Physics Notes on Communication Systems

COMMUNICATION SYSTEMS

• Definition of Communication:
  • The term ‘communication’ refers to sending, receiving, and processing of information electronically.
  • A communication system refers to the setup to transmit information.

Basic Terminology in Electronic Communication System

1. Transducer:

   • Any device that converts one form of energy into another can be termed as a transducer.
   • An electrical transducer is a device that converts some physical variable (pressure, displacement, force, temperature, etc.) into corresponding variations in the electrical signal at its output.

2. Signal:

   • Information converted into electrical form and suitable for transmission is called a signal.
   • Signals can be either analog or digital.

3. Noise:

   • Noise refers to unwanted signals that disturb the transmission and processing of message signals in a communication system.
   • The source generating the noise may be located either inside or outside the system.

4. Transmitter:

   • A transmitter processes the incoming message signal to make it suitable for transmission through a channel and subsequent reception.

5. Receiver:

   • A receiver extracts the desired message signals from the received signals at the channel output.

6. Attenuation:

   • The loss of strength of a signal while propagating through a medium is known as attenuation.

7. Amplification:

   • The process of increasing the amplitude (and consequently the strength) of a signal using an electronic circuit called the amplifier.
   • Amplification compensates for the attenuation of signals in communication systems.
   • It is carried out at points between the source and destination wherever the signal strength becomes weaker than required.

8. Range:

   • The largest distance between a source and destination up to which the signal is received with sufficient strength.

9. Bandwidth:

   • Bandwidth refers to the frequency range over which equipment operates or the portion of the spectrum occupied.

10. Modulation:

    • The original low frequency message/information signal cannot be transmitted over long distances; therefore, information contained in a low frequency signal is superimposed on a high frequency wave acting as a carrier of information.
    • This process is called modulation.

11. Demodulation:

    • The process of retrieving information from the carrier wave at the receiver is termed demodulation.
    • This is the reverse process of modulation.

12. Repeater:

    • A repeater is a combination of a receiver and a transmitter and picks up the signal from the transmitter with a change in carrier frequency.
    • Repeaters are used to extend the range of a communication system.
    • A communication satellite is essentially a repeater station in space.

Analog Signal and Digital Signal

• Analog Signals:

  • Continuous variations of voltage or current; essentially single-valued functions of time.
  • A sine wave is a fundamental analog signal.
  • Sound and picture signals in TV are analog in nature.

• Digital Signals:

  • Signals that can take only discrete stepwise values.

  • The binary system extensively used in digital electronics employs two levels of signals: '0' corresponds to a low level and '1' to a high level.

  • A rectangular wave can be composed into a superposition of sinusoidal waves with frequencies: $<br />\nu<em>0, 2\nu</em>0, 3<br />\nu<em>0, 4\nu</em>0, ext{…}$, where n is an integer extending to infinity and $<br />\nu<em>0 = \frac{1}{T</em>0}$.

  • To reproduce the rectangular wave shape exactly, all harmonics $<br />\nu<em>0, 2\nu</em>0, 3<br />\nu<em>0, 4\nu</em>0…$ are required, implying an infinite bandwidth; however, contributions from higher harmonics can often be neglected for practicality.

• Coding Schemes for Digital Communication:

  • Various coding schemes such as binary coded decimal (BCD) and American Standard Code for Information Interchange (ASCII) are used to represent numbers, letters, and certain characters.

Bandwidth of Signals

• Each type of message signal (voice, music, picture, computer data) has different frequency ranges.
  • Speech Signals:
  • Frequency range: 300 Hz to 3100 Hz; therefore, the required bandwidth: $3100 ext{ Hz} - 300 ext{ Hz} = 2800 ext{ Hz}$.
  • Music:
  • Approximate bandwidth: 20 kHz required due to high frequencies from musical instruments.
  • Audible range: 20 Hz to 20 kHz.
  • Video Signals:
  • Requires about 4.2 MHz of bandwidth for picture transmission.
  • A TV signal (containing both voice and picture): typically allocated 6 MHz bandwidth for transmission.

Bandwidth of Transmission Media

• Various transmission media have different bandwidth capabilities:
  • Wire:
  • Coaxial cable offers bandwidth approximately of 750 MHz, usually operated below 18 GHz.
  • Free Space:
  • Radio waves can propagate over frequencies from hundreds of kHz to a few GHz.
  • Fiber Optic Cable:
  • Optical communication frequency range: 1 THz to 1000 THz; optical fibers can offer transmission bandwidth in excess of 100 GHz.
  • Spectrum Allocation:
  • Arrived by international agreement and administered by the International Telecommunication Union (ITU).

Propagation of Electromagnetic Waves

• Ground Waves:

  • To radiate signals effectively, antennas should have sizes comparable to the wavelength $ext{λ}$ of the signal (at least ~ $ext{λ}/4$).
  • Longer wavelengths (lower frequencies) require larger physical antennas, which often operate near the ground.
  • Standard AM broadcast uses ground-based vertical towers as transmitting antennas, where the ground significantly influences signal propagation (surface wave propagation).
  • A wave induces a current in ground and is attenuated due to energy absorption.

• Space Wave Propagation:

  • Radio waves propagated through the troposphere are known as space waves.
  • The troposphere extends up to 15 km from the Earth's surface.
  • Two components of space wave propagation are:
  • (i) Direct line-of-sight (LOS) component.
  • (ii) Component that reaches the receiver after reflection from the Earth’s surface.
  • Suitable for waves with frequencies above 30 MHz
  • The distance to the horizon $d<em>T$ for a transmitting antenna at height $h</em>T$ is given by: $d<em>T = 2Rh</em>T$, where $R$ is the Earth's radius (approximately 6400 km).

