NKTWOUKS FOR IMPKDANCK FUNCTIONS 



393 



where 



Zo = 



A' + pL 



P = 



7 = (72 + pLy'\G + pcy" 



Z. + Zo 



Z.= ^ log 



r? /o(<ra) 77 luiah) 



^ ^ 27ra Iiiaa) ^ 2Tb K^{<xb) ^ 2t ^ a 



G+pC = 



1 ^ 

 log- 



a 



(go + peo) 



(2-3) 

 (2-4) 

 (2-5) 



(2-(;) 



(2-7) 



h, a, b = cavity length, inner radin.s, outer radius, as shown in Fig. 11, 

 all measured in meters 





(pi^g) 



1/2 



1/2 



(2-8) 



H, g are permeability, conductivity of the conducting material of the walls 

 (for copper: m = -l7r(10^^), g = 5.8(10') in M.K.S. units). 



tin , go, 60 are permeability, conductivity, dielectric constant of the dielec- 

 tric material occupying the cavity (for air: /^o = 4x(10~ ), ^0 = 0, 

 Co = (10~ )/367r in M.K.S. units), p — generalized frequency vari- 

 able. 



Io{z), Ii(z) are Bessel functions of the first kind for imaginary argument 

 and of order 0, 1. 



Ko(z), Ki(z) are Bessel functions of the second kind for imaginary argu- 

 ment and of order 0, 1. 

 Except for ignored small deviations of the field around the corners of 



the cavity, the above formulas are exact. To arrive at results that are 



sufficiently compact to be useful, we make these approximations, at the 



start : 



r7-ni/2 

 Zo = Ko = 



770 1 b 

 2x a 



where 



T?" 



1/2 



= 1207r ohms 



(2-9) 

 (2-10) 



