FLUCTUATION NOISE IN VACUUM TUBES 641 



the shot effect in any of these currents. The general shot effect 

 equations ^ show that the magnitude of shot noise from these grid 

 currents is 



F? ^ 2ei,r,' f df/{l + 47^Vr//2)^ 

 where ig is the sum of the grid currents regardless of sign. 



(9) 



Noise Produced by Secondary Effects 



In this classification are grouped several sources of disturbance 

 whose individual effects are very difficult to calculate and measure 

 under the operating conditions of the vacuum tube. For this reason 

 the following discussion will include only a general consideration of 

 the more obvious contributing causes. 



Although the cathode is the principal source of electrons which 

 reach the plate, in actual practice electrons are produced by ionization 

 of the gas molecules within the tube or by secondary emission resulting 

 from bombardment of the tube elements. Electrons produced in 

 this manner are drawn to the plate and generate noise which is not 

 much affected by the space charge. Assuming a reasonable magnitude 

 for the current produced in this manner it can be shown by the shot 

 equations that noise from this source is usually negligible. In cases 

 where the gas pressure within a tube is above normal, or in screen- 

 grid and multi-grid tubes having high plate resistances and consider- 

 able secondary emission, the shot noise from secondary and ionization 

 electrons may be of the same order of magnitude as thermal noise in 

 the plate circuit. 



Positive ions formed from ionized gas molecules or emitted from 

 the tube elements are much more effective in producing noise since, 

 instead of being drawn oft' to the plate, they are attracted into the 

 space charge region where small disturbances in equilibrium produce 

 large momentary fluctuations in space current. Due to their large 

 mass the motions of the ions are relatively slow, so that they are very 

 effective in this respect. This type of noise is quite disturbing in 

 amplifying tubes for it tends to become a maximum at complete 

 temperature saturation. This is illustrated very clearly in the noise 

 measurements on the tungsten filament shown in Fig. 1. Here positive 

 ions from the filament begin to show their effect as space charge sets 

 in, the number of ions and the amount of noise increasing as tempera- 

 ture saturation is approached. As heard in the loud speaker, this 

 noise consists of sharp crackling sounds which can easily be dis- 

 '•* E.g. Ref. 4 or 5. 



