. The Bell System technical journal . V A \ 10, 7 \\ / / \ \ / y / ^ / /- ^ ^ ADVANCED PHASE LAG IN RADIANS RETARDED >TT Fig. 4—Gain factor yl as a function of phase lag in endfire arrays. If a sinusoidal variation in excitation voltage along the radiator is super-posed on the constant amplitude assumed for (1), we get I sin 7r(p cos Q — ^) , ,. cos 7r(p cos 0 — (3) r = \ a ; r- ::t + U ~ O) 7r(p COS 0-/3) 1 - 4(p COS 9 - ^y (4) where a is defined in Fig. 5. This figure gives patterns of a six wavelengthradiator according to
. The Bell System technical journal . V A \ 10, 7 \\ / / \ \ / y / ^ / /- ^ ^ ADVANCED PHASE LAG IN RADIANS RETARDED >TT Fig. 4—Gain factor yl as a function of phase lag in endfire arrays. If a sinusoidal variation in excitation voltage along the radiator is super-posed on the constant amplitude assumed for (1), we get I sin 7r(p cos Q — ^) , ,. cos 7r(p cos 0 — (3) r = \ a ; r- ::t + U ~ O) 7r(p COS 0-/3) 1 - 4(p COS 9 - ^y (4) where a is defined in Fig. 5. This figure gives patterns of a six wavelengthradiator according to (4) for various values of a. Here 0 is fixed at maximum gain. Tapering symmetrically away from the center de-creases the minor lobes. The gain is also decreased, but to a lesser extent. 842 BELL SYSTEM TECHNICAL JOURNAL Exponential tapering comes about from heat losses and radiation lossesin the feed line. With attenuation a per wavelength, (1) becomes** 2 cosh ap — 2 cos 27r(cos d — ^)ay- + 47r2(p cos d - /3)2 (5). 20 25 30 DEGREES OFF AXIS Fig. 5—Effect of sinusoidal tapering of power upon directional characteristic of a sixwavelength continuous array. Feed line attenuation increases slightly the minor lobe amplitudes and tillsin the nulls. Exponential tai)ering caused by radiation can be reduced oreliminated if the coupling of the radiating elements to the feed line is gradu-ally increased along the line. 4. The Polyrod AntennaIt has been found that a suitably proportioned dielectricrod can act as an efficient endtire radiator. A complete understanding of* hoc. cit. POLY ROD ANTENNAS 843 its operation involves the solution of Maxwells equations subject to theboundary conditions appropriate to the configuration. An analysis of thissort is not available because of its mathematical complexity. However, asatisfactory explanation of polyrod operation, especially for engineeringpurposes, can be obtained by establishing analogies with array theory
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