Sunday, 16 October 2022

Reflection, its law and Application

Light


It is an agent in which produces in us the sensation of sight. It is a form of energy. 

     No doubt this definition of light holds good only for a small portion of light, we shall be mainly concerned with light having this property. 

     Some terms connected with light. Some of the following terms shall be more oftenly during the study of optics. 

     1. Source. A body which emits light in all directions is said to be the source of light. The source may be a point one or an extended one. A source is of two kinds :

     (a) Self luminous. Self luminous source is the source which possesses light of its own, e.g., sun, electric arc, candle, etc. 

     (b) Non-luminous. It is a source of light which does not possess light of its own but receives light from an external source and scatters it to the surroundings, i.e., moon, page of your book, table, etc. 

      2. Medium. Substance through which light propagates or tends to propagate is called a medium. It is of following three kinds :

      (a) Transparent. It is a medium through which light can be propagated easily, e.g., glass, water, etc. 

     (b) Translucent. It is a medium through which light is propagated partially, e.g., paper, ground glass, etc. 

     (c) Opaque. It is a medium through which light cannot be propagated, e.g., wood, iron, etc. 

     3. Ray. The straight line path along which the light travels in a homogenous medium is called a ray. It is represented by an arrow head on a straight line, the arrow head giving the direction of propagation of light. 

     4. Beam. A number of rays combined together is called a beam. 

     5. Pencil. A narrow beam of rays is called a pencil. A pencil is of three kinds. 

     (a) Convergent. It is a pencil in which width of the pencil goes on decreasing as the rays proceed forward. 

     (b) Divergent. It is a pencil in which all the rays meet at a point when produced backward and the width of pencil goes on increasing as the rays proceed forward. 

     (c) Parallel. It is a pencil in which all the rays move parallel to each other and the width of the pencil remains constant throughout. 

Reflection


It is the property of light by virtue of which, light is sent after being obstructed by back into the same medium from which it is coming a surface. 

Fig. 1. Reflection at a plane surface. 



     Consider a ray SO, incident on a shining surface XY. The ray gets reflected along OI (Fig. 1). We define following terms in connection with the phenomenon of reflection. 

1. Incident ray (SO). Ray which approaches the shining surface. 

2. Reflected ray (IO). Ray which departs away from the shining surface. 

3. Normal (ON). It is a perpendicular drawn to the shining surface at the point of incidence O. 

4. Reflecting surface (XY). The shining surface which sends the ray back into the same medium is called reflecting surface. If nearly 100% of light is sent back the reflecting surface is said to be a mirror. 

5. Angle of incidence (i). It is the angle between the incident ray 'SO' and the normal 'ON' to the surface. 

6. Angle of reflection (r). It is the angle between the reflected ray OI and the normal ON. 
     
      The intensity of the reflected ray depends upon the nature, state of polish and smoothness of the reflecting surface. 

7. Angle of deviation during reflection = π - (i + r). It is the angle between initial incident ray after reflection and the reflected ray. 

Law of Reflection :

Phenomenon of reflection is governed by two laws called laws of reflection, given below :

     1. The incident ray, the reflected ray and the normal to the reflecting surface at the point of incidence, all lies in one plane and that plane is perpendicular to the reflecting surface. 

     2. The angle of incidence is equal to the angle of reflection, i.e., 

                        ㄥi = ㄥr. 


Relevant Reference


     We can see a piece of paper but we cannot see our image in the piece of paper, while we can see our image in a mirror. 


     The reason is that reflection occurring in the paper is diffused reflection because it's surface is not smooth. 

     If a parallel beam of light gets reflected from a rough surface (like paper) the reflected beam neither remains parallel nor has the same orientation as it was having before reflection. Thus, reflected beam is not able to reconstruct the image of the object. We just see general illumination. 

Fig. 2. Diffused reflection. 



Image formed by a plane mirror


     (a) Image of a point source. Consider a point source 'S' situated at a certain distance from the reflecting surface (mirror) XY. A ray of light SA incident normally (∴ i = 0) on XY is reflected back along AS (∴  r = 0) (Fig. 3). Another ray SO incident on XY obliquely at an angle of incidence i is reflected along OI, making an angle of reflection r, such that angle i and angle r are equal. Reflected rays AS and OI, meet at I' only when they are produced back. So I' is the virtual image of S as seen through the mirror XY. 

Fig. 3. Image of a point source. 


