TRANSMISSION LINES FOR RADIO SYSTEMS 



435 



If n is even and the termination is a short circuit or if n is odd and the 

 termination is an open circuit, (12) is employed. If n is odd and the 

 termination is a short circuit or if n is even and the termination is an 

 open circuit, (13) is employed. The attenuation factor is given by: 



a = - ^ + 77 GZo napiers per foot, 

 = 4.34 ( y- + GZo ] decibels per foot, 



(14) 



(14a) 



where : 



R = resistance in ohms per foot, 

 G = conductance in ohms per foot, and 

 Zq = characteristic impedance in ohms. 



For all the lines concerned with here tanh [a:(//X/4)3 may be replaced 

 by [q:(//X/4)] without more than 1.5 per cent error. Thus, (12) and 

 (13) reduce to 



Zi = 



8Zo = 



R wX 

 2 4 



2Zo' 



1 + 



n\ 



R 



GZl 

 R 



GZl 

 R 



(12a) 

 (13a) 



BALANCING CONDENSER 



^^ BEATING OSC (PUSH PULL) 



300 KG INT 



FREQ AMPL 



AND 



LF DET 



ATTENUATOR 



w LOCAL SIGNAL OSC 



Fig. 16 — Schematic diagram of apparatus for measuring line loss by means of a 

 resistance substitution method. 



Therefore, except for the small contribution of shunt conductance, 

 Zi is independent of Zq. In cases where G is negligible, the measure- 

 ment of Zi gives directly the high-frequency resistance. 



The method of measurement is shown schematically in Fig. 16 and 

 an experimental set-up appears in Fig. 17. The modified high-fre- 



1^ It is assumed here that the conductance term in (14) is small compared with 

 the resistance term. 



