Study of Radiating Properties of Open - Ended Rectangular - Waveguides

The transverse operator method is used for the analysis of an open-ended rectangular waveguide, in particular as a radiating element. It is shown that the method allows a systematic formulation of problems involving discontinuities whether they are radiating or not. The numerical results concerning the admittance and power patterns of a waveguide aperture surrounded by an infinite conducting flange are compared to those available in the literature, and a good agreement is observed. INTRODUCTTON PERTURE antennas find many applications in A aeronautics, diathermy, and hyperthermia as well as in phased-array systems [l]. The basic radiating structure is the open end of a waveguide, generally terminated by an infinite metallic flange. This subject has been studied by many authors using different approaches such as the variational, correlation matrix, and integral equation methods [1]-[6]. The correlation matrix method proposed by MacPhie is based on the principle of energy conservation through the aperture [5], while Gardiol obtains the aperture admittance using an integral equation method based on the magnetic current concept [6]. The method proposed in this paper, based on the transverse fields calculation through the use of an operator, called the transverse operator, was introduced for the first time by Marcuvitz [7]. The tangential field continuity condition in the spectral domain leads to a simple relation between the electric and magnetic fields. The field expansion in a series of normal transverse electric (TE) and transverse magnetic (TM) modes allows the aperture admittance to be obtained, and the radiation patterns are then determined. THEORY The structure to be studied is that of Fig. 1 where the rectangular waveguide is terminated by an infinite conducting flange. The transverse electromagnetic fields 4 satisfy the following relationship [7]: where L^ is transverse matrix operator defined as Fig. 1. Rectangular waveguide terminated by infinite conducting flange. where Tis the unity matrix and a,=(ax) 9 a; =(a,-ax); The solution of (1) is 4 = ,ilricz-zo) do where I#J~ represents the transverse electromagnetic fields at z = zo, which in our case will be the discontinuity plane (z = 0). The Fourier transform of (2) yields