HIGH Q RESONANT CAVITIES 423 



terms which are a function of frequency and by assuming the conductivity 

 of copper* for the cylinder walls. It then becomes 



13/2 



[. + 0.168 (Ipj 



e^ = 2.77- ^^.^ (6) 



^ 1 + 0.168 



for TE 01 n modes;/ is in megacycles. 



Thus, it is seen that for the design parameters Q and/, selected values of n 

 now define tentative useful points on the mode chart in terms of D/L and n. 



Selection of Operating Area on Mode Chart 



This will be more evident upon examination of Fig. 6, which is a basic 

 design chart for cylindrical cavity resonators using TE Oln modes. The 

 coordinates of (fDY and {D/Ly will be recognized from the previous dis- 

 cussion of the mode chart (Fig. 1) although in this case the range has been 

 expanded by the use of logarithmic coordinates. Mode identification is 

 obtained from equation 2; which, for TE Ohi modes becomes 



(fDY X 10-8 = 2.0707 + 0.3480 n^ {D/iy (7) 



with D and L in inches and / in megacycles. 



A family of TE Olw modes has been drawn on the chart for selected values 



Q 

 of n. To aid in designing for minimum volume a line labelled Max. „ has 



been added (Equation 3). Lines of constant Q^yf are also shown as a 

 series of dashed lines. 



A tentative operating area on this chart may be selected on the basis of 

 the required Q\/f. Using mid-frequency for/, the intersection of the Qy/f 

 line and the minimum volume line will define the operating mode, n, and 

 also locate the center of the operating rectangle. 



An enlarged plot of this area as in Fig. 7 will show all modes possible in 

 the cavity. Some adjustment of the precise location of this area may then 

 be desirable to eliminate certain types or numbers of unwanted modes. For 

 example, it is extremely difficult to suppress TE 02 modes without affecting 

 the TE 01 mode, because of the very close resemblance of the field configura- 

 tions. On the other hand, most TM modes are easy to handle. 



It may be possible to select an operating area such as the rectangle blocked 

 out in Fig. 1 in which all extraneous responses (with the exception of the 

 companion TM HI) are avoided. The largest rectangle which can be 

 inscribed here is limited by the TE 311 and TE 112 modes. This will 



* p = 1.7241 X 10"^ ohm-cni— the International Standard value for copper. 



