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Microstrip Calculator (Hammerstad-Jensen)

Compute microstrip Z0 and effective permittivity, or solve for the trace width that hits your target. Hammerstad-Jensen formulation, accurate to better than 1 percent across typical RF geometries.

Microstrip Calculator

Compute characteristic impedance and effective permittivity of a microstrip trace or inverse solve for width from Z0. Uses the Hammerstad-Jensen formulation accurate to within 1% for 0.1 <= W/h <= 100.

Units
Length
Frequency

Inputs

Width and impedance
Mode?
Ω
mm
Frequency and loss
GHz
W = 1.531 mmh = 0.8 mmεr = 4.40ground plane
Microstrip line
Characteristic impedance Z0
50.00Ω
for W = 1.531 mm
Required trace width W
1.531mm
60.28 mil

More

Effective permittivity eeff3.331
Free-space lambda_0124.914 mm
Guided lambda_g68.439 mm
lambda_g / 4 (quarter-wave)17.110 mm
Dielectric loss only (conductor loss not included)7.22 dB/m

Analytical calculation

Solve trace width
Invert the Hammerstad-Jensen Z0(W) formula by bisection until it matches the target.
Normalised width
Drives every microstrip term.
Effective permittivity
Hammerstad-Jensen 1980. Captures the field split between substrate and air.
Characteristic impedance
Hammerstad-Jensen Z0, better than 1% accurate over 0.1 <= u <= 100.
Wavelengths
Free-space and guided wavelength. lambdaG sets quarter-wave and stub lengths.

Frequently asked

What microstrip width gives 50 ohm on FR-4?

On 1.6 mm FR-4 (er ~ 4.4) with 1 oz copper, a 50 ohm trace is about 3.0 mm wide. On 0.8 mm FR-4 it is about 1.5 mm. Switch to Solve W mode above to compute it for your stackup.

How accurate is this calculator?

Hammerstad-Jensen is better than 1 percent across typical RF geometries. It assumes infinite ground and a lossless conductor and ignores any cover dielectric. To capture soldermask, copper roughness, and etch effects, run the geometry through RayRF on your real stackup.

References

  • PrimaryHammerstad, E. & Jensen, O. "Accurate Models for Microstrip Computer-Aided Design," 1980 IEEE MTT-S International Microwave Symposium Digest, pp. 407-409. The (a, b) effective-permittivity form and the f(u) impedance form are used verbatim.
  • Cross-checkPozar, D. M. Microwave Engineering, 4th ed., Wiley 2011, Sec. 3.8 (microstrip closed form). Pozar uses the simpler Wheeler-Hammerstad piecewise form rather than the HJ 1980 (a, b) form, so this is a ballpark cross-check, not a re-publication.
  • Cross-checkWadell, B. C. Transmission Line Design Handbook, Artech House 1991 (microstrip closed forms with extensive tables).
  • Loss modelPozar, D. M. Microwave Engineering, 4th ed., Sec. 3.8 (microstrip dielectric attenuation with filling-factor correction). Conductor (skin-effect) loss is not included.
  • ConceptMicrostrip (overview)

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