TRANSMISSION LINES FOR RADIO SYSTEMS 425 



length equal to the line spacing, will radiate approximately one half 

 as much power as the line. Therefore, considering both load and gen- 

 erator terminations, the total power dissipated in radiation may be 

 approximately twice that given in (6). The equation is plotted on Fig. 

 9 for the cases of several 600-ohm lines constructed from practical 

 conductor sizes. It may be seen from this figure that the power ra- 

 diated by a practical terminated line is negligible as compared to the 

 power transmitted by the line provided that operations are confined 

 to wave-lengths other than those in the ultra-short-wave region. 



If the currents in the two wires are unequal or are not exactly 

 180 degrees out of phase there is an appreciable amount of power radi- 

 ated by a two-wire line. Unbalances of this kind become evident when 

 the driving voltages, measured to neutral, are incorrectly balanced and 

 phased. Such unbalances also arise if the voltages induced by the 

 antenna set up currents in the line which employ the two conductors in 

 parallel. 



For the purpose of computation unbalanced currents may be con- 

 sidered as flowing in a single conductor parallel to a perfectly reflecting 

 earth. The amplitude of the current in the single wire may be assumed 

 to be the vector sum of the current values in the two conductors. This 

 procedure ignores the mutual interactions of the balanced and un- 

 balanced currents flowing in the two-wire line and hence, the results 

 so obtained are not strictly correct. It is believed, however, that the 

 error is small. 



Based upon these assumptions the power radiated by unbalanced 

 currents is approximately: ^^ 



P 



— = 30 



0.5772 + log. (2L) - sin^ (L) U - ^^) - Ci{2L) 

 2Ci{H) + Cii^UTlP - L) -{- Ci{^U + H^ + L) 



(7) 



in which 



and 



P/P is expressed in watts/ (amps) ^ 

 / = r.m.s. value of current at a position along the line 

 of maximum current, 



H = ,- being the height of the wires above ground 



A X 



in wave-lengths, 



7 / / 



L = —, -being the length of the line in wave-lengths. 

 X X 



1- See appendix. 



