Green's Function Applications in Antenna Array Modeling: A Case Study with Multiple Log- Periodic Array (MLPA) Antennas

Abstract

This paper presents an analytical and simulation-based treatment of the far-field radiation characteristics of a Multiple Log-Periodic Dipole Array (MLPA) antenna using Green’s function–based magnetic vector potential formulations. The study consolidates established electromagnetic theory by explicitly combining log-periodic element scaling, cumulative spatial phase delays, and array-level superposition into a single, transparent analytical workflow. The scalar free-space Green’s function is employed to derive the magnetic vector potential, from which far-field electric field expressions are obtained under standard approximations. Radiation characteristics such as half-power beamwidth, peak directivity, and sidelobe levels are extracted from MATLAB-based simulations and compared with representative theoretical LPDA performance ranges reported in the literature. The results demonstrate consistency with expected broadband LPDA behavior and serve primarily to illustrate the applicability of Green’s function methods to hierarchically structured log-periodic arrays. The work is intended as a reproducible analytical reference and pedagogical baseline for MLPA modeling, rather than as a replacement for full-wave numerical solvers or experimental validation.