HYPER-FREQUENCY TRANSMISSION 321 



Putting 7. = 1 then gives 



2X 



Thus 



eiw aJi{\a) 



^c c r / /o(Xa) V _ 2_ M^a) I 



e ■ »' L \ M^a) / ^o, Ji{\a) J 



= c^lJ^e VI -{fojfr-. (22) 



Now, for the fundamental component Ho of the //-wave, E^, Ep and 

 He are zero and 



//. = C/o(\p), 



//, -^C/i(Xp), (23) 



Ee= -^CJi(Xp), 

 where 



X2 = ^2 _^ OjVz'^ 



and 



X = ro„7a. (/o'(ro„.) = 0.) 



There is no axial current transmitted by this wave but there is a 

 circulating current in the sheath. From (4) this circulating current, 

 1$, per unit length is given by 



le — -^zHz when p = a. (24) 



Thus, for the //o-wave, we calculate the characteristic impedance with 

 respect to unit circulating current per unit length of conductor. This 

 gives 



/o(Xa) 



1 /4 



bTro) 



^(2.aft^l-)\ (25) 



where, as given above, raJ is the mth root of Ja'^Xa), and, by (10), 



c 1 



V = 



V6mVi - UoJIf? 



