HIGH Q RESONANT CAVITIES 413 



Formula (2) represents a family of straight lines, when (D/L)- and (JDy are 

 used as coordinates, and leads directly to the easily constructed and highly 

 useful "Mode Chart" of Fig. 1. 



It will be noted from Table II that the TE Omn and the TM \mn modes 

 have the same frequency of resonance. This is a highly important case of 

 degeneracy. In the design of practical cavities it is necessary to take 

 measures to eliminate this degeneracy, as the TM mode (usually referred 

 to as the companion of its associated TE mode) introduces undesirable 

 effects. This is discussed more at length later. 



Choice of Operating Mode 



8 

 Turning now to the expressions for Q~ these are seen to be of a rather com- 



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plicated nature. For some of the lower order modes, their values are 

 plotted in Figs. 2, 3 and 4. Examination of these leads to the question of 

 which mode has the highest Q for a given volume. It is desirable to keep 

 the volume a minimum, since, as shown by (1), the total number of reso- 

 nances is a function of the volume. Analysis of the problem is somewhat 

 involved, but leads to the conclusion that operation in the TE Oln mode* 

 gives the smallest volume for an assigned Q, and also leads to specific values 

 of n and D/L which give this result. In fact, for maximum Q/V in the 

 TE Oln mode, 



(JDf (~^ = 3.11 X 10« (3) 



which permits easy plotting on a mode chart of the locus of the operating 

 points for best Q/V ratio. 



Extraneous or Unwanted Modes 



In echo boxes for radar testing, where high Q is of the utmost importance, 

 the TE Qhi mode has been used. The values of n var>' from 1 at frequencies 

 around 1 kmc to 50 at about 25 kmc. 



All other modes are then regarded as unwanted or extraneous. The great 

 utility of the mode chart lies in that it permits a quick determination of the 

 most favorable operating area. We consider this now in detail. 



Figure 5 shows a portion of a mode chart. It is clear that the sensible 

 way to construct a tunable cylinder is to keep the diameter fixed and vary 

 the length. With fLxed diameter, the coordinates of the mode chart are 



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essentially p and ( y j and it is convenient to refer to them loosely as fre- 



* Unimportant exceptions occur for values of Q - < 1.2. 



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