HF ANTENNA OPTIMIZATION STUDY (MATHEMATICAL REPRESENTATION OF A LOG-PERIODIC ANTENNA).

This report describes the theory of a mathematical model of a log periodic antenna developed during the first phase of this study. This mathematical model has been based on work done by Dr. K. K. Mei of the University of California. A solution of the current on a dipole, in terms of the length and radius of the dipole, and the applied voltage, is first obtained. Sinusoidal approximations rather than the assumption of many constant current increments along the dipole make it possible to obtain very accurate values for the current on the dipole with a minimum of calculations. After a solution to the current on a single dipole has been obtained, this solution is expanded to describe the currents on a log periodic antenna. The final step in this modeling consists of relating the far field patterns, the absolute gain and the input impedance to the element currents on the log periodic antenna. A description of some experimental model work to verify the validity of the mathematical model is described in this report.