88 BELL SYSTEM TECHNICAL JOURNAL 



Hence the signal-to-noise ratio is 



iwTR.y ('^) 



r„2 WRr \ R, + 



In general, the internal resistance Ri of the signal generator is fixed, 

 so that i?2 is the only available variable. In the usual case of matched 

 impedances where Ri and Ri are equal, the signal-to-noise ratio is 

 3 db poorer than in the ideal case where R^ is made very large com- 

 pared with 7^1. This is one of the few examples where a mismatch of 

 impedances is advantageous. The use of an ideal step-up transformer 

 between R\ and R2 in Fig. 1 will be of no avail, so far as the thermal 

 noise is concerned, because its effect in equation 6 will be only to replace 

 Ri by Rz/N^ where N is the turns ratio of the transformer. 



In some systems the impedance at the input of the amplifier is un- 

 avoidably small. It may be so small that the voltage of the thermal 

 agitation of the input circuit, even when amplified by the first tube, is 

 lower than the noise voltage originating in the output circuit of that 

 tube. Ideally, the noise in the plate circuit also should be caused by 

 thermal agitation only, and the equations for it have been derived.^' ^° 

 In practice, however, the noise in the plate circuit is found to be 

 considerably greater, for reasons that will be discussed presently. 



Shot Effect and Flicker Effect Without Space Charge 



Early in the study of noise arising in vacuum tubes it was shown '• " 

 that under certain conditions a noise is produced that depends on the 

 fact that the electric current is a flow of discrete particles, the electrons, 

 which are emitted from the cathode in a random manner. The random 

 electron emission produces a statistical fluctuation in the current that 

 flows through the tube and coupling impedance. This fluctuation, 

 called the shot effect (German Schroteffekt, in analogy with the random 

 scattering of shot from a shot gun), appears as noise in the output of 

 the amplifier. When the current in the tube is limited by the rate of 

 emission of electrons rather than by the space charge, so that the 

 resistance of the tube is nearly infinite, then the shot effect produces 

 a mean-square voltage across the output impedance of the amplifier 

 given by '-• ^ 



VJ = lei r Z'GhiJ, (7) 



in which 



€ represents the charge on the electron and is equal to 1.59 X lO"''-* 

 coulomb, 



