Test & Measurement

Differential S-Parameters

Q: Why can't I just use regular 4-port S-parameters for a differential pair?

You can, but a raw 4-port S-parameter matrix (S11, S12, S13, S14, etc.) does not directly tell you how the differential signal propagates. It mixes the differential and common mode responses together. A USB 3.2 receiver does not care about the absolute voltage on pin 1 or pin 2 individually. It only cares about the voltage difference between them. Mixed-mode S-parameters perform a mathematical transformation (using the M matrix) that re-expresses the same 4-port data in terms of the modes the receiver actually uses: differential insertion loss (Sdd21), differential return loss (Sdd11), and mode conversion (Sdc21).

Q: What does Sdc21 (mode conversion) physically represent?

Sdc21 measures how much of the differential signal converts into common-mode noise as it propagates through the structure. In a perfectly symmetric differential pair, Sdc21 is zero (negative infinity dB). In practice, any asymmetry such as length mismatch between the P and N traces, different via stub lengths, or connector pin skew creates mode conversion. This converted common-mode energy radiates as EMI. A Sdc21 specification of better than minus 30 dB is typical for a well-designed PCIe Gen 5 channel.

Q: How do you measure differential S-parameters on a VNA?

Connect all four single-ended ports of the differential pair to a 4-port VNA. Perform a full 4-port SOLT or TRL calibration. The VNA measures the complete 4x4 single-ended S-parameter matrix. Then apply the mixed-mode transformation either in the VNA firmware (all modern 4-port VNAs support this) or in post-processing software. The VNA displays the resulting Sdd, Scc, Sdc, and Scd sub-matrices directly. Some VNAs can also apply the transformation in real time so you see differential parameters updating live.

A mixed-mode S-parameter framework that decomposes a multi-port network's scattering behavior into differential-mode (Sdd), common-mode (Scc), and cross-mode (Sdc, Scd) sub-matrices. Instead of describing what happens at each individual port, differential S-parameters describe what happens to the modes the system actually uses. Essential for characterizing balanced transmission lines in high-speed serial links including USB, PCIe, HDMI, and 100GBASE Ethernet.

Category: Test & Measurement

Also called: Mixed-Mode S-Parameters

Reference impedance: Typically 100 Ω differential (2 × 50 Ω)

Understanding Differential S-Parameters

Modern high-speed digital interfaces send data as balanced differential pairs: two conductors carrying equal and opposite signals. The receiver extracts information from the voltage difference between the two lines, rejecting any noise that appears equally on both (common-mode rejection). Standard single-ended S-parameters describe the behavior at each individual port, but they do not directly reveal how the differential signal propagates or how much energy converts between modes.

The mixed-mode transformation solves this problem. Starting from a conventional 4-port single-ended S-parameter matrix (16 elements), a mathematical transformation using the mode-conversion matrix M produces four 2×2 sub-matrices that describe the system in terms of its actual operating modes.

Mixed-Mode Transformation

Mode Conversion Matrix (M):
M = (1/√2) × [+1, −1; +1, +1]

Mixed-Mode S-Matrix:
S_mm = M × S_se × M⁻¹

Resulting 4 sub-matrices:
[Sdd] = differential-to-differential (what the receiver sees)
[Scc] = common-to-common (common-mode propagation)
[Sdc] = differential-to-common (mode conversion, EMI source)
[Scd] = common-to-differential (susceptibility to common-mode noise)

Reference impedances: Z_diff = 2 × Z₀ = 100 Ω, Z_cm = Z₀/2 = 25 Ω

Key Parameters for High-Speed Channels

Parameter	Physical Meaning	Typical Spec (PCIe Gen 5)	Typical Spec (USB 3.2)
Sdd21	Differential insertion loss	≤ −15 dB at 16 GHz	≤ −8 dB at 5 GHz
Sdd11	Differential return loss	≤ −10 dB to 16 GHz	≤ −10 dB to 5 GHz
Sdd22	Far-end differential return loss	≤ −10 dB	≤ −10 dB
Sdc21	Mode conversion (EMI indicator)	≤ −26 dB	≤ −20 dB
Scc21	Common-mode insertion loss	Informational	Informational
Scd21	Common-to-differential conversion	≤ −26 dB	Informational

Common Questions

Frequently Asked Questions

Why can't I just use regular 4-port S-parameters for a differential pair?

A raw 4-port matrix mixes differential and common mode responses together. A USB 3.2 receiver does not care about the absolute voltage on pin 1 or pin 2 individually; it only cares about the voltage difference. Mixed-mode S-parameters perform a mathematical transformation that re-expresses the same 4-port data in terms of the modes the receiver actually uses: differential insertion loss (Sdd21), differential return loss (Sdd11), and mode conversion (Sdc21).

What does Sdc21 (mode conversion) physically represent?

Sdc21 measures how much differential signal converts into common-mode noise during propagation. In a perfectly symmetric pair, Sdc21 is negative infinity dB. Any asymmetry, such as trace length mismatch, different via stub lengths, or connector pin skew, creates mode conversion. This common-mode energy radiates as EMI. A spec of better than −30 dB is typical for well-designed PCIe Gen 5 channels.

How do you measure differential S-parameters on a VNA?

Connect all four single-ended ports to a 4-port VNA. Perform a full 4-port calibration (SOLT or TRL). The VNA measures the complete 4×4 single-ended matrix, then applies the mixed-mode transformation, either in real-time firmware or post-processing. Modern 4-port VNAs display the Sdd, Scc, Sdc, and Scd sub-matrices directly.

Related Terms

← Differential Phase Diffraction →