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BELL SYSTEM TECHNICAL JOURNAL 



conductors is approximately 13, and the optimum diameter ratio for 

 such a structure, as found from Fig. 2, is about 5.25. 



The behavior of the attenuation in the vicinity of the optimum 

 diameter ratio is illustrated in Fig. 3, which shows attenuation plotted 



HZ 6 



-^5 



z=> 



<2 2 



111 ^ ^ 



2.0 2.5 3.0 3.5 4.0 4.6 5.0 5.5 6.0 



DIAMETER RATIO (p) 



Fig. 3 — Variation of optimum diameter ratio of coaxial circuit with conductivity ratio. 



against diameter ratio for the case where n equals unity. It will be 

 seen that near the optimum the attenuation changes very slowly. ^ 

 This is fortunate, since it means that unavoidable departures from the 

 optimum diameter ratio may be permitted without appreciable effect 

 on the attenuation. Other small departures from ideal design are also 

 allowable. Thus, for example, it has been assumed in deriving the 

 condition for minimum attenuation that the two conductors of the 

 circuit are perfectly coaxial or concentric. However, for moderately 

 small departures from perfect concentricity occasioned by practical 

 difficulties of construction, the conditions for minimum attenuation are 

 substantially the same as for a circuit with no eccentricity. The 

 situation is similar for other types of shielded circuits to be considered 

 later, in these cases also only a reasonably close approximation to the 

 ideal being necessary. 



Effect of Dielectric 

 vSuppose now that the capacitance and leakage conductance intro- 

 duced by the insulation are substantial.^ First, it will be assumed that 

 the space between the two conductors is filled with a substantially 

 uniform non-gaseous dielectric material having a dielectric constant e 

 and a power factor p. Such would be the case, for example, if the 

 two coaxial conductors were separated by a continuous rubber insula- 

 tion. The leakage conductance of the circuit now becomes 



G = pcoC = — ^abmhos per cm., 



where, as usual, w equals 27r/. 



(9) 



2 loge ^ 



