End Plate and Side Wall Currents in Circular Cylinder 

 Cavity Resonator 



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



Formulas are given for the calculation of the current streamlines and in- 

 tensity in the walls of a circular cylindrical cavity resonator. Tables are 

 given which permit the calculation to he carried out for many of the lower 

 order modes. 



The integration of / '.,,,'" dx is discussed; the integration is carried out for 

 Jo -^^'-*'"» 

 C = \,2 and 3 and tables of the function are given. 



The current distribution for a number of modes is shown by plates and figures. 



Introduction 



In waveguides or in cavity resonators, a knowledge of the electromagnetic 

 field distribution is of prime importance to the designer. Representations 

 of these fields for the lower modes in rectangular, circular and elliptical 

 waveguide, as well as coaxial transmission line, have frequently been de- 

 scribed. 



For the most i)art, however, these representations have been diagram- 

 matic or schematic, intended only to give a general physical picture of the 

 fields. In actual designs, such as high Q cavities for use as echo boxes,^ 

 accurately made plates of the distributions were found necessary to handle 

 adequately problems of excitation of the various modes and of mode sup- 

 pression. 



One use of the charts is to determine where an exciting loop or orifice 

 should be located and how the held should be oriented for maximum coup- 

 ling to a particular mode. Optimum locations for both launchers and ab- 

 sorbers can be found. Naturally, when attention is concentrated on a 

 single mode these will be located at the maximum current density points. 

 ! If, however, two or more modes can coexist, and only one is desired, com- 

 I promise locations can sometimes be found which minimize the unwanted 

 phenomena. 



Also, in a cylindrical cavity resonator of high Q with diameter large com- 

 pared with the operating wavelength, there are many high order modes of 

 j oscillation whose resonances fall within the design frequency band. Some 

 I of these are undesired and one of the objectives of a practical design is to 

 ! reduce their responses to a tolerable amount. This process is termed 



! ' "High Q Resonant Cavities for Microwave Testing," Wilson, Schramm, Kinzer, 

 I B.S.T.J., July 1946. 



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