MAGNETRON AS GENERATOR OF CENTIMETER WAVES 209 



Similarly, for the loaded and external Qs: 



^'^(Gc + GlV ^^^^ 



Qext = '7^ . (23) 



It follows that the Qs are related thus: 



1 1 1 



K^n+TT' (24) 



The efficiency of the circuit, defined as the fraction of the energy which 

 reaches the useful load is then: 



Vc 



y RF 



r2 , /-. J7-2 



__£ L__e. '■''^ 



Qext Qq Qo 



5.5 Resonators with Distributed Constants. The individual cavities of 

 the magnetron oscillator, however, are circuits in which the parameters are 

 distributed and not lumped. They may be considered to be "strip-type" 

 resonators, three forms of which generally used in magnetrons, are shown 

 in Fig. 21 (a), (b), and (c). Type (a) has been called the slot type resonator; 

 (b), the vane type, deriving its name from a common method of fabrication 

 in which rectangular plates are disposed around and brazed to the inside of 

 a cyUndrical cavity; and (c), the hole and slot type resonator. The forms 

 of these resonators, especially the parallel strip form of Fig. 21 (a), suggest 

 that the resonators may be considered as sections of terminated transmission 

 lines. 



Voltage and current waves traveling down a section of uniform trans- 

 mission ime, terminated at one end by a short circuit and driven by a sinus- 

 oidal voltage at the other end, are reflected at the shorted end. The inter- 

 ference of the incident and reflected waves results in standing waves of 

 voltage and current along the line. Since the voltage and current waves 

 suffer phase changes on reflection differing by tt radians, the corresponding 

 standing waves are shifted by 7r/2 radians relative to one another. Thus 

 the input admittance of the section of Hne is a periodic function of the dis- 

 tance, t, to the shorted end. For a lossless Une, this admittance is given 

 by the expression: 



F = - iFc cot '^-^ ^ -jY, cot ^-^ . (26) 



A C 



