486 



BELL SYSTEM TECHNICAL JOURNAL 



Here the quantity M is the characteristic admittance of the resonator, 

 which dej^ends on resonator shape and is unaffected by scaling from one 

 frequency to another. Gc is the shunt conductance due to circuit and to 

 load. Ye as given by (7.1) represents to the degree of aj^proximation re- 

 quired the admittance of an)^ resonant circuit and load with only one 

 resonance near the frequency of oscillation. 



It is ])rofitable to consider again in more detail a complex admittance 

 plot similar to Fig. 4. In Fig. 12 the straight vertical line is a plot of (7.1). 



-Ye = ye(2J,(X)/x)e-J^Q 



Ae 



UJo = (LC)-'/2 

 Y = G+j2MAuj/u)o 



CONDUCTANCE, G *■ 



Fig. 12. — The resonator and its load can be represented as a shunt resonant circuit 

 with a shunt conductance G. For frequencies near resonance, the conductance is nearly 

 constant and the susceptance B is proportional to frequenc\', so that when susceptance is 

 plotted vs conductance, the admittance Y is a vertical straight line. The circles mark off 

 equal increments of frequency. The electronic admittance is little affected by frequency 

 but much affected by amplitude. Tne negative of an electronic admittance Y ^ having a 

 constant phase angle \6 is shown in the figure. The dots mark off equal amplitude steps. 

 Oscillation will occur at a fref[uency and amplitude specified by the intersection of the 

 curves Y and — Ye ■ 



The circles mark equal frequency increments. Now if we neglect the varia- 

 tion of the electronic admittance with phase, then the negative of the small 

 signal electronic admittance on this same plot will be a vector, the Iccus of 

 whose termination will be a circle. The vector is shown in l-ig. 12. The 

 dots mark off admittance values corresponding to equal amplitude incre- 

 ments as determined by the data of Fig. 5. 



Steady oscillation will take place at the frequency and amplitude repre- 

 sented by the intersection of the two curves. If the phase angle 16 of the 

 — Ye curve is varied by varying the repeller voltage, the point of intersection 

 will shift on both the I'c curve and the — !'« curve. 'I'hc shift along the 



