SHOT NOISE IN DIODES 601 



Unfortunately (32) cannot be integrated because the specific value 

 of the instantaneous deviation in the rate of electron emission is 

 unknown. Moreover, as shown by Fry ^^ there exists no frequency 

 spectrum for this deviation. The reason is because there is no way 

 of foretelling at a particular instant just when the next electron is 

 going to be emitted from a thermionic cathode. It does not follow, 

 however, that Fourier methods are powerless, as the following argu- 

 ment will show. Imagine that the emission in a thermionic system 

 has been going on for a long time, and place a recorder in the system 

 which makes an oscillograph record of the voltage produced across 

 the tube by the fluctuating current. Let the record be made over a 

 long period of time. Then, it is a perfectly possible thing to analyze 

 the record so obtained into a Fourier spectrum. The result will give 

 no information that the Fourier spectrum which would be obtained 

 on the oscillograph during an ensuing time period of equal length 

 would be the same as the one which has been secured during the past. 

 However, when the mean square value of the Fourier spectrum for 

 the recorded interval is computed, it is found that the mean square 

 value of any two records so obtained is the same when they are both 

 produced by random emission. Moreover, the mean square value 

 within a specified frequency interval is also the same in the two 

 records. These facts result from the random character of the events 

 producing the records, as may be seen even more clearly by examina- 

 tion of the mathematical steps in the following equations, particularly 

 as given in the progression from (37) to (38). It follows, then, that 

 one is justified in concluding that the mean square response of an 

 electrical system to a random excitation can be calculated by the 

 Fourier series method, and that the result so obtained applies equally 

 well either to systems which have been measured in the past, or to 

 those which will be measured in the future, provided only that they 

 both are similar in their configuration and external operating con- 

 ditions. 



To obtain the Fourier expression for the emission deviation, it will 

 be assumed that this function repeats itself after a very long period 

 of time. To find this Fourier Series for the instantaneous deviation 

 from the average rate of emission of electrons with x-directed velocities 

 between Uc and iic + duc, the very long period of time, L, is divided 

 into P equal intervals of length, r, where t is assumed to be mathe- 

 matically small. The exact number of electrons emitted during any 

 of these intervals of time with velocities between Uc and Uc + duc per 

 unit area of the cathode is denoted by n„i{uc)T. The average rate of 



