Radio links.

Step 1 of 7

A carrier

In the Unit on waves we saw that a wave carries energy without carrying matter. A radio wave carries information too. The transmitter makes a wave at a fixed frequency, the carrier, and changes it to follow the message. Such a change is called modulation. Decode the signal is at Message, and the charts beside the Scene show the message, the transmitted wave, what reaches the house and what the receiver decodes.

Step 2 of 7

Weaker every kilometre

A radio wave spreads out in every direction, and its power is shared over the area of a sphere, $4\pi r^2$⁠. So the power reaching the house falls like $\dfrac{1}{r^2}$⁠. Meanwhile the receiver always hears the same noise. What matters is the signal-to-noise ratio, measured in decibels:

$\mathrm{dB} = 10 \log_{10}\frac{P_s}{P_n}$$\mathrm{dB} =$$10 \log_{10}\frac{P_s}{P_n}$⁠

The logarithm turns multiplying into adding: a ratio $100$⁠ times smaller is 20 dB less. Distance is locked.

Step 3 of 7

From decibels to a ratio

Decibels are handy for working out, because you add and subtract them, but it is easy to forget how big each one is. To get from decibels back to a ratio, undo the logarithm:

$\frac{P_s}{P_n} = 10^{\mathrm{dB}/10}$$\frac{P_s}{P_n} =$$10^{\mathrm{dB}/10}$⁠

Step 4 of 7

AM against FM

In AM the tone changes the wave’s height, so any noise that changes the height passes straight into the tone. In FM the height is constant and the tone changes the frequency. Distance is locked at 10 km, and Modulation is free.

Step 5 of 7

The price of FM

FM’s cleanness is not free. To write the tone in large swings of frequency, the wave needs a wider band of frequencies, and each station takes a bigger slice of the spectrum. Modulation is locked on FM.

Step 6 of 7

The digital cliff

In digital radio the receiver only has to decide, for each bit, which of two symbols arrived. Modulation is locked on Digital, and the last chart shows the decoded bits and the error rate.

Step 7 of 7

On the edge of the cliff

Real digital systems add error-correcting bits: a code that lets the receiver find and fix wrong bits, as long as there are not too many of them. Distance is free.