Maximum Line-of-Sight Distance

• The maximum distance $d<em>M$ between two antennas of heights $h</em>T$ (transmitting) and $h<em>R$ (receiving) is provided by the formula: $d</em>M = ext{√}(2Rh<em>T) + ext{√}(2Rh</em>R)$.
  • Area covered by transmission $A$ can be expressed as: $A = ext{π}(d_T)^{2}$.

Examples of Communication Systems using Space Wave Propagation

• Television broadcasts, microwave links, and satellite communications.

Solved Numerical Examples

Q) What must be the height of a transmission antenna of an FM radio station so that people in a circular region of 3140 km² can receive the program? Given $R = 6400 ext{ km}$.

• Solution: $A = ext{π}(2h_TR)$
  • $3140 = 3.14 imes 2 imes h_T imes 6400$
  • $h_T ext{= 0.078125 km = 78.125 m}$.

Q) An antenna at the top of a tower has a height of 50m and the height of the receiving antenna is 32m. What is the maximum distance for satisfactory communication in LOS mode? Given $R = 6400 km$.

• Solution:
  • $d<em>m = ext{√}(2R imes h</em>T) + ext{√}(2R imes h_R)$
  • $d_m = ext{√}(2 imes 6400 imes 10^3 imes 50) + ext{√}(2 imes 6400 imes 10^3 imes 32)$
  • $d_m = 25.29 imes 10^3 + 20.23 imes 10^3 = 45.5 ext{ km}.$

Sky Wave Propagation

• Occurs between frequencies 2 MHz to 30 MHz.
• Radio waves reflect from the ionosphere, which acts as a mirror for these waves, allowing reception over long distances.
• The ionosphere contains electrons and anions due to solar radiation, with varying densities leading to different reflection characteristics.
• Only frequencies below 30 MHz are reflected; above 30 MHz they penetrate.

Modulation and Its Necessity

• Low-frequency signals cannot travel long distances due to various factors:

  1. Length of Antenna: For effective transmission, the minimum length of the antenna must be $\frac{λ}{4}$. If transmitted wavelength is 300 km, frequency about 1 kHz, antenna length would be about 75 km, which is impractical.
  2. Power Radiated from Antenna: The power transmitted by an antenna is inversely proportional to the square of the wavelength: $P ext{∝} \frac{1}{λ^{2}}$.
  3. Mixing Signals: Multiple transmitters using audio signals can mix information, necessitating frequency differentiation for proper communication.
  • Definition of Modulation: The process of superimposing low-frequency audio signals on high-frequency waves is called modulation; the low-frequency signal is referred to as the modulating signal, while the high-frequency wave carries the information and is called the carrier wave.

Mathematical Representation of Carrier Wave

• A sinusoidal carrier wave can be represented as: $c(t) = A<em>c ext{sin}( ext{ω}</em>ct + φ)$
  • where $c(t)$ is the signal strength (voltage or current), $A<em>c$ is the amplitude, $ext{ω}</em>c = 2 ext{π}<br />\nu_c$ is the angular frequency, and $φ$ is the initial phase of the carrier wave.

Types of Modulation

• Any of three parameters of the carrier wave (Amplitude, Frequency, Phase) can be adjusted by the message signal, resulting in:
  1. Amplitude Modulation (AM):
  • The amplitude of the carrier wave is varied according to the instantaneous value of the modulating wave while frequency and phase remain constant.
  • It can be represented mathematically as:
    $c<em>m(t) = (A</em>c + A<em>m ext{sin}( ext{ω}</em>mt)) ext{sin}( ext{ω}_ct)$.

Mathematical Form of AM Wave

• Derived from:

  • The modulated signal given by:
    $c<em>m(t) = A</em>c ext{sin}( ext{ω}<em>ct) + A</em>m ext{sin}( ext{ω}<em>mt) ext{sin}( ext{ω}</em>ct)$
  • Which can be simplified and leads to an amplitude modulated wave with maximum and minimum amplitudes:
    $A<em>{ ext{max}} = A</em>c + A<em>m ext{, } A</em>{ ext{min}} = A<em>c - A</em>m$.

• Modulation Index is defined as:
  $ext{μ} = \frac{A<em>m}{A</em>c} = \frac{A<em>{ ext{max}} - A</em>{ ext{min}}}{A<em>{ ext{max}} + A</em>{ ext{min}}}$.

  • Percentage modulation can be given by:
    $ext{μ}( ext{percent}) = \frac{A<em>{ ext{max}} - A</em>{ ext{min}}}{A<em>{ ext{max}} + A</em>{ ext{min}}} imes 100$.

• Example: A 10 MHz sinusoidal carrier wave of amplitude 10 mV is modulated by a 5 kHz sinusoidal audio signal wave of amplitude 6 mV.

  • Frequency components of the modulated wave will include:
  • Original carrier frequency = 10 MHz
  • Upper Side Band (USB) = 10.005 MHz
  • Lower Side Band (LSB) = 9.995 MHz
  • Modulation factor:
    $ext{μ} = \frac{A<em>m}{A</em>c} = \frac{6}{10} = 0.6.$

Production of AM Waves

• AM can be produced using various methods, depicting the modulating signal added to the carrier signal, producing an output that passes through a nonlinear device (square law device).
• The output supports various frequencies, and through band filtering, unwanted frequencies are stripped away, leaving only the modulated wave.

Detection of AM Waves

• Before detection, the modulated signal might be weak post-transmission; thus, a receiver typically includes an amplifier and a detection stage.
  • Detection Process: Recovering the modulating signal from the modulated carrier wave involves rectifying the modulated signal and passing it through an envelope detector.