Coplanar Waveguide (CPW) Calculator
Coplanar waveguide has the signal trace and ground planes on the same side of the substrate. This allows easy shunt connections without vias and is preferred for MMICs and millimetre-wave PCBs. Uses elliptic integral conformal mapping for accurate results.
Equations & Parameters ▸
\(Z_0 = \dfrac{30\pi}{\sqrt{\varepsilon_{eff}}}\dfrac{K(k^\prime)}{K(k)},\quad k=\dfrac{w}{w+2s},\quad \varepsilon_{eff}=1+\dfrac{\varepsilon_r-1}{2}\dfrac{K(k_1^\prime)/K(k_1)}{K(k^\prime)/K(k)}\)
| w | Signal trace width (mm). |
| s | Gap between trace and ground plane (mm). |
| h | Substrate height (mm). Infinite assumed if h >> w+2s. |
| εᵣ | Substrate dielectric constant. |
| Z₀ | Characteristic impedance = 30π/√εeff · K(k′)/K(k). |
| εeff | Effective permittivity via Schnieder/Hammerstad conformal mapping. |
Physical constants used
| c | Speed of light = 2.998×10⁸ m/s |
| µ₀ | Permeability of free space = 4π×10⁻⁷ H/m ≈ 1.2566×10⁻⁶ H/m |
| ε₀ | Permittivity of free space = 8.854×10⁻¹² F/m |
Inputs
mm
signal conductor widthmm
trace edge to groundmm
trace to bottom ground (if any)alumina=9.9, GaAs=12.9, Si=11.9, FR4=4.4
Results
Electrical
Characteristic impedance, Z₀—
Effective εᵣ—
Phase velocity, vₚ—
Guide wavelength at 10 GHz—
Diagram