Reflections on a differential transmission line

Question

I understand why reflections occur when there is an impedance mismatch on a single-wire transmission line. However, when we introduce a differential line, I am having trouble picturing what would occur in the following cases:

Imagine a transmission line with 100-ohm differential impedance and 50-ohm single-ended impedance. What would happen in each of these cases?

(1) There is a discontinuity where the differential impedance remains 100 ohms, but the single-ended impedance changes.

(2) There is a discontinuity where the differential impedance changes, but the single-ended impedance remains 50 ohms.

The reason this could be unavoidable in real-life design is due to restrictions on stackup and trace width/spacing that may be driven by other mandatory design requirements. If I have to design in either one of these types of discontinuities, I want to understand which is worse, and why.

Thank you.

Answer 1

First, in general, closely coupled differential pairs are somewhat above 50 ohms when each side of the pair is measured single ended (60 to 65 ohms is common).

A differential pair with each single ended signal at exactly half the differential impedance cannot (by definition) be coupled to each other, although many such scenarios exist.

That said, in a differential pair scenario, what matters is retaining the differential impedance; if the pair single ended signals move apart but retain the differential impedance, then there is no differential discontinuity.

If the differential impedance changes (regardless of the single ended impedance), there will be a discontinuity as given by \$\Gamma = \frac {Z_1 - Z_2} {Z_1 + Z_2} \$ where \$Z_1\$ and \$Z_2\$ are the differential impedances and \$\Gamma\$ is the reflection coefficient for voltage.