398 



THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1952 



which the pyhndrical wave is propagated. The series impedance and 

 shunt admittance of such a line are functions of the radius and so will be 

 designated Z(r) and Y{r), respectively. Their values are gi\'en below: 



Z{r) 



Yir) 



2ri + icciih 

 2^ 



ico2Treo 

 h 



(3-1) 



(3-2) 



These formulas take into account the losses in the flat walls but assume 

 the conductance of the air between them to be negligible. Losses in the 

 inner and outer "short-circuiting" cylinders will be taken into account by 

 the boundary conditions. 



Z^2n2 I 2h£fn 2(b-a)(fn 



(b-a)L r , , I 



c ^AA, "^m^ 



(b-a)R A 3h >> 

 2 " 2fb-a)^ 





P_ 1 if^W 

 ^~7raV 2g 



'on>" 



b-a 



L^- 



//oH 



C = 



_ 277"afo 





3 (108) 



SEE FIGURE 11 FOR /Jo,€Q,/J,g 



(n = I FOR FUNDAMENTAL MODE) 



Fig. 12 — Toroidal cavity, E axial. 



