470 BELL SYSTEM TECHNICAL JOURNAL 



it is a function of V only and its action is clearly to reduce the small signal 

 value of the admittance until condition (2.6) is satistied. It will be observed 

 that this function affects the magnitude only and not the phase of the 

 admittance. 



Thus, as indicated in Fig. 4, when oscillation starts the admittance is 

 given by the radius vector of magnitude jc , terminating on the spiral, 

 and as the oscillation builds up this vector shrinks until in accordance with 

 (12.6) it terminates on the circuit-admittance line A'B', which is the locus 

 of vectors (— Vr). The electronic admittance vector may be rotated by a 

 change in the repeller voltage which changes the value of 6. This changes 

 the vertical intercept on line A'B', and since the imaginary component of 

 the circuit admittance, that is the height along A'B', is proportional to 

 frequency, this means that the frequency of oscillation changes. It is this 

 property which is known as electronic tuning. 



Oscillation will cease when the admittance vector has rotated to an angle 

 such that it terminates on the intersection of the spiral and the circuit- 

 admittance line A'B'. It will be observed that the greater is the number of 

 cycles of drift the greater is the electronic tuning to extinction. \Miile it is 

 not as apparent from this diagram, it is also true that the greater the number 

 of cycles of drift the greater the electronic tuning to intermediate power 

 points. Vertical lines farther to the left correspond to heavier leads, and 

 from this it is apparent that the electronic tuning to extinction decreases 

 with the loading. By sufficient loading it is possible to prevent some repeller 

 modes (i.e. oscillations of some n values) from occurring. Since losses in 

 the resonant cavity of the oscillator represent some loading, some modes 

 of low n value will not occur even in the absence of external loading. 



III. Power Production for Drift Angle of (« + |) Cycles 



Now, from equation (2.2) it may be seen that Ye will be real and negative 

 for d = On = (n + 4)27r. Because 6 also appears in the argument of the 

 Bessel function this value of 6 is not exactly the value to make the real 

 component of Ye a maximum. However, for the reasonably large values 

 of n encountered in practical oscillators this is a justifiable approximation. 

 Suppose, then, we consider the case of n + f cycles drift, calling this an opti- 

 mum drift time. Using the value of n as a parameter we plot the magni- 

 tude of the radio-frequency electron current in the electron stream returning 

 across the gap given by equation (2.1) as a function of the radio-frequency 

 voltage across the gap. This variation is shown in Fig. 6. As might be 

 expected, the greater the number of cycles the electrons drift in the drift 

 space, the lower is the radio-frequency ga]) voltage required to ])r(){luce a 

 given amount of bunching and hence a given radio frequenc)- electron 

 current. It may be seen from Fig. 6 that as the radio-frequency ga}) voltage 



