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Crib Sheet for RF Wave Propogation

The Properties of a Sine Wave.

On the left is a perfect sine wave and as you can see it consists of a series of perfect peaks and troughs extending above and below the centre line. The four horizontal red lines indicate how we measure wavelength.

Wavelength is measured normally in metres, and it is measured from any point on one wave to any point on the adjacent wave. It really does not matter which you point you pick.

On the left is the same wave but this time we are measuring the amplitude.

On the centre line the amplitude will be 0V and at the peak or trough the amplitude will be Vmax. It is measured in a straight line from the zero point to the peak (or trough). The amplitude is defined as the displacement from the zero line- up or down doesn't matter. Incidentally, although voltage will normally be measured, depending on the application it way well be something else.


Frequency is another kettle of fish. To determine that we need a time base. So let's take the sine wave and give it one, just as on the left. It's marked off in milliseconds (mS) and as you can see each complete cycle (up once and down once)  takes 1 of them. There's a thousand mS in 1 second and so in 1S it'll do this 1000 times. A cycle per second is known as 1 Hertz  (Hz for short) and so this wave has a frequency of 1000 Hz. Not fast enough for radio propogation, it'd have to get at least fifteen times faster.



So let's make those milliseconds microseconds. A microsecond is 1 millionth of a second and it's pretty fast. It'll do it 1,000,000 times a second now, giving us 1 MegaHertz  (MHz) and that's slap in the middle of the AM broadcasting band. Spiffing. Is there maths to relate this? Of course there is, there's always maths. Nothing can just ever be , can it? Here it comes:


C= f l      and  transposing   l = C/f  and f =  C/l


Where  C is the speed of light, f is the frequency, and l is the wavelength. Usually the speed of light is given as 300,000,000 metres per second, f is expressed in Hz and l in metres.(299,792,458 metres per second is the really accurate figure).





So now we know about the amplitude of a wave.  We know about wavelengths and frequencies. We even know about the speed of light. The trouble now is that a wave has two planes, the electric and the magnetic, set 90 degrees apart. The rise and fall of the magnetic field is proportional to the rise and fall of the electric field, and so at any point in a cycle, the conditions in the adjacent cycle at the same point will be the same. On the left is a model, with a vertical plane marked in red and a horizontal in black. Now, one of them will be electrical (e-plane or e-field) and the other magnetic (m-plane or m-field).

Initially then let us assume that the vertical (red) field is electric. The wave is then said to be in vertical polarity.

If the black field were electric, the wave would be in horizontal polarity.  Hence the rule:


The electric field determines the polarity of a wave.

The complicated-looking graphic on the left represents modes of propagation. This is a fancy way of saying "how the wave travels".

The radio station is at the North Pole, and it is of course Santa AM, which he uses to tell the world who's on the naughty list. He also uses it to brief all the Santa impersonators in department stores all round the world, and plays a rolling selection of Christmas tunes from Slade to Lt Kiejke. But not The Pogues because Shane McGowan has been on the naughty list for some considerable time now.

So, Santa has got the technical difficulty of broadcasting all over the World, now how he is going to do it?  Well, the green line terminating in Libya shows a Long Wave Transmission, which is a low frequency      ( up until about 300 kHz) and which follows the ground entirely. It's known as a ground or surface wave and it's capable of going long distances. What it crosses causes more or less attenuation as it goes along,

Modes of Propogation of RF Waves

ground is good, water is very good, sand is bad. Santa could easily reach Europe, Canada, Russia and Japan with a sufficiently powerful transmitter and with some repeaters he could hop on to the southern hemisphere too. He'd have to do it in AM though because at such low frequencies there wouldn't be much available bandwidth for FM. The yellow line to the left shows what happens if Santa goes for a MW system, up to about 3MHz.  These don't follow the ground as closely and sometimes are refracted back to Earth. he might get past the polar ice caps, perhaps even Scotland, but not a deal further and certainly children in Marseilles won't be able to tune in.

The red line on the right shows a skywave, up to about 30 MHz. This is an interesting topic. Make a cuppa now, because this is going to be long and convoluted. Are you sitting comfortably? Then I'll begin.

3 -30 MHz is the HF portion of the spectrum. It's the short wave too, although the top end of the medium wave behaves the same way. Frequencies below 10 MHz propagate most efficiently at night. Frequencies above 10 MHz propagate most efficiently by day. Why? Because they are either being absorbed or refracted by a region of the atmosphere known as the ionosphere.

Those of you like me who proved to be complete duffers at school geography will now be saying "what is an ionosphere, and why should I care?"  and normally I'd be cheering you to the rafters in your assertions, but it so happens that for RF engineering it turns out to be important and I know it's rather like shooting prisoners of war but here we go.

