Ohmforge Microstrip & Stripline Impedance Calculator
PCB trace impedance Z0, εeff and delay (Hammerstad–Jensen, Wheeler), or the width for 50 Ω.
Try an example: FR-4: 0.3 mm trace on 0.17 mm prepreg · Width for 50 Ω on PTFE (εr 2.2, h 1.27 mm) — Pozar example 3.7 · 50 Ω stripline, planes 3.2 mm apart (εr 2.2) — Pozar example 3.5
How it works
Characteristic impedance of a PCB trace: surface microstrip with the Hammerstad–Jensen equations (thickness correction included) or a centred stripline with Wheeler's formula, plus effective permittivity, propagation delay and guided wavelength. Synthesis mode solves the trace width for a target impedance such as 50 Ω with Brent's root finder; every result is cross-checked against an independent formula and the IPC-2141 rule of thumb.
- Microstrip: Hammerstad–Jensen (1980) closed-form equations — Z0 of the air line Z01(u) with u = W/h, effective permittivity εe(u, εr) with their a(u) and b(εr) fits (accuracy better than 0.2 % for 0.01 ≤ u ≤ 100), and the strip-thickness correction Δu (Wheeler's) applied separately to the air line and the dielectric. Z0 = Z01(ur)/√εe(ur).
- Stripline (strip centred between two planes, spacing b): Wheeler's 1978 formula with the thickness correction (about 0.5 % accuracy for W/(b − t) < 10); for t = 0 it is compared with Cohn's exact conformal-mapping result η0/(4√εr)·K(k)/K(k′), k = sech(πW/2b), evaluated with the arithmetic–geometric mean.
- Synthesis solves Z0(W) = target with Brent's method (Proofline numerical engine) over W/h from 0.01 to 100 (stripline: up to 20) on a logarithmic width axis.
- Delay = √εeff / c, guided wavelength = c / (f·√εeff). The IPC-2141 rule-of-thumb formulas are shown for comparison only; they are less accurate, especially outside their range.
Quasi-static, lossless model: no dispersion (microstrip Z0 and εeff rise at high frequency), no solder mask, no roughness, no etch trapezoid and no nearby copper pour. Ask your PCB maker for their stack-up and impedance-controlled width; manufacturing tolerances are typically ±10 %.
Sources
- E. Hammerstad, Ø. Jensen: Accurate Models for Microstrip Computer-Aided Design, IEEE MTT-S Int. Microwave Symposium Digest (1980) (IEEE)
- H. A. Wheeler: Transmission-Line Properties of a Strip on a Dielectric Sheet on a Plane, IEEE Trans. MTT 25(8) (1977) (IEEE)
- H. A. Wheeler: Transmission-Line Properties of a Strip Line Between Parallel Planes, IEEE Trans. MTT 26(11) (1978) (IEEE)
- S. B. Cohn: Characteristic Impedance of the Shielded-Strip Transmission Line, IRE Trans. MTT 2(2) (1954) (IRE / IEEE)
- D. M. Pozar: Microwave Engineering, 4th ed., Wiley 2012 — §2.3 (VSWR, return loss), §3.7–3.8 (stripline, microstrip), §5.1 (L-section matching) (Wiley)
- IPC-2141A: Design Guide for High-Speed Controlled Impedance Circuit Boards (IPC)
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Calculate microstrip and stripline impedance, or the width for 50 Ω
Find the characteristic impedance of a PCB trace or the trace width for a target impedance, with effective permittivity, delay and independent cross-checks.
What it is for
An RF trace, a USB pair or an antenna feed only behaves when its characteristic impedance matches the system, usually 50 Ω. That impedance depends on the trace width, the dielectric thickness to the reference plane, the copper thickness and the board material. This tool calculates it for two common geometries: Microstrip (a trace on an outer layer over a plane) and Stripline (a trace centred between two planes).
Choose Impedance of a given width to check a layout, or Width for a target impedance to design one. Microstrip uses the Hammerstad–Jensen equations, stripline uses Wheeler's formula, and the width is solved numerically with Brent's root finder.
It is a quasi-static calculation. It does not model solder mask, copper roughness, etch shape, dispersion at high frequencies or a nearby copper pour, and it does not replace the stack-up data from your PCB maker.
Worked example
You need a 50 Ω microstrip on a four-layer board with 0.2 mm prepreg (εr 4.2) to the ground plane and 35 µm copper, for a 2.4 GHz antenna feed. Choose Microstrip, Width for a target impedance, enter Dielectric height 0.2 mm, Copper thickness 35 µm, εr 4.2, Target impedance 50 Ω and Frequency 2400 MHz.
The tool answers with a 0.3657 mm trace (W/h = 1.828), an effective permittivity of 3.067 and a delay of 5.842 ps/mm. The guided wavelength at 2.4 GHz is 71.32 mm, so a quarter-wave section is about 17.8 mm long.
The cross-check table shows how the copper affects the result: the same formula at zero thickness gives 52.463 Ω, and Wheeler's independent 1977 formula gives 52.349 Ω for that thin strip, 0.217 % away. The IPC-2141 rule of thumb reads 47.57 Ω, almost 5 % off, which is why it is shown for comparison only.
How to read the result
Z0 is the characteristic impedance; in synthesis mode it equals your target. Trace width W is the answer in synthesis mode. εeff is the permittivity the wave actually sees. A microstrip has field lines partly in air, so it is lower than εr. Delay tells you how long a trace takes to cross, which matters for length matching.
The Cross-checks table compares the result with independent formulas. The difference to the second formula should be a fraction of a percent; a large difference means you are outside the range where the formulas were fitted.
Tips and common mistakes
- Use the dielectric constant your laminate maker gives for your frequency. FR-4 varies from about 4.2 to 4.6.
- For stripline, enter the total distance between both planes as the height, not the distance to one plane.
- Thin copper matters more on narrow traces: 18 µm copper on a 0.15 mm stripline changes Z0 by about 10 %.
- Solder mask over a microstrip lowers Z0 by a few ohms; ask your board house for their controlled-impedance width.
- Plan for ±10 % manufacturing tolerance unless you order controlled impedance.
FAQ
Why does my PCB maker suggest a different width?
They include solder mask, etch factor and their measured material data. Use this tool to understand the design and their numbers for production.
What does the frequency field change?
Only the guided wavelength. The impedance itself is calculated quasi-statically.
Is the result valid for differential pairs?
No. The tool calculates single-ended lines. Coupled pairs need a differential-impedance model.
Which formula is more accurate, Hammerstad–Jensen or IPC-2141?
Hammerstad–Jensen, by a wide margin. Its authors report errors below about 0.2 % over a wide range. The IPC-2141 rule is a quick approximation for a limited range.
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curl -s -X POST https://ohmforgemicrostripimpedance.usefulweb.app/api/v1/calculate \
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