710 BELL SYSTEM TECHNICAL JOURNAL 



9. R. M. Fano and A. W. Lawson, Proc. LR.E., Vol., Vol. 35, #1, pp. 1318-1323, 

 November 1947. 



10. Wilbur L. Pritchard, Journal of Applied Physics, Vol. XVIII, # 10, pp. 862-872, 



October 1947. 



11. M.I.T. Wave Guide Handbook, Supplement Rod. Lab. Rpt. 41, Sec. 21a, (January 23, 



1945). 



12 A. L. Samuel, J. W. Clark and W. W. Mumford, Gas Discharge Transmit-Receive 



Switch. B. S. T. J., Vol. XXV, #1, pp. 48-101, January 1946. 



13 S. A. SchelkunofT, Representation of Impedance Functions in Terms of Resonant Fre- 



quencies. Proc. I.R.E., Vol. XXXII, pp. 83-90, February 1944. 



14. W. P. Mason and R. A. Sykes, B. S. T. J., Vol. XVI, pp. 275-302, July 1937. 



15. Sperry Microwave Transmission Design Data, Publication No. 23-80, Sperry Gyro- 



scope Co. 



16. S. A. Schelkunoff, Quarterly of Applied Math., Vol. I, #1, pp. 78-85, April 1943. 



17. G. C. Southworth, Hyper-Frequency Wave Guides, B. S. T. J., Vol. XV, pp. 284-309, 



April 1936. 



APPENDIX I 



A cavity resonator, consisting of a length of transmission line, /, at each 

 end of which there is an unvarying susceptance, jB, is approximately equiv- 

 alent to a tuned circuit, consisting of an inductance, L, and a capacity, C, 

 in parallel located at the center of a short length of transmission line, 2f, 

 when these two conditions are satisfied: 



(1) The square root of L over C is equal to the surge impedance of the 

 transmission line divided by twice the loaded Q of the cavity. 



(2) The sum of the lengths of the two transmission lines t and 2/' is equal 

 to a half wavelength at resonance. 



The first of these conditions follows from equation 3 of the text above, 

 and the proof of the second condition will be given in the following analysis, 

 based on the schematic drawing of Figures 9 and 10. In this analysis, the 

 loaded Q of the cavity is derived in terms of the susceptance of the obstacles 

 at its ends. 



Since the cavity and the tuned circuit are both symmetrical it is adequate 

 to consider but one half of each in estabhshing the equivalence. Then by 

 setting the short circuit admittance of one equal to the other and setting the 

 open circuit admittance of one equal to the other, the necessary relationships 

 are derived. 



The following symbols will be used in addition to those used in the text : 



Ysc = NormaUzed admittance, short circuited. 



Yoc = Normalized admittance, open circuited. 



The subscripts 1 and x refer to the cavity and the equivalent tuned circuit 

 respectively. 



"' x; ■ 2 



e. J^ ■ (' 

 tx. 



