Microstrip Impedance Calculator (PCB Trace)
Characteristic impedance and propagation delay of a PCB trace over a ground plane, by the IPC-2141 formula, with a check of its range of validity.
Results
What this tool does
A trace on the outer layer of a board with a ground plane underneath is a microstrip, and once its edges are fast its width sets an impedance that must match the source and the load: 50 Ω for most RF and single-ended high-speed lines, and pairs of traces for the 90 Ω of USB or the 100 Ω of Ethernet. This calculator uses the closed-form expression in IPC-2141, which is quick but only good to a few percent, and only for w/h between 0.1 and 2 and εr between 1 and 15. The permittivity of FR-4 varies between suppliers and drops with frequency, from about 4.7 at 1 MHz to about 4.2 at a few GHz, so for a real controlled-impedance board ask the manufacturer for their stack-up and field-solver numbers.
Formula
Z₀ = 87 ÷ √(εr + 1.41) × ln(5.98 h ÷ (0.8 w + t)) · tpd = 85 √(0.475 εr + 0.67) ps/in
Variables
| Symbol | Meaning | Unit |
|---|---|---|
w | Trace width | mm |
h | Dielectric height to the ground plane | mm |
t | Copper thickness (35 µm = 1 oz) | mm |
er | Relative permittivity εr (FR-4 about 4.3) | — |
Z | Characteristic impedance | Ω |
WH | Width-to-height ratio w/h | — |
EF | Effective permittivity (approx.) | — |
TD | Propagation delay | ps/mm |
VA | Validity | — |
Worked example
- Trace width0.33 mm
- Dielectric height to the ground plane0.2 mm
- Copper thickness (35 µm = 1 oz)0.035 mm
- Relative permittivity εr (FR-4 about 4.3)4.3
- Characteristic impedance50.5 Ω
- Width-to-height ratio w/h1.65
- Effective permittivity (approx.)2.713
- Propagation delay5.51 ps/mm
- ValidityInside the range where the formula holds
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.