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.
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)
αd=(πf/c)·(εr/(εr−1))·(εeff−1)/√εeff·tanδ
αc=Rs·(1/W+1/(2g·K(k)/K(k')))/(4Z₀√εeff)
Rs=√(πfμ₀/σ), Np/m×8.686/100=dB/cm
About the CPW / CPWG Calculator
Coplanar waveguide (CPW) is a transmission line structure where the signal trace and its ground returns all lie on the same surface of the substrate. Unlike microstrip, which requires a ground plane on the opposite side, CPW provides grounding directly adjacent to the signal conductor. This makes it especially popular for millimetre-wave (mmWave) PCB designs above 10 GHz, where via-to-ground inductance in microstrip becomes a significant parasitic.
CPW vs CPWG
Standard CPW uses only the top-layer coplanar grounds with air below the substrate — the field extends through the substrate and into the air half-space beneath. CPWG (coplanar waveguide with ground) adds a continuous bottom ground plane, which confines the field to the substrate and increases the effective permittivity. CPWG gives higher impedance for the same geometry, tighter field confinement, and better shielding against substrate radiation. For most practical PCB designs, CPWG is the preferred choice since a bottom ground pour is already present.
Elliptic Integral Method
The impedance of CPW is calculated using the complete elliptic integral of the first kind K(k), where k = W/(W+2g) is the ratio of signal width to total slot pitch. This closed-form result (Wen 1969 for CPW, Ghione-Naldi for CPWG) is highly accurate for substrates with h > W+2g. The key ratio K(k’)/K(k) determines the impedance — making CPW geometry flexible: many combinations of W and g produce the same impedance.
CPW Design Rules
For 50 Ω CPW on FR4 (εr=4.4), a typical starting point is W/g ≈ 2–4 with h > W+2g. Keep the total slot width (W+2g) small compared to the substrate height for accurate results. At mmWave frequencies above 30 GHz, even bond wire inductance in CPW transitions matters — keep gap widths below 100 μm and use tapered transitions to coax connectors.