426 



BELL SYSTEM TECHNICAL JOURNAL 



The equation is plotted on Fig. 10 for two specific heights above 

 ground and for various line lengths. Upon examining Figs. 9 and 10 

 it may be concluded that in practical constructions a thirty per cent 

 unbalance in line currents radiates an amount of power roughly equal 

 to that radiated by the balanced currents in the line. 



It is our experience that losses due to current unbalances are ap- 

 preciably greater and somewhat different in character from those indi- 

 cated by (7). The discrepancy may reside in the assumptions em- 

 ployed in deriving the equation. In particular, the losses in the earth 

 have been ignored. It may well be that the soil over which the line is 

 erected introduces large losses in the line, particularly when the currents 

 are unbalanced. Such losses would augment the attenuati(Mi constant 



200 



160 

 (/i 



Q. 



<^ 



^ 80 



120 



40 



200 



160 



120 



80 



40 



il__L" 



X~2 



— =' — r ■:===; 'F^' 



LINE LENGTH-WAVELENGTHS 



Fig. 10 — Approximate power in watts radiated by an unbalanced current of 1.0 

 r.m.s. amperes in a long two-wire line. Also, the power radiated by a single wire 

 parallel to the earth for 1.0 r.m.s. ampere line current. Two cases, ^ and j wave- 

 lengths above ground are illustrated. 



of the line.^^ At least, the computations indicate the desirability of 



maintaining careful line current balances. 



Some remarks upon the proper procedure for inserting the power 



losses due to radiation into the equations for the line may be of interest. 



Carson ^'^ has shown that the conventional solution of the transmission 



equation for guided waves on wires is incomplete and does not explain 



the phenomena of radiation. He shows that a "principal wave," and 



hence the currents in the conductor associated with this wave, travel 



along the conductors without sensible attenuation due to radiation. 



Radiation from the line results in the attenuation of an infinite number 



of "complementary waves." These are highly attenuated so that the 



"John R. Carson, Bell Sys. Tech. Jour., Vol. V, No. 4, October, 1926. 

 "John R. Carson, Jour. A. I. E. E., p. 908, October, 1924. 



