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Conformal mapping calculations of impedance and effective dielectric constant are presented for coplanar waveguide (CPW) lines with finite-substrate thickness. These calculations and experimental data show a departure from the intinite dielectric approximation as the substrate thickness approaches the guide slot width. The quasi-TEM approximation is retained and calculations of static energy density within the substrate are given. This approximation agrees well with field calculations using a finite-element solution to Laplace's equation.