630 BELL SYSTEM TECHNICAL JOURNAL 



tion. The total voltage impressed on the amplifier is the quantity 

 which determines whether or not it will overload, and the phases as well 

 as the amplitudes of the frequency components in the several channels 

 must be considered in determining this. It is most convenient for 

 analysis to work directly with instantaneous voltages of speech, the 

 frequency of occurrence of the magnitudes being expressed in the form 

 of a distribution function. 



This distribution function has been measured by Dr. H. K. Dunn, 

 using apparatus which measures 4 samples per second of the instantane- 

 ous voltage out of a commercial subset and typical loop. By operating 

 the apparatus until about 1000 successive samples have been measured, 

 usable distribution curves of instantaneous voltage are obtained; this 

 is readily checked by making repeated runs comprising the same 

 number of samples on speech recorded on high quality phonograph 

 records. It is, of course, known that commercial transmitters have 

 considerable asymmetry as regards positive and negative voltages 

 but the poling referred to the toll board is expected to be random. As 

 the measurements were considerably simplified by doing so, it ap- 

 peared desirable to average out this asymmetry by arranging a linear 

 rectifier ahead of the sampling apparatus to obtain equal samples of 

 positive and negative voltages. 



Such measurements have been made for a number of different 

 talkers, different commercial subsets, and different volumes, with the 

 speech input held at substantially constant volume in each test. 

 The various subsets now in commerical use all give essentially the 

 same distribution curve. The resulting distributions, if they are 

 considered as functions of the ratio of instantaneous to rms voltage, 

 are also nearly independent of the speech volume at the subset. 

 Specifically, the only important effect of volume is that which may be 

 ascribed to amplitude limiting in the transmitter; i.e., to the fact that 

 the transmitter itself has a limited load capacity. However, this 

 effect does not appear until the volume is 10 db or more above the mean 

 of the volume distribution curve, and is only of importance for talkers 

 at still higher volumes. For all lower volume talkers, the instantane- 

 ous voltage distribution may be considered as the same for all volumes 

 w^hen expressed as a ratio of instantaneous to rms voltage. The 

 cumulative distribution curve of the quantity EjU, where E is the 

 rectified instantaneous voltage and U the rms voltage, is shown by the 

 curve w = 1 of Fig. 2. 



Voltage Limiting 



While this curve of Fig. 2 is accurate for the bulk of the talkers, it 

 changes for the high volume talkers who overload the subset trans- 



