Mixed-mode S-parameters

A VNA measures single-ended S-parameters. Mixed-mode S-parameters rewrite the same linear network in terms of differential and common-mode waves. They do not add information that was not in the single-ended matrix; they change the basis so a balanced interconnect is readable.

For a 4-port (2 in, 2 out) the mixed-mode matrix is four 2×2 quadrants:

[ SDD  SDC ]
[ SCD  SCC ]

Quadrant	Stimulus	Response	What it tells you
SDD	Differential	Differential	The intended signal path — insertion and return loss of the pair
SCC	Common	Common	How common-mode energy travels
SDC	Common	Differential	Common → differential conversion (imbalance)
SCD	Differential	Common	Differential → common conversion (imbalance / EMI)

A well-behaved differential path has high |SDD21| (low insertion loss), low |SCC21| (common-mode is rejected or at least not guided), and near-zero SDC/SCD (the two legs are balanced).

Why four measurements

One 2-port sweep cannot separate differential from common mode. You need all four port-pair interactions (or a single S4P). Computing “SDD21” from one S2P is not mixed-mode analysis — it is a single-ended trace with a hopeful name.

Port numbering (Bockelman / common textbook order)

Unless the bench notes say otherwise, these docs use:

Port 1 = positive input  (+)
Port 2 = negative input  (−)
Port 3 = positive output (+)
Port 4 = negative output (−)

Sij is still “to i from j.” Always confirm that the files on disk actually follow this numbering before applying conversion formulas.

Sources

This page is an original CloudSprite distillation. Mixed-mode quadrant language and the common port numbering follow the public treatment in Bert Simonovich, “A Guide for Single-Ended to Mixed-Mode S-Parameter Conversions,” Signal Integrity Journal, 31 July 2020 (article).