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Coplanar waveguide calculator

A line that does not care about scale

In a coplanar waveguide the centre conductor and the grounds lie on the same side of the board. Because of that the impedance depends not on absolute dimensions but on their ratio — double the width and the gap and nothing changes. That is what makes CPW convenient where the process limits the smallest feature.

w 2 mmg 0.3 mmh 1.6 mmgroundgroundZ₀
The characteristic impedance is set by the ratio of width to gap, not by the sizes themselves
Relative permittivity εr
Centre conductor width w (mm)
Gap to ground g (mm)
Substrate thickness h (mm)
Shield underneath
Frequency (MHz)
Result
Characteristic impedance Z₀
Effective permittivity εeff
Modulus k = a/b
Wavelength in the line λg
Quarter-wave section

📐 The formulas​

a = w/2            b = w/2 + g            k = a/b
k′ = √(1 − k²)

With no ground underneath (classic CPW):

εeff = (εr + 1) / 2
Z₀ = (30π / √εeff) × K(k′)/K(k)

With ground underneath (CPWG): a second term with k₃ = tanh(πa/2h) / tanh(πb/2h) is added, and εeff rises.

K(·) is the complete elliptic integral of the first kind.

A check point:​

at εeff = 1 and k = 0.5 the ratio K(k′)/K(k) = 1.2793, so Z₀ = 30π × 1.2793 = 120.6 Ω.

Where this calculator stops:
  • The approximation εeff = (εr+1)/2 holds for a thick substrate; if it is thin relative to the line dimensions the calculator warns you
  • Metallisation thickness is not accounted for, and on narrow lines it lowers Z₀ noticeably
  • The grounds on both sides must be stitched together with vias, or a parasitic mode gets excited
  • Losses and dispersion are not accounted for

🎯 In practice​

  • RF boards without through-holes: the ground is beside the trace, not beneath it.
  • Lines on very thin or very thick substrates, where microstrip gives awkward dimensions.
  • Connector transitions: CPW mates naturally with a coaxial launch.
Practical advice:
  1. Try doubling w and g — Z₀ does not change. That is the best illustration of how this line works.
  2. The gap is set by the etching process: 0.1 mm already calls for a decent fabricator.
  3. Stitch the grounds with vias densely — at least every λg/10.
  4. CPWG is more stable, but its impedance does depend on substrate thickness.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Coplanar waveguide calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/lines/coplanar (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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