CROSSTALK BETWEEN COAXIAL TRANSMISSION LINES 159 



Under certain conditions it is easy to obtain approximate values of 

 the denominator of (52) and use them for gauging the limits between 

 which the mutual impedance must lie. If the frequency is so high 

 that the proximity effect has almost reached its ultimate value the 

 external inductance and the internal impedance of the intermediate line 

 are approximately 



Le — ^z^ cosh 



2bib2 



(Zbb)l + (Zbb)2 



lujj. 



bi bi 



+ 



^^1^ 



r- 



62' / 1_ 



b, 



1 



(bi + b^r 

 I 



1 - 



(bi - 62)- 

 / 



(53) 



where bi and &2 are the external radii and / is the interaxial separation. 

 Usually b2 = b\ — b and consequently 



Le = -r- cosh~^ 



ZTT 



{Zbb)i + (Zw)2 =;^\/v^ 





/2 



(54) 



If the proximity effect is disregarded then the external inductance is 

 simply 



Le =- log. 



/ 



/6165 



(55) 



For this case, then, the mutual impedance is given by the expression 



{Zah)\{Zah)2 



Z\2 — 



{Zbh)\ + {Zbh)2 +-^l0ge , 



^ V6162 



(56) 



For two identical coaxial conductors the expression is further 

 simplified to 



Z12 = ^^ -, • (57) 



lAbh + lOge 7 



TT 



Measuring Method 



As defined above, crosstalk between two transmission lines termi- 

 nated in their characteristic impedances is given by the ratios of the 

 induced and disturbing voltages. Consequently, if the input voltage 

 into the disturbing circuit is known and the induced voltage at one of 



