What is the characteristic impedance of a coplanar waveguide with a finite width ground plane?

The characteristic impedance of a coplanar waveguide (CPW) with finite-width ground planes differs from the ideal infinite-ground CPW because the truncated ground planes reduce the ground-return current path and alter the electromagnetic field distribution. For an ideal CPW (infinite ground planes) on a substrate with dielectric constant Er, the characteristic impedance depends on the signal trace width W and the gap S between the signal and ground: Z_0 = (30 pi / sqrt(Er_eff)) x (K'(k) / K(k)) where k = W / (W + 2S) and K(k) is the complete elliptic integral of the first kind. For a finite-ground CPW (FGCPW) where each ground plane has width G_w: the impedance increases as G_w decreases because less ground current is available. The correction factor depends on the geometry: when G_w > 3S (ground plane width is more than 3x the gap), the impedance is within approximately 5% of the infinite-ground value. When G_w < S, the impedance increases significantly (20-50% higher than infinite-ground). The finite-ground CPW impedance is calculated using: Z_0_FG = (30 pi / sqrt(Er_eff_FG)) x (K'(k_FG) / K(k_FG)) where k_FG accounts for the ground plane width using conformal mapping: k_FG incorporates both k1 = W/(W+2S) and k2 = (W+2G_w)/(W+2S+2G_w). CPW-with-ground (CPWG, also called grounded CPW) adds a bottom ground plane, which changes the impedance and suppresses the slot-line mode, making it the preferred structure for most PCB applications.