High-Frequency Coaxial-Line Calculations

Coaxial cables insulated with solid dielectric are used for transmitting electric energy over wide ranges of frequency. During the development of such cables it was important to be able to predict the characteristics of finished cable by calculations based upon the known dimensions and physical properties of the conductors and the insulation. Many comparatively simple formulas were known to be valid at high frequency, but their applicability at lower frequencies was questioned. In the first part of this paper we have presented: 1. The general relations which hold under all conditions of operation. 2. The conditions under which ``skin-effect´´ tables offer a convenient method for obtaining values of resistance and inductance, as well as the conditions under which relatively simple equations for these quantities are sufficiently accurate. 3. The conditions under which the complete expression for attenuation may be considerably simplified to the form generally used in high frequency practice. In the second part of the paper we have presented formulas and graphs for the ratio of terminal voltages as a function of the phase angle of the line for several types of load for both dissipationless and dissipative lines. These relations are helpful in understanding observed voltage variations with frequency caused by reflections, particularly on short lengths of line. In the third part of the paper a derivation is indicated leading to a general equation for the efficiency of transmission.