GENERAL FORMULATION OF THE SPECTRAL DOMAIN TECHNIQUE FOR THE ANALYSIS OF MULTILAYER PLANAR STRUCTURES WITH DIAGONAL ANISOTROPY

The materials usually used in microwave integrated circuits are often assumed isotropic. However, in certain cases anisotropy is introduced unintentionally during the manufacturing process, or deliberately in order to obtain non reciprocal devices, radar absorbers, and so on., or serves to improve circuit performances. In several cases, neglecting the anisotropy of certain substrates induces errors in integrated-circuit design. Hence the characteristics of planar structures containing anisotropic layers must be accurately described in order to secure the circuit design and improve the CAD models. On the other hand, the measurement of dielectric or magnetic anisotropy of materials at microwaves frequencies is of great interest for several applications and as such the planar structures on anisotropic layers can be used in this domain. Several methods enable the propagation characteristics to be calculated for a large number of structures such as microstrip, coplanar waveguides, and slotlines. The spectral domain technique (SDT) is one of the fastest. For anisotropic substrates, the formulation of the spectral domain method can be very difficult and it depends on the form of the relative tensors-epsilon and mu. The main difficulty in considering anisotropic layers is to obtain the Green matrix of the spectral domain technique. The aim of this paper is to extent the SDT for planar lines on anisotropic (electric and/or magnetic) substrates. A generalized formulation for all diagonal-epsilon and mu is presented and used to calculate the propagation parameters for several planar lines.