CPW Calculator
Plain coplanar waveguide, no bottom ground. The trace runs between two ground rails on the top layer. Wadell elliptic-integral formulation.
Inputs
mm
mm
mm
GHz
Coplanar waveguide (CPW)
Z0
62.84Ω
More
eeff2.490
Guided lambda_g32.754 mm
lambda_g / 48.188 mm
Analytical calculation
Every step the calculator runs, with the formula, your numbers plugged in, and the result.
Aspect ratio
CPW master parameter; Z0 depends on this ratio, not W and S separately.
Effective permittivity
Conformal-mapping result; field splits between air and substrate.
Characteristic impedance
Wen 1969.
References
- PrimarySimons, R. N. Coplanar Waveguide Circuits, Components, and Systems, Wiley 2001, Ch. 4 (CPW with finite-thickness substrate). The eeff = 1 + (er - 1)/2 (K(k1)/K(k1′)) / (K(k)/K(k′)) form with k1 = sinh(piW/4h) / sinh(pi(W + 2S)/4h) is from this chapter.
- OriginalWen, C. P. "Coplanar Waveguide: A Surface Strip Transmission Line Suitable for Nonreciprocal Gyromagnetic Device Applications," IEEE Transactions on Microwave Theory and Techniques, vol. 17, no. 12, Dec. 1969, pp. 1087-1090. Introduced CPW assuming an infinitely thick dielectric; the finite-thickness eeff used here is a later extension (commonly attributed to Veyres-Hanna 1980 and Ghione-Naldi 1984).
- K(k)/K(k') approxHilberg, W. "From Approximations to Exact Relations for Characteristic Impedances," IEEE Transactions on Microwave Theory and Techniques, vol. 17, no. 5, May 1969, pp. 259-265. The piecewise log/pi approximation used in the engine matches AGM-exact K(k)/K(k′) to about 3e-6 max relative error across k in (0, 1).
- ConceptCoplanar waveguide (overview)