MAGNETRON AS GENERATOR OF CENTIMETER WAVES 235 



and the input admittance, Y, expressed as 



1 - r 



Y = Yo 



1 + r 



Conversely: 



p = ,« = ;_^;,> = L^«. (30) 



If the line is matched, that is, terminated in its characteristic admittance, 

 Yt = Y(, , it is clear that the input admittance, Y, is equal to Yo , the 

 voltage reflection coefiicient, r, is zero and the voltage standing wave ratio, 

 0", is unity. 



These concepts are recalled here because they are used in specifying the 

 magnetron load. The remaining point of interest with respect to ad- 

 mittance relationships on transmission lines is the transformation of ad- 

 mittance which occurs in going through a line of variable characteristics 

 such as the output circuit of the magnetron. Such a section of nonuniform 

 line may in general be considered as a lossless transducer, the admittance 

 transformation through which is expressed as a bilinear form. In terms of 

 the reflection coefiicient ^2 looking into the load at the output terminals of 

 the transducer, the reflection coefiicient ri , looking into the transducer at 

 its input terminals may be written thus: 



ri = e ^"12 ^ — 5— . (31) 



In this expression the number /3i2 and the angles cxi2 and 0:21 are the three 

 parameters completely describing the transducer, which for lossless trans- 

 ducers are real numbers. 



9. Equivalent Circuit Theory 



9.1 The Equivalent Circuit: From time to time in the discussion thus 

 far, reference has been made to a lumped constant circuit or circuits 

 which may be considered to be equivalent to the resonator system, output 

 circuit, and load of the magnetron oscillator. One is now in a position to 

 appreciate the justification for the use of such a simple, singly resonant 

 circuit to represent as complex a device as the magnetron. As has been 

 pointed out, this justification lies in the abiUty to separate the mode fre- 

 quencies and to diminish sufficiently well, excitation of all modes except the 

 TT mode. Further, in the discussion of the equivalent circuit shown in 

 Fig. 2, it was pointed out how the output circuit and the electronics may 

 be treated by circuit analysis. This particular equivalent circuit will now 



