Wavelength of oscillations along transmission lines and antennas
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It is a well-known experimental fact that the wavelength of an oscillation along an antenna or an open-ended transmission line differs from the wavelength of the same oscillation in free space, but there did not exist a basic scientific explanation of this phenomena until now. The following paper deals with the above problem from a theoretical point of view and demonstrates that the shortening of the wavelength is caused by a terminal effect, due to the change of inductance and capacitance near the end of a transmission line or the top of an antenna. The general differential equations for a transmission line of variable characteristic impedance are derived and solved for the first time for the particular case of the antenna and of the terminal zone of a transmission line. By means of the results obtained, numerical values for the shortening of the first halfwave are computed which are in good agreement with the values known from experience. The above derivations are of particular practical and theoretical importance for transmitting antenna design.