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BELL SYSTEM TECHNICAL JOURNAL 



straight line CEK represents an asymptote of the type just described, 

 with a slope of 18 db per octave. Since the asymptote may be assumed 

 to represent the practical upper limit of gain in the high-frequency 

 region, the effect of the parasitic elements can be obtained by replacing 

 the theoretical cutoff by the broken line characteristic ABDEK. In 

 an actual circuit the corner at E would, of course, be rounded off, but 

 this is of negligible quantitative importance. Since EF and EK diverge 

 by 8 db per octave the effect can be studied by adding curves of the 

 type shown by Fig. 5 to the original cutoff characteristic. 



220 



uj 160 



ca 140 



0.5 0.6 0.8 1.0 



20 30 40 50 



2 3 4 5 6 8 10 



X 

 fo 

 Fig. 13 — Phase characteristics corresponding to gain characteristics of Fig. 12. 



The phase shift in the ideal case is shown by Curve I of Fig. 13. 

 The addition of the phase corresponding to the extra slope of 8 db per 

 octave at high frequencies produces the total phase characteristic 

 shown by Curve V . At the point B where \ix&\= 1, the additional 

 phase shift amounts to 35 degrees. Since this is greater than the 

 original phase margin of 30 degrees the amplifier is unstable when 

 parasitic elements are considered. In the present instance stability 

 can be regained by increasing the coefficient k to 1-5/6, which leads to 

 the broken line characteristic AGKH in Fig. 12. This reduces the 

 nominal phase margin to 15 degrees, but the frequency interval be- 

 tween G and K is so much greater than that between B and E that the 

 added phase is reduced still more and is just less than 15° at the new 



