Maximum Subscriber Loop Formula

The cable sizes of 19, 22, 24 and 26 gauge are the most commonly used cable for different dc resistance of various subscribers. The higher the gauge number the smaller the wire diameter. With 26-gauge wire a loop distance of only about 6.4372 Km (4 miles) is possible. With 19-gauge wire the loop distance might be extended to as much as about 28.96 Km (18 miles).

Example 3.4. For a 24 gauge loop and a 1250 ohm loop resistance find the loop length. Sol. From the table 3.3, for 24 gauge cable, the Rdc is 84.22 Q/km. Hence, the length of the cable

Maximum permissible loop length. The method of determing the maximum subscriber loop length using the attenuation or loop loss is called the basic transmission design, the maximum loop length is calculated from the formula

Attenuation limit

loss per km

Example 3.5. For 24 gauge loop and a 6 dB loss, find the maximum loop length.

Sol. For 24 gauge cable, the loss per km is 1.05 dB/km

3.5.5. Inductive Loading

Attenuation limits arise from the ac response of the loop and refers to loop loss in decibels. The amplifiers/loop extenders or inductive loading coil methods are used to admit the loop length to increase beyond the limit. Inductive loading is the process of inserting series inductances (loading coils) into the loop at fixed intervals. These will reduce the transmission loss on subscriber loops. This methods enables the designer to increase the loop length without using higher diameter copper wire.

The attenuation loss in twisted pair cable is because of the capacitance between wire pair. The wires of the local loop have a capacitance of approximately 0.1335 MicroFarad per km regardless of the cable gauge. The longer the cable pairs the higher the capacitance. The capacitance can be reduced by separation of the conductors but practically difficult. Heavyside in 1887 proved that the distortion can be reduced by satisfying the equation RC = LG, where R is the resistance, C is the shunt capacitance, G is the conductance and L is the inductance. All are measured per unit length.

By inserting loading coils with proper inductance and at appropriate distances, the distortion can be minimized and high-speed transmission can be achieved Table 3.5 gives the standard letters and its associated spacing. B, D and H are the most, commonly and spacing. To offset the mutual capacitance (0.1335 MicroFarad), load coils having 88 mH inductances are placed at 1.8288 km (6000 ft) intervals on the cable. The frist load coil placed at 0.9144 km (3000 ft) from the local exchange. Then for every 1.8288 km, one loading coil is placed till the subscriber premises. The loading is not necessary, for the loop shorter than 4.83 km. For local loop length, above 18000 ft (5.48 km), loading coils are necessary. Fig. 3.19 (b) shows typical load coil spacing.

Table 3.5. Standard letters and spacing of loading

Letter code

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