  
           ㄥNOS = ㄥOSA = ㄥi (alternate angles) 
           ㄥNOI = ㄥSI'O = ㄥr (corresponding angles) 

     According to the law of reflection
   
                ㄥi = ㄥr       ∴    ㄥOSA = ㄥAI'O

     In ∆ ASO and ∆ AI'O, OA is common. 

             ㄥOSA = ㄥAI'O      (just proved) 
             ㄥSAO = ㄥI'AO = 90°

     Therefore, the triangles are congruent
    
     ∴           SA = AI'

     i.e., the image I' lies as much behind the mirror as the object is in front of it. 

     Therefore, the image formed by a plane mirror has the following characteristics :
   
     (i) It is virtual. 
    (ii) It lies as much behind the mirror as the object lies in front of it. 
   (iii) It is of same size. 
   (iv) It is literally inverted. 

     Since the image is virtual it cannot be taken on a screen or photographed. 

     (b) Image of an extended source. Consider an extended source AB held before a plane mirror XY (Fig. 4). A beam of light from A is reflected into eye by the mirror when the beam meets the mirror at 'a' and 'a'. Reflected rays meet at A₁ only when produced back. Thus, A₁ is the virtual image of A through the mirror. It may be noted that A and A₁, are both equidistant from the mirror. Similarly a beam of light starting from B, gets reflected from b, b' and enters the eye thereby giving a virtual image of B at B₁, when produced back. B and B₁ are also equidistant from the mirror. Thus, A₁B₁ is the virtual image of an extended object. 

Fig. 4. Image of an extended source. 



     The image as seen through a plane mirror is always laterally inverted, i.e., left side of the object appears as the right of the image and vice versa. If you raise your right hand in front of a mirror, the image will appears to raise the left hand. 

Rotation of a mirror


Consider a plane mirror in position X₁Y₁. An incident ray SO gets reflected along OI₁. Let the mirror rotates through an angle ∝ to the position  X₂Y₂. The reflected ray now goes to OI₂. Draw N₁O and N₂O perpendiculars to the two positions of the mirror (Fig. 5).

     ∴      ㄥN₁ON₂ = ㄥX₂OX₁ = ∝

     Applyinɡ the law of reflection in position X₂Y₂.

                  ㄥi₂ = ㄥr₂

     From the diaɡram 

                          ㄥi₂ = ㄥi₁ + ㄥ∝
and                   ㄥi₂ = ㄥr₁ − ㄥ∝ + ㄥβ
     ∴     ㄥi₁ + ㄥ∝ = ㄥr₁ − ㄥ∝ + ㄥβ
     But              ㄥi₁ = ㄥr₁     (law of reflection)

     Therefore,  ㄥ∝ = - ㄥ∝ + ㄥβ
or                        ㄥβ = 2ㄥ∝

Thus, the angle turned by the reflected ray is twice the angle turned by the mirror. 

Fig. 5. Rotation of a mirror. 



     So if a mirror turns through a certain angle the reflected ray turns through double that angle. 

Important notes


In case of reflection from a plane mirror

(i) The image is virtual and erect. 

(ii) The image lies as much behind the mirror as the object is in front of it. 

(iii) Magnification is 1.

(iv) There is lateral inversion. 

(v) If the mirror turns through certain angle, the reflected ray turns through double that angle. 

Relevant Reference


1. Whenever a wave get reflected through a danser medium, an additional phase difference of π radian (or path difference of λ/2) is introduced

Fig. 6(i). 


yi = A sin (ωt - kx) 

yr = A sin [ωt - k (x + λ/2)] 

   = A sin [ωt - kx - kλ/2]

yr = A sin [ωt - kx - π ]         [∵ k = 2π/λ]

or    yr = A sin (ωt + kx)


2. [Refer Fig. 6(i)] if there are two mirrors inclined to each other at an angle θ. Then, number of images formed 'n', of an object are given as :

     (i) If 360/θ = even integer, n = (360/θ -1) ; for any position of object (A or B). 

    (ii) If 360/θ = odd integer, then :

         (a) n = (360/θ - 1); for object on the angle bisector of mirrors (A) 

         (b) n = 360/θ; for object anywhere else (B). 

Fig. 6(ii).



3. [Refer Fig. 6(iii)] If there are two mirrors perpendicular to each other, and a ray is incident on one of them such that, it suffers only one reflection from each of them, then the final ray will be antiparallel to the incident ray, no matter, what is the angle of incidence. 

