u = w/h and the effective dielectric constant
Ereff, which sits between 1 and Er because the field is
partly in the board and partly in air. For u ≤ 1,
Z₀ = (60/√Ereff) · ln(8/u + u/4); above that,
Z₀ = 120π / (√Ereff · (u + 1.393 + 0.667·ln(u + 1.444))). Accuracy is
around 1 % for 0.05 < w/h < 20. Two cautions. Er is not a constant —
FR-4 is quoted near 4.3 at 1 MHz and falls towards 4.0 at GHz frequencies, and it varies by
weave and resin content. And the number that matters is your fabricator's stackup, not this one:
if impedance is controlled, send them the target and let them adjust the width.
| FR-4 (typical) | 4.2 – 4.5 | At 1 MHz; falls towards 4.0 at GHz frequencies |
|---|---|---|
| FR-4 (high-speed grade) | 3.8 – 4.2 | Lower resin content, tighter tolerance |
| Rogers RO4350B | 3.48 | Common RF laminate, FR-4 processing |
| Rogers RO4003C | 3.38 | |
| PTFE / Teflon | 2.1 | Lowest loss, hardest to fabricate |
| Polyimide (flex) | 3.4 | Flexible circuits |
| Alumina (ceramic) | 9.8 | Thick-film hybrids |
| Air | 1.0 | The reference case |
Er is not a constant. It varies with frequency, with the glass-weave pattern under the trace, and between production lots. For controlled impedance, send the target to your fabricator and let them adjust the width to their measured stackup.