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Grounded CPW Calculator (GCPW, Conductor-Backed)

Grounded coplanar waveguide impedance from Simons 2001 Eq. 4.29. The dominant RF transmission line above 10 GHz. Tight EM containment, via fencing for shielding, low radiation loss.

Grounded CPW (GCPW) Calculator

GCPW adds a backside ground to plain CPW. A common workhorse above ~10 GHz on thick substrates: tight EM containment, low radiation loss, and via fencing for shielding.

Units
Length
Frequency

Inputs

mm
mm
mm
GHz
W = 0.6 mmS = 0.2 mmSh = 0.508 mmεr = 3.66
Grounded coplanar waveguide
Z0
59.14Ω

More

eeff2.502
Guided lambda_g18.954 mm
lambda_g / 44.738 mm

Analytical calculation

Aspect ratios
k captures the top CPW; k3 adds the bottom-ground coupling.
Effective permittivity
Combines the top-CPW and bottom-microstrip-like contributions.
Characteristic impedance

Frequently asked

How dense should via stitching be?

Place fence vias every lambda_g/20 along the side grounds. At 24 GHz on RO4350B (default geometry above) lambda_g is about 7.9 mm, so lambda_g/20 is about 0.4 mm pitch; that is easy on a 4-mil-class process. If your design rules push you wider, lambda_g/10 (~0.8 mm at 24 GHz) is still acceptable for most shielding applications.

Why does GCPW work well at 24 GHz / 77 GHz?

Fields are mostly contained between the centre conductor and the side grounds, so trace dimensions can shrink with frequency without exploding loss. Microstrip on a thick substrate starts to excite surface waves and radiate measurably above ~10 GHz; on a thin substrate (h/lambda_0 well below 0.05) microstrip stays clean further. GCPW suppresses both effects with the side rails and backside ground.

References

  • PrimarySimons, R. N. Coplanar Waveguide Circuits, Components, and Systems, Wiley 2001, Ch. 4 (conductor-backed CPW). The eeff = (K(k)/K(k′) + er K(k3)/K(k3′)) / (K(k)/K(k′) + K(k3)/K(k3′)) form with k3 = tanh(piW/4h) / tanh(pi(W + 2S)/4h) is from this chapter.
  • Cross-checkWadell, B. C. Transmission Line Design Handbook, Artech House 1991 (conductor-backed CPW closed forms).
  • ConceptCoplanar waveguide (conductor-backed variant)

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