// Calculators › Transmission Lines
Coplanar Waveguide Calculator
CPW (coplanar waveguide) and CPWG (grounded CPW) impedance, effective permittivity, wavelength, phase velocity and attenuation using the elliptic integral method (Wen 1969 / Ghione-Naldi). No via-to-ground required for CPW stubs — preferred for mmWave designs.
// Parameters
mm
mm
mm
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⚠ Please check your inputs.
// Results
Impedance (Z₀)—Ω
Effective εr (εeff)—
k = W/(W+2g)—
Wavelength (λ)—mm
λ/4 Length—mm
λ/2 Length—mm
Phase Velocity—× c
Skin Depth (δs)—μm
Dielectric Loss (αd)—dB/cm
Conductor Loss (αc)—dB/cm
Total Attenuation—dB/cm
Loss per 10 cm—dB
Elliptic integral method (Wen 1969 / Ghione-Naldi)
k = W/(W+2g) · k' = √(1−k²)
CPW: εeff=(1+εr)/2 Z₀=30π/√εeff · K(k')/K(k)
CPWG: k₁=tanh(πW/4h)/tanh(π(W+2g)/4h)
q=½·(K(k')/K(k))/(K(k')/K(k)+K(k₁')/K(k₁))
εeff=1+q·(εr−1) Z₀=30π/√εeff/(K(k)/K(k')+K(k₁)/K(k₁'))
αd = (π·f/c)·(εr/(εr−1))·(εeff−1)/√εeff·tan δ Np/m
αc = Rs·(1/W + 1/(2g·K(k)/K(k'))) / (4·Z₀·√εeff) Np/m
k = W/(W+2g) · k' = √(1−k²)
CPW: εeff=(1+εr)/2 Z₀=30π/√εeff · K(k')/K(k)
CPWG: k₁=tanh(πW/4h)/tanh(π(W+2g)/4h)
q=½·(K(k')/K(k))/(K(k')/K(k)+K(k₁')/K(k₁))
εeff=1+q·(εr−1) Z₀=30π/√εeff/(K(k)/K(k')+K(k₁)/K(k₁'))
αd = (π·f/c)·(εr/(εr−1))·(εeff−1)/√εeff·tan δ Np/m
αc = Rs·(1/W + 1/(2g·K(k)/K(k'))) / (4·Z₀·√εeff) Np/m