Coplanar Waveguide (CPW) Calculator

Calculate CPW characteristic impedance using elliptic integral conformal mapping. Supports standard CPW and conductor-backed CPW (CBCPW).

What is a coplanar waveguide?

A coplanar waveguide is like a microstrip's cousin — instead of a ground plane underneath, CPW has ground strips alongside the signal trace, like guard rails on either side of a highway. The signal travels in the gap between the center trace and those ground rails.

Why it matters: CPW is used in 5G antenna feeds and high-frequency test equipment because the ground is right next to the signal, making it easier to connect probes and components without drilling through the board.

CPW Parameters
Enter trace width, gap, substrate height, and dielectric constant.

Width of the center signal trace. Wider trace = lower impedance.

Space between the signal trace and the ground strips on each side. Narrower gap = lower impedance.

Board thickness. Standard FR4 is 1.6 mm.

How much the board material slows the signal vs. air (air = 1.0). FR4 ≈ 4.4.

Operating frequency — used to calculate wavelength and propagation delay.

Conductor-Backed CPW

Ground plane under substrate

Impedance Z₀
55.64 Ω
Effective εᵣ
2.816
Results
CPW
Characteristic Impedance Z₀
55.641Ω
Effective Permittivity εe
2.8161
k = w/(w+2s)
0.714286
k' = √(1−k²)
0.699854
K(k)

Complete elliptic integral

1.862818
K(k')

Complementary

1.845525
Guided Wavelength

at 2.4 GHz

74.488mm
λ/4 Length
18.622mm
Propagation Delay
5.594ps/mm
Z₀ = 55.6 Ω — adjust trace width or gap to approach 50 Ω. Current k = 0.7143.