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This work discusses an alternative geometrical optics (GO) technique to synthesize omnidirectional dual-reflector antennas with uniform aperture phase distribution together with an arbitrary main-beam direction for the antenna radiation pattern. Sub- and main reflectors are bodies of revolution generated by shaped curves defined by local conic sections consecutively concatenated. The shaping formulation is derived for configurations like ADC (axis-displaced Cassegrain) and ADE (axis-displaced ellipse) omnidirectional antennas. As case studies, two configurations fed by a TEM coaxial horn are designed and analyzed by a hybrid technique based on mode matching and method of moments in order to validate the GO shaping procedure.

The spectral congestion in urban centers and large data rates required by the next generation technology (5G) of broadband mobile communication have forced the development of systems operating at higher frequencies [

For high-gain or omnidirectional antennas, several works have dealt with the shaping of circularly symmetric dual-reflector for prescribed equiphase field distribution at the aperture by solving an ordinary differential equation derived from geometrical optics (GO) principles [

The present work generalizes the formulation presented in [

The shaped dual-reflector configurations are composed of two circularly symmetric (bodies of revolution) reflectors with a common symmetry axis (the

Geometry of the shaped omnidirectional ADE-like antenna.

Geometry of the shaped omnidirectional ADC-like antenna.

Each pair of conics

The iterative process closely follows that of [

Equation (

To obtain a uniform phase distribution over the conical aperture, the optical path from

The constant optical path

So, observing once more that consecutive conic sections share a common point, the third shaping equation is obtained from (

The fourth equation also comes from (

After

Then,

To illustrate the GO shaping technique described in Section _{e} and _{i} were adjusted to match the radiation pattern provided by the electromagnetic analysis (_{e} = 1.1_{i} = 0.3

Model for the TEM feed radiation pattern.

The initial shaping parameters are defined with the help of a classical ADE configuration, established from the design procedure of [

Generatrices and ray tracing of the classical omnidirectional ADE antenna.

Figures

Generatrices and ray tracing of the shaped omnidirectional ADE antenna.

A full-wave analysis based on the MoM/MMT technique [_{0} = 12.79 dBi, 95% efficiency) is more directive than the classical one (D_{0} = 11.67 dBi, 73% efficiency), as it was designed to have a uniform field distribution over its conical aperture (from a GO perspective). When compared to the classical omnidirectional ADE configuration, the aperture uniform illumination rises the side lobes close to the main beam, and, due to the increase of the density of rays toward the main reflector edge (see Figure

MoM/MMT and CST radiation patterns of the classical ADE antennas.

MoM/MMT radiation patterns of the classical and shaped ADE antennas.

In the second case study, an ADC-like configuration is shaped to provide a uniform aperture illumination, as in the previous case. The initial parameters are established for a classical ADC configuration [

Generatrices and ray tracing of the classical omnidirectional ADC antenna.

Figures _{0} = 12.58 dBi, 90% efficiency) is more directive than classical one (D_{0} = 11.94 dBi, 78% efficiency), as the former was shaped to provide a uniform aperture GO illumination. Once more, one observes the increase of the side lobe level of the shaped antenna due to the increase of the main reflector spillover.

Generatrices and ray tracing of the shaped omnidirectional ADC antenna.

MoM/MMT and CST radiation patterns of the classical and shaped ADE antenna.

MoM/MMT radiation patterns of the classical and shaped ADC antennas.

To investigate the numerical convergence of the proposed technique, surface RMS errors as a function of the number of steps (

Maximum error of shaped ADE and ADC antennas as function of

To illustrate the usefulness and versatility of the shaping technique, the ADE and ADC geometries were shaped once more, now to reduce the side lobe levels observed in Figures

GO aperture power density distributions

Figures

Generatrices and ray tracing of the shaped ADE antenna (−30 dB attenuation at

Generatrices and ray tracing of the shaped ADC antenna (−30 dB attenuation at

MoM/MMT radiation patterns of the classical and shaped ADE antennas.

MoM/MMT radiation patterns of the classical and shaped ADC antennas.

Figure

Maximum error of shaped ADE and ADC antennas (−30 dB attenuation at

A method for the GO synthesis of omnidirectional dual-reflector antennas with equiphase field in a conical aperture has been presented. The sub- and main reflector generatrices were represented by the consecutive concatenation of local conic sections, and, by imposing geometrical optics principles, their shapes were obtained by solving liner equations. Omnidirectional ADE- and ADC-like configurations were successfully designed for uniform and tapered power distributions at the equiphase conical aperture. The concatenation of conic sections allowed an efficient representation of the shaped reflectors, with numerical convergence similar to that observed in [

The authors declare that they have no conflicts of interest.

This work was partially supported by FINEP/FUNTTEL Grant no. 01.14.0231.00, under the Radio Communications Reference Center (CRR), CAPES-PROCAD Grant 068419/2014-01, CNPq, and FAPEMIG.