Fig. 6(iii).



Conceptual questions with answers


Q. 1. What is the difference between regular and irregular reflection ? 
 
  Ans. The reflection is said to be the regular if it takes place in accordance with the law of reflection. It takes place from a smooth surface whether plane or spherical. When a beam of parallel rays is incident on an irregular surface, light is sent back into same medium but not in accordance with the law of reflection. This reflection is called irregular; or diffused surface. 

Q. 2. A ray of light is incident on a plane mirror at a certain point. The mirror is capable of rotation about an axis passing through some other point. Prove that if the mirror turns through a certain angle, the reflected ray turns through double the angle ? 

  Ans. Let XY be the position of mirror initially [Fig. 7]. A ray AO reflected at O goes along OB. 

Fig. 7.



                   ㄥAON = ㄥ BON
     ∴          ㄥAOY = ㄥBOX = ∝ (say) 

     Let the mirror be rotated to a new position XY' . The incident ray, now, gets reflected from O' along O'B'. O'N' is the new position of normal. 

     According to the law of reflection, 

                   ㄥAON = ㄥBON
     ∴           ㄥAOY = ㄥBOX = ∝
     Also      ㄥXO'O = ㄥAO'Y' = ∝
     ∴         ㄥB'O'O = 2∝'     

     Due to rotation of mirror the reflected ray turns through an angle BCB' = ፀ. 

                ㄥBCB' = ㄥO'CO = ፀ 
                ㄥO'OC = 180° - 2∝

     In ∆OO'C,     ፀ + 180° - 2∝ + 2∝' = 180°
or                                                    ፀ = 2(∝ -  ∝') 
     In ∆XOO',                                  ∝ = ф + ∝'
     ∴                                                ф = ∝ - ∝'
     Substituting for ф in (i)        ф = 2ф

Q. 3. A mirror was rotated through a certain angle but it was observed that the reflected ray did not turn through any angle. How would you explain ? 

  Ans. If the mirror rotates in its own place about the normal as the axis, there is no turning of reflected ray due to a rotation of mirror. 

Q. 4. Prove that if a ray of light is obliquely incident on one of the two mirrors inclined at angle 'ፀ' with each other, the net deviation of ray, after reflection from both the mirrors is independent of the angle of incidence ? 

  Ans. Consider a ray SA getting reflected from A at the first mirror and successively from B at the second mirror (Fig. 8). Finally, the ray proceeds towards BI. Let i₁ and i₂ be the angles of incidences at the two mirrors. 

           ㄥBAO = 90 - i₁  and  ㄥ ABO = 90 - i₂

           In ∆OAB, 
      
           θ + ㄥBAO + ㄥABO = 180°
           θ + 90 - i₁ + 90 - i₂ = 180°   
or       θ = i₁ + i₂

              Deviation at A = π - 2i₁
              Deviation at B = π - 2i₂

Fig. 8.



     Net deviation δ of the ray is given by 

            δ = π - 2i₁ + π - 2i₂ = 2π - 2(i₁ + i₂) 
or        δ = 2(π - θ) 

     Thus, the deviation only depends upon the angle between the two mirrors. It does not depends upon the angle of incidence. 

Friday, 7 October 2022

What is Space Communication ?

 Space Communication

Introduction

Communication of message from one place to another has always been an important feature of our everyday life. Earlier, communication was done by beating of drums, by smoke signals or through pigeons. With the development of science, a necessity was felt for faster communications. Now we are relying on communication through electrical waves, which travel with velocity of light (3 × 10⁸ ms-1).

     The basic idea is to convert our primary information (may be speech or a set of printed letters) into electrical wave form (signal) which propagates through a channel. As the signal propagates, it becomes weaker due to resistance and some noises also creep in. Noises may creep in due to man made faulty contact switches, make and break of electrical circuits, ignition radiation, etc. There are some natural phenomena like sun's radiation, lightning and electrical storms which also add to the noise introduced into the signal. Always our effort is to keep the noise low and signal strong. So, we should always strive for a higher value of 'S/N' i.e., signal to noise ratio. 

     The speed of communication depends upon the number of signals transmitted in one second i.e., the frequency of signals. If we want to increase the speed of communication, we shall have to compress the waveforms in a certain time so that greater number of signals are transmitted in one second. This necessitates a greater band-width of the channel. S/N ratio and the band-width B are connected to each other by Shannon Hartley law 

                 C = B log (1 + S/N) 

where 'C' is called the channel capacity or rate of message transmission. According to this relation , if we intend to maintain a higher S/N ratio, a narrow band-width can be used while a broader band-width will be required if we have smaller value of S/N.

