LIMITS TO AMPLIFICATION 89 



i represents space current in amperes, 



Z represents the magnitude in ohms of the coupUng impedance, 



G represents the voltage gain of the amph'fier from Z to the output, 



/ represents frequency in cycles per second, 



For an amplifier having a flat frequency response curve over frequency 



range F the expression becomes, for the effective shot noise across the 



impedance Z 



F/ = 31.8 X Ur^HZ^F. (8) 



The expression holds quite accurately for tubes in which the cathode 

 is made of either clean or thoriated tungsten and for high-vacuum 

 photo-electric tubes, and it has been used in determining the charge 

 on the electron." 



When an oxide coated cathode is used, fluctuations of a larger 

 magnitude ^^ are superimposed on the true shot effect. These fluctua- 

 tions are inappreciable above about 10 k.c, but increase rapidly in 

 magnitude toward the lower frequencies. They also increase with the 

 current at a faster rate than the shot effect fluctuations. This dis- 

 turbance has been ascribed to a state of flux and change in the 

 activating material on the surface of the cathode, ^^' ^^ and the phe- 

 nomenon has been called the " flicker effect " (from the analogy of a 

 flickering candle). 



There are two practical circuits in which the pure shot effect may 

 set the ultimate noise level. One of these is the circuit in which the 

 grid of an amplifying tube is left " floating " at its equilibrium potential 

 as usually is done in the first stage of amplifiers used for ion counters 

 and other instruments for measuring very small charges.^*' ^^ The 

 grid then emits a few electrons and receives positive ions and electrons 

 from the surrounding space. These currents are very small, but are 

 not subject to space charge limitation so far as the grid is concerned. 

 Because the grid impedance is very high, the shot voltage developed 

 by the small grid current may exceed the thermal voltage of the grid 

 impedance. The second circuit is that in which a photo-electric cell 

 works into the amplifier.^"- -''■ -^ Vacuum cells generate shot noise of 

 very nearly the theoretical value given by equation (7), while gas 

 filled cells give even greater noise. 



The total noise generated in the output of the vacuum photo- 

 electric cell is the sum of the shot noise and thermal noise across the 

 coupling resistance R, as given by equations (8) and (2). The mean 

 square of the signal voltage, however, is {MRf/2 where Ai is the 

 amplitude of the current variation. The ratio of signal to noise is 

 then 



