Communication Systems


Notes for Communication System chapter of class 12 physics. Dronstudy provides free comprehensive chapterwise class 12 physics notes with proper images & diagram.

 

Communication System

A communication system is the set-up used in the transmission of information from one place to another. The present day communication system are electrical, electronic or optical in nature.

In principle, a communication system consists of the following three parts :

(i) Transmitter

(ii) Communication Channel

(iii) Receiver

A schematic model of an electrical communication system is shown in Figure 1.

(i) A transmitter :transmits the information after modifying it to a form suitable for transmission. The key to communication system is to obtain an electrical signal (voltage or current), which contains the information. For example, a microphone converts speech signals into electrical signals. Similarly, piezoelectric sensorsconvert pressure variations into electrical signals. Light signals are converted into electrical signals by photo detectors. The devices like microphone, piezoelectric sensors and photo detectors, which convert a physical quantity (called information, here) into electrical signal are known as Transducers. Such an electrical signal contains the information to be transmitted.

We define a signal as a single valued function of time (that conveys the information). This function has a unique value at every instant of time.

Most of the speech or information signals cannot be transmitted directly over long distances.  These signals have to be loaded or superimposed on a high frequency wave, which acts as the carrier wave. This process is known as modulation. The signal so obtained is called modulated signal/wave. The power of the signal is boosted signal using a suitable amplifire. The modulated signal is then radiated into space with the help of an antenna called transmitting antenna. The arrangement is shown in Fig.2

(ii) Communication Channel : The communication channel carries the modulated wave from the transmitter to the receiver. In ordinary conversation, the air through which sound travels from the speaker to the listener serves as the communication channel. In case of telephony and telegraphy, communication channel is the transmission lines, which connect the transmitter and the receiver. In radio communication (or wireless communication), the free space through which the modulated signal travels serves as the communication channel.

(iii)The receiver : In the radio communication or wireless communication, the receiver consists of :

(a) a pick up antenna to pick the signal,

(b)a demodulator, to separate the low frequency audio signal from the modulated signal,

(c) an amplifier, to boost up suitably the audio signal, and

(d) the transducer, like loud speaker to convert the audio signal (in the form of electrical pulses) into sound waves.

The receiver part of the communication system is shown schematically in Fig.3

Antenna 

An antenna plays a vital role in a communication system. It is used in both, the transmission and reception of radio frequency signals.

Infact, an antenna is a structure that is capable of radiating electromagnetic waves or receiving them, as the case may be. Basically, an antenna is generally a metallic object, often a wire or collection of wires, used to convert high frequency current into electromagnetic waves and vice-versa. Thus, a transmitting antenna converts electrical energy into electromagnetic waves, whereas a receiving antenna converts electromagnetic waves into electrical energy. Apart from their different function, transmitting and receiving antennas behave idenically i.e. their behaviour is reciprocal.

When a transmitting antenna is held vertically, the electromagnetic waves produced are polarized vertically.

A Hertz antenna is a straight conductor of length equal to half the wavelength of radio signals to be transmitted or received i.e. l = /2.

A  Marconi antenna is a straight conductor of length equal to a quarter of the wavelength of radio signals to be transmitted or received i.e. l = /4. It is held vertically with its lower end touching the ground. The ground provides a reflection of the voltage and current distributions set up in the antenna. The electromagnetic waves emitted from (Marconi) antenna ground system are the same as those emitted from Hertz antenna, which is not grounded.

The design of an antenna depends on frequency of carrier wave and directivity of the beam etc. Two common types of antenna are :

(i) Dipole antenna, shown in Fig.4 is used in transmission of radio waves. It is omni directional.

(ii) Dish type antenna, shown in Fig.5 is a directional antenna.

Such an antenna has a parabolic reflector with an active element, called the dipole or horn feed at focus of the reflector. The dish type antenna can transmit waves  in a particular direction. Also, it can receive only those waves which are directed towards it. For transmission, the signal is fed to the active element, which directs it on to the reflector. The signal is then transmitted in the form of a parallel beam as shown in Fig.5. For reception, the waves directed towards the dish are reflected on to the active element, which converts them into electrical signals. The dish type antennas are commonly used in radar and satellite communication.

Message Signals

Message signals are electrical signals generated from the original information to be transmitted, using an appropriate transducer. A message signal is a single valued function of time that conveys the information. This function has a unique value at every instant of time. These signals are of two type :

(i) Analog signals                (ii) Digital signals

(i) Analog signals. An analog signal is that in which current or voltage value varies continuously with time.

