Microstrip resonators on anisotropic substrates

Analysis of Unilateral Fin-Line Resonators on Biaxial Substrates Via Spectral Domain Technique

“…At millimeter frequencies, it has been found that substrate anisotropy plays an important role in determining the characteristics of ICs [1][2][3]. Regardless whether anisotropy occurs naturally or is purposely implanted, it must be considered.…”

“…In the isotropic regions, the fields in general can be written in terms of Hertz potential functions [3]. The solutions for the z component of the electric field in the three regions after applying the boundary conditions are:…”

Accurate and Efficient Modeling of Interconnects in Lossy Layered Media

“…For the biaxial anisotropic materials it is not possible to decouple the TE y and TM y modes into two independent transmission lines as is possible for the uniaxial case [66]. Hence, we introduce a new conjoint transfer impedance parameter in order to consider the remaining field components i.e.Ẽ v for the TE y mode andH u for the TM y mode.…”

“…Their Fourier transforms areJ ui and J vi , respectively. The TM y self impedance corresponding to i th metallization plane is defined as It is obtained by taking the reciprocal of the sum of admittances looking up (Ỹ e vi up ) and down (Ỹ e vi down ) from the interface with the metallization assuming that there is no metallization present in any of the other layers.Z Conjoint Impedance ParameterFor the biaxial anisotropic materials it is not possible to decouple the TE y and TM y modes into two independent transmission lines as is possible for the uniaxial case[66]. Hence, a conjoint impedance parameter[64] is used in order to consider the remaining field components i.e.Ẽ v for the TE y mode andH u for the TM y mode.…”