Mathematics BASIC TERMINOLOGY USED IN COMMUNICATION SYSTEMS, BANDWIDTH AND PROPAGATION OF ELECTROMAGNETIC WAVES

### Topic Covered

color{blue}{star} ELEMENTS OF A COMMUNICATION SYSTEM
color{blue}{star} BASIC TERMINOLOGY USED IN ELECTRONIC COMMUNICATION SYSTEMS
color{blue}{star} BANDWIDTH OF TRANSMISSION MEDIUM
color{blue}{star} PROPAGATION OF ELECTROMAGNETIC WAVES

### INTRODUCTION

color{blue} ✍️Communication is the act of color{brown} {"transmission of information."}

color{blue} ✍️ Every living creature in the world experiences the need to impart or receive information almost continuously with others in the surrounding world.

color{blue} ✍️For communication to be successful, it is essential that the sender and the receiver understand a common language.

color{blue} ✍️Modern communication has its roots in the 19th and 20th century in the work of scientists like J.C. Bose, F.B. Morse, G. Marconi and Alexander Graham Bell. The pace of development seems to have increased dramatically after the first half of the 20th century.

color{blue} ✍️The aim of this chapter is to introduce the concepts of communication, namely the mode of communication, the need for modulation, production and deduction of amplitude modulation.

### ELEMENTS OF A COMMUNICATION SYSTEM

color{blue} ✍️Communication pervades all stages of life of all living creatures. Irrespective of its nature, every communication system has three essential elements "transmitter, medium/channel and receiver."

color{blue} ✍️The block diagram shown in Fig. 15.1 depicts the general form of a communication system.

color{blue} ✍️In a communication system, the transmitter is located at one place, the receiver is located at some other place (far or near) separate from the transmitter and the channel is the physical medium that connects them.

color{blue} ✍️Depending upon the type of communication system, a channel may be in the form of wires or cables connecting the transmitter and the receiver or it may be wireless.

color{blue} ✍️The purpose of the transmitter is to convert the message signal produced by the source of information into a form suitable for transmission through the channel.

color{blue} ✍️If the output of the information source is a non-electrical signal like a voice signal, a transducer converts it to electrical form before giving it as an input to the transmitter.

color{blue} ✍️When a transmitted signal propagates along the channel it may get distorted due to channel imperfection. Moreover, noise adds to the transmitted signal and the receiver receives a corrupted version of the transmitted signal.

color{blue} ✍️The receiver has the task of operating on the received signal. It reconstructs a recognisable form of the original message signal for delivering it to the user of information.

color{blue} ✍️There are two basic modes of communication: "point-to-point and broadcast."

color{blue} ✍️In point-to-point communication mode, communication takes place over a link between a single transmitter and a receiver. Telephony is an example of such a mode of communication.

color{blue} ✍️In contrast, in the broadcast mode, there are a large number of receivers corresponding to a single transmitter. Radio and television are examples of broadcast mode of communication.

### BASIC TERMINOLOGY USED IN ELECTRONIC COMMUNICATION SYSTEMS

color{blue} ✍️By now, we have become familiar with some terms like information source, transmitter, receiver, channel, noise, etc.

color{blue} ✍️It would be easy to understand the principles underlying any communication, if we get ourselves acquainted with the following basic terminology.

color{brown}((i)bbul ("Transducer") : ) Any device that converts one form of energy into another can be termed as a transducer. In electronic communication systems, we usually come across devices that have either their inputs or outputs in the electrical form.

color{blue} ✍️An electrical transducer may be defined as a device that converts some physical variable (pressure, displacement, force, temperature, etc) into corresponding variations in the electrical signal at its output.

color{brown}((ii)bbul ("Signal") : ) Information converted in electrical form and suitable for transmission is called a signal. Signals can be either analog or digital. Analog signals are continuous variations of voltage or current.

color{blue} ✍️They are essentially single-valued functions of time. Sine wave is a fundamental analog signal. All other analog signals can be fully understood in terms of their sine wave components.

color{blue} ✍️Sound and picture signals in TV are analog in nature. Digital signals are those which can take only discrete stepwise values. Binary system that is extensively used in digital electronics employs just two levels of a signal. ‘0’ corresponds to a low level and ‘1’ corresponds to a high level of voltage/ current.

color{blue} ✍️There are several coding schemes useful for digital communication. They employ suitable combinations of number systems such as the binary coded decimal (BCD)*. American Standard Code for Information Interchange (ASCII)** is a universally popular digital code to represent numbers, letters and certain characters.

color{brown}((iii)bbul ("Noise") : ) Noise refers to the unwanted signals that tend to disturb the transmission and processing of message signals in a communication system. The source generating the noise may be located inside or outside the system.

color{brown}((iv)bbul ("Transmitter") : ) A transmitter processes the incoming message signal so as to make it suitable for transmission through a channel and subsequent reception.

