Channel loss budget estimator

Nyquist frequency f is half the baud rate at the IEEE 802.3 electrical lane rates: 10.3125 Gb/s NRZ → 5.16 GHz, 25.78 Gb/s NRZ → 12.89 GHz, 53.125 Gb/s PAM4 → 13.28 GHz, 106.25 Gb/s PAM4 → 26.56 GHz, 212.5 Gb/s PAM4 → 53.13 GHz. PAM4 carries 2 bits per symbol. (OIF CEI-112G quotes 112 Gb/s, i.e. 28 GHz; the difference is under 6%.)

The dielectric term is the standard first-order approximation for a homogeneous dielectric. The smooth-copper conductor term has the √f / w form of Bogatin's rule of thumb α_c ≈ 36·√f / (w·Z₀), with the constant calibrated to a published field-solver result (0.404 dB/in of conductor loss for a 5 mil, 100 Ω stripline pair at 14 GHz, Signal Integrity Journal); the plain rule of thumb at Z₀ = 50 Ω gives 0.72, about 33% higher. Copper roughness is applied with the Hammerstad–Jensen correction, which rises with frequency as the skin depth δ shrinks and saturates at 2× for foil much rougher than δ. As an independent check, for a 5 mil trace on FR-4 at 4 GHz with standard foil the model gives about 0.80 dB/in, against about 0.78 dB/in reported by Bogatin for a PCIe Gen3 channel of that construction.

RMS roughness per foil class is a planning assumption: conventional ED foil measures about 1.2–4 µm Rq on its treated side, very-low-profile foils about 0.47–0.7 µm, and HVLP3-class foil is specified at Rz ≤ 1.1 µm; the Rq values in the selector sit inside those ranges. Hammerstad under-predicts loss for the roughest foils above about 20 GHz, where a Huray-model field solver is the better tool. Laminate Dk and Df are the supplier's datasheet values at 10–14 GHz and are held constant across frequency; real laminates drift slightly upward in Df with frequency. Via, connector, package and crosstalk losses are not included.

Budget defaults: IEEE 802.3ck 100GBASE-KR1 allows 28 dB at 26.56 GHz and IEEE 802.3dj 200GBASE-KR1 allows 40 dB at 53.125 GHz, both die-to-die including packages and connectors. The PCB trace gets only part of that; if you have a trace allocation, enter it as the budget.

Budget status: green up to 85% of the budget, yellow above 85%, red above 100%. When a 112G or 224G channel exceeds the budget, the estimator reports the length at which this construction would use the full budget, as the point beyond which a retimer or a lower-loss laminate is needed.

Result accuracy is about ±20%: use it to compare laminates and foils, not to sign off a channel. Channel sign-off needs a field-solver or measured S-parameter model of the actual stackup.