HF-Guiding structures: Modelling and calculations

Guides vary in geometry and material composition depending on their application and operating frequency. The theoretical foundations of guided propagation, as well as examples of commonly used structures, are presented in the article “HF Guide Structures—Propagation and Geometry” [E1170] . While analytical solutions exist for canonical cases, it is generally necessary to use numerical methods to determine the field configuration and relevant parameters associated with the waveguide. This difficulty stems not only from the geometry of the waveguide cross-section but also from the inhomogeneity of the propagation medium (air and dielectric substrate, for example). Indeed, this results in complex boundary conditions, particularly at the air-dielectric interface, which make solving the Helmholtz equation difficult. Due to this difficulty, various approximate methods have been proposed to determine the propagation constant and the fields propagated in a planar line. Among these methods, the following can be cited for application to the microstrip line:

• quasi-static methods (conformal transformation, finite differences, integral equation) used in the context of a TEM approximation of the propagation;

• guide-mode patterns (ribbed-guide pattern, coupled TE and TM wave patterns).

The drawback of these methods is that they are only valid for limited geometries and frequency ranges.

Rigorous numerical approaches have been developed thanks to the emergence of new computational tools. Methods based on integral equations, finite differences, or the Fourier transform have led to a precise understanding of propagation phenomena in this type of waveguide structure. For example, the spectral method, which relies on fast Fourier transform (FFT) algorithms now available on most computers, has proven highly effective for these types of structures. However, it does not apply to structures with arbitrary geometries. It is therefore important to note that numerical methods cannot be applied or be effective for all types of structures.

The most commonly used numerical methods are presented in the article [E1030]...