Transmission lines at very high radio frequencies

Radiation resistance, although ordinarily neglected, is actually of dominant importance in determining the selectivity factor Q and the input impedance Zsfor both parallel-wire and concentric lines at high radio frequencies, and therefore materially changes the optimum design of the line, whether used as a low-loss inductive or capacitive reactance or to give high selectivity or high impedance as a resonant line. Accurate design equations for maximum selectivity and for maximum impedance are developed in this paper for both parallel-wire and concentric lines, and curves are included showing radiation resistance, selectivity, input impedance, optimum values of spacing, conductor radius, etc. It is shown that for maximum Q the optimum ratio of spacing to wire radius for parallel-wire lines is D/r = 6.186, and the ratio of outer conductor radius to inner conductor radius for concentric lines is b/a = 4.22, as compared with values of about 3.6 for both ratios when radiation resistance is neglected. For maximum impedance corresponding values are D/r = 20.96 and b/a = 14.3, as compared with values of 8 and 9.2, respectively, predicted neglecting radiation resistance. Moreover, Q and Zsare not proportional to D and b as indicated in previous analyses; instead definite values of D and b give maximum Q and slightly larger values give maximum Zs, and even a small departure from the best value produces a large decrease in Q or in Zs. Q and Zsfor optimum design are both inversely proportional to the cube root of the frequency for parallel-wire lines and inversely proportional to the 0.4 power of the frequency for concentric lines, whereas previous analyses showed both increasing as the square root of the frequency.