CAD Model for Microstrips on r-cut Sapphire Substrates

Journal article, 1994

Simple and correct formulas are derived for calculation of an effective isotropic dielectric constant, which characterizes the wave propagation in microstrip lines on anisotropic substrates made of r-cut sapphire crystals. The r-plane is extensively used for epitaxial growth of high-Tc superconductor YBa2Cu3O7 films as applied to microwave integrated circuits. In contradistinction to previous models developed for z-cut sapphire, the nondiagonal dielectric permittivity tensor of r-cut sapphire is used. The effective dielectric constant of a microstrip line on r-cut sapphire substrate is found as a function of the strip-line geometry and the orientation of the crystallographic axes with respect to the symmetry plane of the microstrip line