Electromagnetic Scattering at the Waveguide Step between Equilateral Triangular Waveguides

Abstract

The analysis of the electromagnetic scattering at discontinuities between equilateral triangular waveguides is studied. The complete electromagnetic solution is derived using analytical closed form expressions for the mode spectrum of the equilateral waveguide. The mathematical formulation of the electromagnetic scattering problem is based on the quasi-analytical Mode-Matching method. This method benefits from the electromagnetic field division into symmetries as well as from the plane wave formulation presented for the expressions involved. The unification of the surface integrals used in the method thanks to the plane wave formulation is revealed, leading to expressions that are very well suited for its implementation in an electromagnetic analysis and design code. The obtained results for some cases of interest (building blocks for microwave components for communication systems) are verified using other numerical methods included in a commercial software package, showing the potential of the presented approach based on quasi-analytic expressions.

Wave Propagation in Periodic Metallic Structures with Equilateral Triangular Holes

“…being the wavenumber in the z-direction of the triangular waveguide, h hole the hole depth, and k ti the transverse wavenumber, which here corresponds to the cutoff wavenumber (k c,mn ) of the triangular waveguide [26]. The tangential fields in the gap region can be described as the following Floquet-series expansion [23]:…”

“…The longitudinal modal functions (electric field for TM modes and magnetic field for TE modes) in an equilateral triangular waveguide are calculated as [26][27][28]:…”

“…Figure 2 plots the normalized magnitude of the tangential modal functions Φ i (x, y) in the equilateral triangular waveguide. The fourteen considered modes are ordered according to their increasing cutoff frequency f c,mn = k c,mn c/(2π), k c,mn = 4π √ m 2 + n 2 + mn/(3e) being the cutoff wavenumber [26]. Additionally, the modes are labeled following the notation TM/TE s/a mn .…”

“…The isotropic behavior of the structures can be related to the electrical size of the equilateral triangular hole and the cutoff frequency of the equivalent triangular waveguide. If the modal functions in the equilateral triangular waveguide are sorted according to their cutoff frequencies, the cutoff frequency of the first mode (labeled as #1 in Figure 2) is much higher compared to other canonical waveguides, such as the square or circular waveguides of the same lateral size [26,30]. This means that, in comparison with the same geometric size, the "effective" electrical size of the triangular hole is much smaller compared to other holes used in isotropic periodic holey structures.…”

Higher-Order Mode Electromagnetic Analysis of a Material Sample between Two Flanged Coaxial Probes for Broadband Modelling of Dielectric Measurement Setups

“…This formulation has been used in the past many times. Examples of the inner-cross product computation for different waveguide steps can be found in [25,30,31]. After this computation, the cascading of the GSM of each step in the problem is carried out systematically [14,28], as it will be explained in the next section for the two proposed models.…”