206 BELL SYSTEM TECHNICAL JOURNAL 



resonator like one of the magnetron cavities. ^^ This is important not only 

 because the magnetron resonator system comprises a number of such cavities 

 but also because the resonator system as a whole may under certain circum- 

 stances be considered to resonate at but one frequency, in which case it 

 behaves like a simple single frequency resonator. 



Concerned with the simple electromagnetic resonator are the funda- 

 mental ideas of a natural frequency of resonance, of the rate of energy loss or 

 the sharpness of resonance, and of the characteristic admittance or the 

 energy storage capacity. The electromagnetic resonator, whether it has 

 lumped or distributed constants, consists of a device in which energy is trans- 

 ferred between electric and magnetic fields cyclically in a manner entirely 

 analogous to the transfer of energy between potential and kinetic in the 

 simple swinging pendulum. Each of these oscillations, electromagnetic or 

 mechanical, is described by a second order differential equation in terms of 

 a parameter such as voltage or current on the one hand, and angular dis- 

 placement of the pendelum bob on the other. The solutions represent 

 simple harmonic oscillations, the one for the simple electrical circuit having 

 the frequency, 



COo 



1 



This occurs when the susceptances of the two components of the circuit, L 

 and C, are equal, or when 



— 7 = cooC. (18) 



The fact that a finite time is required to transfer the energy between the 

 electric and magnetic fields is a lumped constant circuit is not surprising 

 since a finite time is required for a condenser to charge or discharge, and for 

 a current to build up or decay in an inductance. 



5.3 The Q Parameters: The type of oscillation of the simple L-C circuit 

 discussed above is its natural or free oscillation, not constrained by the ap- 



'■' In the next sections of this paper, material has been drawn from the theorj- of a single 

 resonant circuit having either lumped or distributed constants, the theory of coupled 

 circuits, and the theory of centimeter wave transmission in coaxial lines and wave guides, 

 treatments of which are to be found in the following representative texts: 



L. Page and N. I. Adams, Principles of Electricity, D. Van Nostrand Co., New York 



(1931). 

 E. A. Guilleman, Commimication Networks, Vols. I and II, John Wiley and Sons, New 



York (1931). 

 J. G. Brainerd, G. Koehler, H. J. Reich, and L. F. Woodruff, Ultra-High Frequency 



Techniques, D. Van Nostrand Co., New York (1942). 

 J. C. Slater, Microwave Transmission, McGraw-Hill Book Co., New York (1942). 

 R. I. Sarbacher and W. A. Edson, Hyper and Ultrahigh Frequency Engineering, John 



Wiley and Sons, New York (1943). 

 S. A. Schelkunofif, Electromagnetic Waves, D. Van Nostrand Co., New York (1943). 



