526 



BELL SYSTEM TECHNICAL JOURNAL 



may cut such a curve at more than one pohit : thus, oscillation at more than 

 one frequency is possible. Actually, there may be three intersections per 

 loop. The two of these for which the susceptance B is increasing with fre- 

 quency represent stable oscillation; the intersection at which B is decreasing 

 with frequency represents an unstable condition. 



The loops are of course due to reactance changes associated with varia- 

 tion of the electrical length of the line with frequency. Slight changes in 

 tuning of the circuit or slight changes in the length of the line shift the loops 

 up or down, parallel to the susceptance axis. Thus, whether the electronic 

 admittance line actually cuts a loop, giving two possible oscillating fre- 

 quencies, may depend on the e.xact length of the line as well as on the ex- 



D-O.l 



BETWEEN POINTS 



k 



k^ 



J/ 



0.5 0.6 0.7 



CONDUCTANCE, G 



Fig. 42. — Susceptance vs conductance for line 500 wave lengths long terminated by a 

 load having a standing wave ratio of 1.11. Circles mark off relative frequency increments 

 of 10"''. Characteristic admittance to the resonator equals 100. 



istence of loops. The frequency difference between loops is such as to 

 change the electrical length of the line by one-half wavelength. 



The existence or absence of loops and their size depend on all three pa- 

 rameters. Things which promote loops are: 



Low ratio of Mr/M ^ or Qe 



Large n or 6 



High 0- 



As any parameter is changed so as to promote the existence of loops, the Y 

 curve first has merely a slight periodic variation from the straight line for a 

 resistiveiy loaded circuit. Further change leads to a critical condition in 

 which the curve has cusps at which the rate of change of admittance with 

 frequency is zero. If the electronic admittance line passes through a cusp, 



