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BELL SYSTE}f TECHNICAL JOURNAL 



We use this together with (2.22) 



t = 





(2.22) 



We obtain the overall equation 



1 



iVoU^e - r) 



"rri(£V/3'p) 

 L 2(ri - r) 



coCi_ 



(7.9) 



In terms of the gain parameter C, which was defined in Chapter II, 



we can rewrite (7.8) 



(i/3e - 



C' = (£'V/32p)(/o/8Fo) 





{Ti - r 



a:C,{E-/l3'P) 



(2.43) 



(7.10) 



We will be interested in cases in which Y and Fi differ from 13^ by a small 

 amount only. Accordingly, we will write 





(7.11) 

 (7.12) 



The propagation constant F describes propagation in the presence of 

 electrons. A positive real value of 8 means an increasing wave. A positive 

 imaginary part means a wave traveling faster than the electrons. 



The propagation constant Fi refers to propagation in the circuit in the 

 absence of electrons. A positive value of b means the electrons go faster 

 than the undisturbed wave. A positive value d means that the wave is an 

 attenuated wave which decreases as it travels. 



If we use (7.11) and (7.12) in connection with (7.10) we obtain 



[1 + C(2j8 - a')][l + C(b - >/)] 



8 = 



[-b + jd + j8 + Cijbd 



byi + dyi + 5V2)] 



_ 4/3. [(1 + C{2j8 - C8'')\C 

 a;Ci(£V^-^) 



(7.13) 



We will now assume that | 5 | is of the order of unity, that | b | and | d \ 

 range from zero to unity or a little larger, and that C <5C 1 . We will then neg- 

 lect the parentheses multiplied by C\ obtaining 



1 



{-h+jd+j8) 



4QC 



Q = 



a;Ci(£V^''^) 



(7.14) 

 (7.15) 



