HIGH Q RESONANT CAVITIES 421 



small relocations of the coupling points to discriminate against a residual 

 undesired mode. 



Principle of Similitude 



One other theorem generally applicable to all cavities has been useful 

 in design. It is the principle of similitude, which maybe stated as follows^-: 



A reduction in all the linear dimensions of a cavity resonator by a 

 factor 1/w (if accompanied by an increase in the conductivity of the 

 walls by a factor m) will reduce the wavelengths of the modes by a 

 factor 1/m. 



The condition given in parentheses is necessary for strict validity; for 

 high Q cavities, it need not be considered. 



Application of Theory 



An illustration of an engineering application of the basic information 

 just presented, is the design of an echo box test set for use in radar main- 

 tenance. 



The test set has a number of components, but only the cavity proper and 

 its coupUngs will be considered at this time. 



Design Requirements 



The basic design requirements of the cavity set by the radar are: (1) the 

 working decrement, and (2) the tunable frequency limits (/] and/o). Service 

 use of these test sets in the 3 kmc and 9 kmc bands has shown that a working 

 decrement of about 3 db per microsecond gives satisfactory results. 



As seen in the discussion above, () is a more useful design parameter for 

 the resonant cavity than decrement, (/. Hence the conversion 



Q = '-^^ (4) 



where d is expressed in db per microsecond, and / is in megacycles, gives the 

 loaded or working Q to be realized. 



Determi)iing the Theoretical Q Required 



For design purposes, however, there are several factors which dictate the 

 use of a value for theoretical Q which is somewhat higher than the loaded () 

 just computed. The input and output couplings reduce the theoretical () 

 of the cavity due to their loadings. The coupling factor, s, expressed as the 

 ratio of loaded to unloaded Q, has values for echo boxes of about 0.90 for 

 the input coupHng and from 0.90 to 0.99 for the output coupling. In addi- 

 tion, other factors such as the means used for mode suppression may degrade 



