724 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



or 



Y. = -F. 



2.5b 



Attainment of this condition is preceded by a period during which 

 the RF gap voltage increases from its initial, near-zero value to its 

 final steady state amplitude. Concurrently, the net conductance across 

 nodes 1 and 2 changes from its maximum negative value to zero and 

 the electronic admittance vector shrinks from Yen to Ye . 



This process of build-up of oscillations and the final steady state may 

 be conveniently studied by the graphical representation of Fig. 4. Here, 

 the negative of the passive circuit admittance, F, has been superimposed 

 on the small-signal electronic-admittance spiral. Since the net con- 

 ductance across the interaction gap (nodes 1 and 2 in Fig. 3) must be 

 negative in order for oscillations to build up, we see at once that the 

 (— F) plot, sometimes also referred to as "load line," divides the com- 

 plex admittance plane into two regions: the one to its left, in which the 



REGION OF 

 OSCILLATION 



REGION OF NO 

 OSCILLATION 



^ = (1 + 3^)277-^. 

 (2 + 3^)277' 

 (3 + 3^)27r. 



FREQUENCY 

 INCREASING 



LOCUS OF SMALL SIGNAL 

 ■-ELECTRONIC ADMITTANCE 

 VECTOR, Yes 

 (SEE EG. 2.2) 



Fig. 4 — Complex admittance plane representation showing the superposition 

 of the negative of the circuit input admittance upon the small signal electronic 

 admittance spiral. Each point on spiral corresponds to a particular value of re- 

 peller transit angle, 0, and hence repeller voltage, Vr , and each division on the 

 (— F) locus to an equal frequency increment. 



1 



I 



