Communication Systems

Communication is the transfer of information from one point to another. A typical communication system has three main components:

``` Information → [TRANSMITTER] → [CHANNEL] → [RECEIVER] → Information ```

Key elements:

• Transducer: Converts non-electrical signal (sound, image, temperature) into electrical signal. Example: microphone, camera.
• Transmitter: Processes signal (amplifies, modulates) for transmission.
• Channel: The physical medium connecting transmitter and receiver (wire, optical fibre, free space).
• Receiver: Extracts the original signal from the received signal.
• Noise: Unwanted random electrical signal that distorts information.
• Repeater: Amplifies the signal en route to compensate for losses (used in long-distance communication).

Signal Types:

Bandwidth: Range of frequencies necessary to transmit a signal. Different signals require different bandwidth:

Bandwidth of transmission medium:

Attenuation: Loss of signal strength along the channel. Amplification: Boosting signal strength (compensates attenuation). Range: Maximum distance between transmitter and receiver beyond which signal is too weak to recover.

EM waves are used for wireless communication. Three modes of propagation are used depending on frequency:

1. Ground Wave (Surface Wave) Propagation:

• Wave travels along Earth's surface
• Used for: AM broadcast ($530$ kHz – $1710$ kHz)
• Range: Few hundred km (high attenuation at higher frequencies)
• Frequency: $< 2$ MHz typically

2. Sky Wave Propagation:

• Wave is reflected by ionosphere back to Earth
• Used for: short-wave broadcasting, amateur radio
• Frequency: $2-30$ MHz (HF)
• Multiple bounces possible — long-distance global coverage
• Limited by ionosphere conditions (day/night, solar activity)

3. Space Wave (Line-of-Sight) Propagation:

• Wave travels directly from transmitter to receiver
• Used for: TV, FM, microwave links, satellite communication, mobile phones
• Frequency: $> 30$ MHz (VHF, UHF, microwave)
• Higher frequencies penetrate ionosphere → useful for satellite communication

Line-of-Sight Distance for Antenna of Height $h_T$: $$d_T = \sqrt{2Rh_T}$$ where $R$ = Earth's radius. For both antennas (transmitter $h_T$, receiver $h_R$): $$d_M = \sqrt{2Rh_T} + \sqrt{2Rh_R}$$

Ionosphere Layers:

Critical Frequency: Maximum frequency reflected back at vertical incidence. Above this, wave penetrates the ionosphere.

MUF (Maximum Usable Frequency): Highest frequency that gives reflection from ionosphere for given path.

Satellite Communication: Satellites act as relay stations. Geostationary satellites at $36000$ km appear stationary; three suffice for global coverage. Frequencies used: GHz range (microwaves).

Why Modulation? Direct transmission of low-frequency audio (kHz range) faces several problems:

1. Antenna size: Effective antenna length $L \geq \lambda/4$. For $f = 1$ kHz: $\lambda = 300$ km, so $L \geq 75$ km — impossibly large. For high $f$ (MHz), antenna is just metres.
2. Power radiated: Power radiated by antenna $\propto (l/\lambda)^2$. Higher frequency → much more efficient radiation.
3. Mixing of signals: If many transmitters all radiated at audio frequency, signals would overlap. Different carrier frequencies allow many channels simultaneously.

Modulation: Process of superimposing low-frequency (modulating/message) signal on a high-frequency carrier wave.

Three Basic Types:

Amplitude Modulation (AM):

Carrier: $c(t) = A_c\sin\omega_c t$. Message: $m(t) = A_m\sin\omega_m t$.

AM signal: $c_m(t) = (A_c + A_m\sin\omega_m t)\sin\omega_c t = A_c(1 + \mu\sin\omega_m t)\sin\omega_c t$

where modulation index $\mu = A_m/A_c$; ranges $0 \leq \mu \leq 1$. Over-modulation ($\mu > 1$) causes distortion.

Expanding: $$c_m(t) = A_c\sin\omega_c t + \frac{\mu A_c}{2}\cos(\omega_c - \omega_m)t - \frac{\mu A_c}{2}\cos(\omega_c + \omega_m)t$$

AM signal contains three frequencies:

• Carrier $\omega_c$
• Upper side band (USB) $\omega_c + \omega_m$
• Lower side band (LSB) $\omega_c - \omega_m$

Bandwidth of AM = $2\omega_m$ (or $2f_m$ in Hz).

In terms of voltage amplitudes from waveform: $$\mu = \frac{V_{\max} - V_{\min}}{V_{\max} + V_{\min}}$$

Power in AM:

• Carrier power: $P_c = V_c^2/(2R)$
• Each sideband: $P_{SB} = \mu^2 P_c/4$
• Total power: $P_t = P_c(1 + \mu^2/2)$
• Efficiency: $\eta = \mu^2/(2 + \mu^2)$. For $\mu = 1$: $\eta = 1/3 = 33.3\%$

Frequency Modulation (FM): Instantaneous frequency of carrier varied in proportion to message amplitude. Carrier amplitude remains constant.

$$f(t) = f_c + k_f m(t)$$

Advantages of FM over AM:

• Better noise immunity (noise mostly affects amplitude, which FM ignores)
• Higher fidelity sound quality
• Used for high-quality audio broadcasting ($88-108$ MHz commercial FM band)

Disadvantages:

• Requires larger bandwidth (typically $200$ kHz vs $10$ kHz for AM)
• More complex circuitry

Carson's Rule (FM bandwidth): $$BW_{FM} = 2(\Delta f + f_m)$$ where $\Delta f$ = peak frequency deviation, $f_m$ = highest modulating frequency.

Phase Modulation (PM): Phase of carrier varied with message: $$\phi(t) = \phi_c + k_p m(t)$$

PM and FM are closely related — differentiating phase gives frequency.

Comparison: AM vs FM

Demodulation (Detection): Process of recovering the original message signal from the modulated wave.

AM Demodulation: Uses an envelope detector = diode + RC low-pass filter. The diode rectifies the AM wave (positive envelope), and the RC filter smooths it, leaving the audio envelope.

Time constant $\tau = RC$ should satisfy: $$\frac{1}{f_c} \ll RC \ll \frac{1}{f_m}$$

FM Demodulation: Uses frequency discriminator circuits (slope detector, ratio detector, PLL — phase-locked loop). More complex than AM detection.

Production of AM: Square-law modulator with carrier and message inputs, followed by band-pass filter to keep $\omega_c \pm \omega_m$ components.

Production of FM: Voltage-controlled oscillator (VCO) — frequency depends on input voltage.