Principles of communication systems
A communication system moves information from one place to another.
- Transmitter: turns the message (sound, text, video) into a signal and sends it.
- Channel: the path the signal travels along.
- Receiver: picks up the signal and turns it back into the message.
On the way, the signal gets weaker (attenuation) and picks up unwanted signals (noise). Repeaters and amplifiers boost it.
Analogue and digital
An analogue signal can take any value. A digital signal uses only a few levels, usually 0 and 1. Digital signals can be cleaned up (regenerated) at each repeater, so noise does not build up. Sampling turns analogue into digital; the sampling rate must be at least twice the highest frequency in the signal.
Bit rate = number of bits sent per second (bit/s).
Transmission media
- Copper wire (twisted pair, coaxial cable): cheap, easy to join. Signal fades quickly and picks up noise. Coaxial cable has a shield, so less noise.
- Optical fibre: light pulses travel by total internal reflection in thin glass. Huge bandwidth, very low loss, no electrical noise, secure. Harder to join, costs more to lay.
- Radio waves (free space): no cables needed, good for mobile users. Range depends on frequency: low frequencies follow the ground or bounce off the ionosphere; high (microwave) frequencies need line of sight or satellites.
Signals in cables and fibre travel at about 2×10⁸ m/s; radio in air at about 3×10⁸ m/s.
Time-division multiplexing (TDM)
Multiplexing means many signals share one channel. In TDM, each digital signal is given a short time slot in turn. A group of one slot per signal is a frame. At the far end the receiver splits the slots back out, in step (synchronised) with the sender.
If n signals each need a bit rate R, the channel must carry at least n × R.
Example: 30 phone calls at 64 kbit/s each need 30 × 64 = 1920 kbit/s on the shared line.
Amplitude (AM) and frequency modulation (FM)
Modulation puts the message onto a high-frequency carrier, because high frequencies travel well and need small aerials.
AM
The carrier's amplitude follows the message. A message of frequency fm on a carrier fc makes side frequencies fc ± fm. Bandwidth = 2fm.
FM
The carrier's frequency follows the message. The biggest shift is the frequency deviation Δf. Carson's rule: bandwidth ≈ 2(Δf + fm).
Compare
- AM: narrow bandwidth, simple receiver, long range, but noisy (noise changes amplitude).
- FM: better sound, less noise, but wider bandwidth and shorter range.
Key formulas and definitions
- AM bandwidth = 2 fm
- AM side frequencies = fc ± fm
- FM bandwidth ≈ 2(Δf + fm) (Carson's rule)
- TDM channel rate ≥ n × R
- sampling rate ≥ 2 × highest signal frequency
- v = d / t (signal delay)
Worked examples
1. A 5 kHz audio tone is sent by AM on a 900 kHz carrier. Find the side frequencies and bandwidth.
895 kHz and 905 kHz. Bandwidth = 2 × 5 = 10 kHz.
2. An FM station has Δf = 75 kHz and fm = 15 kHz. Estimate the bandwidth.
2(75 + 15) = 180 kHz.
3. 24 signals at 64 kbit/s share one TDM line. Minimum line rate?
24 × 64 = 1536 kbit/s.
4. Sound up to 20 kHz is digitised. Minimum sampling rate?
2 × 20 = 40 kHz (CDs use 44.1 kHz).
5. A signal travels 3000 km of optical fibre at 2×10⁸ m/s. Find the delay.
t = 3×10⁶ / 2×10⁸ = 0.015 s = 15 ms.
6. A geostationary satellite is 36 000 km up. Time for a signal up and down?
t = 7.2×10⁷ / 3×10⁸ = 0.24 s.
Common mistakes
- Mixing up AM and FM: in AM the height changes, in FM the spacing (frequency) changes.
- Saying AM bandwidth equals fm. It is 2fm, because there are two side frequencies.
- Thinking TDM sends signals at the same instant. They take turns, very quickly.
- Using 3×10⁸ m/s for signals in fibre or cable; there it is about 2×10⁸ m/s.