2 BELL SYSTEM TECHNICAL JOURNAL 



quency. When continuous oscillation is necessary it is desirable to provide 

 adequate margin against intermittent operation. When intermittent opera- 

 tion is desired the opposite is true. In either case an understanding of the 

 same general problem is necessary. 



The present analysis applies only to oscillators of the feedback type. Xo 

 method of extending it to cover negative resistance oscillators such as the 

 Dynatron and the Transitron has been found. Relaxation oscillators as 

 such are not considered here inasmuch as they are seldom affected by inter- 

 mittent operation. No specific frequency limits apply but it is sometimes 

 difficult at very high frequencies to achieve desirable values of the constants. 

 At very low frequencies oscillators employing automatic output control are 

 relatively unsuitable because their performance tends to be unduly sluggish. 



The term linear oscillator is used to indicate an oscillator in which the 

 range of operation is controlled within such limits that the harmonic content 

 of the output is inappreciable. 



The general equation describing a simple amplitude-modulated wave is 



V = Vo{\ -\- m sin 2vjt) sin l-wFt 



This may be taken as defining the modulation factor m, a complex number 

 which is limited to magnitudes between zero and one. 



II. General Theory of Oscillation 



It is found that three separate functions are necessary and sufficient for 

 the operation of an oscillator of the feedback type.^ These are indicated 

 in the block diagram of Fig. 1. 



The amplifier must be provided to overcome the losses of the rest of the 

 system. The power output, if any, depends upon the fact that the output 

 of an amplifier is greater than the input. 



Selectivity must be provided to insure that the output has a definite 

 frequency. Ordinarily a tuned circuit of relatively high Q is used although 

 some excellent oscillators employ resistance-capacitance networks. The 

 term filter is employed as being sufficiently general to include these extremes. 



A limiter of some form is necessary to establish the level at which sustained 

 oscillations occur. In many circuits the functions of amplifier and limiter 

 are performed simultaneously in the vacuum tube. In an important class 

 of oscillators the limiter is a thermal device such as a tungsten lamp. In the 

 Meacham circuit the functions of limiter and filter are combined in a bridge 

 employing a tuned circuit and a tungsten lamp. 



To simphfy the analysis it is convenient to assume that the amplifier of 

 Fig. 1 is completely linear and operates with equal gain at all frequencies 



^ This topic is discussed more fully in "Hyper and Ultra-High Frecjuency Engineering," 

 R. I. Sarbacher, and W. A. Edson, John Wiley & Sons, Inc., 1943. 



