nicn Q RESONANT CAVITIES 409 



Due to their interesting properties the history of resonators of the cavity 

 type in which a dielectric space is enclosed by a conducting material, goes 

 back many years. In 1893 J. J. Thompson' derived expressions for resonant 

 frequencies of the transverse electric modes in a cylinder. Lord Rayleigh'' 

 published a paper in 1897 dealing with such resonant modes. The early 

 work was almost entirely theoretical but some experiments were carried out 

 in 1902 by Becker^ at 5 and 10 centimeters. In recent years, the subject 

 has been fairly thoroughly investigated (at least theoretically) for several 

 simple shapes. 



However, many of the presentations are highly mathematical with con- 

 siderable space devoted to proofs; the results which would be most useful 

 to an engineer are thus sometimes obscured. The purpose of this paper is 

 to present certain engineering results together with information upon the 

 application of the tunable cylindrical cavity to radar testing. 



Defimtioxs and Fundamental Formulas 

 Modes 



By fundamental and general considerations, every cavity resonator, re- 

 gardless of its shape, has a series of resonant frequencies, infinite in number 

 and more closely spaced as the frequency increases. The total number .V 

 of these having a resonant frequency less than/ is given approximately by:^ 



N=^Vf (1) 



in which 



V = volume of cavity in cubic meters. 



c = velocity of electromagnetic waves in the dielectric in meters per 

 second. 



/ = frequency in cycles per second. 

 With each resonance there is associated a particular standing wave pattern 

 of the electromagnetic fields, which is identified by the term "mode." 



In right cylinders (ends perpendicular to axis) the modes fall naturally 

 into two groups, the transverse electric (TE) and the transverse magnetic 

 {TM). In the TE modes, the electric lines everywhere lie in planes per- 

 pendicular to the cylinder axis, and in the TM modes, the magnetic lines 

 so lie. Further identification of a specific mode is accomplished by the 

 use of indices. 



The MS Factor 



With the cylinder further restricted to a loss-free dielectric and a non- 

 magnetic surface, there is associated with each mode a value of Q (quality 

 factor)^ which depends on the conductivity of the metallic surface, on the 



