On the Theoretical Maximum Directivity of a Radiating Aperture From Modal Field Expansions

Abstract

This communication addresses the maximization of the directivity from a radiating aperture through the derivation of a closedform expression for the modal field amplitudes whose field distribution at the aperture maximizes the directivity in a desired direction. This closedform expression arises from a convex formulation of the maximization problem (as a ratio of two Hermitian forms), which mathematically ensures that the achieved directivity value is the global maximum for a specified number of propagating modes. The proposed technique, which is valid for any aperture shape and polarization, is discussed and compared with previous work. Several numerical examples considering different main lobe directions, aperture geometries, and polarizations are presented. To verify the numerical results, radiation patterns and directivity values are computed using both commercial tools and in-house developed software.

Generalized Design Methodology of Highly Efficient Quad-Furcated Profiled Horns With Larger Apertures

“…The radiating element's axial profile length is 127.46 mm (4.97λ 0 ). It achieves aperture efficiency above 90% for a wide frequency bandwidth (over 14%); it is noted that the maximum theoretical level has been calculated 95.1% [15]. 1 includes the radiating elements that provide the better aperture efficiency than the Q-FPH optimized by the presented generalized methodology.…”

“…The first is that a greater number of aperture modes is involved, while the second relates to the potential of generating more excitation modes in the form of TE m0 , m = 1, 2, 3, ..., at the four feeding waveguide parts. The first factor suggests that the theoretical maximum aperture efficiency bounds are enlarged up to 95.1% [3,15]. This also adds complexity in the design since more modes should be considered at the calculations.…”

“…The vector on the left side of Eq. ( 7) represents the required modal distribution for the optimal approximation of a uniform electric field at the aperture, that is [3,15]:…”

Quad-Furcated Profiled Horn: The Next Generation Highly Efficient GEO Antenna in Additive Manufacturing

“…An ideal radiating aperture that achieves aperture efficiency of 100% is excited with a uniform radiating field in amplitude and phase. For a horn antenna, the radiated field can be decomposed as a superposition of propagating waveguide modes associated with the transverse section of its aperture [32]- [34]. The size of the aperture will then define which modes are propagating and hence contributing to the radiation.…”

Numerical Study on the Orthogonality of the Fields Radiated by an Aperture

“…Several analysis and synthesis techniques [9][10][11][12][13][14] perform a modal expansion of the aperture field distribution in order to compute the total radiated field as the summation of the fields radiated by each modal field function weighted by their corresponding complex modal amplitudes. As is well known, these modal fields are orthogonal between them, since they constitute an orthogonal basis for the fields at the aperture [15].…”