color{brown}((v)bbul ("Receiver") : ) A receiver extracts the desired message signals from the received signals at the channel output.

color{brown}((vi)bbul ("Attenuation") : ) The loss of strength of a signal while propagating through a medium is known as attenuation.

color{brown}((vii)bbul ("Amplification") : ) It is the process of increasing the amplitude (and consequently the strength) of a signal using an electronic circuit called the amplifier . Amplification is necessary to compensate for the attenuation of the signal in communication systems.

color{blue} ✍️The energy needed for additional signal strength is obtained from a DC power source. Amplification is done at a place between the source and the destination wherever

color{brown}((viii)bbul ("Range") : ) It is the largest distance between a source and a destination up to which the signal is received with sufficient strength.

color{brown}((ix)bbul ("Bandwidth") : )Bandwidth refers to the frequency range over which an equipment operates or the portion of the spectrum occupied by the signal.

color{brown}((x)bbul ("Modulation") : )The original low frequency message/information signal cannot be transmitted to long distances because of reasons given in Section 15.7.

color{blue} ✍️Therefore, at the transmitter, information contained in the low frequency message signal is superimposed on a high frequency wave, which acts as a carrier of the information. This process is known as modulation. As will be explained later, there are several types of modulation, abbreviated as AM, FM and PM.

color{brown}((x i)bbul ("Demodulation") : ) The process of retrieval of information from the carrier wave at the receiver is termed demodulation. This is the reverse process of modulation.

color{brown}((x ii)bbul ("Repeater") : ) A repeater is a combination of a receiver and a transmitter. A repeater, picks up the signal from the transmitter, amplifies and retransmits it to the receiver sometimes with a change in carrier frequency.

color{blue} ✍️Repeaters are used to extend the range of a communication system as shown in Fig. 15.2.
A communication satellite is essentially a repeater station in space.

### BANDWIDTH OF SIGNALS

color{blue} ✍️In a communication system, the message signal can be voice, music, picture or computer data. Each of these signals has different ranges of frequencies.

color{blue} ✍️The type of communication system needed for a given signal depends on the band of frequencies which is considered essential for the communication process.

color{blue} ✍️For speech signals, frequency range 300 Hz to 3100 Hz is considered adequate. Therefore speech signal requires a bandwidth of 2800 Hz (3100 Hz – 300 Hz) for commercial telephonic communication.

color{blue} ✍️To transmit music,an approximate bandwidth of 20 kHz is required because of the high frequencies produced by the musical instruments. The audible range of frequencies extends from 20 Hz to 20 kHz.

color{blue} ✍️Video signals for transmission of pictures require about 4.2 MHz of bandwidth. A TV signal contains both voice and picture and is usually
allocated 6 MHz of bandwidth for transmission.

color{blue} ✍️In the preceeding paragraph, we have considered only analog signals.

color{blue} ✍️Digital signals are in the form of rectangular waves as shown in Fig. 15.3.

color{blue} ✍️One can show that this rectangular wave can be decomposed into a superposition of sinusoidal waves of frequencies ν_0 , 2ν_0 , 3ν_0 , 4ν_0 ... nν_0
where n is an integer extending to infinity and ν_0 = 1/T_0.

color{blue} ✍️The fundamental (ν_0 ), fundamental (ν_0) + second harmonic (2ν_ 0), and fundamental (ν_0) + second harmonic (2ν_0) + third harmonic (3ν_0), are shown in the same figure to illustrate this fact. It is clear that to reproduce the rectangular wave shape exactly we need to superimpose all the harmonics ν_0 , 2ν_0 , 3ν_0, 4ν_0..., which implies an infinite bandwidth.

color{blue} ✍️However, for practical purposes, the contribution from higher harmonics can be neglected, thus limiting the bandwidth.

color{blue} ✍️As a result, received waves are a distorted version of the transmitted one. If the bandwidth is large enough to accommodate a few harmonics, the information is not lost and the rectangular signal is more or less recovered. This is so because the higher the harmonic, less is its contribution to the wave form.

### BANDWIDTH OF TRANSMISSION MEDIUM

color{blue} ✍️Similar to message signals, different types of transmission media offer different bandwidths. The commonly used transmission media are wire, free space and fiber optic cable.

color{blue} ✍️Coaxial cable is a widely used wire medium, which offers a bandwidth of approximately 750 MHz. Such cables are normally operated below 18 GHz. Communication through free space using radio waves takes place over a very wide range of frequencies: from a few hundreds of kHz to a few GHz.

color{blue} ✍️This range of frequencies is further subdivided and allocated for various services as indicated in Table 15.2. Optical communication using fibers is performed in the frequency range of 1 THz to 1000 THz (microwaves to ultraviolet). An optical fiber can offer a transmission bandwidth in excess of 100 GHz.

color{blue} ✍️BANDWIDTH OF TRANSMISSION MEDIUM Spectrum allocations are arrived at by an international agreement. The International Telecommunication Union (ITU) administers the present system of frequency allocations.

