92 BELL SYSTEM TECHNICAL JOURNAL 



nance, only resistance is introduced into the plate circuit, L5, G, and 

 fp, in parallel with the d-c feed of 8000 ohms, with which it is coupled. 

 Hence, if the plate circuit likewise operates at series resonance, a 

 change in resistance of any part of the circuit will change only the 

 resistance into which the tube works and therefore will leave the fre- 

 quency unaltered. 



In a more general sense, any of the oscillator forms discussed may 

 be stabilized even when the resistance in the external circuit is not in- 

 appreciable, the effect of the external resistance manifesting itself in 

 two ways: first, a value of stabilizing reactance slightly different from 

 that given in the above formulas may be required, and second, the 

 frequency, instead of being absolutely independent of battery voltage 

 variations, goes through a maximum or a minimum as the battery 

 voltages change, the voltage at which this maximum or minimum 

 occurs depending upon the exact value of the stabilizing reactance. 

 An exact mathematical analysis of this more general case yields for- 

 mulas for the stabilizing reactances which involve fg or Vp and hence 

 are not as useful even in a case where the resistance in the external 

 circuit is of importance as are the formulas presented above. The 

 latter may be used as first approximations in any event. 



In practice it has been found that when ordinary precautions are 

 taken to insure a low-loss external circuit, the relations given above 

 hold very accurately and any variations in frequency then existing as a 

 result of varying battery voltages may be traced to either one of two 

 causes, both of which may be guarded against: first, the interelectrode 

 capacities of the tube may be sufficient to enter into the impedance 

 relations. In this event, a change in the form of circuit, such as the 

 use of the tuned plate-tuned grid arrangement of Fig. 17, where the 

 interelectrode capacities form a part of the external circuit, will elimi- 

 nate the difficulty. Second, the harmonic currents caused by the 

 nonlinear characteristics of the vacuum tube may introduce the effect 

 of a reactive impedance back into the fundamental which may vary 

 with battery voltage and so change the frequency. The remedy for 

 this is to provide a low reactance path for the harmonics so that they 

 have no opportunity to build up a reactive voltage across the tube, and 

 also to use grid leaks and other such well-known devices for reducing 

 the harmonic currents generated by the tube. 



For the purpose of providing information as to the order of stability 

 which may be expected from the several methods of stabilization out- 

 lined above, various quantitative experimental tests have been con- 

 ducted. The general results of these tests may be summarized by 

 saying that a close adherence to the theoretical requirements results 



