912 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1952 



where ^1(71)) and Z-^iyo) are the radial impedances looking into the stacks 

 at pi and p2 respectively, and Z„(7()) and Zhiji)) are the radial impedances 

 looking into the core and the outer sheath. From equations (44) and 

 (45) of Section II, the atteiuiation and phase constants of a coaxial C'log- 

 ston 1 cable with infinitesimally thin layers, Clogston's condition being- 

 satisfied exactly, are 



Zi(yo)/pi + Z2(yo)/p2 ... ,. 



oi = Re — — -— , (114) 



2r?o log (po/pi) 



/3 / I T^ Zl(yo)/Pl + ^2(to)/P2 /,,.x 



/3 = coVMotu + Im — — ^- , (llo) 



2r/o log (po/pi) 



where Zi{yo)/pi and Z2(yo)/p2 are given by (113). 



The impedances Za{yo) and Zb(yn) may be computed if we know the 

 structure of the core and the sheath. For a solid, homogeneous core and 

 a homogeneous sheath of effectively infinite thickness, we have 



. . r]K /o(Ka) 7 t \ '"^' ^^o('^^^) mnX 



Zaiyo) = — rT~\ ' Zbiyo) = — , (116) 



a i]{Ka) <T Ki{kO) 



where 



K = Va- - 75 , (117) 



but of course the intrinsic propagation constant a and the intrinsic im- 

 pedance 7] need not be the same for the core and the sheath. If the sheath 

 is of finite electrical thickness or has a laminated structure (alternate 

 layers of copper and iron, for example, to provide effective shielding), 

 its surface impedance may be calculated by a straightforward but longer 

 procedure. We shall not go into this matter here, but shall merely observe 

 that in many cases of interest Za(yo) and ^6(70) are so large that we 

 may neglect the terms containing their reciprocals in (113). This means 

 that we neglect the total conduction and displacement currents flowing 

 in the core and the sheath, compared to the conduction currents in the 

 stacks. Then the expressions for the attenuation and phase constants 

 become 



1 



a = 



1 



+ 



(118) 



2r]fig log (p2/pi) \_Si{a + |si) 82(6 - ^82) 

 /3 = u>V^o, (119) 



and again to this approximation there is neither amplitude nor phase 

 distortion. 



The formulas which have just been derived on the assumption of 



