(35) 



238 BELL SYSTEM TECHNICAL JOURNAL 



The condition for oscillation stated earlier requires that: 



Y,-[-Y, = 0, 

 or: 



G, + jB. + a + i2Fo. '^^^ + (f J (Gl + jB',) = 0. (34) 



Separating real and imaginary parts, this reduces to the pair of equations: 



a + G, = 0, or. Ge + a + {^ Gl = 0, 



B. + B.^ 0, or, B. + 27,.'^-^ + (f J^l = 0. 



Since ( — ) G'l is equal to G'/, one may write the first of equations {3S) in 

 terms of the Qs defined by (21), (22), (23) and (24) thus: 



-G. = G.= F..(i- + i-}=y^l. (36) 



9.2 The Rieke Diagram: The electronic conductance and susceptance, 

 being functions of the parameters such as Vrf , V, and B which govern 

 the electronic behavior of the magnetron, are not known a priori except for 

 the fact that they are undoubtedly slowly varying functions of frequency. 

 The circuit conductance and susceptance are given by equation (33) . Equa- 

 tions (35) state that the circuit conductance and susceptance must be the 

 ftegative of the electronic conductance and susceptance respectively. It is 

 from these relations that the behavior of the oscillator under changes of 

 load is to be inferred. 



Suppose now that one were to vary the load in such a way that only Bl 

 changes, G'l remaining constant. Then, by the first of equations (35), Gs 

 and hence Ge would not change. If, further, the frequency of oscillation 

 changes such that 



2F., ^ + (^y ABl = 0, (37) 



COO \ ^ / 



by equations (35) Bs and hence Be remain constant as well and the electronic 

 operation of the magnetron involving the RF voltage, Vrf , is undisturbed. 

 Since the power delivered by the magnetron is 



P = -GeVlF = G^VIf , (38) 



contours of constant G'l on a plot of performance versus load. Fig. 32 (a), 

 are thus contours of constant output power. Along any such constant 



