684 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



weakest signals, regardless of the shape of the characteristic in the non- 

 linear region. Equation (8) implies 



{vie) 



e^O 



(AVAe)e^o = M/log (1 + m) 



so that for each ^'alue of ju, the constant companding improvement for 

 the weakest signals is 



20 logio [M/log (1 + m)] db 



which is plotted in Fig. 9. Fig. 8 supplements Fig. 9 in revealing the ac- 

 tual volumes required for the realization of this weak signal saturation, 

 as well as the detailed behavior for stronger signals. 



D. Companding Improvement for en 7^ 



Since we will usually regard a nonzero \'alue of Cq as an undesirable 



I 



30 



28 



26 



SIGNAL POWER IN DECIBELS BELOW FULL LOAD SINUSOID 

 5 10 15 20 25 30 35 40 45 50 



24 



22 



20 



18 



2 16 



> 



O 



Q. 



2 



14 



12 



(J) 



z 



Q 



Z 



o 



10 



6 8 10 



20 40 60 



C 



100 



200 



400 600 1000 



Fig. 11 — The effect of a "dc component" on companding improvement for 

 M = 200. For further detail.s, see the caption of Fig. 10. 



