Physics › Electronics › Data communication
Data communication
A microphone's few kilohertz cannot cross a country on their own, so they ride a carrier wave, printed on its amplitude or on its frequency. Each choice buys something and costs something, and the modern move is to send the wave as a stream of numbers instead.
Builds on Digital signal processing.
IN THIS TOPIC
- Distinguish baseband from modulated transmission, and say what a carrier buys.
- Find sideband frequencies and bandwidth for AM, and bandwidth for FM.
- Weigh AM against FM on bandwidth, noise and cost.
- Choose a sampling rate, and follow a signal through pulse-code modulation.
- Compare time-division with frequency-division multiplexing, and copper, fibre and radio as media.
WHAT YOU PROBABLY THINK
FM radio sounds cleaner than AM because it is broadcast at higher power.
Baseband, and the case for a carrier
Send a signal in its own natural range of frequencies and you are transmitting at baseband. A telephone landline does exactly this, speech from about 300 Hz to 3.4 kHz travelling down a private pair of wires, and on a private wire baseband is fine. Radio has no private wires. Every transmitter shares the same air, and if each station broadcast baseband audio they would all occupy the same few kilohertz and land on top of one another.
There is a second, more physical objection. An efficient aerial needs to be a respectable fraction of a wavelength long, and a 3 kHz radio wave is 100 km long. Nobody builds that aerial. Both problems fall to the same trick: print the programme onto a high-frequency carrier wave. The carrier's short wavelength suits real aerials, and each station is allotted its own carrier frequency, so a tuned circuit at the receiver, resonance from earlier in this unit, can select one station and reject the rest. Printing the programme on is called modulation, and the two classic schemes divide this lesson between them.
Amplitude modulation
Amplitude modulation keeps the carrier frequency fixed and makes its amplitude follow the programme, loud passages swelling the envelope. The surprise is what this does to the spectrum. Modulate a carrier with a single audio tone of frequency and you transmit exactly three frequencies, the carrier itself plus two sidebands at and . The audio is not sent at its own frequency; it appears as the pair of new frequencies flanking the carrier.
Real programmes are a band of tones up to some maximum audio frequency , so each sideband spreads into a band, and the transmission occupies everything from to . The occupied width is the bandwidth:
WORKED EXAMPLE
Medium wave arithmetic
A medium-wave station on a 909 kHz carrier transmits audio limited to 4.5 kHz. Find the frequencies it occupies and its bandwidth.
Sidebands run from 909 − 4.5 = 904.5 kHz up to 909 + 4.5 = 913.5 kHz.
The bandwidth is 2 × 4.5 = 9.0 kHz, and medium-wave stations are duly spaced 9 kHz apart across the band.
The audio ceiling of 4.5 kHz is the price of that tight packing. Music loses its top octaves before it ever leaves the transmitter.
Frequency modulation
Frequency modulation holds the amplitude constant and swings the carrier's frequency instead, above and below in step with the programme. Louder audio swings it further; the maximum swing is the frequency deviation . The occupied band must cover the deviation and the modulating structure on top of it, so
WORKED EXAMPLE
Broadcast FM's appetite
A broadcast FM station uses a deviation of 75 kHz and carries audio up to 15 kHz. Find its bandwidth, and compare it with the medium-wave station's.
Bandwidth = 2 × (75 + 15) = 180 kHz.
That is twenty times the 9 kHz an AM station occupies. FM buys its quality with spectrum, and the wide channels only fit because the FM band sits up near 100 MHz, where there is room.
What does 180 kHz buy? Noise, whether from motors, lightning or distant sparks, adds to a wave's amplitude. An AM receiver reads the amplitude, so it faithfully reproduces the noise. An FM receiver reads only the frequency, and it clips the amplitude flat before detection, shaving nearly all of that noise away. FM also carries audio to 15 kHz rather than 4.5, and its constant amplitude lets the transmitter run steadily at full efficiency. AM's rejoinder is thrift, a twentieth of the spectrum per station and receivers simple enough to build with a diode.
| AM | FM | |
|---|---|---|
| bandwidth per station | narrow, , about 9 kHz | wide, , about 180 kHz |
| response to noise | noise adds to amplitude, and is heard | amplitude clipped flat, so most noise is removed |
| audio quality | limited, about 4.5 kHz of audio | up to 15 kHz of audio |
| transmitter and receiver | simple and cheap | more complex circuitry |
| carrier frequencies used | long and medium wave, longer range | VHF, roughly line of sight |
YOUR TURN
A narrowband compromise
A marine two-way radio uses FM with a deviation of 2.5 kHz and speech limited to 3.0 kHz. Find its bandwidth, and explain in one sentence why it accepts a far smaller deviation than broadcast FM.
Show the working
Bandwidth = 2 × (2.5 + 3.0) = 11 kHz.
Small deviation keeps each channel narrow, so many ships share the band; speech only needs to be intelligible, not high fidelity, and the noise advantage of FM survives in miniature.
Sending numbers instead: sampling and PCM
The last lesson argued that digital signals shrug off noise and can be regenerated without loss. To give an analogue signal those advantages, digitise it. Step one is sampling, measuring the signal's value at regular instants. Sample too rarely and wiggles between samples are missed entirely, and the rule has a sharp edge. The sampling rate must be greater than twice the highest frequency present in the signal. Sampled slower than that, a high frequency masquerades as a low one and the corruption cannot be undone afterwards.
