Edge-Coupled Embedded Microstrip Calculator
Calculate differential and common-mode impedance for an edge-coupled pair under soldermask, coating or prepreg — with a separate effective permittivity per mode, so the skew the cover introduces is visible.
Formula
Reference: Filling factors fitted to the layered method-of-moments solver committed in src/lib/pcb/__tests__/solver, which reproduces Hammerstad–Jensen to 0.1% and the fully-embedded limit to 0.005%.
How It Works
A differential pair on an outer layer is rarely bare. Soldermask, conformal coating or a laminated prepreg sits over it, and that cover changes the impedance by more than its thickness suggests, because the field between two closely spaced traces is concentrated exactly where the cover sits.
What makes a covered surface pair different from a stripline pair is that the dielectric is not homogeneous. Part of the field is in the substrate, part in the cover, and part still in the air above. The two modes divide that field differently: the odd mode drives its field through the gap between the traces, while the even mode spreads laterally. So the two modes see different effective permittivities and travel at different speeds.
That speed difference is real and it matters. A pair whose modes travel at different speeds converts differential signal into common mode as it propagates — mode-conversion skew — and a long covered pair accumulates it. A stripline pair does not, because its medium is uniform.
This calculator separates geometry from dielectric. The air-mode impedances depend only on the width and spacing relative to the substrate height, and are fitted as ratios to the single line, so an uncoupled pair recovers the single-line result exactly. Each mode then receives its own effective permittivity, built from the share of its energy already in the substrate plus the share of the remainder that the cover captures.
That construction has a property worth stating: because the cover can only capture energy that is not already in the substrate, the effective permittivity can never exceed the largest permittivity present. That bound is not a check bolted on afterwards — it holds by construction. A covered-microstrip model that violates it, as a previous model in this codebase did, is not merely inaccurate; it is describing something that cannot exist.
On a bare pair the even mode carries the higher permittivity, because the odd mode drives its field through an air gap. Put a thick cover over a tight gap and that ordering can invert, since the region the odd mode works hardest in is now dielectric rather than air. The model reproduces the inversion because it was fitted to a layered field solve rather than assumed.
Worked Example
Take a 0.2 mm pair on 0.2 mm spacing over a 0.2 mm FR4 substrate at εr = 4.2, 1 oz copper, under 25 µm of soldermask at εrc = 3.5.
The single trace on its own, covered, is 64.13 Ω. With its partner alongside:
Z_odd = 53.76 Ω, Z_even = 73.82 Ω Z_diff = 2 × 53.76 = 107.52 Ω Z_common = 73.82 / 2 = 36.91 Ω
Now the part a homogeneous model cannot show. The two modes see different effective permittivities:
εeff,odd = 3.122, εeff,even = 3.472
which gives propagation delays of 5.894 ps/mm for the odd mode and 6.215 ps/mm for the even mode. That is 0.321 ps/mm of skew between the modes. Over a 100 mm route it accumulates to 32 ps of differential-to-common-mode conversion — which is why the calculator raises it as a warning rather than leaving it in a table.
Set the cover dielectric constant to 1.0 and the calculator returns the bare surface pair exactly, which is a useful way to see what the mask is actually costing you.
Practical Tips
- ✓Run the geometry twice, once with the cover dielectric at 1.0 and once at its real value. The difference is what the cover is doing, isolated from everything else.
- ✓For a long pair, look at the two propagation delays before the impedances. If the skew is significant over your route length, that is a stronger argument for moving to an inner layer than the impedance is.
- ✓A thicker cover is more predictable than a thin one, because once the cover contains the field, further thickness stops mattering. Thin mask is the sensitive region.
- ✓If the design is impedance-critical and the pair must stay on the surface, ask the fabricator to hold and report mask thickness rather than assuming a nominal figure.
- ✓Check the validated-range flag when using unusually wide or unusually tightly spaced traces.
- ✓Compare against the internal symmetric calculator for the same electrical target — if both are viable, the buried pair removes the skew question entirely.
Common Mistakes
- ✗Ignoring soldermask because it is thin. Twenty-five micrometres of mask sits precisely where the odd-mode field is strongest, and it moves the differential impedance by several ohms.
- ✗Using one effective permittivity for both modes. That erases the skew, which is the main reason a covered surface pair behaves differently from a buried one.
- ✗Assuming the even mode always has the higher permittivity. It does on a bare pair, but a thick cover over a tight gap can invert the ordering.
- ✗Taking the mask thickness as the value in the fabricator's datasheet. Mask over a trace is thinner than mask over bare laminate, and it is the thickness over the copper that matters here.
- ✗Treating a covered pair and a stripline pair as interchangeable for long routes. Only one of them accumulates mode-conversion skew.
Frequently Asked Questions
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