DIELECTRIC CONSTANTS AND POWER FACTORS 



129 



/o 



V. 



1 + tanh" {a€ + af) • tan 



IttSC 



V 



I 



/ 



+ 



Forming the current values | /m | = | /02 1 = 



1 + — -Tj tanh {at + <i^) 

 /o(resonant) 



tan" 



lirht 



K 



, dividing to elimi- 



nate I /(I I and discarding squares and products of small quantities in com- 

 parison with unity leaves, 



Vk^- - 1 = 



tan 



iwdC 



+ tanh {a€ + c^) 



/■ 



or 



Vk^ - 1 



85^ 



(6) 



Vl 



+ tanh (a^ + af) 



which becomes our "Q" when A' = \/2. 



In most practical situations the "tan" and "tanh" are equal to their 



TT 



4 

 angles. For this condition (J = -^ . If we now put, by defini- 



1/. 



+ al-\-a( 



tion, Qt^ 



4at 



_xl/i 



(the Q of the line itself), Qo = 7- -^^^ — , Qf = ~. — , we have 



4 Zo 



Aat 



i _ 1 1 1 



(? ~ e, ^ ^0 "^ <2^ 



(7) 



the law of Q composition relating the resultant Q to line and terminal Q's. 



