Transmission Media & Shannon Capacity
Transmission media is the physical path between transmitter and receiver. The choice of medium determines maximum data rate, distance, cost, and immunity to electromagnetic interference.
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1. Guided (Wired) Media
Guided media uses a physical conductor to guide signals:
| Medium | Max Speed | Max Distance | Cost | EMI Immunity | Typical Use |
|---|---|---|---|---|---|
| UTP Cat5e | 1 Gbps | 100 m | Very low | Poor | Office LANs, patch cables |
| UTP Cat6a | 10 Gbps | 100 m | Low | Poor | Modern office LAN, server rooms |
| STP | 10 Gbps | 100 m | Medium | Good (shielded) | Industrial environments, Token Ring |
| Coaxial (Thin) | 10 Mbps | 185 m | Medium | Good | Early Ethernet, cable TV local drop |
| Coaxial (Thick) | 10 Mbps | 500 m | Medium | Good | Cable TV trunk lines |
| Single-mode Fibre | 100 Gbps+ | 100+ km | High | Excellent (no EMI) | WAN backbone, ISP, undersea cables |
| Multi-mode Fibre | 10 Gbps | 2 km | High | Excellent | Campus backbone, data centre interconnects |
Why Twisted Pair Cables Work
Twisting the two conductors causes the magnetic fields from each wire to cancel each other out, reducing crosstalk and electromagnetic interference. More twists per metre = better noise rejection. STP adds a metallic foil or braid shield for additional protection in high-noise environments.
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2. Unguided (Wireless) Media
| Medium | Frequency Range | Range | Obstacle Penetration | Use Case |
|---|---|---|---|---|
| Radio Waves | 3 kHz – 1 GHz | Long (national/global) | Penetrates walls | AM/FM broadcast, mobile networks |
| Microwaves | 1 – 300 GHz | Short, line-of-sight | Blocked by hills and buildings | Satellite, Wi-Fi (5 GHz), 4G/5G cellular |
| Infrared | 300 GHz – 400 THz | Very short (metres) | Cannot penetrate walls | TV remote, IrDA devices |
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3. Signal Impairments
3.1 Attenuation
Attenuation is the loss of signal energy as it travels through the medium. Signal power decreases with distance. Measured in decibels (dB). Compensated by amplifiers (analog) or repeaters (digital).
3.2 Distortion
Distortion changes the shape of the signal. In composite signals, different frequency components travel at slightly different speeds (phase velocity varies with frequency), causing them to arrive at different times. This is called dispersion.
3.3 Noise
| Noise Type | Cause | Impact |
|---|---|---|
| Thermal (Johnson) Noise | Random electron motion due to temperature | Unavoidable; sets minimum noise floor; proportional to temperature |
| Induced Noise | Electromagnetic fields from motors, fluorescent lights | Corrupts data on cables running near sources |
| Crosstalk | Signal from one conductor induces voltage in adjacent conductor | Common in UTP bundles |
| Impulse Noise | Sudden spikes from lightning, power surges, switching | Causes burst errors; difficult to prevent |
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4. Performance Metrics
| Metric | Definition | Formula / Unit |
|---|---|---|
| Bandwidth | Range of frequencies the channel can carry | Hz (Hertz) |
| Throughput | Actual measured data rate (always ≤ bandwidth) | bps |
| Propagation Speed | Speed signal travels through medium | ~2×10⁸ m/s in copper/fibre |
| Propagation Time | Time for signal to travel from sender to receiver | Distance ÷ Propagation Speed |
| Wavelength | Physical distance signal travels in one period | λ = v ÷ f |
| Latency | Total delay: Propagation + Transmission + Queuing + Processing | milliseconds |
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5. Shannon Capacity Theorem (Noisy Channel)
Shannon's theorem gives the theoretical maximum data rate for a noisy channel:
C = B × log₂(1 + SNR)
- C = Maximum channel capacity (bps)
- B = Bandwidth of the channel (Hz)
- SNR = Signal-to-Noise Ratio (linear value, not dB)
Converting SNR dB to linear: SNR_linear = 10^(SNR_dB ÷ 10)
Worked Example 1 — Standard Telephone Channel
Problem: Telephone channel B = 3000 Hz, SNR = 30 (linear). Find maximum capacity C.
C = B × log₂(1 + SNR)
C = 3000 × log₂(1 + 30)
C = 3000 × log₂(31)
C = 3000 × 4.954
C ≈ 14,862 bps ≈ 14.86 kbpsAnswer: Maximum capacity ≈ 14.86 kbps
Worked Example 2 — Finding Required SNR
Problem: Channel B = 4000 Hz, required C = 20,000 bps. Find the minimum SNR needed.
20000 = 4000 × log₂(1 + SNR)
5 = log₂(1 + SNR)
2⁵ = 1 + SNR
32 = 1 + SNR
SNR = 31Exam Tip: Shannon formula is C = B × log₂(1+SNR). Always confirm if SNR is linear or dB — if dB, convert first using SNR_linear = 10^(SNR_dB/10). This numerical appears in most exams.
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6. Nyquist Theorem (Noiseless Channel)
For a noiseless channel, the Nyquist theorem gives:
C_Nyquist = 2 × B × log₂(M)
Where M = number of discrete signal levels.
| Feature | Shannon Theorem | Nyquist Theorem |
|---|---|---|
| Channel | Noisy (realistic) | Noiseless (theoretical) |
| Variable | SNR | Signal levels M |
| Formula | C = B × log₂(1+SNR) | C = 2B × log₂(M) |
| Use | Absolute upper bound | Guides modulation design |
Study Deep: Shannon in Real Systems
- ADSL uses Shannon's theorem to dynamically adjust modulation to line quality — different frequency bands on the telephone line get different modulation levels based on their measured SNR. This is why broadband speed varies by distance from the telephone exchange.
- Wi-Fi 6 and 5G use QAM-1024 modulation to approach the Shannon limit on high-SNR channels, packing 10 bits per symbol.
- Shannon capacity is a hard upper bound: no encoding or modulation scheme, however clever, can exceed it on a given channel.
- When both Shannon and Nyquist apply, the actual maximum capacity is the lower of the two values.