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The results of several studies on network models of log-periodic structures are described. A nonuniform, continuously scaled transmission line is introduced to simulate the near-field behavior of the log-periodic dipole array. The frequency-independent performance of the continuously scaled line represents the ideal, which is approximated by using lumped elements in a log-periodic structure. It is particularly significant to note that 1) the continuously scaled model predicts the observed input impedance behavior of log-periodic dipole arrays even when the frequency is approaching the high-frequency limit of the antenna, 2) phase velocity on the transmission line model in the active region and at the input region is also found to agree with experimental data, 3) increasing the of the loading element increases the coupling to the reflected wave, resulting in increased variations of impedance. Decreasing the angle of taper of the antenna will compensate for the increase in . Based on this model, it is shown that true size reduction may be achieved only at the expense of efficiency.