Foundations of Amateur Radio

If you walk into your radio shack and switch on a light, the result is instantaneous, one moment it's dark, the next it's not. What if I told you that as immediate as it appears, there is actually a small delay between you closing the circuit and the light coming on. Likely the distance between your switch and your light is less than say 10 meters, so the delay is likely to be less than 33 nanoseconds, not something you'd notice unless you're out to measure it.

What if your light switch is 3,200 km away? That's the length of the first transatlantic telegraph cable in 1858.

Let's start with the notion that between the action of closing a switch, or applying a voltage at one end of the cable and it being seen at the other end takes time. If we ignore the wire for a moment, pretending that both ends are separated by vacuum, then the delay between the two ends is just over 10 milliseconds because that's how long it takes travelling at the speed of light. One of the effects of using a cable is that it slows things down. In case you're curious, the so-called Velocity Factor describes by how much. A common Velocity Factor of 66 would slow this down by 66%.

This means that there is a time when there is voltage at one end and no voltage at the other.

There are a few other significant and frequency dependent things going on, we'll get to them, but before we go any further, it's important to consider a couple of related issues.

Ohm's Law, which describes the relationship between voltage, current and resistance in an electrical circuit was first introduced in 1827 by Georg Ohm in his book: "The Galvanic Chain, Mathematically Worked Out". Initially, his work was not well received and his rival, Professor of Physics Georg Friedrich Pohl went so far as to describe it as "an unmistakable failure", convincing the German Minister for Education that "a physicist who professed such heresies was unworthy to teach science."

Although today Ohm's Law is part and parcel of being an amateur, it wasn't until 1841 that the Royal Society in London recognised the significance of his discovery, awarding the Society's oldest and most prestigious award, the Copley Medal, in recognition for "researches into the laws of electric currents".

I'll point out that Ohm only received recognition because his work was changing the way people were starting to build electrical engines and word of mouth eventually pressured the Royal Society into the formal recognition he deserved.

I also mentioned the speed of light in relation to the delay between applying a voltage and it being seen at the other end, but it wasn't until 1862 when James Clerk Maxwell published a series of papers called "On Physical Lines of Force" that light speed was actually derived when he combined electricity and magnetism and proved that light was an electromagnetic wave, and that there were other "invisible" waves, which Heinrich Rudolph Hertz discovered as radio waves in 1888.

How we understand transmission lines today went through a similar discovery process. Your radio is typically connected to an antenna using a length of coaxial cable, which is a description for the shape the cable has, but the nature of the cable, what it does, is what's known as a transmission line.

If you looked at the submarine telegraph cable of 1858, you'd recognise it as coaxial cable, but at the time there wasn't much knowledge about conductance, capacitance, resistance and inductance, let alone frequency dependencies. James Clerk Maxwell's equations weren't fully formed until 1865, seven years after the first transatlantic telegraph cable was commissioned and the telegraph equations didn't exist until 1876, 18 years after the first telegram between the UK and the USA.

In 1854 physicist William Thomson, was asked for his opinion on some experiments by Michael Faraday who had demonstrated that the construction of the transatlantic telegraph cable would limit the rate or bandwidth at which messages could be sent. Today we know William Thomson as the First Lord Kelvin, yes, the one we named the temperature scale after. Mr. Thomson was a prolific scientist from a very young age.

Over a month, using the analogy with the heat transfer theory of Joseph Fourier, Thomson proposed "The Law of Squares", an initial explanation for why signals sent across undersea cables appeared to be smeared across time, also known as dispersion of the signal, to such an extent that dits and dahs started to overlap, requiring the operator to slow down in order for their message to be readable at the other end and as a result, message speed for the first cable was measured in minutes per word, rather than words per minute.

Today we know this phenomenon as intersymbol interference. 

It wasn't until 1876 that Oliver Heaviside discovered how to counter this phenomenon using loading coils based on his description of what we now call the Heaviside condition where you can, at least mathematically, create a telegraph cable without dispersion. It was Heaviside's transmission line model that first demonstrated frequency dependencies and this model can be applied to anything from low frequency power lines, audio frequency telephone lines, and radio frequency transmission lines.

Thomson worked out that, against the general consensus of the day, doubling the line would actually quadruple the delay needed. It turns out that the length of the line was so significant that the second cable laid in 1865, 560 km shorter, outperformed the original cable by almost ten times, even though it was almost identical in construction, providing physical proof of Thomson's work.

It has been said that the 1858 transatlantic telegraph cable was the scientific equivalent of landing man on the Moon. I'm not sure if that adequately explains just how far into the unknown we jumped. Perhaps if we blindfolded Neil Armstrong whilst he was landing the Eagle...

I'm Onno VK6FLAB