Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 27

During the period 1840–1850, several persons conceived the idea of telegraph across the Atlantic Ocean. Finally, in the year 1850, the first under‐sea telegraphy, between Dover (Kent, England) and Calais (France), was made operational. However, no cable theory was available at that time to understand the electrical behavior of signal transmission over the undersea cable.

In 1854, Kelvin modeled the under‐sea cable as a coaxial cable with an inner conductor of wire surrounded by an insulating dielectric layer, followed by the saline sea‐water acting as the outer conductor [J.18, B.1]. The coaxial cable was modeled by him as a distributed RC circuit with the series resistance R per unit length (p.u.l.) and shunt capacitance C p.u.l. It was the time of the fluid model of electricity. Kelvin further conceived the flow of electricity similar to the flow of heat in a conductor. Fourier analysis of 1D heat flow was in existence since 1822. Following the analogy of heat equation of Fourier, Kelvin obtained the diffusion type equation for the transmitted voltage signal over the under‐sea coaxial cable:

(1.1.3)

This is the first Cable Theory; Kelvin called the above equation the equation of electric excitation in a submarine telegraph wire. Kelvin's model did not account for the inductance L p.u.l. and the conductance G p.u.l. of the cable. The cable inductance L is due to the magnetic effect of current, and G is due to the leakage current between the inner and outer conductors. However, cable theory was a great success. Following the method of Fourier, he solved the equation for both the voltage and current signals. At any distance x on the cable, a definite time‐interval was needed to get the maximum current of the received signal. The galvanometer was used to detect the received current. This time‐interval called the retardation time of the received current signal also depends on the square of the distance. Moreover, the telegraph signals constituted of several waves of different frequencies, and their propagation velocities were frequency‐dependent. It limited the speed of signal transmission for long‐distance telegraphy. The conclusions of Kelvin's analysis were ignored, and 1858 transatlantic cable worked only for three weeks. It failed due to the application of 2000 V potential pulse on the cable. The speed of transmission was just 0.1 words per minute. Finally, following Kelvin's advice and using a very sensitive mirror galvanometer invented by him, the transatlantic telegraph was successfully completed in 1865 with eight words per minute transmission speed [B.1–B.3].