Some Results on Cylindrical Cavity Resonators 



By J. P. KINZER and I. G. WILSON 



Certain hitherto unpublished theoretical results on cylindrical cavity reson- 

 ators are derived. These are: an approximation formula for the total number 

 of resonances in a circular cylinder; conditions to yield the minimum volume cir- 

 cular cylinder for an assigned (^; limitation of the frequency range of a tunable 

 circular cylinder as set by ambiguity; resonant frequencies of'the elliptic cylinder; 

 resonant frequencies and ^ of a coaxial resonator in its higher modes; and a brief 

 discussion of fins in a circular cylinder. 



The essential results are condensed in a number of new tables and graphs. 



Introduction 



THE subject of wave guides and the closely allied cavity resonators was 

 of considerable interest even prior to 1942, as shown in the bibliography. 

 It is believed that this bibliography includes virtually everything published 

 up to the end of 1942. During the war, many applications of cavity reso- 

 nators were made. Among these was the use of a tunable circular cylinder 

 cavity in the TE 01« mode as a radar test set; this has been treated in pre^ 

 vious papers. ^'^ During this development, a num.ber of new theoretical 

 results were obtained; some of these have been published.^ Here we give 

 the derivation of these results together with a number of others not previ- 

 ously disclosed. 



In the interests of brevity, an effort has been made to eliminate all 

 material already published. For this reason, the topics are rather discon- 

 nected, and it is also assumed that the reader has an adequate background 

 in the subject, such as may be obtained from a study of references 3 to 7 

 of the bibliography, or a text such as Sarbacher and Edson.** 



A convenient reference and starting point is afforded by Fig. 1, taken from 

 the Wilson, Schramm, Kinzer paper.- This figure also explains most 

 of the notation used herein. 



Acknowledgement 



In this work, as in any cooperative scientific development, assistance and 

 advice were received from many individuals and appropriate appreciation 

 therefor is herewith extended. In some cases, explicit credit for special 

 contributions has been given. 



Contents 



1. Approximation formula for number of resonances in a circular cylin- 

 drical cavity resonator. 



2. Conditions for minimum volume for an assigned (). 



410 



