172 BELL SYSTEM TECHNICAL JOURNAL 



is thus the same field as that to which energy is transferred. In this sense the 

 magnetron oscillator is perhaps more properly analogous to the reflex type 

 of velocity variation oscillator, in which a single cavity is used both as 

 "buncher" and "catcher"; the electrons, after traversing the gap once, are 

 turned back in the proper phase in the drift space so as to pass through the 

 gap again in the opposite direction. 



Each type of oscillator has a resonator in which energy is stored and which 

 synchronizes the flow of energy from the electrons into it by the means of 

 self excitation. In each type, energy is extracted from the resonator by an 

 output circuit at a rate which, under steady state conditions, equals that of 

 influx from the electron interaction, minus the losses in the resonator itself. 



1.3 Use of Equivalent Circuits: In many instances the understanding of 

 electromagnetic oscillators is made easier and analytic trea tment made pos- 

 sible by use of an equivalent circuit with lumped constants. Of several 

 possible types, one of the simpler and more frequently used for the magne- 

 tron oscillator is shown in Fig. 2. This may appear in the case of the multi- 

 cavity magnetron to be an oversimplification as it does not account for the 

 fact that the resonant frequency of the magnetron resonator system is many 

 valued. A magnetron resonator, being made up of a number of coupled 

 resonating cavities, is capable of supporting several modes of oscillation. 

 These modes of oscillation have different resonant frequencies and corre- 

 spond to different configurations of the electromagnetic fields. By means 

 to be discussed, however, magnetron resonators can be made to oscillate 

 "cleanly" in one of these modes and may thus be represented for many pur- 

 poses by a simple L-C circuit having a single resonance. 



The output circuit of the oscillator is also amenable to treatment by 

 equivalent lumped constant circuits which account for its behavior with 

 accuracy. More general, four terminal network theory has also been applied 

 in the study and design of impedance transformations in this part of the 

 oscillator. 



Finally, the electrons, which in a sense are connected to the circuit formed 

 by the resonator and the load, may also be treated by circuit concepts. 

 The electrons moving in the space between the cathode and anode, by virtue 

 of their presence and motion, induce charge fluctuations on the anode seg- 

 ments. The time deriv'ative of these fluctuations is equivalent to an RF 

 current flowing into the anode from the interaction space. This current and 

 the RF voltage on the anode, bearing a definite phase relationship, make 

 possible the definition of an admittance called the average electronic admit- 

 tance, I'e = Ge -\- jBg. Since the electrons are being driven against RF 

 fields in the interaction space, this admittance looking into the electron 

 stream has a negative conductance term. Unlike usual circuit admittances, 

 the electronic admittance is nonlinear, being a function of the voltage 



