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This paper presents an analytical expression that models the tilt angle of directors in a nematic liquid crystal (LC), depending on its elastic properties, its dielectric anisotropy, and the quasi-static electric field applied. The analytical solution obtained is fast and easily computable in comparison with numerical estimations and is of special interest in radiofrequency; for instance, for the LC modeling in full-wave electromagnetic simulators in the design process of electronically tunable devices, such as microwave phase shifters or electronically steerable antennas for satellite communications. Subsequently, a comparison is made between numerical approaches (self-implemented shooting method) and the analytical formulas when varying the parameters of the LC, being demonstrated its usefulness. The average LC director is then obtained and used to form the full permittivity tensor that completely characterizes the electrical properties of the material. Finally, an electromagnetic simulation is carried out to show the capabilities of the LC as a tunable phase shifter. It is shown that only 5 cm of a commercial 200-µm LC mixture is necessary to achieve 360 • of the maximum variable phase shift at the 30-GHz band. INDEX TERMS Liquid crystal, nematic phase, analytical expression, microwave, phase shifting.

This paper presents a compact and low-loss V-band waveguide phase shifter based on glidesymmetric pin configuration. This kind of higher symmetry permits the control and improvement of the electromagnetic behavior or radiofrequency devices, as it is the case of the proposed phase shifter. The study of the dispersion diagram of the phase shifter unitary cell demonstrates that the pin configuration is a proper option for introducing a phase shift in a waveguide-based system. There is a significant increase in terms of phase shift when using a glide-symmetric pin distribution compared to its corresponding nonglide-symmetric configuration. Through this paper, the key geometrical parameters are also determined. The complete phase shifter is composed of an optimized cascade of tailored unitary cells so that the desired final phase shift value is achieved. A prototype has been manufactured in order to validate the theoretical approach through the comparison of phased shifters with both non-glide-symmetric and glide-symmetric configurations. The measurement results demonstrate the higher performance and compactness of the glidesymmetric phase shifter. For the same distance, the glide-symmetric version of the phase shifter provides more than 60% of phase shifting compared to the non-glide-symmetric phase shifter. Both phase shifters have a good impedance matching between 46 and 60 GHz and an insertion loss lower than 1 dB, thus clearly enabled as a 5G technology. INDEX TERMS Phase shifter, millimeter-wave, glide symmetry, gap waveguide.

This paper analyzes thoroughly the dispersion and filtering features of periodic holey waveguides in the millimeterwave frequency range. Two structures are mainly studied depending on the glide and mirror symmetries of the holes. A parametric study of the dispersion characteristics of their unit cells is carried out. Glide-symmetric holey waveguides provide a higher propagation constant and a low dispersion over a wide frequency range regarding hollow waveguides. This property is particularly useful for the design of low-loss and low-dispersive phase shifters. We also demonstrate that glide-symmetric holey waveguides are less dispersive than waveguides loaded with glide-symmetric pins. Furthermore, we perform a Bloch analysis to compute the attenuation constants in holey waveguides with mirror and broken glide symmetries. Both configurations are demonstrated to be suitable for filter design. Finally, the simulation results are validated with two prototypes in gap-waveguide technology. The first one is a 180 o phase shifter based on a glide-symmetric holey configuration that achieves a flat phase shift response over a wide frequency range (27.5% frequency bandwidth). The second one is a filter based on a mirror-symmetric holey structure with 20-dB rejection from 63 GHz to 75 GHz.

A multilayer aperture antenna array in millimeterwave band is presented in this article. The antenna array is based on glide-symmetric holey gap-waveguide technology combined with E-plane insertion gaps for a low-cost and low-loss design. The radiating part of the antenna array is formed by an array of sixteen aperture antennas, grouped in four sets of 2x2 antenna subarrays in E-plane configuration. The 2x2 subarrays are fed by a one-to-four corporate feeding network in E-plane with holey gap-waveguide technology. The antenna array has been manufactured with high precision stereolithography (SLA) and subsequent metal plating. This design procedure yields a low-cost and low-weight manufacturing process for functional prototypes. The complete array has been manufactured and measured, comparing its performance with the simulation results. Measurements show an input reflection coefficient below -10 dB which ranges from 68 GHz to 74 GHz. The measured radiation patterns suit adequately the defined ones in the design stage. Moreover, gain above 19 dBi in the entire operating frequency band is achieved with a 74.1% mean antenna efficiency.

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