PROPORTIONING OF CIRCUITS FOR ATTENUATION 



251 



size of the outer conductor, and the further fact that the thick- 

 ness of the outer conductor will ordinarily be determined by 

 mechanical considerations or by shielding requirements. 

 4. That the frequency is high enough to permit the use of certain 

 approximate formulas as noted below. Practically, this means 

 that at the frequency considered the currents are largely 

 crowded toward the inner surface of the outer conductor and 

 the outer surface of the inner conductor. 



The problem is to discover the proportioning which will make the 

 high-frequency attenuation of the circuit a minimum under such 

 conditions. It is well known that the attenuation of a transmission 



Fig. 1 — Coaxial conductor circuit. 



circuit at high frequencies may be represented by the following 

 approximate formula:^ 



R fC , G \L 



(1) 



where R, L, G and C designate, respectively, the linear resistance, 

 inductance, conductance and capacitance of the circuit. Except as 

 otherwise indicated, values in this and subsequent formulas are ex- 

 pressed in c.g.s. electromagnetic units. 



When the dielectric loss is negligible, the second term of formula (1) 

 evidently disappears. 



Let a and b represent, respectively, the inner and outer radii of the 

 inner conductor, c and d the inner and outer radii of the outer con- 

 ductor, / the frequency, Xi and mi, respectively, the conductivity and 



