Isosceles right triangular waveguides with boundary conditions of composite electric and magnetic walls

Isosceles right triangular waveguides with six kinds of boundary conditions of composite electric and magnetic walls are discussed in this paper. The completed closed-form modal solutions are derived for both transverse electric and transverse magnetic modes. These exact solutions not only serve as accuracy standards for approximate methods, but also solve a fundamental problem. Their corresponding electric field distributions are plotted for the dominant modes of the six kinds of isosceles right triangular waveguides. Finally, electric field distributions excited in the quarter-mode substrate integrated waveguide and eighth-mode substrate integrated waveguide are studied, and they are in good agreement with theoretical predictions.