402 



THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1952 



where, as before, 5„ is the "skin depth" e([ual to the real part of o-„ . That 

 is, 



, _ /cOOnMg 



To gain an idea of numerical magnitudes, consider the same cavity used 

 in example 2. The dimensions are, as before, h ^ .5 cm,, b — a = .5 cm. 

 For the square cross-section chosen, the first resonance again occurs at 

 30,000 megacycles, very nearly, and we can make the following direct 

 comparison of the Q's for the two modes of oscillation: 



Due to the asymptotic approximations used, the results for example 3 

 are not as accurate as those for example 2; the two sets of results show 

 only that the Q of the cavity is substantially the same for the two differ- 

 ent modes of oscillation. 



The poles of Y are given by 



1 



P-n 



Pn = —Oin 



i^n 



Oin = Won 



2hbn "^ ih 



/3„ = COOn 1 + 



and the residues are 



An = ttn + ibn , 



an = 



irn 



Hoiajwon 



1 



2)^ 



- a)8j 

 {b - a)8nj 



(3-15) 



A_n — An — dn tOn 



bn = 



irn 



1 - 



1 



1 



2h8n 



+ 



2(b - a) 5 J 

 1 



(3-16) 



_2h8n 2(b - a)8n_ 



Applying formulas (6) gives the following values for the n*"" branch of 



