Coplanar Waveguide Calculator & Formula

Coplanar waveguides (CPW) are popular in RF and microwave PCB design due to their easy integration and low dispersion. Accurate calculation of impedance and effective permittivity is essential for reliable circuit performance.

EXAMPLE:

INPUTS:

• Center Conductor Track Width (S) = 2.5 mm
• Gap Width (W) = 1.5 mm
• Dielectric Thickness (h) = 2.0 mm
• Relative Dielectic Constant (Er) = 4.2

OUTPUTS:

• Effective Dielectric Constant (Eeff) = 3.22
• Characteristic Impedance = 70.76 Ohms

Coplanar Waveguide (CPW) Formula

Summary: This page explains CPW fundamentals and provides formulas with a calculator to determine key transmission line parameters, making it useful for RF layout and microwave circuit design.

References for further study

1. Pozar, Microwave Engineering (CPW impedance uses elliptic integrals)
2. SciPy Documentation - ellipk(m) definition and parameter convention
3. Research paper: Open source numerical algorithms for elliptic integrals (AGM, Gauss Legendre, etc.)
4. Abramowitz & Stegun, Handbook of Mathematical Functions