Terms connected with a communicating system

Following terms are often, used in connection with a communication network. 

     (i) Source. Our main purpose is to transform data from one place to another. The agent responsible for production of that data is called source. If we intend to transform sound from one place to the other, the person producing that sound is the source. It may be a sheet of paper having text written on it or a photograph to be transferred to a newspaper office by a journalist. 

    (ii) Information. The sound produced by the man, the text on the sheet or the photograph is the information. The information in its own real form can be communicated over short distances. To send this information over long distances, we shall have to change its shape. 

   (iii) Signal. In order to achieve speed in communication we have to depend on electric wave form, since they propagate with the speed of light. The information is first converted into electrical waveform by suitable circuits. The waveforms are generally time varying quantities (current and voltages). The variations correspond to the information. The instrument which converts information into a signal is called 'transducer'. The signal is transmitted and received at the destination where another transducer converts it back into information. 

   (iv) Channel. A channel is the medium through which signal propagates from sending station to receiving station. It may be a white link, a co-axial cable, an optical fibre or a radio link. We can think about a channel as a pipe with information flowing through it. A channel's carrying capacity (or band-width) limits the amount of information through it can handle. For example, the band-width of a telephone wire is 4 kilohertz, allowing it to carry about 28000 bits per second of information. The band-width of a television channel is 6 megahertz and it will handle 27 × 10⁶ bits per second. 

    (v) Noise. As the signal propagates through the medium it becomes weak due to the resistance of the medium. At the same time it gets distorted also due to some factors external as well as internal. The presence of distorted in the signal is termed as noise. Some of the external factors are lightning in atmosphere, solar radiation, ignitions and sparks in some electrical instruments. Some of the internal factors for production of noise are motion of electrons in inductors and diffusion and combination of charge carriers. 

Analog and Digital signals

Analog signal. When speech is converted into electrical oscillations using a microphone, the electrical signal is sinusoidal in nature. It is a continuously varying signal. Same is the case when vaccum tubes or semi-conductor amplifiers and oscillators are operated. 

     The term 'analog' is derived from the word analogous which means "similar to" or "compatible with". It refers to the relationship between an original and a representative of that original. Analog specifies that there is a one to one relationship between the parts of an original and the parts of its representative. For example, an analog watch represents the movement of the sun around the earth. For convenience, the 12 hours of both night and day are compressed on to one circle. 

     When a person speaks in front of a microphone, the vibrations of vocal cords produce a corresponding electrical oscillations in the electrical circuits. These oscillations are analogous to oscillations of vocal cords and hence the name 'analog'. Human beings are capable of producing oscillations of 50 Hz to 5000 Hz. It has been established that the bulk of the energy of speakers lies in the range of about 4000 Hz. Therefore, it is not necessary to transmit the entire voice signals through a telephone network for the man at the other end to be able to understand and recognise the speaker. Generally, the signals are transmitted through a 'band-width filter' which remove all frequencies except those carrying maximum energy of the signal. This filtered signal is then frequency multiplexed with other analog signals for onward transmission through telephone network. 

Digital signal. It is a signal which is discrete in nature and is represented by discontinuous curves diagrammatically. The concept of digital signal transmission is not a new one. About a hundred years ago, Samuel Morse used his Morse code of dashes and dots for transmission of messages from one place to other. One hundred years before that an American P. Revere used one lantern signal and two lantern signals to signify two previously decided messages to be conveyed to distant places.  

     A digital signal is one which consists of a sequence of symbols taken from a finite set. The text of this book can be considered to be an example of digital signal. The text consists of a number of discrete letters along with punctuation signs and numerical figure. The simplest digital signal, a binary signal uses only two symbols or states denoted by 0 and 1. These binary digits are called bits. [Fig. 1] shows two types of binary representations.

Fig. 1. Binary representations. 

 

     (i) Positive logic. In this case the voltage used to represent binary 1 is higher than that used for binary 0 [Fig. 1(i)].

    (ii) Negative logic. In this case the voltage used to represent binary 1 is lower than that used for binary 0 [Fig. 1(ii)].

