Right, let's pick this up — Page 20, Lesson 21

Right, let's pick this up. We've just established the inverse square law — that signal strength falls off with the square of the distance. Now I want to show you the practical consequence of that, because it's a number every pilot and engineer should have at their fingertips. The practical effect is this: if you want to double the effective range of a transmitter, you don't double the power. You have to increase the power by a factor of 4. That's the direct consequence of the inverse square law — the signal strength drops as the square of distance, so to overcome that squared loss over twice the distance, you need four times the power. Keep that relationship in mind; it comes up again and again. Now, let's talk about something that degrades all of this — static interference. There's a large amount of static electricity generated in the atmosphere, and it comes from three main sources: weather, human activity, and geological activity. Now here's the key point about frequency: the effect of static interference is greater at lower frequencies. At VHF and above — that's Very High Frequency — the effect of interference is generally negligible. But there's a catch: radio waves travelling through the ionosphere will collect interference at all frequencies. So even at high frequencies, if the signal path goes through the ionosphere, you pick up noise. And it's not just the atmosphere. The circuitry in the receivers and transmitters themselves also produces static interference. So the static, from whatever source, does two things: it reduces the clarity of communications and it reduces the accuracy of navigation systems. Now, how do we express this relationship? We use something called the signal to noise ratio, abbreviated S/N. That's the strength of the required signal compared to the amount of interference. And for the best clarity or accuracy, the unwanted noise needs to be reduced to the lowest possible levels. That's the whole game — maximise the signal, minimise the noise. Next, let's look at fading. Transmissions can follow different paths — for example, through reflections — and those signals can arrive at a receiver simultaneously. But here's the problem: the two signals will not necessarily be in phase. In extreme cases, the two signals will be in anti-phase — that means one is at its peak while the other is at its trough — and they will cancel each other out. So what do you observe? Signals going in and out of phase are indicated by alternate fading and strengthening of the received signal. That's the classic flutter you hear or see on a receiver. Now, back to power. An increase in the power output of a transmitter will increase the range, but — and this is the crucial limit — only within the limits of the inverse square law. And as I said at the start, to double the range, you need the power increased by a factor of 4. Then there's receiver sensitivity. If the internal noise in a receiver can be reduced, then the receiver will be able to process weaker signals. That means it can hear signals that are further away, hence increasing the effective range at which a useable signal can be received. But — and this is the practical catch — this is an expensive process. Reducing internal noise costs money. Finally, directivity. If the power output is concentrated into a narrow beam, then there will be an increase in range, or alternatively, a reduction in power required for a given range. But there's a trade-off: the signal will only be usable in the direction of the beam. So you gain range in one direction, but you lose coverage everywhere else. And that brings us back to the formula that ties it all together: P ∝ 1/R². That reads: power is proportional to one over R squared, where R is the range. That's the inverse square law in its mathematical form — and it's the foundation for everything we've just discussed, from the factor-of-4 rule to why directivity helps.