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THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



is completely determined by its performance at single frequencies, and this 

 permits the solution to be developed in terms of simple sinusoidal functions 

 of time. 



New symbols are needed for the small signal theory, and to avoid an undue 

 number of subscripts they are introduced in the following manner : In the 

 preceding general equations the dependent variables were indicated by 

 capital letters; in the following small signal theory, the same capital letters 

 are used to indicate the d-c. components, and the corresponding small 

 letters then indicate the complex ampHtudes of the a-c. components. This 

 gives the following list of symbols : 



Amplitude of AC 

 mponent 



Total current density 



Conduction current density 



Voltage 



Electric intensity 



Electron velocity 



This symbolism has the disadvantage of using e to indicate both electric 

 intensity and the base of the natural logarithms, but the duplication causes 

 no serious confusion, for the meaning of the symbol is always evident from 

 the text. As examples of the new nomenclature, the conduction current 

 density is now Q + ^e^"*, and the electron velocity is Z7 + ue"^ . It should 

 be noted that the a-c. amplitude in each of these expressions is a complex 

 space-varying amplitude, which is sometimes called the space part of the a-c. 

 component. 



Before passing it is well to write the following useful relations, which 

 follow immediately from the fundamental equations (5) and (6) : 



9 = ^ + ^coee 



(25) 



e — 



ceo 



their substitution in (11) and (23) give 



S ^ ^E^Ii-^S e^"* 



5 = e£ - ^^ e^"' 



(26) 



With this introduction to the change in symbolism, we now express the 

 general solution (22) and (24) in terms of the new symbols, and neglect all 



