FLUCTUATION NOISE IN VACUUM TUBES 643 



and of the vacuum tube. In such a combination R{j) is related to 

 the pure resistance R and the total capacitance c according to equation 

 (7). In all the measurements described here the factor Air'^c^R'^P is so 

 small in comparison with unity that it may be neglected without 

 appreciable error. Under these conditions equation (1) reduces to 



AkTR f \G,(f)\'df, (10) 



where R is the direct current value of the resistance between control 

 grid and cathode of the tube under test. 



The voltage fluctuations arising from conditions within the tube 

 produce a mean square voltage output En"^ according to the equation 



E?^ f\Vif)\'\G,(f)\Hf, (11) 



where | V{f) | ^ is the tube noise at the frequency / for unit frequency 

 band width, expressed in volts squared and referred to the input 

 circuit. Letting Vf"^ be the effective value of | V{f)\^ over the band 

 width of the amplifier we obtain 



U If 



Gr{f)M. (12) 



Since the integrals in equations (10) and (12) are identical it is found 

 on dividing one equation by the other and solving for Ff^ that : 



TV = 4:kTR{E?/E?). (13) 



Equation (13) enables one to calculate the magnitude of tube noise 

 in the frequency range F, per unit cycle band width, in terms of the 

 thermal noise generated in a resistance R placed in the input circuit. ^^ 

 Since this equation contains no integral the measurements are sim- 

 plified in that neither standard signal generator nor calibrated amplifier 

 is required. 



Apparatus 



The experimental arrangement used in the measurements to be 

 reported here is given in schematic form in Fig. 2. The system in- 

 cludes the tube under test, a high gain amplifier, appropriate filters, 

 an attenuator, and an output measuring device. 



" It is assumed that tube noise does not vary with frecjuency, or that the hand 

 width of the amplifier is so narrow that no appreciable error is introduced in applying 

 the result. 