### PROPAGATION OF ELECTROMAGNETIC WAVES

color{blue} ✍️In communication using radio waves, an antenna at the transmitter radiates the Electromagnetic waves (em waves), which travel through the space and reach the receiving antenna at the other end.

color{blue} ✍️As the em wave travels away from the transmitter, the strength of the wave keeps on decreasing. Several factors influence the propagation of em waves and the path they follow.

color{blue} ✍️At this point, it is also important to understand the composition of the earth’s atmosphere as it plays a vital role in the propagation of em waves. A brief discussion on some useful layers of the atmosphere is given in Table 15.3.

color{brown}bbul("Ground wave")
color{blue} ✍️To radiate signals with high efficiency, the antennas should have a size comparable to the wavelength λ of the signal (at least  λ//4). At longer wavelengths (i.e., at lower frequencies), the antennas have large physical size and they are located on or very near to the ground.

color{blue} ✍️ In standard AM broadcast, ground based vertical towers are generally used as transmitting antennas. For such antennas, ground has a strong influence on the propagation of the signal. The mode of propagation is called surface wave propagation and the wave glides over the surface of the earth.

color{blue} ✍️A wave induces current in the ground over which it passes and it is attenuated as a result of absorption of energy by the earth. The attenuation of surface waves increases very rapidly with increase in frequency.

color{blue} ✍️The maximum range of coverage depends on the transmitted power and frequency (less than a few MHz).

color{brown}bbul("Sky waves")
color{blue} ✍️In the frequency range from a few MHz up to 30 to 40 MHz, long distance communication can be achieved by ionospheric reflection of radio waves back towards the earth.

color{blue} ✍️This mode of propagation is called sky wave propagation and is used by short wave broadcast services. The ionosphere is so called because of the presence of a large number of ions or charged particles. It extends from a height of ~ 65 Km to about 400 Km above the earth’s surface.

color{blue} ✍️Ionisation occurs due to the absorption of the ultraviolet and other high-energy radiation coming from the sun by air molecules. The ionosphere is further subdivided into several layers, the details of which are given in Table 15.3. The degree of ionisation varies with the height.

color{blue} ✍️The density of atmosphere decreases with height. At great heights the solar radiation is intense but there are few molecules to be ionised. Close to the earth, even though the molecular concentration is very high, the radiation intensity is low so that the ionisation is again low.

color{blue} ✍️However, at some intermediate heights, there occurs a peak of ionisation density. The ionospheric layer acts as a reflector for a certain range of frequencies (3 to 30 MHz). Electromagnetic waves of frequencies higher than 30 MHz penetrate the ionosphere and escape.

color{blue} ✍️These phenomena are shown in the Fig. 15.4. The phenomenon of bending of em waves so that they are diverted towards the earth is similar to total internal reflection in optics.

color{brown}bbul("Space wave")
color{blue} ✍️Another mode of radio wave propagation is by space waves. A space d_T = sqrt(2Rh_T) wave travels in a straight line from transmitting antenna to the receiving antenna.

color{blue} ✍️Space waves are used for line-of-sight (LOS) communication as well as satellite communication. At frequencies above 40 MHz, communication is essentially limited to line-of-sight paths.

color{blue} ✍️At these frequencies, the antennas are relatively smaller and can be placed at heights of many wavelengths above the ground. Because of line-of-sight nature of propagation, direct waves get blocked at some point by the curvature of the earth as illustrated in Fig. 15.5.

color{blue} ✍️If the signal is to be received beyond the horizon then the receiving antenna must be high enough to intercept the line-of-sight waves.

color{blue} ✍️If the transmitting antenna is at a height h_T, then you can show that the distance to the horizon d_T is given as where R is the radius of the earth (approximately 6400 km). d_T is also called the radio horizon of the transmitting antenna.

color{blue} ✍️With reference to Fig. 15.5 the maximum line-of-sight distance d_M between the two antennas having heights h_T and h_R above the earth is given by

color{blue}(d_M=sqrt(2Rh_T)+sqrt(2Rh_R))

...........(15.1)

color{blue} ✍️where h_R is the height of receiving antenna.

color{blue} ✍️Television broadcast, microwave links and satellite communication are some examples of communication systems that use space wave mode of propagation. Figure 15.6 summarises the various modes of wave propagation discussed so far.

Q 3159880714

A transmitting antenna at the top of a tower has a height 32 m and the height of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in LOS mode? Given radius of earth 6.4 × 10^6 m.
Class 12 Chapter 15 Example 1
Solution:

d_m = sqrt(2xx64xx10^5xx32)+sqrt(2xx64xx10^5xx50)m
= 64xx10^2xxsqrt(10)+8xx10^3xxsqrt(10)m
144xx10^2xxsqrt(10)m=45.5km