In the simplest form of an analog signal, amplitude of the signal varies sinusoidally with time. It is represented by the equation

E = E0 sin (t + f)

where E0 is max. value of voltage, called the amplitude, T is time period and  =  is angular frequency of the signal. In fig.6, f represents the phase angle. Such signals can have all sorts of values at different instants, but these values shall remain within the range of a maximum value (+ E0) and a minimum value ( – E0).

Examples of analog signals are speech, music, sound produced by a vibrating tuning fork, variations in light intensity etc. These are converted into current/voltage variations using suitable transducers. The information bearing signals are called base band signals.

(ii) Digital signals. A digital signal is a discontinuous function of time, in contrast to an analog signal, wherein current or voltage value varies continuously with time.

Such a signal is usually in the form of pulses. Each pulse has two levels of current or voltage, represented by 0 and 1. Zero (0) of a digital signal refers to open circuit and (1) of a digital signal refers to closed circuit. Zero (0) is also referred to as 'No' or space and (1) is referred to as 'Yes' or mark. Both 0 and 1 are called bits.

A typical digital signal is shown in Fig.7.

The significant characteristics of a digital signal are : Pulse amplitude ; Pulse Duration or Pulse Width and Pulse Position, representing the time of rise and time of fall of the pulse amplitude, as shown in Fig.7.

Examples of digital messages are :

(i) letters printed in this book

(ii) listing of any data,

(iii) output of a digital computer,

(iv) Electronic transmission of a document at a distant place via telephone line i.e. FAX etc.

An analog signal  can be converted suitably into a digital signal and vice-versa.

Note. As stated above, a digital signal is represented by binary digits 0 and 1 called bits.

A group of bits is called a binary word or a byte. A byte made of 2 bits can give four code combinations : 00, 01, 10 ; 11.

Types Of Communications Systems

There is no unique way of classifying communication systems. However, for the sake of convenience, we can classify them broadly on the basis of -

(i) nature of information source,

(ii) mode of transmission,

(iii) type of transmission channel used,

(iv) type of modulation employed, as detailed below :

(a)Based on nature of information source

(i) Speech transmission as in radio

(ii) Picture as well as speech transmission as in television

(iii) Facsimile transmission, as in FAX

(iv) Data transmission as in computers

(b) Based on mode of transmission

(i) Analog communication, where the modulating signal is analog. The carrier wave may be sinusoidal or in the form of pulses. For example, in telegraphy, telephony, radio network, radar, television network, teleprinting, telex etc.

(ii) Digital communication, where the modulating signal is digital in nature. For example, Fax, mobile phone network, e-mail, teleconferencing, telemetry, communication satellites and global positioning system are all digital communication systems.

(c)  Based on transmission channel

(i) Line communication

1. Two wire transmission line

2.Co-axial cable transmission

3. Optical fibre cable communication

(ii) Space communication

(d) Based on the type of modulation

(i) For sinusoidal continuous carrier waves, the types of modulation are :

1. Amplitude Modulation (AM)

2. Frequency Modulation (FM)

3. Phase Modulation

(ii) For pulsed carrier waves, the modes of modulation are

1. Pulse Amplitude Modulation (PAM)

2. Pulse Time Modulation (PTM). It includes

– Pulse Position Modulation (PPM),

– Pulse Width modulation (PWM),

– Pulse Duration Modulation (PDM)

3. Pulse Code Modulation (PCM)

5. An important step in communications modulation and it’s need

Suppose we wish to transmit an electrical signal in the audio frequency (AF) range (20 Hz to 20 kHz) over a long distance. We cannot do it, as such because of the following reasons :

Size of the antenna or aerial. An antenna or aerial is needed both for transmission and reception. Each antenna should have a size comparable to the wavelength of the signal, (atleastl/4 in size), so that time variation of the signal is properly sensed by the antenna.

For an audio frequency signal of frequency n = 15 kHz, the wavelength, {c \over v}{{3 \times {{10}^8}} \over {15 \times {{10}^3}}} = 20000 m. The length of the antenna = {\lambda \over 4} = {{20000} \over 4} = 5000 metre. To set up an antenna of vertical height 5000 metre is practically impossible. Therefore, we need to use high frequencies for transmission.

Effective Power radiated by antenna. Theoretical studies reveal that power P radiated from a linear antenna of length l is

 \propto {1 \over {{l^2}}}

As high powers are needed for good transmission, l should be small i.e. antenna length should be small, for which wavelength l should be small or frequency n should be high.

Mixing up of signals from different transmitters. Suppose many people are talking at the same time. We just cannot make out who is talking what. Similarly, when many transmitters are transmitting baseband information signals simultaneously, they get mixed up and there is no way to distinguish between them. The possible solution is, communication at high frequencies and allotting a band of frequencies to each user. This is what is being done for different radio and T.V. broadcast stations.

