Telegraphist's Equations

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• 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 ...
  

History, Theory, and Practice of the Electric Telegraph By George Bartlett Prescott

History, Theory, and Practice of the Electric Telegraph By George Bartlett Prescott:

On Monday March 12th 1860 there were transmitted over one wire from Boston to New York 204 private messages containing 7,456 words and 600 words of press news and from New York to Boston over the same wire 253 messages containing 8,957 words making a total of 17,013 words The time occupied in transmitting this large number of words was nine hours The length of the circuit operated is 260 miles and the weather was rainy during the day The despatches were all printed in plain Roman letters by the Combination instrument and accurately punctuated Messrs Grace and Edwards were the operators at the Boston and New York termini of the line