The atmosphere consists of layers like on the left. The ionosphere is a region that covers several layers and consists of  three, four or five layers of its own depending on how you're counting. Confused? You just wait, cos you ain't seen nothing yet.


The first layer of the ionosphere is the D layer, but only in the day. At night the D layer disappears completely.

In the day it sits about 60 km above the Earth's surface and extends to about 100 km or so. Any frequency below 10 MHz gets all its energy absorbed and is not returned to Earth; as the frequency gets higher the absorption gets proportionally less. Those of you old enough to remember Radio Luxembourg now know why you couldn't get it in the daytime. Why does the D Layer disappear at night?  The answer is in bold print below: skip it if you want to.




During the day, nitric oxide gets ionised by radiation at a wavelength of 121.5 nM creating a block for anything under 10MHz. After sunset, this radiation is no longer present and the D Layer disappears.

Next is the E Layer which can reflect frequencies lower than about 10 Mhz, anything above goes through.

Again it can only do it in the day, and only if the D Layer is weak. The E layer appears because of  1-10 nm wavelengths ionising molecular oxygen (O2).

BUT- there is sometimes a second part to the E Layer and this is the Es Layer the s in which stands for sporadic. It's been known to go as high as 225 MHz reflection. It occurs because- well nobody knows for sure. It can mean that signals can get 2000 miles past their intended destination, but it can last for days, minutes or hours, and so it is completely unpredictable. It occurs in the summer months.


The F layer sits at about 200 km up and extends to 500 km and beyond.The upper part, F2, is the only layer permanently there night and day. It reflects everything up to about 30 MHz and after that signals go into space. It's represented on our diagram by the green circle, and the white line going through it is Santa using a UHF signal. Only the polar bears will know who's getting presents this year, and then only if they've got a line of sight with the transmitter.


There are lots of things that can upset this delicate balance. Temperature, lightning, solar activity and the aurora borealis will upset it completely. There is no solution, you just have to wait for things to calm down. Remember- RF engineering is not a science so much as an occult practice.

Speaking of which, let's talk about Tropospheric Ducting. This occurs when the moisture content of the air is high but not raining, usually early in the morning and can mean that the upper portions of VHF and above can dramatically increase their range by more than 1000 miles. But not for long; a few hours at most.

Then there's meteor scattering. Yes, you skip on the intensely ionised air caused by meteors in the VHF band. The MOD played with this. It's awful.


So remember- Long and Medium waves are ground waves. Short waves, VHF and FM and TV Broadcasts normally need a line of sight with the transmitter. Microwaves go up into space.


Santa, by the way, got fed up with the whole shebang and put the lists on a website instead. He still does the tunes, though, it helps the elves relax.

So, now we know about properties of a sine wave, polarities and modes of propagation. All that's left is to look at modulating methods. For analogue systems there are two, amplitude modulation (AM) and frequency modulation (FM).  The two are more fully dicussed here:




In this crib sheet we'll just delve in to the basics.

Amplitude Frequency

On the left you see a wave in red which has a constant frequency. It has variations, however, in its amplitude. The blue dotted line above it is an audio signal and you will notice that the constant frequency waveform follows the rises and falls of the audio signal. The audio signal is provided by an amplifier and the rises and falls are caused by how loud the sound is and the frequency of it. Through a modulating device, which is nothing more than a transformer, the audio wave is heterodyned (which means joined on to) the constant

frequency wave which is in fact an RF frequency wave. It adds to or subtracts from the voltage of the wave.

It produces three different frequencies, the nominal, the sum and the difference. Sum frequency is that of the nominal + the highest frequency modulated, difference is that of the nominal minus the highest frequency modulated. As the amplitude of the waveform is modulated, we call this amplitude modulation.

The lower waveform on the diagram on the left represents frequency modulation, and that above it the audio signal causing it. The amplitude of the wave does not change but the frequency at which it oscillates variates. How loud the sound is causes the deviation of the frequency of the carrier waveform (the lower one, which is an RF frequency) and the frequency of the audio signal controls how many times it does it per second. In the United Kingdom the BBC and commercial broadcasters are allowed to broadcast sounds with a frequency up to 15 kHz on FM and only 4.5 kHz on AM, making FM vastly superior for music broadcasting. In addition FM is impervious to most natural and man-made interference as the interference is generally on the amplitude of the waveform- in receivers it is filtered through limiters and does not appear at the output. However, FM will not allow a weaker signal to break over a stronger one. This is good if you are a broadcaster, bad if you are trying to get an emergency signal across with failing batteries.

In recent years a new technology has emerged, that of digital radio. For a discussion of this technology, click on the link below.

Digital Radio