How is microstrip impedance calculated?
Microstrip is a conductor strip of width W on a dielectric of thickness h above a ground plane. Because the field lies partly in air, it supports a quasi-TEM mode with effective permittivity between 1 and εr. Widely used closed-form approximations (Hammerstad–Jensen) give, for W/h ≥ 1, Z0 = 120π / [√εeff·(W/h + 1.393 + 0.667·ln(W/h + 1.444))].[1][2]
How is effective permittivity estimated?
εeff ≈ (εr + 1)/2 + ((εr − 1)/2)·(1 + 12h/W)−1/2. For W/h ≤ 1: Z0 = (60/√εeff)·ln(8h/W + W/(4h)).[2] These ignore conductor thickness, which slightly lowers Z0; field solvers and simulator line calculators include it.
What width gives 50 ohms?
Roughly W/h ≈ 1.9 on FR-4 (εr ≈ 4.3) and ≈ 2.2 on εr = 3.5 material; on a 0.508 mm RO4350B core, about 1.1 mm. Always confirm with the fabricator’s stackup and a field solver, since the design Dk and copper thickness shift the result.[3]
What are the limitations of microstrip?
- Dispersion: εeff rises toward εr with frequency.
- Radiation from discontinuities and open ends, increasing at mmWave.
- Higher-order modes when W or h approach a fraction of a wavelength in the dielectric.
- Coupling to nearby lines; spacing of about 3h or more reduces crosstalk.
- Exposed to solder mask, which lowers Z0 slightly.
How lossy is microstrip?
Total loss = conductor loss (∝ √f, increased by roughness) + dielectric loss αd = k0εr(εeff − 1)tan δ / (2√εeff(εr − 1)) Np/m.[2] On FR-4 at a few GHz, dielectric loss dominates.
Frequently asked questions
Is microstrip TEM?
No, quasi-TEM, because the field is in two different media.
Does solder mask change impedance?
Yes, typically lowering Z0 by a few ohms; include it in the stackup model.
When should I use CPW instead?
At high frequencies or when tight ground control and easy shunt connections are needed.
See also
References
Online sources accessed October 21, 2026; printed works cited by edition. See all sources.
- “Accurate Models for Microstrip Computer-Aided Design”. E. Hammerstad and Ø. Jensen, IEEE MTT-S International Microwave Symposium Digest, pp. 407-409. 1980.
- “Microwave Engineering, 4th ed.”. D. M. Pozar, Wiley. 2012.
- “RO4000 Series High Frequency Circuit Materials data sheet (RO4350B)”. Rogers Corporation. data sheet.