A CAD model for microstrips on r‐cut sapphire substrates

Abstract

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-T, superconductor YBa,Cu,O, 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.

Development of CAD tool for a design of microwave planar HTS filters

“…All these characteristics are temperature dependent. Propagation characteristics of the HTS planar transmission lines have been presented in [14] and [16] and [18]- [20]. The nonhomogeneous current density distribution in the line cross section is taken into account.…”

“…The simulated characteristics are in a good agreement with the experimental data. The simulation procedure was based on using the equivalent isotropized dielectric constant of the anisotropic sapphire substrate [18]- [20]. In this case,…”

Modelling and investigation of HTS planar resonators and filters on sapphire substrate

“…The simulation of the characteristics of the lines on sapphire substrates is complicated by the anisotropy of the dielectric permittivity. The tensor components depend on the wave propagation direction with respect to the crystallographic axes of sapphire [7].…”

“…The tensor components lie in the range 9.3-11.6 and depend on the wave propagation direction with respect to the crystallographic axes of sapphire. Accurate closedform models of propagation characteristics have been derived for microstrip lines and coplanar waveguides (CPWs) on sapphire substrates [7][8][9]. A model of coupled microstrip lines on sapphire substrates was also proposed [10] and verified by a comparison with full-wave analysis results [11].…”

Accurate CAD-Model Analysis of Multilayer Microstrip Line on Anisotropic Substrate

“…We must take into account the effect of w/h-ratio of the microstrip for accurate determination of the equivalent isotropic relative permittivity using some closed-form expression. Vendik et al [8] have incorporated the effect of w/h ratio using perturbation approach considering the electrostatic energy per unit length of line. However this approach seems to be accurate but the method is rigorous and difficult to implement with CAD applications.…”