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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.

Model & assumptions: these are first-order estimates from the closed-form conformal-mapping solutions of Wen (1969) for CPW and Ghione & Naldi (1984) for CPWG — quasi-static models that assume zero conductor thickness and ideal boundaries. They hold up best when the substrate height satisfies h ≳ W+2g. Real PCB copper thickness, high-frequency dispersion, and (for CPWG) ground-via stitching pitch are not captured here — for thin substrates, thick copper, or tight-tolerance production designs, cross-check against full-wave EM simulation. Further reading: CPW overview, Wen 1969, Ghione & Naldi 1984.
Parameters
SUBSTRATE (εr, h) GND g W g GND h Air half-space above
Trace Width W
mm
Gap Width g
mm
Substrate Height h
mm
Permittivity εr
—
Loss tan δ
—
Frequency
⚠ Please check your inputs.
Propagation
Impedance (Z₀)—Ω
Eff. εr (εeff)—
k = W/(W+2g)—
Phase Velocity—× c
Wavelength (λ)—mm
λ/4 Length—mm
λ/2 Length—mm
CPW — Wen (1969)
k=W/(W+2g), k'=√(1−k²)
εeff=(1+εr)/2 (ideal: zero thickness, air above)
Z₀=30π/√εeff·K(k')/K(k)
Loss & Attenuation
Skin Depth (δs)—μm
Dielectric Loss (αd)—dB/cm
Conductor Loss (αc)—dB/cm
Total Attenuation—dB/cm
Loss per 10 cm—dB
Attenuation
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 a quasi-static, zero-conductor-thickness model, and is most accurate for substrates with h > W+2g and copper thickness t ≪ h. The key ratio K(k’)/K(k) determines the impedance — making CPW geometry flexible: many combinations of W and g produce the same impedance. Real PCB copper thickness, dispersion at high frequency, and (for CPWG) ground-via stitching are not captured by this ideal model — treat the results as a first-order estimate and validate against full-wave EM simulation for production designs.

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.

Further Reading

C. P. Wen, "Coplanar Waveguide: A Surface Strip Transmission Line Suitable for Nonreciprocal Gyromagnetic Device Applications," IEEE Trans. Microwave Theory Tech., vol. 17, no. 12, pp. 1087–1090, 1969 (abstract). G. Ghione and C. Naldi, "Analytical Formulas for Coplanar Lines in Hybrid and Monolithic MICs," Electronics Letters, vol. 20, no. 4, pp. 179–181, 1984 (abstract). See also the Wikipedia overview of coplanar waveguide for background theory.