FLUCTUATION NOISE IN VACUUM TUBES 635 



Often, in the use of high-gain amplifiers, the impedance of the input 

 circuit is naturally high or may effectively be made high by the use of 

 a transformer. In this case the contribution of noise from the vacuum 

 tube is small compared with the noise arising from thermal agitation in 

 the input circuit. This is a desirable condition since it furnishes the 

 largest ratio of signal to noise for a given input power. Sometimes, 

 however, the input impedance is perforce so small that the tube noise 

 may be comparable with or greater than the thermal agitation noise. 

 Such conditions may arise, for example, in amplifiers where the frequency 

 dealt with is high or the frequency range is wide. It is, therefore, 

 desirable to know the noise level to be expected from different types 

 of tubes that may be used in the first stage of high-gain amplifiers as 

 well as to be able to calculate the thermal noise level of the input 

 circuit. 



The noise of thermal agitation ^ arises from the fact that the electric 

 charge in a metallic conductor shares the thermal agitation of the 

 molecules of the substance so that minute variations of potential 

 difference are produced between the terminals of the conductor. 

 The mean square potential fluctuation is proportional to the absolute 

 temperature and to the resistive component of the impedance of the 

 conductor, but is independent of the material. The thermal noise 

 power is distributed equally over all frequencies although the apparent 

 magnitude depends on the electrical characteristics of the measuring 

 system as well as on those of the conductor itself. From purely 

 theoretical considerations the following equation has been derived ^ 

 to give the thermal noise voltage at the output of an amplifier due to 

 the thermal agitation of electric charge in an impedance at the input: 



x 



R{I)\G,{j)\'df. (1) 



Et^ is here the mean square thermal noise voltage across the measuring 

 device, k is Boltzmann's constant (1.37 X 10~^^ watt second per 

 degree), T the temperature of the impedance expressed in degrees 

 Kelvin, R{j) the resistive component of the impedance at the fre- 

 quency/, Gy{f) the voltage amplification between the input impedance 

 and the measuring device at the frequency /, and F the frequency 

 band within which the amplification is appreciable. 



While the thermal noise in the circuit is accurately predictable, 

 the noise originating within the vacuum tube is not completely under- 



1 J. B. Johnson, Phys. Rev., 32, 97 (1928). 



2 H. Nyquist, Phys. Rev., 32, 110 (1928). 



