Edge-Coupled Asymmetric (Offset) Stripline Calculator
Calculate differential and common-mode impedance for an edge-coupled pair sitting off-centre between two reference planes — the usual case in an asymmetric stack-up.
Formula
Reference: S. B. Cohn, IRE Trans. MTT-3 (1955) for the centred case; offset correction fitted to the committed solver in src/lib/pcb/__tests__/solver.
How It Works
Most differential pairs are not centred between their reference planes. A pair on an inner signal layer usually has a thin prepreg to one plane and a thicker core to the other, and that asymmetry moves the impedance by more than the tolerance the fabricator is holding.
The offset case has no exact closed form, so this calculator is built as an exact base with a correction on top. The base is the exact centred coupling ratio applied to the offset single line — both of which are already known quantities. What that decomposition misses is a residual correction, and that correction was fitted to a two-dimensional method-of-moments field solver committed alongside the calculator.
The important property of the correction is that it vanishes identically when the two dielectric heights are equal. That means the reduction to the exact symmetric case holds by construction rather than by luck: set h₁ = h₂ and this calculator returns the symmetric calculator's answer to the last digit, not merely to within a tolerance.
Offsetting the pair moves it closer to one plane, which raises the capacitance to that plane and lowers every mode impedance. The effect is not subtle. Moving a pair from centred to a quarter of the plane spacing typically drops the differential impedance by 10 to 20%, which is why treating an offset pair as centred is a common way for a controlled-impedance board to come back out of specification.
The model's residual against the solver is 1.85% worst case on a mode impedance and 0.44% rms, over trace widths of 0.05 to 0.8 of the plane spacing, spacings of 0.05 to 1.0, and a nearer gap between 0.125 and 0.5 of the plane spacing. Outside that range the result is still returned, but it is flagged as extrapolated.
Worked Example
Take a 0.13 mm pair on 0.2 mm spacing, sitting 0.2 mm above the lower plane and 0.5 mm below the upper one, 1 oz copper, FR4 at εr = 4.2.
The total plane separation is 0.7 mm and the offset ratio |h₁ − h₂|/(h₁ + h₂) is 0.4286 — the pair sits well off centre.
The single trace on its own in that offset position has an impedance of 59.44 Ω. With its partner 0.2 mm away, the modes come out at:
Z_odd = 51.51 Ω, Z_even = 66.70 Ω Z_diff = 2 × 51.51 = 103.02 Ω Z_common = 66.70 / 2 = 33.35 Ω
Now the comparison that matters. Centre the same pair between the same planes — 0.35 mm each side — and the differential impedance rises. The offset costs real impedance, and it costs it in the direction that a 100 Ω design cannot absorb if it was already at the bottom of tolerance.
Propagation delay is 6.836 ps/mm, the same as any stripline in this dielectric, because the medium is homogeneous regardless of where in it the traces sit.
Practical Tips
- ✓Run the centred case first as a reference, then apply the real offset. The difference between the two is the number to take to a stack-up review.
- ✓If the offset is large and the impedance target is tight, ask whether the pair can move to a more balanced layer before adjusting width and spacing to compensate.
- ✓Check the extrapolation flag before trusting a number. Very thin outer gaps in particular fall outside the fitted range.
- ✓An offset pair is also asymmetric in its coupling to the two planes, so plane-referencing discontinuities matter more; keep a continuous reference under the whole route.
- ✓Where the two heights are nearly equal, use the symmetric calculator — its answer is exact rather than fitted, so there is no residual at all.
- ✓Compare the odd-mode impedance against the single-trace value to see how much of the result is coupling and how much is placement.
Common Mistakes
- ✗Averaging the two dielectric heights and using the symmetric calculator. The relationship is not linear in the offset, so the average gives the wrong answer in the direction that flatters the design.
- ✗Taking the heights from the drawing rather than from the fabricator's actual stack-up. Prepreg thickness after lamination is not the thickness on the datasheet, and it is the built value that sets the impedance.
- ✗Ignoring which plane is nearer. The model is symmetric under swapping the two heights, so only the offset matters — but confusing the two while reading a stack-up produces the wrong offset entirely.
- ✗Treating the extrapolation flag as cosmetic. Outside the validated range the model has no stated accuracy, and a fit outside the geometry it was fitted over is not a calculation, it is a guess.
- ✗Forgetting that the copper thickness sits inside the plane-to-plane distance. The dielectric heights are measured from the copper faces, not from the layer centreline.
Frequently Asked Questions
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