All the three reasons explained above suggest that there is a need for  transmissions at high frequencies. This is achieved by a process, called modulation, where in we superimpose the audio frequency baseband message or information signals (called the modulating signals) on a high frequency wave (called, the carrier wave). The resultant wave is called the modulated wave, which is transmitted.

In the process of modulation, some specific characteristic of the carrier wave is varied in accordance with the information or message signal. The carrier wave may be

(i) Continuous (sinusoidal) wave, or

(ii) Pulse, which is discontinuous

A continuous sinusoidal carrier wave can be expressed as E = E0 sin (t + ).

Three distinct characteristics of such a wave are : amplitude (E0), angular frequency (w) and phase angle (f). Any one of these three characteristics can be varied in accordance with the modulating baseband (AF) signal, giving rise to the respective Amplitude Modulation ; Frequency Modulation and Phase Modulation.

Notes. Phase modulation is not of much practical importance. We shall, therefore, confine ourselves  to the study of amplitude and frequency modulations only.

Again, the significant characteristics of a pulse are : Pulse Amplitude, Pulse Duration or Pulse Width and Pulse Position (representing the time of rise or fall of the pulse amplitude). Any one of these characteristics can be varied in accordance with the modulating baseband (AF) signal, giving rise to the respective, Pulse Amplitude Modulation (PAM), Pulse Duration Modulation (PDM) or Pulse Widhth Modulation (PWM) and Pulse Position Modulation (PPM).

Application 1

Show that the minimum length of antenna required to transmit a radio signal of frequency 10 MHz is 7.5 m.

Solution                  

Here, f = 10 MHz = 107 Hz

\lambda = {c \over f} = {{3 \times {{10}^8}} \over {{{10}^7}}} = 30 m,    Minimum length of antenna = {\lambda \over 4} = {{30} \over 4} = 7.5 m

Amplitude Modulation

When a modulating AF wave is superimposed on a high frequency carrier wave in a manner that the frequency of modulated wave is same as that of the carrier wave, but its amplitude is made proportional to the instantaneous amplitude of the  audio frequency modulating voltage, the process is called amplitude modulation (AM).

Let the instantaneous carrier voltage (ec) and modulating voltage (em) be       represented by

ec = Ec sin ct               ....(1)

em = Em sin mt          ....(2)

Thus, in amplitude modulation, amplitude A of modulated wave is made proportional to the instantaneous modulating voltage em

i.e. A = E+ k em                ....(3)          where k is a constant of proportionality.

In amplitude modulation, the proportionality canstant k is made equal to unity. Therefore, max. positive amplitude of AM wave is given by

A = Ec + em = Ec + Em sin mt         ....(4)

It is called top envelope

The maximum negative amplitude of AM wave is given by

– A = – Ec – em

= – (E+ Em sin mt) ....(5)          This is called bottom envelope

The modulated wave extends between these two limiting envelopes, and its frequency is equal to the unmodulated carrier frequency. Fig.8(a) shows the variation of voltage of carrier wave with time. Fig.8(b) shows one cycle of modulating sine wave and Fig.8(c) shows amplitude modulated wave for this cycle.

As is clear from Fig.8(c)

Em = {{{{\rm{E}}_{{\rm{max}}}}{\rm{ - }}{{\rm{E}}_{{\rm{min}}}}} \over {\rm{2}}}

and   E= Emax – Em

= Emax – {{{{\rm{E}}_{{\rm{max}}}}{\rm{ - }}{{\rm{E}}_{{\rm{min}}}}} \over {\rm{2}}}

Ec = {{{{\rm{E}}_{{\rm{max}}}}{\rm{ + }}{{\rm{E}}_{{\rm{min}}}}} \over {\rm{2}}}    ....(6)

In amplitude modulation, the degree of modulation is defined by a term, called modulation index or modulation factor or depth of modulation represented by ma. It is equal to the ratio of amplitude of modulating signal to the amplitude of carrier wave i.e.

m{{{{\rm{E}}_{\rm{m}}}} \over {{{\rm{E}}_{\rm{c}}}}} = {{{{\rm{E}}_{{\rm{max}}}} - {{\rm{E}}_{{\rm{min}}}}} \over {{{\rm{E}}_{\max }} + {{\rm{E}}_{{\rm{min}}}}}}  ....(7)

Obviously, modulation index (ma) is a number lying between 0 and 1. Often, ma is expressed in percentage and is called the percentage modulatoion. Importance of moduation index is that it determines the quality of the transmitted signal. When modulation index is small, veriation in carrier amplitude will be small. Therefore, audio signal being transmitted will be weak. As the modulataion index increases, the audio signal on reception becomes clearer.

