422 BELL SYSTEM TECHNICAL JOURNAL 



the Q. But, in simple designs, these may be negligible. Therefore, it is 

 expedient to design for a theoretical Q of about 15 to 25 per cent in excess of 

 the working Q to be realized. 



The working Q's of a number of echo box designs are cited here to indicate 

 the order of magnitude required at several frequencies: 



1 kmc 70,000* 



3 40,000 



9 100,000 



25 200,000 



Finding the Cavity Dimensions 



With the frequency and theoretical Q known, the dimensions of the cavity 



can be evaluated but the formulas of Table I require some simplification for 



engineering use. 



5 ... 



The mode-shape {MS) factor, Q-,may also be termed its selectivity which 



A 



for the TE 01 w modes may be expressed as follows: 



13/2 



X 



where: 



[, + . »(|y.-j 



Q \ = 0.610 ^ ^Yy -" (5) 



1 + 0.168(^)w' 



1 / 

 5 = the skin depth in cm. = t^A/ 



lO^p 



/ 



p = the resistivity in ohm-cm. 



The skin depth is a factor which recognizes the dissipation of energy in 

 the walls and ends of the cylinder. With increase of resistivity of these 

 surfaces the currents penetrate deeper and the resulting Q is lower. 



A comparison of the relative Q's computed from the resistivity of several 

 metals will show the importance of this factor: 



Therefore, a brass cavity will have about one-half of the Q that a similar 

 cavity would have if made of copper. Similarly, the silverplating of a copper 

 cavity will gain about 3 per cent in Q. 



Equation 5 may be made more convenient for calculations by combining 



* This value reflects the higher Q required on ground radars. 



