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Differential Pair Calculator (Edge-Coupled Microstrip, 100 Ohm)

Edge-coupled microstrip differential impedance Zdiff for USB, Ethernet, PCIe, MIPI, and HDMI. Hammerstad-Jensen single-line plus the Hammerstad even-odd coupling correction.

Differential Pair Calculator

Edge-coupled microstrip differential pair; the workhorse for USB, Ethernet, PCIe, MIPI, and HDMI. Computes differential and common-mode impedance from W, S, and stackup.

Units
Length
Frequency

Inputs

Ω
mm
mm
GHz
W = 0.381 mmWS = 0.2 mmh = 0.2 mmεr = 4.04ground plane
Edge-coupled differential microstrip
Differential Z
100.00Ω
Required width W
0.381mm
15.02 mil

More

Z0 single52.05 Ω
Even mode Z0e42.48 Ω
Odd mode Z0o50.00 Ω
Common mode Z21.24 Ω
Guided lambda_g34.13 mm

Analytical calculation

Every step the calculator runs, with the formula, your numbers plugged in, and the result.

Solve trace width
Invert Z_diff(W) by bisection to hit the target differential impedance.
Single-ended impedance
Hammerstad-Jensen on one trace alone, ignoring the partner.
Even / odd modes
Empirical Hammerstad coupling correction. Wide S means both modes converge to the single-ended value.
Differential impedance
Twice the odd-mode impedance.

Frequently asked

What W and S give 100 ohm diff on 0.2 mm prepreg?

For h = 0.2 mm, S = 0.18 mm and er ~ 4.0, Solve W gives about W = 0.38 mm to land Zdiff = 100 ohm. Tighter S means tighter coupling and a narrower W; loosen S to ~3 h and you can use roughly the same W as a 50 ohm single-ended trace. Use Solve W mode with your actual stackup for an exact answer.

Should I match length on diff pairs?

Yes. Aim well under 10 ps of intra-pair skew as a routing budget for USB 3 / PCIe Gen 4 / 10G Ethernet; the relevant specs (USB 3.2, PCIe base 4.0/5.0) state intra-pair skew limits in the 8 to 15 ps range at the receiver, so you want a comfortable margin. Length tuning is not impedance; both matter independently.

References

  • PrimaryHammerstad, E. & Jensen, O. 1980 (single-ended Z0). Even/odd-mode coupling factors 1 - 0.48 exp(-0.96 S/h) and 1 - 0.48 exp(-2.5 S/h) follow the edge-coupled microstrip approximation collected in Wadell 1991 and in Garg, Bahl & Bozzi, Microstrip Lines and Slotlines, 3rd ed., Artech House 2013.
  • Cross-checkWadell, B. C. Transmission Line Design Handbook, Artech House 1991 (edge-coupled microstrip, even/odd-mode closed forms).
  • NoteThese empirical coupling factors are accurate to a few percent for typical PCB geometries (S/h roughly 0.2 to 3); outside that band, especially at very tight S/h, cross-validate with a 2.5D solver.

Closed-form is just the start.

These calculators hand you the analytical starting point. RayRF takes you the rest of the way: antennas, filters, feedlines, and more, simulated on your real stackup with copper losses, dielectric loss, and finite ground. Roughly a second per iteration.

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