Application 2

An audio signal of amplitude one half the carrier amplitude is used in amplitude modulation. Calculate the modulation index ?

Solution 

Here, Em = 0.5 Ec

Emax = Ec + Em = Ec + 0.5 Ec = 1.5 Ec

Emin = Ec – Em = Ec – 0.5 Ec = 0.5 Ec

Ma = {{{{\rm{E}}_{{\rm{max}}}} - {{\rm{E}}_{{\rm{min}}}}} \over {{{\rm{E}}_{\max }} + {{\rm{E}}_{{\rm{min}}}}}} = {{{\rm{1}}{\rm{.5}}{{\rm{E}}_{\rm{c}}} - 0.5{{\rm{E}}_{\rm{c}}}} \over {{\rm{1}}{\rm{.5}}{{\rm{E}}_{\rm{c}}} + 0.5{{\rm{E}}_{\rm{c}}}}} = {{{{\rm{E}}_{\rm{c}}}} \over {{\rm{2}}{{\rm{E}}_{\rm{c}}}}} = 0.5

6.1  Frequency Spectrum of AM wave

A detailed study of amplitude modulation reveals that the amplitude modulated wave consists of three discrete frequencies, as shown in Fig.9. Of these, the central frequency is the the carrier frequency (fc), which has the highest amplitude. The other two frequencies are placed symmetrically about it. Both these frequencies have equal amplitudes-which never exceeds half the carrier amplitude. These frequencies are called side band frequencies i.e. fSB = fc ± fm

Frequency of lower side band is      fLSB = fc – fm              ....(8)

and frequency of upper side band is      fUSB= fc + fm       ....(9)

Band width of amplitude modulated wave is = fUSB – fLSB           

= (fc + fm) – (fc fm) = 2fm             ....(10)

Band width = twice the frequency of the modulating signal

6.2  Power and Current Relations in AM wave

Average power/cycle in the unmodulated carrier wave is  Pc = {{{{\rm{E}}_{\rm{c}}}^2} \over {{\rm{2R}}}}   ....(11)

where R is resistance (of antenna) in which power is dissipated.

It can be shown that total power/cycle in the modulated wave is Pt = Pc \left( {1 + {{{{\rm{m}}_{\rm{a}}}^2} \over {\rm{2}}}} \right)       ....(12)

{{{{\rm{P}}_{\rm{t}}}} \over {{{\rm{P}}_{\rm{c}}}}} = 1 + {{{{\rm{m}}_{\rm{a}}}^2} \over {\rm{2}}}              But {{\rm{P}}_{\rm{t}}}{\rm{ = }}{{\rm{I}}_{\rm{t}}}^{\rm{2}}{\rm{R}}  and {{\rm{P}}_{\rm{c}}}{\rm{ = }}{{\rm{I}}_{\rm{c}}}^{\rm{2}}{\rm{R}}

{{{{\rm{I}}_{\rm{t}}}^2} \over {{{\rm{I}}_{\rm{c}}}^2}} = 1 + {{{{\rm{m}}_{\rm{a}}}^2} \over {\rm{2}}}   or  {{{{\rm{I}}_{\rm{t}}}} \over {{{\rm{I}}_{\rm{c}}}}} = \sqrt {1 + {{{{\rm{m}}_{\rm{a}}}^2} \over {\rm{2}}}}    ....(13)

Amplitude Modulated Wave Production

The following is the block diagram of a modulator for obtaining an AM signal:

The message signal or modulating signal Am sin ωmt is added to the carrier signal Ac sin ωct to obtain the signal x(t). This signal is passed through square law device which is a non – linear device which produces output of the from y(t) = B x(t) + C x(t)2 where B and C are constants.

The signal y(t) is then passed through bandpass filter centred at ωc to remove other unwanted signals if present. Hence, we get AM signal.

Amplitude Modulated Wave Detection

The block diagram of AM wave detection is shown below:

 

The received AM signal is firstly passed through an amplifier as the transmitted signal gets attenuated while propagating through channel. After that, the carrier frequency is changed to a lower frequency known as an intermediate frequency before passing it to the detector.

Following is the detailed block diagram of detector:

The AM Wave after being converted to IF frequency is passed through a rectifier to convert it into DC signal as shown in (b). Now, in order to retrieve message signal m(t), the signal is passed through an envelope detector which can be a simple RC circuit. Finally, the message signal is passed through an amplifier to obtain the clean transmitted message signal.

