📡 Based on Simons (2001) and Wadell (1991) equations • Uses elliptic integral K(k) method • Units are consistent

Relative Dielectric Constant (εr)

Track Width (S) — signal conductor width

Gap Width (W) — space between track and ground

Substrate Thickness (h) — dielectric height

Conductor Thickness (t) — optional, for correction

Unit System

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Characteristic Impedance Zo (Ω)

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Effective Dielectric Constant (ε_eff)

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k / k' Ratio (k = S/(S+2W))

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Guide Wavelength (λ_g)

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Phase Velocity (×10⁸ m/s)

Calculation Method: Standard Coplanar Waveguide (No Bottom Ground)

k = S / (S + 2W) | k' = √(1 − k²)

K(k) = Complete elliptic integral of the first kind

ε_eff = 1 + (ε_r − 1) · K(k')·K(k₁) / (2·K(k)·K(k₁'))

Z₀ = 60π / √ε_eff · K(k) / K(k')

Coplanar waveguide structure diagram - signal track with ground planes

CPW structure: Signal conductor (S) with gap (W) to ground planes on both sides

What is Coplanar Waveguide (CPW)?

Coplanar waveguide is a planar transmission line where the signal conductor and ground planes are all on the same side of the substrate. This structure offers lower dispersion, easier shunt mounting of components, and reduced radiation loss compared to microstrip lines.

How to Use This Calculator

Select Mode: Choose Standard CPW (no bottom ground) or Grounded CPW (with bottom ground plane)
Enter εr: Relative dielectric constant of your substrate (FR-4: 4.6, Rogers 4003: 3.55, Alumina: 9.8)
Enter Track Width (S): Width of the center signal conductor
Enter Gap Width (W): Spacing between signal conductor and ground planes
Enter Substrate Thickness (h): Height of dielectric material
Optional Conductor Thickness (t): For fine correction (default 1 oz copper ≈ 0.035mm)
Select Units: Any consistent unit system works (mm, mils, µm, inches)

Design Guidelines & Best Practices

To avoid microstrip modes: Ensure h > (S + 2W) and ground planes extend > 3W from the edges
Typical impedance targets: 50Ω for RF circuits, 75Ω for video, 100Ω for differential
Gap to track ratio: For 50Ω on FR-4 (εr=4.6), S/(S+2W) ≈ 0.4–0.5
Conductor thickness: Effects are minor below 10GHz; for precision designs, use full-wave EM simulation
Air bridges: Use bonding wires or plated bridges to suppress parasitic slotline modes

Standard Substrate Properties

FR-4: εr = 4.2–4.8, tanδ = 0.02, h typical = 0.8–3.2mm
Rogers RO4003C: εr = 3.55, tanδ = 0.0027, low loss for RF
Rogers RO4350B: εr = 3.48, tanδ = 0.0037, good for microwave
Alumina (Al₂O₃): εr = 9.8, tanδ = 0.0002, high frequency
PTFE (Teflon): εr = 2.1, tanδ = 0.0002, very low loss

Formulas & Theory

The calculator uses the conformal mapping method based on elliptic integrals. For standard CPW (no bottom ground):

k = S / (S + 2W) — ratio for air region
k₁ = sinh(πS/2h) / sinh(π(S+2W)/2h) — includes substrate thickness effect
K(k) = complete elliptic integral of the first kind (approximated by polynomial)
ε_eff = 1 + (ε_r - 1) · K(k')·K(k₁) / (2·K(k)·K(k₁'))
Z₀ = 60π / √ε_eff · K(k) / K(k')

References

R. Simons, "Coplanar Waveguide Circuits, Components, and Systems", Wiley, 2001
B. C. Wadell, "Transmission Line Design Handbook", Artech House, 1991
K. C. Gupta, et al., "Microstrip Lines and Slotlines", Artech House, 1996

Frequently Asked Questions

What's the difference between CPW and microstrip? — CPW has ground planes on the same side as the signal, allowing easier component integration and lower radiation.
Why do I need a bottom ground? — Grounded CPW (conductor-backed) reduces radiation loss and provides better heat dissipation but can excite parallel-plate modes.
What is the recommended gap width? — Typically 0.1–0.5 mm for standard PCB fabrication; smaller gaps increase impedance sensitivity.
How accurate is this calculator? — Accurate to ~2-5% for typical geometries; precision designs should use 3D EM simulation.
Does conductor thickness matter? — Minor effect below 10 GHz; this calculator includes approximate correction.

Coplanar Waveguide Calculator