Coplanar Waveguide (CPW) Calculator
Estimate characteristic impedance, effective dielectric constant, propagation velocity, and guided wavelength.
What this coplanar transmission line calculator does
A coplanar transmission line (usually called a coplanar waveguide or CPW) places the signal trace and ground conductors on the same PCB layer. This calculator gives you a quick first-pass estimate of:
- Characteristic impedance (Z0)
- Effective dielectric constant (εeff)
- Propagation velocity
- Guided wavelength at a chosen frequency
- Equivalent per-meter capacitance and inductance
Input parameters explained
1) Center trace width (w)
This is the width of the RF trace in the middle. Increasing w generally reduces impedance.
2) Gap to ground (s)
This is the spacing between the center trace and each adjacent ground conductor. Increasing s generally increases impedance.
3) Substrate thickness (h)
The board thickness influences field distribution in air versus dielectric. For thin substrates, geometry is more tightly confined.
4) Relative dielectric constant (εr)
Use the laminate dielectric constant from your stackup data. Typical values: FR-4 can range around 3.8 to 4.6 depending on frequency and resin content.
5) Frequency
Frequency is optional. It is used to compute guided wavelength only. The impedance model here is quasi-static, so it is best for initial design and not final high-frequency signoff.
Equations used in this calculator
This page uses standard closed-form CPW approximations with complete elliptic integrals of the first kind.
Where K(·) is the complete elliptic integral and k' = √(1 - k²). These formulas are widely used for CPW estimation, but they still simplify real-world behavior.
Design workflow for a 50-ohm CPW line
- Choose your laminate and confirm εr and thickness.
- Pick a manufacturable minimum gap based on your PCB fabricator rules.
- Adjust trace width and gap until Z0 is near 50 Ω.
- Reserve solid ground copper beside the trace and ensure good return current paths.
- Run an EM solver for final dimensions and launch transitions (SMA, vias, bends, connectors).
Practical RF layout tips
Use via fences
Stitch top ground rails to the bottom ground plane with periodic vias. This lowers parasitic modes and improves field confinement.
Control solder mask effects
Solder mask over CPW changes effective dielectric constant and impedance. For tighter control, many RF designers keep CPW regions mask-free.
Account for copper thickness and roughness
At higher frequencies, copper roughness and finite conductor thickness increase loss and can shift impedance slightly from ideal formulas.
Minimize discontinuities
Sharp corners, abrupt width changes, and poor connector transitions dominate mismatch in practical boards. Use smooth mitered bends and tapered launches.
Important limitations
- Quasi-static model: good for early design, not a replacement for full-wave EM simulation.
- Material dispersion and dielectric loss tangent are not included.
- Conductor loss and radiation loss are not included in the displayed results.
- Ground geometry is assumed idealized; real clearances and nearby objects matter.
Bottom line
Use this calculator to quickly size and compare CPW geometries, then verify with your PCB vendor stackup data and a field solver before release. It is fast, practical, and excellent for front-end design decisions.