How microstrip impedance is calculated

A microstrip is a trace on an outer layer running over a ground plane. Its impedance depends mostly on the ratio of trace width to dielectric height and on the board's dielectric constant. Part of the field runs through the air above the trace, so the signal sees an effective permittivity somewhere between 1 and εr. EngBench uses the Hammerstad–Jensen equations, the closed-form model that field solvers are usually checked against.

• Impedance: Z₀ = Z₀₁(u) / √εeff, with u = w/h
• Effective permittivity: εeff = (εr+1)/2 + (εr−1)/2 · (1 + 10/u)^(−a·b)
• Delay: t = √εeff / c

Worked example: 50 Ω on 1.6 mm FR-4

A 3.0 mm trace on 1.6 mm FR-4 (εr 4.4) with 1 oz copper has an effective permittivity of 3.30 and an impedance of 50.2 Ω. Signals travel at 0.55 times the speed of light, about 6.1 ps per millimetre.

Good to know

• A wider trace or a thinner dielectric lowers impedance. On a 4-layer board with 0.2 mm prepreg, a 50 Ω trace is only about 0.36 mm wide.
• Solder mask over the trace typically lowers impedance by 1–3 Ω. Specify impedance with a tolerance (usually ±10%) and let the fabricator tune the width.
• The εr of FR-4 ranges from about 4.0 to 4.7 depending on glass style, resin content and frequency. Ask your fabricator for the value of their laminate.
• Pro solves the width for a target impedance and adds quarter-wave length and the impedance-vs-width curve.

Related calculators