Differential Signaling
Theory: taking the difference of two lines
Overview
I've been told to route USB as a '100 Ω differential' pair. I just put two 50 Ω traces side by side, right?
Only if they're well apart. Differential pairs are usually routed close together, so their fields couple and the impedance differs from each trace alone. In the odd mode, with opposite signals, capacitance to the neighbour lowers impedance. So two 50 Ω traces placed close give less than 100 Ω; width and spacing must be designed together for the differential impedance.
Odd and even modes
Opposite signals on the two lines form the odd mode (the differential signal); identical signals form the even mode (common-mode noise). Differential impedance is twice the odd-mode impedance and falls below the single-line value $Z_0$ as coupling strengthens.
Approximate formulas
Rule-of-thumb formulas for surface microstrip (IPC-2141 style). $h$ is dielectric thickness, $w$ width, $t$ copper thickness, $s$ spacing and $\varepsilon_r$ relative permittivity. Accuracy is about ±10%, so confirm final values with 2D field solvers or the board fabricator.
From twisted-pair telephone lines to high-speed serial links
Sending signals on two wires to cancel noise goes back to twisted-pair telephone lines of the late 19th century. In digital electronics, LVDS (low-voltage differential signaling) was standardised in the 1990s, sending fast signals of only about 0.35 V swing with low radiation. Today's USB, PCIe, SATA and HDMI are all differential high-speed serial links, reaching tens of Gbps per lane. With rise times of tens of picoseconds, even slight length differences and bends in the routing matter.
Worked examples
Example 1: width, spacing and differential impedance
Approximate calculation for surface traces on FR-4 (εr 4.3), 0.10 mm dielectric, 35 μm copper:
| Width | Single Z0 | Spacing 0.10 mm | 0.15 mm | 0.20 mm | 0.30 mm |
|---|---|---|---|---|---|
| 0.146 mm | 50.0 Ω | 81.6 Ω | 88.6 Ω | 93.0 Ω | 97.3 Ω |
| 0.120 mm | 55.3 Ω | 90.2 Ω | 98.0 Ω | 102.8 Ω | 107.6 Ω |
| 0.100 mm | 60.0 Ω | 98.0 Ω | 106.4 Ω | 111.6 Ω | 116.8 Ω |
Two 50 Ω lines at 0.1 mm spacing drop to 82 Ω.
Right. For 100 Ω differential you might narrow the traces (0.12 mm here) and space them 0.15–0.20 mm. Wider spacing approaches 100 Ω, but weaker coupling reduces noise cancellation within the pair and increases crosstalk to neighbours. Tight or loose coupling is a design choice, but either way changing spacing along the route changes impedance and causes reflections — keep it constant.
Example 2: length mismatch and mode conversion
| Length mismatch | Skew | 50 ps rise | 100 ps rise |
|---|---|---|---|
| 0.5 mm | 3.0 ps | ≈6% | ≈3% |
| 1.0 mm | 6.0 ps | ≈12% | ≈6% |
| 2.0 mm | 11.9 ps | ≈24% | ≈12% |
With an effective permittivity of 3.19 (surface), skew is about 6 ps per millimetre. During the skew the two signals aren't opposite, and that portion becomes common mode, which isn't cancelled at the receiver and radiates from cables and enclosures as EMI. Inner/outer length differences at bends accumulate too, so serpentine routing equalises lengths.
Design and analysis
Routing basics
- Constant spacing: route both traces together around parts and vias.
- Match length: correct near where the mismatch arises; correcting all at the receiver leaves common mode along the way.
- Don't cross plane splits: gaps in the reference plane disturb impedance and increase common mode.
- Vias and connectors: via stubs and connectors easily break impedance; check with 3D analysis.
Analysis flow
- Use 2D cross-section analysis for odd/even impedances to set width and spacing.
- Analyse vias, connectors and packages in 3D and extract S-parameters.
- Cascade the whole channel and evaluate eye diagrams and differential-to-common-mode conversion.
“Lengths matched, yet radiation is high”
A differential pair matched perfectly in total length still failed EMI at odd harmonics. The mismatch had been corrected by a serpentine just before the receiver, so along the way one trace ran ahead and common mode flowed through that whole stretch. Matching the total doesn't remove intermediate mismatch; correct near where it arises, such as right after a bend. In analysis, looking at common-mode amplitude section by section, not just at the ends, makes this clear.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Assuming 2 × 50 Ω = 100 Ω | Low differential impedance | Design including coupling |
| Spacing changes along the route | Reflections | Keep spacing constant |
| Correcting length only at the receiver | Common mode and radiation en route | Correct near the source |
| Crossing plane splits | Impedance discontinuity | Route over continuous planes |
| Finalising with rule-of-thumb formulas | Off by ±10% | Confirm with 2D solver or fabricator |
I'd like to try differential impedance and eye diagrams myself.
Try the differential pair impedance calculator for differential impedance, the transmission line simulator for transmission lines, the coupled-line crosstalk tool for coupling and the eye diagram tool for eye diagrams. Related topics are covered in crosstalk, S-parameters, via modelling and eye diagram evaluation.
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