     There are other ways also of representing these binary digits. [Fig. 2(i)] represents two different binary slabs by a change in frequency while [Fig. 2(ii)] shows two binary slabs by turning on and off a single frequency. 

Fig. 2. Binary representations. 


Merits of digital signals

As the signals travel (through cable or space) attenuation takes place. As a result of this noise creeps in. Thus, the resultant signal is not exactly similar to one which was transmitted. This effect is relatively more prominent in analog signals where we have to use various vaccum tubes/semi-conductor devices. 

     Main important feature of the digital signals is that the effect of noise and interference can be virtually eliminated. The block diagram of a system illustrating this characteristics is shown in [Fig. 3(a)] necessary. 

Fig. 3. Part of a binary digital transmission system. 


     The essential components of the system are as follows :

     (i) Transmitter. This is a device which sends a binary data in which a binary 1 is represented by a positive voltage for the duration of complete symbol period and binary 0 us represented by zero volt. The waveform of the transmitted data is shown in [Fig. 3b (i)].

    (ii) Transmission channel. As the signal travels through the channel (may be a co-axial cable) it gets attenuated. The clear transition between the two voltage levels becomes indistinct. Along with that some delay is also accompanied with. The attenuated signal is shown in [Fig. 3b (ii)]. 

   (iii) Equaliser. The attenuated signal is allowed to pass through a circuit called 'equaliser'. This circuit makes the relationship of equaliser output to the original binary symbol more predominant. The output of equaliser is shown in [Fig. 3b (iii)].

   (iv) Threshold detector. It is a circuit whose output is one of the two voltage levels depending on whether the output is greater or less than a pre-set threshold level. As output of equaliser passes through it, a binary signal very similar to the transmitted one is obtained. The signal is said to have been regenerated. It will be observed that the regenerated signal [waveform (iv)] is slightly out of step with the original signal [waveform (i)].

    (v) Retiming circuit. Final processing of the signal is its retiming. If this is not done, the irregularities present in waveform (iv) will soon build up to produce error. A regular timing reference signal [waveform (v)] is derived from the received waveform by a special circuit and is mixed with output of threshold detector to give a final regenerated digital signal [Fig. 3b(vi)].

     Thus, it can be seen that inspite of presence of noise, the regenerated signal is almost similar to the original transmitted signal but is slightly delayed. Therefore, transmission through digital signals helps us in maintaining data integrity. 

     By using large scale integrated circuit, we have been able to reduce the cost and size of equipment to be used in digital transmission while this has not been done in analog transmission. 

     Use of very high band-width (satellites and optical fibres) increases the capacity to be utilized. This benefit can be encashed only in case of digital transmission. 

Modulation

While sitting at home, we watch a cricket match being played thousands of kilometer away. To broadcast a programme over such large ranges, we need modulation.

  Modulation is the process of superimposing the signal to be transmitted on other wave of high frequency called carrier wave so that is can be transmitted to large distances. The technique of superimposing depends on the type of modulation. To understand how does modulation make a signal to be received over greater distance, let us consider the following example. 

     Suppose you buy a cup of ice cream about 1 km away from your house. If you return on foot, the ice cream will melt. But if you return on a motorbike, you can bring it in very good condition. Same is the case with an audio signal. It travels at a speed of only 330 ms-1. By the time it reaches 100 m, it dies off because of rigidity of the medium. But if it is superimposed on a carrier wave moving with speed of light, it can travel a much greater distance. 

     Modulation is also used to keep the dimensions of receiving antenna within practical limits. At this stage, it might be difficult to understand. Length of antenna bears an inverse relation with the frequency of signal to be received. For audio ranges, the length can be calculated to be 10 - 20 km which is quite impractical. Modulation makes signal frequency equal to carrier frequency. So, length of antenna is reduced to about 2 m. For the same reason, antenna use in UHF range has smaller length as compared to ordinary VHF antenna. 

     A carrier wave in general, us represented by the equation, 

                      Vc = Vcm sin (ωc + θ)

     Impression of the signal can be superimposed over the carrier wave in following ways :

     (i) By changing Vcm keeping ωc and θ constant. In this method the amplitude of the carrier wave varies in accordance with the amplitude of the signal. This method of modulation is called amplitude modulation. 

    (ii) By changing ωc keeping Vcm and θ constant. In this method, the frequency of carrier wave change according to the amplitude of modulation signal. This method of modulation is called frequency modulation. 

