Microstrip Trace Impedance Calculator

Microstrip transmission lines emerged in the 1950s at ITT Labs as a compact alternative to waveguide for microwave electronics. The first practical formulas for characteristic impedance were developed by Harold Wheeler (Hewlett-Packard) in 1964, refined by Erik Hammerstad at SINTEF Norway in 1975, and extended by Hammerstad and Øystein Jensen in 1980 into the widely-used H-J formula this calculator implements.

The H-J formulas achieve ±2% accuracy across the practical trace-geometry range (0.05 < w/h < 20) by empirically fitting to numerical-field-solver data. They account for the fact that the field doesn't completely fill the substrate — it fringes into air above the trace — requiring the "effective dielectric constant" correction εe.

Modern field solvers (Ansys HFSS, CST Microwave Studio, Polar Si9000) give sub-1% accuracy but require substantial compute time and software cost. The H-J closed-form formulas remain the go-to for first-pass design and educational use, and still power the built-in impedance calculators in every major ECAD tool (Altium, KiCad, Mentor Graphics).

Enter microstrip geometry: trace width W, substrate height H, trace copper thickness T, and dielectric constant εr. The tool computes Z₀ using the Hammerstad-Jensen formula and effective εr for the propagation-delay correction.

Common targets: 50Ω for SMA connectors and most RF, 75Ω for video coax, 90Ω for USB 2.0 differential, 100Ω for DDR memory and Ethernet. For tight tolerance (±5%), use a field solver and validate with TDR on a prototype board. Everything runs client-side.