Miniaturized Multibeam Reflectarray Antenna Based on Mathematical Unit Cell Design

This paper presents a novel mathematical approach for the design of miniaturized reflectarray antenna elements. The unit cell geometry is generated analytically using combined trigonometric and logarithmic functions, allowing systematic and continuous control of the reflection phase through a single geometrical tuning parameter, α. The proposed unit cell is implemented on a single-layer RO4003 substrate with a thickness of 1.57mm and a periodicity of 0.26λ0at 10 GHz, corresponding to a 1.92× size reduction relative to conventional 0.5λ0reflectarray (RA) unit cells. By varying α, a reflection phase range of 352° is achieved with an average reflection loss of approximately 0.2 dB. This compactness supports dense element integration, increasing the number of elements across the aperture from 104 to 424 and reducing the phase quantization step from 6.11° to 3.18°, leading to smoother aperture phase distributions and reduced phase errors. These characteristics also contribute to improved phase stability of the unit cell under oblique incidence angles up to 30°. A single-feed multibeam RA antenna is synthesized and evaluated numerically and experimentally based on the proposed unit cell using the addition theorem, showing a decent performance balance between the four intended beams and low sidelobes, owed to the compact unit cell geometry and smooth phase profile on the surface of the RA. The measurements show peak gains ranging from 15.33 to 16.84 dBi, and the measured 3 dB gain bandwidths varying between 7.44% and 15.32% over the 9–11 GHz frequency band. The measured results are in good agreement with full-wave simulations, validating the theoretical and numerical analyses.