Hong Life CalculatorsUnderstanding the microstrip impedance calculator — concept and principle
A microstrip is a copper trace on the outer layer of a printed circuit board, separated from a ground plane by the board's dielectric. This calculator estimates its characteristic impedance from trace width, dielectric height, copper thickness and permittivity. It is used to route controlled-impedance lines such as 50 Ω RF feeds and to sanity-check high-speed traces.
How it is calculated
The calculator uses the IPC-2141 approximation:
Z₀ = 87 / √(εᵣ + 1.41) · ln(5.98 h / (0.8 w + t))
- w (mm): trace width. Wider traces lower the impedance.
- h (mm): dielectric thickness between trace and ground. Thicker boards raise the impedance.
- t (mm): copper thickness; 1 oz copper is about 0.035 mm.
- εᵣ: relative permittivity of the board material; FR-4 is roughly 4.3, varying with frequency and supplier.
All lengths must use the same unit. The formula is intended for about 0.1 < w/h < 2.0.
The principle
Like any transmission line, the impedance is √(L/C) per unit length. A wider trace or a thinner dielectric increases capacitance to ground and lowers Z₀; a narrow trace far from ground has more inductance and less capacitance, raising Z₀. Because part of the electric field runs through air above the board, the wave sees an effective permittivity between 1 and εᵣ, which is why the formula uses εᵣ + 1.41 instead of εᵣ alone. The logarithm comes from the same field geometry that gives the coaxial ln(D/d) term; the constants 87, 5.98 and 0.8 are empirical fits to measured and computed data.
Worked example
- √(4.3 + 1.41) = √5.71 ≈ 2.3896, so 87 / 2.3896 ≈ 36.408.
- Numerator: 5.98 × 1.6 = 9.568.
- Denominator: 0.8 × 3 + 0.035 = 2.435.
- ln(9.568 / 2.435) = ln(3.929) ≈ 1.3685.
- Z₀ = 36.408 × 1.3685 ≈ 49.82 Ω, close to the 50 Ω target. Here w/h = 1.875, inside the valid range.
| Dielectric height (mm) | Impedance (Ω) |
|---|---|
| 0.4 | -0.6486849758 |
| 0.8 | 24.58767186 |
| 1.2 | 39.34999426 |
| 1.6 | 49.82402869 |
| 2 | 57.94832097 |
| 2.4 | 64.58635109 |
| 3.2 | 75.06038552 |
How to read the result
Common targets are 50 Ω single-ended for RF, about 90 Ω differential for USB and about 100 Ω differential for Ethernet and many serial links. On a 1.6 mm FR-4 board a 50 Ω microstrip is roughly 3 mm wide; on a thin 0.2 mm layer of a multilayer board it is only a few tenths of a millimetre. Fabricators usually hold impedance to about ±10%, so a result within a few ohms of target is a good starting point.
Common mistakes
- Using the total board thickness instead of the distance from the trace to its reference plane.
- Applying the formula outside 0.1 < w/h < 2.0, where errors grow quickly.
- Ignoring solder mask, which lowers impedance by a few ohms.
- Treating FR-4 εᵣ as exact; it varies roughly from 3.8 to 4.8.
Frequently asked questions
What width gives 50 Ω on 1.6 mm FR-4?
About 2.98 mm with this formula (εr 4.3, 35 µm copper); check with your fabricator's stack-up.
How is stripline different?
A stripline is buried between two ground planes, so all of the field is in the dielectric and different formulas apply.
Sources: IPC-2141A, Design Guide for High-Speed Controlled Impedance Circuit Boards · Wadell, Transmission Line Design Handbook, Artech House