Characterization of anisotropic substrate materials for microwave applications

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

“…The ERP obtained from the present model has also been compared with results obtained by Fritsch and Wolff [6] in Table 1 considering Spectrum Domain Analysis (SDA) using Galerkin method [6] and maximum deviation of about 0.5% with our present model is seen that proves the validity of our model. Before calculating the e Moreover, these results are also obtained from the EM simulator-EMPIRE v-4.20 [11] considering the same set of parameters as considered by Alexopoulos and Krowne [3] in Figs.…”

“…Figure 6 (a and b) compares the results against the experimental results of Fritsch and Wolff [6]. The present model has been used along with the dispersion model of Jensen et al [14] to compute the dispersion in microstrip line on Sapphire substrate for h=0.4 mm and w=0.4 mm, 0.6 mm up to 30 GHz.…”

“…In another approach [5] they have given a closed-form expression to get an equivalent isotropic relative permittivity applicable only to the Sapphire substrate. Fritsch and Wolff have used the full-wave method [6] to include this dependency. However these methods considered the dependence of w/h ratio on equivalent isotropic relative permittivity but all these are either numerical or full wave that can not be easily implemented in CAD applications.…”

Dielectric Anisotropy of Modern Microwave Substrates

“…The substrate gyrotropy will not be considered here. Initially the uniaxial anisotropy is connected mainly with the crystallography properties of the optical glasses, microwave ceramics (van Heuven & Vlek, 1972;Fritsch & Wolff, 1992) and liquid crystals (Gaebler et al, 2008). These materials are homogeneous, but anisotropic due to their crystalline anisotropy -different dielectric parameters along to their main crystallographic axes.…”

Equivalent isotropic relative permittivity of microstrip on multilayer anisotropic substrate

“…An effort has been made by several investigators to account for the effect of anisotropy on the effective relative permittivity and characteristic impedance of a microstrip line Owens, Aitken and Edwards 1976;Alexopoulos and Krowne 1978;Alexopoulos 1985;Tsalamengas, Uzunoglu and Alexopoulos 1985;Hoffmann 1987;Fritsch and Wolff 1992). The closed-form expressions are reported that convert the anisotropic substrate to the equivalent isotropic substrate with equivalent substrate thickness.…”