How do I determine the correct microstrip trace width for 50 ohm impedance on FR4 at a given frequency?
Microstrip Design on FR4
The characteristic impedance of a microstrip line depends on the ratio of trace width (W) to dielectric height (h), the dielectric constant (εr), and the trace thickness (t). For W/h ratios typical of 50 Ω (1.5-2.0), the impedance decreases with wider traces and increases with thinner traces. The effective dielectric constant is lower than the bulk εr because part of the field propagates in air above the trace.
FR4 is the most common and least expensive PCB substrate, but its electrical properties limit high-frequency performance. The dielectric constant varies from 4.2 to 4.6 across manufacturing lots and even within a single panel, causing ±5% impedance variation. The loss tangent (tan δ = 0.020-0.025) causes significant insertion loss above 3-4 GHz: approximately 0.5 dB/inch at 5 GHz for a 50 Ω microstrip on 0.031-inch FR4.
For impedance-controlled designs on FR4, specify the target impedance (50 Ω ± 10%), the stackup dimensions, and the copper weight to the PCB fabricator. They will calculate the trace width using their specific εr data and etch compensation factors. Most PCB shops achieve ±10% impedance control on FR4; tighter tolerances require more expensive substrates like Rogers or Isola.
(for W/h < 2, Hammerstad approximation)
For FR4 (εr=4.4), h=0.031":
W ≈ 0.059" for Z₀ = 50 Ω
W ≈ 0.108" for Z₀ = 35 Ω
W ≈ 0.012" for Z₀ = 100 Ω
Frequently Asked Questions
Does copper thickness matter?
Yes. Standard 1 oz copper (35 μm) slightly lowers the impedance compared to 0.5 oz (17 μm) for the same trace width. The effect is about 1-3 Ω for typical 50 Ω lines. Thicker copper (2 oz) has a larger effect and must be accounted for in the impedance calculation.
What about inner layers?
Inner layer traces (stripline) are surrounded by dielectric on both sides, giving a higher effective εr and requiring narrower traces for 50 Ω. On the same 0.031-inch FR4, stripline requires approximately 12 mil trace width for 50 Ω, compared to 59 mil for microstrip.
Can I use FR4 above 6 GHz?
With difficulty. Above 6 GHz, FR4 dielectric loss exceeds 1 dB/inch, εr dispersion causes phase errors, and the εr tolerance makes impedance control unreliable. For serious work above 6 GHz, use Rogers 4003C (εr=3.55, tan δ=0.0027), Isola I-Tera (εr=3.45, tan δ=0.0031), or similar low-loss laminates.