946 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1952 



Ko(kPi)Ii(kP2) + KiiKpo)Io(Kpi) 



J_ y (Kt)"" 1 ^ (m + DUO""""' 



Kpi 

 1 



m=o i2m)l (kpiY m=o (2w+ 1)! 



= — ch K^ 



liP2 



1 



(xpi)- _ 



1 rf 





2/cpij 



ch /v'/ — 



^ -J- {x sh x) 

 2 a.r 



1 



(A6) 



2(kpi)- 



sh d. 



The other three equations may he treated similarly. Doing so, and 

 remembering that 



P2/P1 = 1 + //pi , (A7) 



we obtain the results which were quoted in Section III, namely 



Kp'iiKoiIn + Ki2l(n) 



1 + TT- I ch d — - — sh d, 



Kp2{KoiIo2 — K02I01) 



KpiiKnIvi — Knhi) 



zpi 



' + 2k] ''' ^■^' 

 1 + -^1 sh d, 



-plj 



2kpi 



(A8) 



/ 



2pi_ 



ch d + - — sh d, 

 2kpi 



Kp2{KnL)2 + Knoln) 

 up to first order in t/pi . 



Table of Symbols 



Note: Rationalized MKS units are employed throughout. The sub- 

 scripts 0, 1,2 applied to symbols representing material constants, such 

 as €, /i, g, (T, and r], have the significance that refers to the main dielec- 

 tric in a Clogston line, while 1 refers to the conducting layers and 2 re- 

 fers to the insulating layers in the stacks. Bars denote a^'erage ^'alues. 

 Subscripts not included in the present table are explained in the context 

 where they are used, 

 a, (B, e, 3D: Elements of the general circuit parameter matrix (Section 



III). 

 a: Distance between outer sheaths of plane Clogston line. 



Radius of inner core of coaxial Clogston line. 

 b: Thickness of main dielectric in plane Clogston line. Inner 



radius of outer sheath of coaxial Clogston line. 



