Telephones operate in the frequency range 200 to 3400 Hz. There is no reason why the cables connecting them to the exchange should have a greater frequency range than this. Yet they do as ADSL is commonplace.
The table below gives the characteristics of some standard BT cables, per kilometer. The numbers assume a 2 wires cable. So a single conductor of 0.32mm diameter wire has a resistance of 217Ω per km.
Characteristics of some standard BT cables, per kilometer
| Weight/mile (lb) | Cu or Al | Dia (mm) | Res (Ω) | Loss @ 800Hz (dB) | Loss @ 1600Hz (dB) |
| 2½ | Cu | 0.32 | 434 | 2.06 | 2.8 |
| 4 | Cu | 0.4 | 275 | 1.31 | 2.2 |
| 6½ | Cu | 0.5 | 168 | 1.18 | 1.79 |
| ? | Al | 0.5 | 287 | 1.9 | 2.7 |
| 10 | Cu | 0.63 | 109 | 0.91 | 1.38 |
| ? | Al | 0.8 | 112 | 1.2 | 1.7 |
| 20 | Cu | 0.9 | 55 | 0.62 | 1.04 |
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The simplest possible model of 1 km of "typical" local line cable could be modelled as below and would display a simple first-order frequency response.
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In order to make the model more representative of a real cable a the single 1 km section could be replaced by two or more shorter sections.
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The graph on the left shows simulated results as the number of sections is increased as far as 20 (with R and C values adjusted to give the correct totals.) The results for 10 and 20 sections are very similar, so it seems unnecessary to model the line as more than 10 sections.
The cable should be terminated in a complex impedance as shown below.
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Running the simulator with the line modelled as 1 section, and as 10 sections, shows that terminating the line with this impedance has introduced an extra loss of 3 dB between 2 kHz and 20 kHz.
The model shown above, a resistance/capacitance combination, takes no account of line inductance. Each wire has an inductance of around 3 mH per kilometre and the resonant frequency of 3 mH and 50 nF is only 13 kHz.
Using a multiple section model as shown below a more realistic simulation can be performed,
The simulation shows that including the wires' inductance in the model makes a huge difference. The response is now substantially flat to about 250 kHz.
Above that frequency it drops like a stone, and is 250 dB down by 500 kHz. Attenuation for telephone cables is typically 7dB at 100 kHz over 1km.
