Maximizing Gain of Endfire Arrays Based on Electrical Dipoles Using Spherical Harmonics

This article proposes a new model based on the spherical wave expansion (SWE) theory to synthesize efficient and highly directive endfire arrays of electric dipoles, which are known to be suitable for superdirective purposes. When extremely compact dimensions are considered, the high-order spherical harmonics required to construct a directive radiation pattern become mainly dissipative, causing radiation efficiency drops. To account for the impact of the losses, the proposed synthesis procedure integrates a specific formulation of the modal dissipation factor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$({\delta }_{n})$ </tex-math></inline-formula> associated with the excited spherical harmonics. The excitation coefficients, results of the optimization, demonstrate improved efficiency for endfire arrays of two, three, and four elements if compared to a superdirective solution. These results are scalable to a higher number of elements as well as other element distributions and types of radiators. In addition to the numerical validation through full-wave electromagnetic simulations, a prototype based on a four-element array is designed and experimentally characterized to validate the proposed analysis. The experimental results show a maximum gain of 9.8 dBi achieved for a radiansphere of 1.75, which is in good agreement with the theory and simulation results.