A MFIE/EFIE Fast Multipole Volume/Surface Integral Equation Approach for Substrate Integrated Waveguide Structures and Leaky-Wave/Slot Antennas Using the Duality Principle

Substrate Integrated Waveguide (SIW) components and antennas have the advantage of being characterized and fabricated as quasi-planar structures thus they can be integrated easily together with other microstrip/coplanar components. SIWs with slots in the upper groundplane are very attractive building blocks for the design of e.g. leaky-wave antennas with transverse slots or resonant slot arrays with longitudinal slots. For the characterization of the slots, magnetic surface currents are introduced within an integral equation approach using the duality principle whereas the SIW is modeled by two rows of vias modeled by volume current basis functions within a parallel-plate medium described by extended Green's functions. The integral equation is solved with a fast multipole approach utilizing branch cut contributions and especially the pole contributions of the parallel-plate waves. Furthermore the volume basis functions are used as field monitors to extract amplitudes and propagation constants of the waves within the SIW for S-parameter determination and leaky-wave characterization.