Electric Green's dyadics for modeling resonance and surface wave effects in a waveguide-based aperture-coupled patch array

Abstract

Electric Green's dyadics for a serni-infinite partially filled rectangular waveguide are developed for the full-wave analysis of a waveguide-based aperture-coupled patch aniplifier array. The Green's functions are derived in the form of a double series expansion over tlie coniplct,e systcm of cigenfuiict,ioiis of the Helmholtz operator. In this represcnliLf.ioii, tlic oii~-diiirc,ision~,l clmract.cristic Green's functions along the waveguide provide a physical iiiaight on rebonance and surface wave effects occurring in overrnoded layercd waveguide transitions. Particularly, this is related to the coupling of waveguide modes to surface waves propagating in the transverse direction. This is demonstrated for the example of an aperture-coupled patch amplifier array in the N-port waveguide transition, although the analysis is applicahle to other waveguide-based antenna structures, which allow for the propagation of surface waves.

Magnetic Potential Green's Dyadics of Multilayered Waveguide for Spatial Power Combining Applications

“…(r, r ) is the electric dyadic Green's function of the second kind for a semi-infinite rectangular waveguide filled with dielectric with permittivity ε n+1 and terminated by a ground plane at z = z n (obtained similar to that presented in [14]). The electric DGFs G (is) e1 and G…”

“…Each of the continuity conditions (13), for q = 1, 2, ..., n−1, provides four equations for these coefficients, and the boundary condition (12) provides two additional equations. Instead of solving the system of 4n − 2 equations for 4n − 2 unknown coefficients by brute force, we propose a method of reducing this system to a system of only four equations for the four key unknown coefficients, B The representation (14) subject to the boundary and continuity conditions (12), (13) results in the expressions for coefficients C (is) x in terms of the key coefficients B (1s)…”

“…The properties of completeness and orthogonality of eigenfunctions in the waveguide cross-section allow for reduction of the three-dimensional problem to a one-dimensional Sturm-Liouville boundary value problem for the unknown characteristic Green's functions. In [14], electric DGFs for a semiinfinite partially filled rectangular waveguide are obtained for the fullwave analysis of a waveguide-based aperture-coupled patch amplifier array. The derived characteristic Green's functions provide a physical insight into resonance and surface wave effects occurring in overmoded layered waveguide transitions.…”

“…An alternative method of developing Green's dyadics for rectangular waveguides and cavities utilizes a partial eigenfunction expansion as a double series expansion over the complete system of eigenfunctions of the transverse Laplacian operator [13,14]. The unknown coefficients in this expansion represent one-dimensional characteristic Green's functions along the waveguide.…”

“…In the past few decades, considerable amount of research has been devoted to the development of DGFs of rectangular waveguides and cavities [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. They are traditionally constructed in the form of a double series expansion using the Hansen vector wave functions [1][2][3][4][5][6][7][8][9][10].…”