Telegram for you: for good communications, leaky cables are best

In Wicklow town, an obelisk commemorates Robert Halpin, a master mariner born at the nearby Bridge Tavern. Halpin, one of the more important mariners of the 19th century, "helped to make the world a global village" by connecting continents with submarine telegraph cables.

Halpin left home aged 11 and had many nautical adventures before taking command of the leviathan SS Great Eastern, a brainchild of Brunel. Its mission was to lay a telegraph cable across the Atlantic Ocean, from Valentia Island to Newfoundland, some 2,600 miles. The consulting engineer was William Thomson, later Lord Kelvin, the Belfast-born scientist who oversaw the laying of the cables.

Telegraph speed on the first cable, completed in 1858, was very slow, and it failed within a week. A second cable was more robust and faster; it could carry messages at eight words a minute (about one Morse character per second). Thompson had analysed the transmission properties of cables and had argued that electrical resistance and leakage should be minimised for best results.

As signals travel along a telegraph cable, they lose energy and also suffer distortion. Different signal components travel at different speeds, causing corruption of the message. To ensure distortion-free transmission, components of different frequencies must travel at the same speed. Early cables were designed to reduce energy loss, with no effort to avoid distortion.

Thomson had used an equation of parabolic type, with solutions that diffuse and dampen out but that are not wave-like. However, he omitted a crucial factor: when a current flows through a wire, it generates a magnetic field, which acts back on the current, inhibiting the flow. This self-inductance has a major impact on the transmission characteristics of a telegraph cable.

Oliver Heaviside, a self-educated and eccentric English electrical engineer, derived a mathematical equation, the telegraph equation, which included inductance. This effect completely changes the nature of the solutions so that they have a wave-like character. Mathematicians call equations of this type hyperbolic equations.

Heaviside’s idea was simple: a signal that has been damped can easily be amplified, but one that is distorted is difficult if not impossible to recover. So the design should focus on removing distortion. He showed that, to achieve distortion-free transmission, some electrical leakage between the conductors of a cable is essential.

Heaviside found that two quantities, one involving resistance and one involving leakage, must have their arithmetic and geometric means equal. But this happens only if the quantities are themselves equal. This gave him a condition on the properties of the cable that are needed to avoid distortion of the signal.

The upshot of Heaviside’s mathematical analysis was that cable designers should not try to reduce leakage but, rather, should increase the inductance to achieve the balance required for distortion-free transmission.

Heaviside was a controversial character who came into regular conflict with the scientific establishment, and the engineers responsible for cable construction were not inclined to listen to him. They either did not understand or did not believe his theory.

As a result, it was several decades before Heaviside's brilliant ideas were implemented. But from the beginning of the 20th century, distortion-free telegraphy was widely implemented and became an industry standard. Transmission speeds could then exceed 100 words per minute.

[ thatsmaths.com ]