RF / Transmission Line Impedance
Calculate characteristic impedance of PCB microstrip transmission lines for RF matching.
Microstrip Impedance Formula (IPC-2141):
Z₀ = (87 / sqrt(ε_r + 1.41)) × ln(5.98h / (0.8w + t)) Ω
This equation yields highly accurate matching predictions for typical PCB dielectric substrates (like FR-4) when trace dimensions are in the range of 0.1 < w/h < 3.0.
Impedance Match Status compares Z₀ to the 50 Ω RF standard: <1Ω Optimal, ≤5Ω Good, otherwise mismatch (needs a matching network). Widen the trace or reduce dielectric height to lower Z₀.
When you need it: Computing the characteristic impedance and propagation delay of a microstrip or stripline trace when you need a controlled-impedance route (USB, RF, high-speed digital).
Worked example: On FR-4 (εr ≈ 4.3), a 50 Ω microstrip is roughly 1.8× as wide as the dielectric is thick, and propagation delay is about 6 ps/mm (effective εr ≈ 3).
Tips & gotchas:
- Route over a solid, unbroken reference plane; a gap under the trace ruins the impedance and radiates.
- Microstrip's effective εr sits between air and the laminate because part of the field is in air.
- Either keep the trace short relative to a wavelength/rise-time or terminate it properly.
- Er and stackup tolerances shift impedance — get the actual stackup from your fabricator before finalising widths.