  (iii) By charging θ keeping Vcm and ωc constant. This impression of modulation signal can also be incorporated into carrier wave by changing its phase in accordance with the amplitude of modulation signal. This method of is called phase modulation. 

   (iv) There is yet another mode of modulation provided the carrier wave is taken in the form of pulses of short duration. This type of modulation us called pulse modulation. 

Amplitude Modulation (AM) 

In this type of modulation, amplitude of the carrier wave is varied in direct proportionality with the amplitude of modulating signal [Fig. 4]. Suppose the signal is

                                 Vs = Vsm sin ωst

and the carrier is        Vc = Vcm sin ωct 

     In amplitude modulation (AM) , amplitude of the carrier varies according to the instantaneous signal value. New value of  Vcm is

             V' cm = Vcm + Ka Vsm sin ωst    

     Here Ka is a factor that determines the extent of variation of modulated signal with audio signal. 

Fig. 4. Amplitude modulation. 

      ∴     Modulated signal has Instantaneous value as

     Vc = (Vcm + Ka Vsm sin ωst sin ωct

     = Vcm sin ωct + Ka Vsm sin ωst sin ωct

    = Vcm sin ωct + Ka Vsm/2 (2 sin ωst sin ωct) 

    = Vcm sin ωct + Vcm Ka Vsm/2Vcm 

                         [cos (ωc - ωs) t - cos (ωc + ωa) t]


or    Vc = Vcm sin ωc t + Vcm m/2

                         [cos (ωc - ωs) t - cos (ωc + ωs) t]


     Here m = Ka Vsm/Vcm is called "modulation index". 

Therefore, the modulated signal consists of 

     (i) Vcm sin ωct i.e., original unmodulated carrier. 

    (ii) Frequencies ωc - ωs and ωc + ωs each with an amplitude of  Vcm .m/2.

     These two frequency components are called side bands. The word band may sound confusing because band is not a single frequency but a range if frequencies. ωc - ωs is not a single frequency. When we transmit audio signal say speech, it had components ranging from 200 Hz to 15000 Hz. So, ωs is a band of frequencies. If we use a carrier of 50 kHz frequency. 

        ωc - ωs will range from 49.8 - 35 kHz. 

        This is called lower side band. 

        ωc + ωs will range from 50.2 to 65 kHz. 

        This is called upper side band. 

     This figure 5 shows the side bands for a signal having frequencies between 200 and 15000 Hz. The signal can be reproduced equally well from either of the two side bands. For transmission we transmit only one side band. This is called single side band transmission. 

Fig. 5. Side bands of a signal. 


     Nonlinear modulation. From the article on energy density of electromagnetic waves, we get that energy per unit volume in an electric field. 

                  uE = ½ ε₀ E²

     This gave an idea for nonlinear modulation. In this case, we use devices having nonlinear V-I characteristic like a triode. For a device having square law relation between input current I and output voltage V, 

           I = aV²

where a is a constant. 

      V is modulated output voltage. 

     Clearly, the output contains frequencies 2 ωs, 2 ωc.These are two harmonics. The useful frequencies in the  output are ωc - ωs andωc + ωs, i.e., the two side bands. Also there is d.c. component, i.e., a/2 (sm + V²cm). All the frequency component except ωc - ωs and ωc + ωs are eliminated using a parallel LC circuit which has resonant frequency at ωc. The output frequency characteristics of LC circuit and the modulation circuit are shown in Fig. 6.

     LC circuit attenuates frequencies lower than ωc - ωs and those higher than ωc + ωs

Fig. 6. Modulation circuit and frequency characteristics. 

Frequency Modulation (FM) 

Inthis case, the frequency of the carrier is changed according to the amplitude of modulating signal. In AM, the zero carrier frequency was fixed while the carrier amplitude was varied. In FM reverse is the case. The modulating signal, carrier and modulated signal all are shown in Fig. 7. 

     In this case when modulating signal has zero amplitude, i.e., at ωt = 0, π, 2π, the carrier frequency remains unchanged. When amplitude is greater than zero, the carrier frequency increases and when the amplitude is less than zero, the carrier frequency decreases. Let fc be carrier frequency at zero signal amplitude, fmax be carrier frequency at maxima of modulating signal and be that at the  minima. 

     The fmax - fc = fc = fmax is called frequency deviation 

     Fig. 7 shows that concept of frequency modulation when there is no signal, the frequency of modulated wave remains constant and is same as that of carrier wave [Fig. 7(i)]. During positive half of modulating signal, the frequency of modulated wave increases while during negative half it decreases. This effect is illustrated in [Fig. 7(ii) and (iii)] using two modulating signals of different frequencies. 

