428 BELL SYSTEM TECHNICAL JOURNAL 



and the component of increasing wave excited by this voltage, V\t , will be, 

 from (9.4), 



Vlt = kTBKt I (1 - h/b,){\ - 8,/8i} I -2 (10.5) 



The noise figure of an amplifier is defined as the ratio of the total noise 

 output power to the noise output power attributable to thermal noise at the 

 input alone. We will regard the mean-square value of the initial voltage Vi 

 of the increasing wave as a measure of noise output. This will be substantially 

 true if the signal becomes large prior to the introduction of further noise. 

 For example, it will be substantially true in a tube with a severed helix if 

 the helix is cut at a point where the increasing wave has grown large com- 

 pared with the original fluctuations in the electron stream which set it up. 



Under these circumstances, the noise figure F will be given by 



F = \^ {e/kT)(8Vlc'/IoKt) | 6,8, \^ (10.3) 



Now we have from Chapter II that 



C' = loKc/^Vo 

 whence 



F = 1 + 2(eVo/kT)C I 5253 |- (10.4) 



The standard reference temperature is 290°K. Let us assume b = d ^ 

 QC = 0. For this case we have found | So | = | Ss | = 1. Thus, for these as- 

 sumptions we find 



F = 1 + 807oC (10.5) 



A typical value of Vo is 1,600 volts; a typical value of C is .025. For these 

 values 



F = 3,201 



In db this is a noise of 35 db. 



This is not far from the noise figure of traveling-wave tubes when the 

 cathode temperature is lowered so as to give temperature-limited emission. 

 The noise figure of traveling-wave tubes in which the cathode is at normal op- 

 erating temperature and is active, so that emission is limited by space-charge, 

 can be considerably lower. In endeavoring to calculate the noise figure for 

 space-charge-limited electron flow from the cathode we must proceed in a 

 somewhat different manner. 



