LAMINA TKI) TRANSMISSION LINKS. I 



Si)3 



TluMi from (33) and (84) the bouiulary coiiditioiis are 



AIo{koPi) — BKo{koPi) _ ry ^ s 



.4/i(koP2) + BKiiKopi) 



m\ 



Avhero 



K'O — (ffo 



7 



'/(tp 



Ko 



go + ?"coe(i 



r7o(l — y'/(Tu)\ (37. 



If e(iuatious (36) are to he satisfied by values of A and B which are not 

 both zero, it is easily shown tluit a necessary and sufficient condition is 



r]i)f,Ki,{Kupi) + Zi{y)Ki{Kopi) 77op/vo(^oP2) — ^2(7) A'l(^■oP2) 



VOpIo(Kopi) — Zi('y)Ii(koPi) 



rjOp/o(KoP2J + Z2(y)Il{KQP2) 



(38) 



and (38) is a transcendental e(iuation for the determination of the propa- 

 gation constants of all the circular magnetic modes in the coaxial line. 

 As ill the discussion of the parallel-plane line, we shall confine our 

 attention to the principal mode and shall assume forthwith that the wall 

 losses are small." Since for the principal mode we expect that 7 will be 

 nearly equal to ctq , we may write 70 for o-q and eyaluate Zi and Z2 at 70 ; 

 and we may replace the modified Bessel functions in (38) by their ap- 



Fig. 2 — Transmission line bounded l)y coaxial inii)edance cylinders. 



^ J. A. Stratton, Electrumniinctic Theori/, McGraw-Hill, New York, 1941, pp. 

 551-554, gives a similar treatment of the jMiiicipal mode in an ordinary coaxial 

 cable with solid metal walls. 



