CROSSTALK BETWEEN COAXIAL CONDUCTORS 



365 



conductor while Z44 would equal one-half of the surface self-Impedance 

 of a single outer conductor (neglecting the self-impedance of the lead 

 sheath in comparison with the iron outer conductors). Thus, neglect- 

 ing differences in external inductance and in proximity effects I/Z33 

 would equal I/4Z44 and the crosstalk would vanish. Actually, the 

 observed reduction in crosstalk due to these opposing terms is about 

 32 db at 50 kilocycles in a 145-foot section of twin coaxial with quads 

 and sheath shorted to the coaxials at the ends only. Physically this 

 means that the current due to the voltage on the outer conductor 

 surface of the disturbing coaxial flows mainly in the sheath and quads 

 rather than on the high impedance surface of the disturbed coaxial. 



Now let us consider the case where the sheath is insulated from the 

 coaxial outer conductors. For this case equations (1) and (2) may 

 also be added directly to give 



Fi = 



2Z 



Z33 



/ 



74^ 



4Z44 74^ - 7^ 



74 



+ 



74 / 74^ + 7^ 



4Z44V(742 - y^)\ 

 -(.yt-y)i f.-lyA+y)i 



+ 



4Z44\2(74 - 7)2 2(74 + 7)' 



(5) 



This equation appears quite formidable but it has been split purposely 

 into three terms which will be examined individually. The first term 

 is directly proportional to length, the second term is independent of 

 length and the third term involves length exponentially. For lengths 

 where the tertiary circuit is electrically long the third term vanishes 

 and we have 



Fi = 



^a0 



IZ 



_z_ 



Z33 



/ 



74^ 



+ 



74 / 74' + 7^ 



4Z44 74^- 7V 4Z44V(742 - 7^)=^ 



(6) 



In electrically short lengths we get 



Fi = 



Z^ 

 2Z 



Z33 



/ 



74^ 



4Z44 74== 



2Z L 



+ 



Z33 



74 



4Z 



44 



74^ 



74 l^ 



4Zu ' 2 



-y 2)\ 



- 2Z LZ33J' 



(7) 



in which it is seen that terms two and three of (5) combine to cancel 

 the second half of term one. 



From equations (5), (6) and (7) we are now ready to build a physical 

 picture of what takes place as / is increased for cable sections where 

 the sheath is insulated from the coaxial outer conductors but ter- 

 minated to them at each end in characteristic impedance, Z4. Starting 

 with equation (7) we see that for very short lengths the term involving 



