PROPORTIONING OF CIRCUITS FOR ATTENUATION 



255 



By substituting in formula (1), the high-frequency attenuation is 

 found to be 



''=Yc^l\^p 



+ V«)2l 



1 



Oge 9 



-\ ^ — nepers per cm. (10) 



Since w, p, and e are not functions of the ratio cjb, the second term of 

 this expression is constant for purposes of differentiation with respect 

 to that ratio, and the condition for minimum attenuation is identical 

 with that previously found, as given in formula (7). 



A high-frequency transmission property of smaller interest than the 

 attenuation is the characteristic impedance. This is given by the 

 familiar formula "^ 



Zo = A /-^abohms. (11) 



For the coaxial circuit with dielectric constant e the high-frequency 

 characteristic impedance is 



2 loge p 

 Zo — F abohms. 



Ve 



(12) 



There now comes the case where the space between the conductors 

 consists of a combination of gaseous and non-gaseous dielectrics. 

 Perhaps the simplest example occurs when the conductors are separated 

 by insulating discs or washers extending continuously between the 

 two conductors with flat sides perpendicular thereto. Such a con- 

 struction is illustrated in Fig. 4. Let the thickness of each insulating 



Fig. 4 — ^Coaxial structure with disc insulation. 



disc be designated w, the spacing between centers of adjacent discs, s, 

 the dielectric constant of the air dielectric, ei, and that of the disc 

 material eo. 



