Differential Pair Impedance Calculator
Two parallel surface traces driven differentially. The single-ended impedance comes from Hammerstad-Jensen; the coupling correction is the IPC-2141 exponential fit, which is the industry default but is genuinely approximate - the deviation output tells you how hard it is working.
Choosing something to solve for makes Differential impedance an editable target and computes the chosen input from it.
Formula
| w | width of one trace (m) |
| s | edge-to-edge separation (m) |
| h | dielectric height (m) |
| Z0 | single-ended impedance of one trace (ohm) |
| Zdiff | impedance seen across the pair (ohm) |
What this model assumes, and where it stops
Assumptions
- Quasi-TEM propagation: the cross-section is small against a wavelength.
- Static (low-frequency) solution - no dispersion, so Dk and Z0 do not change with frequency.
- Perfect conductors and a lossless, homogeneous, isotropic dielectric.
- Infinitely wide reference plane with no splits, voids or stitching gaps under the trace.
- A uniform, straight, infinitely long line - no bends, vias, stubs or terminations.
- Both traces identical, parallel, coplanar and equally spaced from the plane.
- Perfectly balanced drive: equal and opposite signals with no skew.
- Only the two traces couple; nothing else is nearby.
Limitations
- The 0.48/0.96 coupling fit is an empirical curve from IPC-2141, not a field solution. For tight coupling (s/h below about 0.5) it can be several ohms out, and that is exactly where high-speed pairs live.
- It never quite reaches 2 x Z0 even at large separation, which is a known artefact of the exponential form rather than real coupling.
- Broadside-coupled and edge-coupled stripline pairs are different geometries and are not covered here.
- Intra-pair skew, glass-weave fibre effects and mode conversion are all invisible to this model.
- No loss, no dispersion, no roughness.
When you need a 3D field solution instead
Closed-form models like the one above hold on idealised geometry. These are the cases where they stop being good enough and a full 3D electromagnetic and thermal solution is the only way to get a trustworthy answer:
- Reference-plane splits, voids or antipads under the trace, which the infinite-plane assumption cannot see.
- Vias, layer transitions and connector launches, where the discontinuity dominates the impedance budget.
- Tight bends, taper transitions and length-matching serpentines.
- Anything above roughly 5 GHz, where dispersion, surface roughness and dielectric loss stop being negligible.
- Trace-to-trace coupling beyond a single adjacent pair, and coupling between layers.
- Etch-factor trapezoidal cross-sections, where the top and bottom widths differ enough to shift Z0 by several percent.
- Tightly coupled pairs where the IPC fit is outside its comfortable range and a couple of ohms matters.
- Length-matching serpentines, where the pair couples to itself around the bends.
- Differential vias and connector breakouts, where common-mode conversion is decided.
- Broadside-coupled pairs and any stack where the two traces are not coplanar.
Common questions
Why is differential impedance less than twice the single-ended impedance?
Because the two traces couple. Field from one trace terminates on the other rather than on the plane, which lowers the impedance seen across the pair. The tighter the coupling, the larger the reduction - this page reports the coupling factor explicitly.
How accurate is the IPC-2141 coupling formula?
It is an empirical fit, not a field solution. For loosely coupled pairs it is reasonable; below about s/h = 0.5, which is where most high-speed pairs live, it can be several ohms out. It also never quite reaches twice the single-ended value even at large separation, which is an artefact of its exponential form.
Does this cover broadside-coupled pairs?
No. This is edge-coupled microstrip only, with both traces on the same layer. Broadside pairs on adjacent layers are a different geometry with different behaviour.
References
- IPC-2141A - Design Guide for High-Speed Controlled Impedance Circuit Boards
- Hammerstad & Jensen - Accurate Models for Microstrip Computer-Aided Design, 1980