Frequency Modulation

When a modulating AF wave is superimposed on a high frequency carrier wave in such a way that the amplitude of modulated wave is same as that of the carrier wave, but its frequency is varied in accordance with the instantaneous value of the modulating voltage, the process is called frequency modulation (FM).

Let the instantaneous carrier voltage (ec) and modulating voltage (em) be represented by

ec = Ec sin ct        ....(15)                     em = Em sin mt             ....(16)

Fig.10(a) represents the variation of carrier voltage with time, and Fig.10(b) represents the variation of modulating AF voltage with time.

In frequency modulation, the amount by which carrier frequency is varied from its unmodulated value (fc = c/2) is called the deviation. This deviation is made proportional to the instantaneous value of the modulating voltage. The rate at which the frequency variation takes place is equal to the modulating frequency. Fig.10(c) represents an exaggerated view of frequency modulated wave. Fig.10(d) shows the frequency variation with time in the FM wave. This is identical to the variation of the modulating voltage with time, Fig.10(b). Note that

(i) All signals having same amplitude will change the carrier frequency by the same amount, whatever be their frequencies

(ii) All modulating signals of same frequency, say 1 kHz, will change the carrier frequency at the same rate of 1000 times, per second-whatever be their individual amplitudes

(iii) The amplitude of the frequency modulated wave remains constant at all times, being equal to the amplitude of the carrier wave

If ƒ is frequency of FM wave at any instant t and ƒc is constant frequency of the carrier wave, then

deviation (in frequency),  = (ƒ – ƒc)       ....(17)

By definition of frequency modulation,

  em

or     Em sin mt

 = k Esin mt                              ....(18)

where k is a constant of proportionality, Using (17), we get

= ƒ –ƒc = k Em sin mt

or   ƒ = ƒc + k Em sin mt     ....(19)

The deviation will be maximum, when

(sinmt)max = ± 1

From (19), ƒmax = ƒ± k Em                   ....(20)

or   dmax = ƒmax – ƒc = ± k Em                ....(21)

The modulation index (mƒ) of a frequency modulated wave is defined as the ratio of maximum frequency deviation to the modulating frequency i.e.

mƒ = {{{\delta _{\max }}} \over {{f_m}}} = {{ \pm {\rm{k}}{{\rm{E}}_{\rm{m}}}} \over {{f_m}}}   ....(22)

Clearly, modulating index increases, as modulating frequency (ƒm) decreases. mƒ has no units, it being the ratio of two frequencies.

The instantaneous amplitude of frequency modulated wave is given by

A = A0 sin 

where  is the function of carrier angular frequency (c) and modulating angular frequency (m). Infact,

 = \left( {{{\rm{\omega }}_{\rm{c}}}{\rm{t}} + {\delta \over {{f_m}}}\sin {{\rm{\omega }}_{\rm{m}}}{\rm{t}}} \right) ....(23)

The frequency spectrum of FM wave is far more complex than the frequency spectrum of AM wave. Infact,

(i) The output of an FM wave consists of carrier frequency (ƒc) and almost an infinite number of side bands, whose frequencies are (ƒc ± ƒm), (ƒc ± 2ƒm), (ƒc ± 3ƒm),... and so on. The sidebands  are thus separated from the carrier by ƒm, 2ƒm, 3ƒm ....etc i.e. they have a recurrence frequency of ƒm.

(ii) The number of sidebands depends on the modulation index (mƒ). The number of sidebands increases, when frequency deviation () is increased, keeping (ƒm) constant. Similarly, number of sidebands decreases, when frequency of modulating signal (ƒm) is increased keeping frequency deviation constant

(iii) The sidebands are disposed symmetrically about the carrier. Further, sidebands at equal distances from the carrier have equal amplitudes.

(iv) As the distance of sidebands from carrier frequency increases, their amplitude decreases. Therefore, number of significant sideband pairs is limited

(v) In frequency modulated wave, the information (audio signal) is contained in the sidebands only. Since the sidebands are separated from each other by the frequency of the modulating signal (ƒm), therefore,

Band width = 2n × (ƒm)  ....(24)

where n is the number of the particular sideband pair.

Application 3

As audio signal of 2.8 kHz modulates a carrier of frequency 84 MHz and produces a frequency deviation of 56 kHz. Calculate

(i) frequency modulation index

(ii) frequency range of FM wave

Solution

Here, ƒm = 2.8 kHz, ƒc = 84 MHz ;  = 56 kHz

(i) Frequency modulation index = mƒ = {\delta \over {{f_m}}} = {{56} \over {2.8}} = 20

(ii) Frequency range of FM wave  = ƒc ± ƒm = (84 ± 2.8 × 10–3) MHz = 84.0028 MHz and 83.9972 MHz



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