Z 1 = P — tanh (K x 1,+^) 



(62) 



The parameter \L can be eliminated between the latter two 

 equations by use of the identity 



tanh (a+(3) 



tanh a + tanh 6 

 1 + tanh a tanh 8 



The resulting relation is 



tanh A' I 



i i 





Z+Z 



1 + 



5 

 p Q 



4*i 



(63) 



which represents an implicit relation for K in terms of fi 

 and the boundary impedances Z x and Z x . This relation can 

 be augmented by the corresponding two equations for the 

 coordinate directions 2 and 3. These three equations, 

 together with 



fi 3 = o 3 K 3 +KJ +K„ 



(64) 



allow an evaluation of the K^ and Q in terms of the boundary 

 impedances. 



The real parts of Q and K^ correspond to the temporal 

 and spatial attenuation coefficients and these are regarded 

 as small compared to the imaginary parts. Consequently 

 the approximations 



K? = -h 7 - 3 + 1 2 h 7 - a. 



7, 1, <-> 1,1 



q3 = _ w 2 + j 2ls) a t 



49 