Fig. 7. Frequency modulation. 

Comparison of AM and FM

Following comparison between AM and FM will show that FM is advantageous over AM. 

AM

FM

(i) In case of AM, a large amount of power component is of carrier frequency which is of no use. For modulation index m = ½, 90% power is in carrier and only 10% inside bands. So wastage of power is there. Thus FM has higher efficiency than AM. 


(ii) The frequency range of modulation of AM is less than that of FM. 
(i) FM is immune to almost all forms of noise existing in nature. Most forms of noise consists of variations in amplitude to which FM receiver is not sensitive. It can detect only variations in frequency. So transmission is noise free. 

(ii) The frequency range of modulation of FM is higher than that of AM. 


     These advantages are clear from the fact that sound of a TV set (FM) is so much better quality than that of a radio set (AM). 

Phase Modulation

In this type of modulation, the phase angle of the carrier waves undergoes and change depending upon the amplitude of modulating signal. Let the carrier wave and the modulating signal be represented as

Vc = Vcm sin (ωct + θ) 

and      Vs = Vsm sin ωmt

     If θt is the instantaneous value of phase angle of modulated wave, 

θt = θ0 + KVs

     where θ₀ is the initial phase angle at the = 0 and K is the phase deviation constant. Since is a constant value, it does not effect the modulation, therefore, it can be ignored. 

∴           θt = KVsm sin ωmt = ∆θ sin ωmt

     Here ∆θ = K Vsm is known as peak phase deviation. 

     Phase modulated wave is given by Vc = Vcm sin (ωct + KVsm sin ωmt).

Pulse Modulation

In this type of modulation, the carrier wave consists of high frequency discontinuous pulses whose characteristics get changed due to the superimposition of signal. Depending upon the change in characteristics there are various types of pulse modulation. 

     (i) Pulse amplitude modulation. Superimposition signal results in change in amplitude of carrier pulses. 

    (ii) Pulse duration modulation. In this case, the time interval between the consecutive pulses gets affected due to superimposition of signal. 

   (iii) Pulse code modulation. The chain of pulses represents the binary coded representation of signal. 

Demodulation 

As the modulated signal reaches the destination, we need to extract information from it. The process of unloading the information from the modulated wave is called demodulation. 

     (i) Amplitude demodulation. Fig. 8 shows a circuit diagram where we have used a crystal diode for demodulation. 

Fig. 8. Junction diode as demodulator. 

     The function of the LC circuit is to select a particular frequency out of a large number of frequencies. It is used for turning the demodulation to only one station transmitting the programme. Now this modulated signal has two halves that is positive and negative. The diode is used to cut off negative part as shown in Fig. 9.

Fig. 9. Demodulation. 

    To obtain audio signal from it, we use smoothening circuit containing capacitor and resistor. 

Fig. 10. Smoothening output audio signal. 

     In Fig. 10 carrier peaks are marked A, B, C ect. When peak A comes, the capacitor starts getting charged. When input climbs down from peak A, the capacitor discharges slowly through the resistance so that output is not zero till another peak B comes. So the capacitor joins all the peaks of the carrier with one another to get the audio signal as output. In this case output is  somewhat spiky. So some noise is always there. 

    (ii) Frequency demodulation. The modulated wave has different frequencies in its different region. To extract the information of modulating signal from this, the basic principle are as follows. The reactance of an inductor or capacitor depends upon the frequency of incident wave. The modulated wave shall produce a current (in an inductor or capacitor) which is an image of modulating signal. This current when allowed to flow through a resistor will produce a varying voltage signal similar to the modulating signal. 

Earth's atmosphere and electro-magnetic radiation

Electro-magnetic radiation interacts with the earth's atmosphere. For a proper study of their interaction, we must know the constitution of earth's atmosphere can be broadly divided into following four regions [Fig. 11]. Actually there are no sharp boundaries dividing these regions. Their heights are variable. Whatever is given below is their average behaviour over a long duration of time. 

Fig. 11. Different regions of atmosphere. 


     (i) Troposphere. It is the region of atmosphere in contact with the surface of earth and extends up to a constituent of the atmosphere are contained in this region. Its density varies from 1 kg m-3 at the source of 0.1 kg m-3 at its top. The rate of fall of temperature in this region is 6 K per km of height. This region is separated from the next higher one by gap called troposphere. 

