MAGNETRON AS GENERATOR OF CENTIMETER WAVES 



253 



distributed continuously throughout a band, Fig. 37 (a'). The energy 

 distributions in time and frequency are related mathematically by the 

 Fourier transform. 



The breadth of the frequency distribution is inversely proportional to 

 the modulating pulse width as shown in Fig. 37. The spectrum widths of 

 operating magnetrons may exceed the theoretical width by a factor of not 

 more than two for reasons not altogether clear. 



10.6 Oscillation Buildup- — Starting: Of importance in the design and 

 operation of pulsed magnetrons are the phenomena associated with the 

 buildup of oscillation when the voltage is applied. Here will be discussed 

 briefly what is known about the problem, the factors upon which the rate of 

 buildup of oscillation in the circuit depends, how this is related to the rate 



KT- 



(0) 



(b) 



(c^ 



(b) 

 sArtA 



Av/ 



FREQUENCY 



Fig. 37. — Plots of DC voltage pulse shapes (a), (b), and (c) and the frequency spectra 

 (a'), {b'), and (c') resulting from each, respectively. These are shown for the idealized 

 case of perfectly rectangular voltage pulse shapes. 



of voltage buildup and to pulser characteristics, and how these factors result 

 in various types of magnetron starting behavior. 



The rate of buildup of oscillation in the magnetron depends not only 

 upon the circuit characteristics but also upon the electronic behavior with 

 increasing DC and RF voltages. Because of the nonlinear nature of the 

 electron interaction, the amount of energy fed to the circuit per cycle is 

 dependent upon the amplitude of the oscillation. Considering the condition 

 for oscillation given by the first of equations (35) and expanding it to 

 include during buildup a term to account for the energy being stored in the 

 resonators, one may derive a simple expression for the rate of increase of RF 

 voltage amplitude. The energy stored in the circuit at any instant being 



IF = CVrp , the rate at which energy is being stored is -^- = ICVrf — —. 



at at 



