ε), and so the differential impedance becomes 2*(ZO-ε).

Note, there have been a number of Q&A's about this topic just in the past 2 years or so that I've been here.

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