A Theory of the Log-periodic Dipole Antenna†

Abstract

ABSTRACT On the basis of experimentally known electrical properties, a log-periodic dipole (LPD) antenna can be divided into three regions, namely, (1) a short dipole region, (2) an active dipole region, and (3) an unexcited long dipole region. A mathematical expression for the radiation pattern of a LPD antenna is developed, assuming (a) the far field radiation pattern entirely due to the active dipole region, (b) the scaling factor T close to unity, (c) the existing mutual coupling effect to be approximately represented by the introduction of the end-fire antenna array condition, and (d) the unexcited long dipole region to function as a parasitic reflector. To simplify the analysis the proposed parasitic reflector is further assumed to be positioned just adjacent to the resonant dipole and is included in the active dipole region. Radiation patterns computed from the mathematical expression are compared with experimentally known patterns and found to be in reasonably good agreement.