Saturday, July 12, 2008

Telegraphist's Equations

  • at Google Book Search
  • Page 82:
    • As an historical example, we can analyze the first transatlantic telegraph cable, laid in 1865. The cable was 3,600 km long and weighed 5,000 tons. The insulator was a vegetable gum called gutta-percha . For this cable L = 460 nH/m, C = 75 pF/m, and R = 7 mQ/m. At a frequency of 2.4 kHz, wL = R, and so the high-resistance assumption is well satisfied for frequencies below 100 Hz. At 12 Hz, we can write a and v as
      • a = v/wRC/2 = 4.4 x 10...
      • v = ...
    • The loss for the entire line is al = 140 dB and the delay is l/v = 210 ms. For comparison, at 3 Hz, the loss in dB and the delay change by a factor of 2, to 70 dB and 420 ms. Thus the 12-Hz component attenuates 70 dB more than the 3-Hz component. In addition, the 12-Hz component arrives 210 ms ahead of the 3-Hz component. In order to improve these characteristics, the signalling speed had to be drastically reduced, to about one word per minute, which was twenty times slower ...

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