20.7.4.4 Determination ofunlinearity noise from a multi­channel load

The technique used (Bennett, 1940) is to show that, for the purpose of calculating unlinearity or intermodulation noise, a channel loaded with a single sinusoid can be considered equivalent to a channel loaded with gaussian (or speech ) noise by the application of a suitable factor k(x) to the noise contribution. A band of n speech channels thus becomes a band of n sinusoids and the problem is reduced to one of counting intermodulation products falling into the channel of interest for each product (A + B, 2A- B, etc.).

The total intermodulation noise in any particular channel is the summated power contribution from each of these products.

Bennett's formula, rearranged to give the weighted noise con­tribution W(x) within a specified channel is as in Equation 20.19.

The suffix (x) refers to the type of intermodulation under con­sideration i.e. H(A + B) etc. (Table 20.7) In Equation 20.9 PJx) is the power of the intermodulation product (x) in dBmO at the output of the system for OdBmO fundamentals; k(x) is the speech tone modulation factor (a factor in dB to convert the sinusoid P (x) to the equivalent intermodulation product power for bands of 4kHz gaussian noise); P is the power in a single average talker in dBmO (see Table 20.6); g is the standard deviation of the distribution of all talkers from loud to soft (see Table 20.6); e(x) and d(x) are factors to account for the relationship between the power in the talker (the fundamental signal) and the resulting intermodulation product (e(x) is a factor to modify the talker volume P_vo and d(x) to modify the standard deviation of talker volumes g); t is the transmission activity factor or the probability that a particular channel is active (see Table 20.6); u(x) is the number of channels involved in forming the particular intermodulation product and therefore t^u'^x' is the prob­ability that the particular intermodulation product from a particular set of channels is present; C is the psophometric weighting correc­tion factor for 4kHz and is 3.6dB. U(x) is the number of intermodulation products for a particular type (i.e. A + B, A + B, etc.) falling in a particular channel of interest.

The factor U(x) is derived from Bennett's formulae but for sim­plicity are usually shown in graphical form as in Figure 20.12.

These graphs are valid for systems of greater than 500 channels (Bell, 1971).

20.7.4.5 Approximate value for the weighted intermodulation noise contribution

For wide band systems there are three major intermodulation con­tributors A + B, A- B and A + B - C. Assuming the CC1TT accepted values for channel loading (see Table 20.6) a rule of thumb calcula­tion can be made for unlinearity contributions using Equations 20.20 to 20.22, where W (x) is the approximate noise power in a selected channel, P_m(x) is the power of the (x) product in dBmO for OdBmO fundamentals, U (x) is the factor obtained from Figure 20.13 for a channel at frequency f.