Microstrip Line Impedance Calculator
Microstrip is the most common transmission line on RF boards: a signal trace on top of a solid ground plane. Enter the laminate and dimensions to get the characteristic impedance, or synthesize the width for 50 Ω, including copper thickness and dispersion.
What is a microstrip line?
A microstrip is the most common transmission line on printed circuit boards: a copper trace on the top layer runs over a solid ground plane, separated by the PCB dielectric. Because part of the electric field travels in air and part in the substrate, the wave sees an effective permittivity εeff between 1 and εr, which sets both the characteristic impedance and the guided wavelength. The impedance rises when the trace gets narrower or the dielectric gets thicker, and falls when εr increases.
Microstrip is easy to fabricate, probe and tune, which is why RF modules, antenna feeds and evaluation boards usually start with a 50 Ω microstrip. Its limits are radiation and crosstalk on dense boards and sensitivity to solder mask and laminate tolerance. When top-layer ground pour comes closer than about three trace widths, the line behaves as grounded coplanar waveguide, so use the GCPW calculator for that layout. The 50 Ω reference widths under Design tips were calculated with this page for the stated laminate, thickness and copper weight; confirm the final width with your fabricator's stack-up.
How to use
- Enter the laminate relative permittivity εr, substrate height h (dielectric between the signal layer and its ground plane) and copper thickness t (1 oz ≈ 35 µm).
- Enter the frequency f in MHz; it is used for dispersion and the quarter-wavelength result.
- Known width: enter W and press Analyze to get the characteristic impedance Zo.
- Known target: enter Zo (e.g. 50 Ω) and press Synthesize to get the required width W.
Theory and formulas
The tool uses Wheeler's microstrip equations with a thickness correction, then applies Getsinger's dispersion model:
W′ = W + ΔW · (1 + 1/εr)/2
Z = 42.4/√(εr+1) · ln{ 1 + (4h/W′)·[ (14+8/εr)/11 · 4h/W′ + √( ((14+8/εr)/11 · 4h/W′)² + π²(1+1/εr)/2 ) ] }
εeff(0) = (Zair / Z)² (Zair: same geometry with εr = 1)
εeff(f) = εr − (εr − εeff(0)) / [ 1 + G·(f/fp)² ], fp = Z/(0.8πh) GHz (h in mm), G = 0.6 + 0.009Z
Zo(f) = Z · √( εeff(0) / εeff(f) )
k = 1/√εeff λ/4 = k · c / (4f)
Synthesis adjusts W by bisection until the calculated impedance is within 0.001 Ω of the target.
Design tips
- 50 Ω reference widths (from this tool): FR-4 (εr 4.4, 35 µm copper) 1.6 mm thick ≈ 3.0 mm; 0.8 mm ≈ 1.49 mm; RO4350B (design Dk 3.66) 0.508 mm ≈ 1.07 mm. Rule of thumb on FR-4: a 50 Ω trace is about 1.9 × the dielectric height.
- On multilayer boards, h is the dielectric between the signal layer and the adjacent reference plane, not the full board thickness. Ask your fabricator for the stack-up.
- Solder mask lowers the impedance by roughly 1–3 Ω. For ±10 % or tighter, order controlled impedance with a test coupon.
- Keep top-layer ground pour at least 3W away from the trace; otherwise it behaves as grounded CPW — use the GCPW calculator.
- FR-4 permittivity falls with frequency (about 4.7 at 1 MHz, 4.3 at 1 GHz); use the value at your operating frequency.
FAQ
- What εr should I use for FR-4?
- Typically 4.3–4.6; around 2.4 GHz 4.3–4.4 is common. For accurate work use the Dk your fabricator specifies at a stated frequency.
- How much does copper thickness matter?
- Thicker copper widens the effective trace and slightly lowers impedance. This tool gives only about 0.3 Ω difference between 1 oz (35 µm) and 2 oz (70 µm) for a 3.0 mm trace on 1.6 mm FR-4, but about 1.5 Ω for a 0.35 mm trace on 0.2 mm dielectric.
- What is the quarter wavelength used for?
- A λ/4 line serves as an impedance transformer, an RF choke for bias feeds, or an open/short stub filter. The length is the guided wavelength, already including εeff.
Microstrip vs CPW vs GCPW vs coplanar strips
Pick the calculator that matches your board stack-up. The structures differ mainly in where the return (ground) conductor is:
| Line type | Conductors and ground | Typical use | Calculator |
|---|---|---|---|
| Microstrip | Trace on the top layer over a solid ground plane on the other side of the dielectric | General RF routing and 50 Ω feeds on FR-4; easy to fabricate and tune | This page |
| Coplanar waveguide (CPW) | Signal trace between two ground planes on the same layer; no backside ground | Ceramic or single-sided boards, many shunt parts, GSG probe measurements | Open Coplanar waveguide calculator |
| Grounded CPW (GCPW / CPWG) | CPW plus a backside ground plane, top grounds stitched with vias | RF modules, antenna feeds and dense layouts needing low radiation and crosstalk | Open Grounded CPW calculator |
| Coplanar strips (CPS) | Two equal parallel strips, balanced, no ground plane | Printed dipole and folded-dipole feeds, baluns, differential lines | Open Coplanar strips calculator |
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