DIELECTRIC CONSTANTS AND POWER FACTORS 127 



For all lines usable as transmission devices tlie following approximations 

 hold: 



y/DZ = c.-Vi^ "=21/1 + 14/1 /3 = a,VZC = ^ = ^ 



= a/ ^ , C = -^r^ , L = -^ , V = 3 X 10^" cm/sec. 



for air. 



For the case of near-end input and output the second of equations (1) can 

 be rewritten as 



, Zf , 



cosh yjDZ t + — y= sinh \/DZ t 



/o= ° 



i/^ — ^ cosh ^DZ i + sinh \/ DZ I (3) 



\ T) 



+ — j^ /cosh \/dZ C + — k sinh \/dZ t 



If now we assume a quarter-wave line, the condition of resonance implies 



1 /zl 1 /zl 



that Rfy>\ A/ —\ and Ra<^\ A/ -^\- The condition of reasonable short- 

 * \ y D\ \ y D\ 



ening of the line (or lengthening) by the terminal reactance implies that 

 ^f^\]/W'^'^ ]/l)\- Hence weshallhave |Z^| »|y^||, 



I ^0 1 « I y^ 



Fo tanh {VdZ ^ + 6) 



If we put -?-- — = tanh 6, we get 



(4) 



J\ 1 + ~^tanh (V£>Z I + ^) 



We now make the assumption that "Zo" is a pure resistance (which is no 

 limitation on the measurement to be discussed) and put ^ = a^ + ihi . 



