410 



BELL SYSTEM TECHNICAL JOURNAL 



Let us first differentiate (7.13) with respect to 5 and d 



-j dd - j db 



2b db = 



{-b+jd-\-jbr- 



(8.29) 



0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.0 



QC 

 Fig. 8.13 — h curve giving the rate of change of x\ with attenuation parameter d for 

 J = and for various values of the space-charge parameter QC. For small values of QC 

 the gain of the increasing wave is reduced by \ of the circuit loss; for large values of QC 

 the gain of the increasing wave is reduced by \ of the circuit loss. 



0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 



d 



Fig. 8.14 — A curve showing the variation of .vi with QC for QC = and for various 

 values of the attenuation parameter d. 



By using (7.13) we obtain 

 db = 



-j2b 



- 1 



dd 



(8.30) 



(6^ -h AQCy 



If we allow d to be small, we can use the values of b of Figs. 8.7-8.9 to \)\oi 

 the quantity 



Re(dbi/dd) = dxjdd (8.31) 