Step two is quantisation. Each sample is rounded to the nearest of fixed levels, and the level is named by an n-bit binary code. The rounding error is the quantisation error, shrunk by adding bits, since each extra bit doubles the number of levels and halves the step between them. The stream of codes, sent as pulses, is pulse-code modulation, PCM. From then on the signal enjoys every digital privilege, regeneration included, and noise stops accumulating along the route.
WORKED EXAMPLE
The telephone's budget
Telephone speech is limited to 3.4 kHz, sampled at 8.0 kHz with 8 bits per sample. Check the sampling rate and find the bit rate.
Twice the highest frequency is 6.8 kHz, and 8.0 kHz clears it, with margin left for imperfect filters.
Bit rate = 8000 samples per second × 8 bits = 64 000 bits per second, the standard worldwide figure for one digital phone call.
Sharing the channel, choosing the medium
One cable or one band is always shared, and there are two ways to slice it. Frequency-division multiplexing gives each user a permanent slice of the spectrum, every broadcaster transmitting continuously on its own carrier, which is precisely how the radio dial works. Time-division multiplexing gives each user the whole channel for a brief repeating time slot. Digital signals suit TDM perfectly, because samples are short pulses with dead time between them, and interleaving thirty phone calls into the gaps is routine.
| medium | attenuation | bandwidth | weaknesses and strengths |
|---|---|---|---|
| copper cable | high, repeaters every few km | modest, tens of MHz | picks up electrical interference and crosstalk; cheap and everywhere |
| optic fibre | very low, repeaters tens of km apart | enormous, many GHz | immune to electrical interference, secure, light and thin |
| radio and microwave link | spreads and fades with distance and weather | limited by the allocated band | no cable to lay, reaches moving and remote users, but shared and interceptable |
The comparison that examiners reward is argued through attenuation and bandwidth. Fibre loses least per kilometre, so its repeaters are furthest apart; it carries the most, and being an insulator carrying light it ignores electrical interference completely. Copper is the cheap incumbent for the last mile. Radio is the only choice when the receiver moves, and the price is a shared, weather-dependent medium in which whatever you transmit can be received by anyone.
TRY IT UNSEEN
How many stations fit
The FM broadcast band runs from 87.5 MHz to 108.0 MHz, and each station is allocated 200 kHz of it. How many stations fit, and how many 9 kHz AM stations would the same span hold?
Show the working
The band spans 108.0 − 87.5 = 20.5 MHz = 20 500 kHz. At 200 kHz per station that is 20 500/200 = 102.5, so 102 stations.
At 9 kHz per station the same span would hold 20 500/9 ≈ 2277 stations.
The units are the usual trap. Convert the megahertz span into kilohertz before dividing, or the answer arrives a thousand times too small.
THE EXAM BIT
- A carrier modulated by one tone transmits three frequencies, the carrier and one sideband each side. Writing one sideband, or four frequencies, is the standard sideband slip.
- Bandwidth is the full occupied width, for AM, never . Halving it is the most common lost mark in the topic.
- Keep kHz and MHz apart. Convert the audio frequency and the carrier to the same unit before adding or subtracting, and check the sidebands sit close to the carrier, not at it.
- FM bandwidth needs both terms, . Dropping the is the examiners' favourite error to punish.
- State the sampling rule with its inequality, more than twice the highest signal frequency, and multiply samples per second by bits per sample for any bit-rate mark.
- Media comparisons score through attenuation and bandwidth, argued in pairs. Fibre: least loss, widest band, immune to interference. Say all three, each against its rival.
CHECK YOURSELF
A station broadcasts speech limited to 4.0 kHz by AM on a 1.2 MHz carrier. Find the range of frequencies transmitted and the bandwidth. A rival carries the same speech by FM with a deviation of 6.0 kHz. Find the FM bandwidth, and state one advantage each listener holds over the other.
Show a hint
Convert the carrier to kHz first. AM occupies fc − fM up to fc + fM; FM needs the deviation as well.
Show the answer
The carrier is 1200 kHz, so the transmission runs from 1196 kHz to 1204 kHz, a bandwidth of 2 × 4.0 = 8.0 kHz.
FM bandwidth = 2 × (6.0 + 4.0) = 20 kHz, two and a half times the spectrum per station.
The FM listener hears less noise, because the receiver clips away amplitude disturbances. The AM listener's station spends far less bandwidth, so more stations fit in the band, and the receiver is simpler and cheaper.
One modulating tone makes three frequencies: the carrier with a sideband either side.
AM occupies 2fM of spectrum; FM occupies 2(Δf + fM) and shrugs off amplitude noise.
Sample faster than twice the highest frequency, round to a level, send the code: PCM.
Fibre loses least, carries most, and ignores electrical interference.
WORKBOOK
Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.
CHECK YOUR PROGRESS
Rate how confident you feel with each objective for this lesson. Ratings are saved in this browser, on this device only.
- Distinguish baseband from modulated transmission, and say what a carrier buys.
- Find sideband frequencies and bandwidth for AM, and bandwidth for FM.
- Weigh AM against FM on bandwidth, noise and cost.
- Choose a sampling rate, and follow a signal through pulse-code modulation.
- Compare time-division with frequency-division multiplexing, and copper, fibre and radio as media.
Open the full revision checklist to track your progress across the whole unit.