enuation increases as the square root of the frequency. tion coefficient. The imaginary part B is called the phase coefficient. The relationship between the attenuation and phase coefficients 15.2.2 Loaded lines and the primary coefficients is given by Equation 15.4. A special case arises if LG = RC. Substituting this condition in tanh a+jB)=[(R+jwl)(G+ jwc) = + (15.4) Equation 15.5, then the attenuation coefficient a = ( RG ) 112 which at voice frequencies is independent of frequency. In a real cable, RC By expanding real and imaginary parts, Equations 15.5 and 15.6 will be larger than LG and increasing G would increase the attenu- can be obtained. ation. However, L can be increased by inserting lumped inductance in each leg of a pair. Loading a line in this way was an important (15.5) technique for providing long distance audio circuits. However, the lumped inductance forms a low pass filter with cable capacity which limits the line bandwidth as illustrated in Figure 15.1. (15.6) In order to apply PCM systems to such cables the loading coils have to be removed. Hence the term 'deloaded audio'. -1/2(RG-w2LC))" 15.2.3 Performance of balanced pair cables At low frequencies, wL <<R and wC<<G giving Equation 15.7. Table 15.3 gives typical performance characteristics of 0.9mm star quad cable at audio frequencies. In this table 44mH/1800m indi- a=(RG)) (15.7) cates 44mH loading coils placed at 1800m. The line would only be operated at about 75% of the cut-off frequency. It will be seen that At audio frequencies wL <<R but wC>>G giving Equation loading can reduce attenuation to one third of the unloaded value, 15.8. but at the expense of restricted bandwidth. Table 15.4 gives typical data for unit twin cable and shows how a=(1/2wcr) (15.8) conductor size influences attenuation and impedance. At very high frequencies wL >> R and wC>>G giving Equa- tion 15.9. Table 15.3 Performance of 0.9mm star quad cable Parameter Non-loaded 44mH/1800m (15.9) 88mH/1800m Impedance 1130Q @ 1kH The value of Z is given by Equation 15.10. A