636 BELL SYSTEM TECHNICAL JOURNAL 



stood and cannot be calculated accurately. It is known, however, 

 that tube noise arises from a number of different causes, chief among 

 which are: (1) thermal agitation in the internal plate resistance of 

 the tube, (2) shot effect and flicker effect from space current in the 

 presence of space charge, (3) shot effect from electrons produced by 

 collision ionization and secondary emission, and (4) space charge 

 fluctuations due to positive ions. Each of these sources of noise will 

 be discussed in the following section : 



Origin of Noise in Thermionic Amplifier Tubes 



Thermal Agitation in the Internal Plate Resistance of the Tube ^ 

 Just as voltage fluctuations are produced by thermal agitation in 

 resistances comprising the input circuit, so the resistance component 

 of the impedance between plate and cathode is a source of thermal 

 noise. This impedance consists of the internal plate impedance of 

 the vacuum tube in parallel with the external load impedance. 

 Llewellyn ^ has shown that the resistive component of the internal 

 plate impedance produces thermal noise as if it were at the temperature 

 of the cathode. The following formula has been developed by him to 

 cover the case where the tube impedance and load impedance are 

 pure resistances: 



E? = Akl{r,r,)l{r, + r,y-]{T,r, + Tfr,) f \G,{f)\W (2) 



J F 



Here rp is the internal plate resistance of the tube, ro the external load 

 resistance in the plate circuit, G^if) the voltage amplification between 

 the load resistance ro and the measuring device, and To and T/ re- 

 spectively the temperatures of the external load resistance and cathode 

 expressed in degrees Kelvin. The relationship between Gi{f) and 

 G2(f) is given by 



Gi(/) = C?2(/)(/xro)/(ro + r,), (3) 



where /j, is the voltage amplification factor of the tube. By assuming 

 Giij), in equation (2), to be constant over the frequency range F and 

 substituting for it the value given by equation (3), it is found on 

 integrating that the thermal noise in the plate circuit of the tube 

 produces the same effect in the measuring device as a signal applied 



^ During the preparation of this paper a paper by E. B. MoulHn and H. D. ElHs 

 entitled "Spontaneous Background Noise in Amplifiers Due to Thermal Agitation 

 and Shot Effects" appeared in /. E. E. Jour., 74, 323 (1934). The authors there 

 contend that no the,rnial noise is produced in the plate impedance of a thermionic 

 vacuum tube and that shot noise is not altered by the presence of space charge. 

 With these contentions I cannot agree and I hope to state my definite reasons 

 therefor at a later date. 



^ F. B. Llewellyn, Proc. I. R. £., 18, 243 (1930). 



