Figure 5.4 is a simplified model of a subscriber loop. Distance D in the figure is the length of the loop. As we mentioned above, D must be limited in length owing to (1) attenuation of the voice signal on the loop and (2) dc resistance of the loop for signaling.

The maximum loop loss is taken from the national transmission plan.5 In North America, it is 8 dB measured at 1000 Hz. We will use the maximum resistance value calculated above, namely 1700 Q (wire only).

Figure 5.4 Subscriber loop model.

5National transmission plan for North America, see Bellcore, BOC Notes on the LEC Networks, latest edition (Ref. 5).

Figure 5.4 Subscriber loop model.

5National transmission plan for North America, see Bellcore, BOC Notes on the LEC Networks, latest edition (Ref. 5).

5.4.3.1 Calculating the Resistance Limit. To calculate the dc loop resistance for copper conductors, the following formula is applicable:

0.1095

where Rdc = loop resistance (fi/mi) and d = diameter of the conductor (inches).

If we want a 17-mile loop, allowing 100 fi per mile of loop (for the 1700-fi limit), what diameter of copper wire would we need? Apply Eq. (5.1).

100 = 0.1095/d2 d2 = 0.1095/100 = 0.001095 d = 0.0331 inches or 0.84 mm or about 19 gauge

By applying resistance values from Table 5.1, we can calculate the maximum loop length for 1700-fi maximum signaling resistance. As an example, for a 26-gauge loop,

This, then, is the signaling limit for 26-gauge (copper) subscriber loop. It is not the loss (attenuation) limit, or what some call the transmission limit.

Another guideline in the design of subscriber loops is the minimum loop current offhook for effective subset operation. For example, the North American 500-type subset requires at least 20 mA for efficient operation.

5.4.3.2 Calculating the Loss Limit. For our discussion here, the loss at 1000 Hz of a subscriber loop varies with diameter of the wire and the length of the loop. Table 5.2 gives values of loss (attenuation) per unit length for typical subscriber low-capacitance wire pair.

Ohms/1000 ft |
Ohms/Mile |
Ohms/km | |

AWG |
of Loop |
of Loop |
of Loop |

28 |
132 |
697 |
433 |

26 |
83.5 |
440 |
268 |

24 |
51.9 |
274 |
168.5 |

22 |
32.4 |
171 |
106 |

19 |
16.1 |
85 |
53 |

Table 5.2 |
Loss per Unit Length of Subscriber Wire Pairs | ||

Loss/1000 ft | |||

AWG |
(dB) |
dB/km |
dB/mi |

28 |
0.615 |
2.03 |
3.25 |

26 |
0.51 |
1.61 |
2.69 |

24 |
0.41 |
1.27 |
2.16 |

22 |
0.32 |
1.01 |
1.69 |

19 |
0.21 |
0.71 |
1.11 |

16 |
0.14 |
0.46 |
0.74 |

Work the following examples based on a maximum loss of 8 dB. Here we are to calculate the maximum loop length for that 8-dB loss. Use simple division with the values in column 2 of Table 5.2. The answers, of course, will be in kilofeet.

28 |
gauge: |
8/0.615 |
= 13.0 kft |

26 |
gauge: |
8/0.51 |
= 15.68 kft |

24 |
gauge: |
8/0.41 |
= 19.51 kft |

22 |
gauge: |
8/0.32 |
= 25.0 kft |

19 |
gauge: |
8/0.21 |
= 38.1 kft |

16 |
gauge: |
8/0.14 |
= 57.14 kft |

Copper is costly. Thus, many telecommunication companies employ gauges with diameters no greater than 22 gauge in the local trunk plant and 26 gauge in the subscriber loop plant.

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