Basic Concepts in Telecommunications: Set 3 - Power, Signals, and Wireless Fundamentals

This comprehensive HTML notes page covers key definitions and concepts in telecommunications, particularly related to energy, power, signals, propagation, and system performance. Each concept includes detailed descriptions, formulas, examples, and visual illustrations for better understanding.

1. Energy

Energy is the ability of a system to do work or cause change. In telecommunications, energy is required to operate transmitters, receivers, and other equipment, such as powering signals over time.

Formula: E = P × t

Where: E = energy (Joules, J), P = power (Watts, W), t = time (seconds, s)

Example: If P = 10 W and t = 5 s, then E = 50 J.

Real-life application: The energy consumed by a mobile phone transmitter during a call determines battery life.

Illustration showing energy as the capacity to perform work.

Diagram of gravitational potential energy increasing with height.

2. Power

Power is the rate at which energy is used or transferred. It indicates how strong a signal is in communication systems.

Formula: P = E / t

Example: If E = 100 J and t = 10 s, then P = 10 W.

Real-life application: Higher transmit power in base stations extends cellular coverage.

Diagram illustrating power as rate of energy transfer.

Example of power calculation in physical systems.

3. Units of Power

Power is measured in Watts (W).

• 1 W = 1000 mW (milliwatts)
• 1 kW = 1000 W (kilowatts)

In telecom, signals are often in dBm (decibels relative to 1 mW).

4. Decibel (dB)

The decibel is a logarithmic unit used to express gain or loss of power, making large ratios easier to handle.

Formula: dB = 10 log₁₀(P₂ / P₁)

Example: If P₂ = 100 W and P₁ = 10 W, gain = 10 dB.

Real-life: Amplifier gain in receivers is specified in dB.

Decibel scale showing power ratios.

Common decibel values for sound and power.

Decibel chart for quick reference.

5. Efficiency

Efficiency measures how much input power is converted into useful output power, critical for amplifiers and transmitters.

Formula: η = (P_out / P_in) × 100%

Example: If P_in = 100 W and P_out = 80 W, efficiency = 80%.

Efficiency calculation diagram.

Visual representation of input vs output power.

6. Speed of Electromagnetic Waves

Electromagnetic waves, including radio signals, travel at a constant speed in free space.

Formula: c = 3 × 10⁸ m/s (speed of light)

Electromagnetic spectrum showing wave speeds.

Illustration of light and EM waves.

7. Frequency, Wavelength, Period, and Speed

These describe wave behavior in signal propagation.

Formulas: c = fλ , T = 1 / f

Example: If f = 100 MHz, then λ = 3 m.

Sine wave showing frequency and wavelength.

Diagrams illustrating wave parameters.

8-9. Phase and Phase Shift

Phase represents the position of a wave within one complete cycle. Phase shift is the change in phase between two signals due to delay or transmission effects.

Illustrations of phase shift in sine waves.

10-13. Analog and Digital Signals

Analog signals vary continuously; digital use discrete levels (usually binary).

Analog: x(t) = A sin(ωt + φ)

Digital: x(t) ∈ {0, A}

Comparison of analog and digital waveforms.

14-15. Channel and Free Space Propagation

A channel is the medium for signal travel. Free space propagation is through open space without obstacles.

EM wave propagation in free space from antennas.

16-17. Antenna and Antenna Gain

An antenna converts electrical signals to EM waves and vice versa. Gain measures directional focus.

Radiation patterns showing antenna gain.

18-20. Path Loss

Path loss is signal power reduction during propagation, increasing with distance.

Linear: L = P_t / P_r

Graphs of path loss vs. distance.

21-22. Receiver Sensitivity and Link Budget

Sensitivity: Minimum power for reliable reception. Link budget: Pr = Pt + Gt + Gr − L

Link budget diagrams for wireless links.

23. Signal-to-Noise Ratio (SNR)

SNR = P_s / P_n

Illustrations of SNR in signals.

24. Bit Error Rate (BER)

BER = error bits / total bits

Measures digital communication reliability, affected by SNR.

25-29. Multiplexing and Interference

Multiplexing shares channels (e.g., TDM, FDM). Interference degrades signals, including ISI and co-channel.

Multiplexing techniques (FDM, TDM).

Inter-symbol interference (ISI) diagrams.

Conclusion

These concepts form the foundation of wireless telecommunications, enabling design of efficient and reliable communication systems like cellular networks, Wi-Fi, and satellite links.