544 BELL SYSTEM TECHNICAL JOURNAL 



tant, although (3) may be appreciable. An analysis of the induction of 

 noise in the resonator is surprisingly com])licated, for the electron stream 

 acts as a non-linear load impedance to the noise power giving rise to a com- 

 plicated variation of noise with frequency and with amplitude of oscillation. 

 On the basis of analysis and experience it is pcssible, however, to draw 

 several general conclusions concerning reflex oscillator noise. 



first, it is wise to decide just what shall be the measure of noise. The 

 noise is important only when the oscillator is used as a beating r scillator, 

 usually in connection with a crystal mixer. A power P is supplied to the 

 mixer at the beating oscillator frequency. Also, the oscillator supplies at 

 signal frequency, separated from the beating oscillator frequency by the 

 intermediate frequency, a noise power P„ proportional, over a small fre- 

 quency range, to the band-width B. An adequate measurement of the 

 noisiness of the oscillator is the ratio of P„ to the Johnson ncise po\^er, kTB. 

 The general facts which can be stated about this ratio and seme explanaticn 

 of them follow: 



(1) Electrons which cross the gap only once contribute to noise but not 

 to power. Likewise, if there is a large spread in drift angle amcng various 

 electron paths, some electrons may contribute to noise but not to power. 



(2) The greater the separation between signal frequency and beating 

 oscillator frequency (i.e., the greater the intermediate frequency) the less 

 the noise. 



(3) The greater the electronic tuning range, the greater the ncise for a 

 given separation between signal frequency and beating oscillator frequency. 

 This is natural; the electronic tuning range is a measure of the relative mag- 

 nitudes of the electronic admittance and the characteristic admittance of 

 the circuit. 



(4) The degree of loading affects the noise through affecting the bunching 

 parameter X. The noise seems to be least for light loading. 



(5) Aside from controlling the degree of loading, resonator losses do not 

 affect the noise; it does not matter whether the unused power is dissipated 

 inside or outside of the tube. 



(6) When the tube is tuned electronically, the noi?e usually increases at 

 frequencies both above and below the optimum power frequency, but the ■ 

 tube is noisier when electronically tuned to lower frequencies. At the opti- ^ 

 mum frequency, the phase of the pulse induced in the circuit when an elec- 

 tron returns across the gap lags the pulse induced on the first crossing by 

 270°. When the drift time is shortened so as to tune to a higher frequency, 

 the angle of lag is decreased and the two pulses tend to cancel; in tuning 

 electronically to lower frequencies the pulses become more nearly in phase. 



An approximate theoretical treatment leads to the conclusion that aside 

 from avoiding loss of electrons in reflection, or very wide spreads in transit 



