668 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



111 (8), V represents the output voltage corresponding to an input signal 

 voltage e, and /x is a dimensionless parameter which determines the degree 

 of compression. 



Typical compression characteristics, corresponding to various choices 

 of the compression parameter, m, 'n\ (8a), are shown in Fig. 3. The log- 

 arithmic replot of Fig. 4 provides an expanded picture of small amplitude 

 behavior, as well as evidence of the probable realizabilit}^ of such char- 

 acteristics. 



Although restriction of attention to (8) may at first appear to impose 

 serious limitations on the generality of the analysis, this impression is not 

 confirmed b}^ more careful scrutin}^ of the problem. 



Perusal of Fig. 3 indicates that (8) generates a considerable variety of 

 curves which meet the general requirements already enunciated in con- 1 

 nection with Fig. 2. Thus, the constant factor, F/log (1 + m), has been 

 chosen to satisfy the condition 



[vUv = V (9) 



Evidence of the significance of the M-characteristics may be derived 



1.0 



> 



0.9 



0.8 



0.7 



0.6 



0.5 



0.4 



0.3 



0.2 



0.1 







0.1 0.2 0.3 0.4 0.5 0.6 



(e/v) 



.7 0.8 0.9 1.0 



Fig. 3 — Typical logarithmic compression characteristics determined by 

 equation (8a). The symmetrical negative portions, corresponding to equation 

 (8b), are not shown. 



