Editing Loading coil (section)

===Oliver Heaviside===
[[File:Heaviside cropped.png|thumb|Oliver Heaviside]]
The origin of the loading coil can be found in the work of [[Oliver Heaviside]] on the theory of [[transmission line]]s. Heaviside (1881) represented the line as a network of infinitesimally small circuit elements. By applying his [[operational calculus]] to the analysis of this network he discovered (1887) what has become known as the [[Heaviside condition]].<ref>Heaviside, O, "Electromagnetic Induction and its propagation", ''The Electrician'', 3 June 1887.</ref><ref>Heaviside, O, ''Electrical Papers'', vol. 1, pp. 139-140, Boston, 1925.</ref> This is the condition that must be fulfilled in order for a transmission line to be free from [[distortion]]. The Heaviside condition is that the series [[electrical impedance|impedance]], Z, must be proportional to the shunt [[admittance]], Y, at all frequencies. In terms of the [[primary line coefficients]] the condition is:

:<math>\frac{R}{G}=\frac{L}{C}</math>

where:

:<math>R</math> is the series resistance of the line per unit length
:<math>L</math> is the series self-inductance of the line per unit length
:<math>G</math> is the shunt leakage [[Electrical resistance and conductance|conductance]] of the line insulator per unit length
:<math>C</math> is the shunt capacitance between the line conductors per unit length

Heaviside was aware that this condition was not met in the practical telegraph cables in use in his day. In general, a real cable would have,

:<math>\frac{R}{G} \gg \frac{L}{C}</math>

This is mainly due to the low value of leakage through the cable insulator, which is even more pronounced in modern cables which have better insulators than in Heaviside's day. In order to meet the condition, the choices are therefore to try to increase G or L or to decrease R or C. Decreasing R requires larger conductors. Copper was already in use in telegraph cables and this is the very best conductor available short of using silver. Decreasing R means using more copper and a more expensive cable. Decreasing C would also mean a larger cable (although not necessarily more copper). Increasing G is highly undesirable; while it would reduce distortion, it would at the same time increase the signal loss. Heaviside considered, but rejected, this possibility which left him with the strategy of increasing L as the way to reduce distortion.<ref>Brittain, pp. 39-40</ref>

Heaviside immediately (1887) proposed several methods of increasing the inductance, including spacing the conductors further apart and loading the insulator with iron dust. Finally, Heaviside made the proposal (1893) to use discrete inductors at intervals along the line.<ref>''The Electrician'', 1887 and reproduced (according to Brittain) in Heaviside, O, ''Electromagnetic Theory'', p. 112</ref> However, he never succeeded in persuading the British [[General Post Office|GPO]] to take up the idea. Brittain attributes this to Heaviside's failure to provide engineering details on the size and spacing of the coils for particular cable parameters. Heaviside's eccentric character and setting himself apart from the establishment may also have played a part in their ignoring of him.<ref>Brittain, p. 40</ref>