    (ii) Stratosphere. It is the region of atmosphere which extends from a height of 12 km to 50 km. It is a region which forms practically clear sky. The density in this region varies from 10-1 kg m-3 to 10-3 kg m-3. This region has a later of ozone at its upper extreme. This layer protects the life on earth from the harmful effects of ultraviolet light of sun. This region is separated from the next higher region by a gap called stratosphere. 

   (iii) Mesosphere. It is the region of atmosphere extending from a height of 50 km to 80 km. The density at this region varies from 10-3 kg m-3 to 10-5 kg m-3. Temperature in this region decreases from 290 K to 180 K. 

   (iv) Ionosphere. It is the region of atmosphere extending from the height of 80 km to about 400 km above the surface of earth. This is the outermost part of the region and receives maximum energy from sun. The constituents of this region are free electrons and positively charged ions. That is why it is rightly called ionosphere. This is further divided into different regions on the basis on the density of free electrons. Lowest region called D-layer contains a few electrons. As we move upward, the density of free electrons increases. Beyond 150 km, the region is E-layer up to a height 300 km. Its free electron density is higher than that of  D-layer. 300 - 400 km region contains F₁ layer and F₂ layer. Reflection of radio waves occurs im E-layer and F-layer. Density of ionosphere region varies from 10-5 kg m-3 to 10-10 kg m-3 while the temperature rises from 180 K to 700 K. 

     As the electro-magnetic radiations from sun pass through the atmosphere, some of them are absorbed by it while other reach the surface of earth. The renge of wave length which reaches earth lies in infrared region. This increases the temperature of earth. The radiations emitted by earth (in accordance with Planck's radiation formula) travel towards the atmosphere but are unable to escape. Heavier gases like CO₂ present in the stratosphere region reflect these radiations back to the surface of earth. This keeps the surface of earth warm. This effect is called green house effect. 

     The other short wave length constituents (ultraviolet light, X-rays, γ-rays) of radiations from such are harmful to the living tissues. These constituents are absorbed by the ozone layer and are eliminated, thus keeping the life on earth safe. 

Propagation of radio waves through atmosphere

Radio waves from an important tool for communicating messages from one place to another. Propagation of radio wave can take place in any of the following three modes :

     (i) Ground waves. Radio waves emitted by a transmitter T travel in a straight line. As such these are not able to reach distant point due to the curvature of the earth. The station situated close to the transmitter can however catch these rays directly. Such waves called ground waves (Fig. 12). Due to their absorption by ground, the signals received at distant station are weaker and then absorption increases with an increase in frequency of wave. 

Fig. 12. Ground waves and sky waves. 


   (ii) Sky waves. The stations, which become inaccessible to ground waves due to the curvature of earth, can receive waves after reflection from the ionosphere. These waves are called sky waves. 

     The refractive index μ of the atmosphere for radio waves depends upon the frequency of radio waves as well as the di-electric constant of the medium. The di-electric constant of the medium (ionosphere region) depends upon its free electron density. It decreases with an increase in free electron density. As we go up in ionosphere, the electron density increases, thus decreasing di-electric constant. Since refractive index is proportional to square root of di-electric constant, it also decreases as we move up. A radio wave finds itself travelling from denser to rare medium. It continuously bends away from the normal layer after layer, till its angle of incidence increase up to the critical angle. Then it suffers total internal reflection and it set back towards the earth. Thus, it is able to reach distant points which were otherwise inaccessible to ground waves. These waves are called sky waves. 

     Low frequency waves are reflected by E-layer and high frequencies are reflected by F₁ and F₂ layer. Still hiɡher frequencies (> 300 MHz) cannot be reflected by the ionosphere and get transmitted through it. 

  (iii) Space waves. The ionosphere does not help in reflecting wave of frequencies greater than 300 MHz. This range of frequencies is generally used in T.V. transmission. These waves can travel from transmitting station to receiving station along the line of sight. Thus, their propagation takes place in between two highly placed antenna. This is the region that transmission antenna is generally very high. We can calculate the distance 'd' up to which the signals from an antenna of higher 'h' can be received. 

     Consider a transmission antenna 'T' of height 'h' at P (Fig. 13). From T, draw tangents TA and TB touching the earth's surface at A  and B respectively. Let O be the centre of earth. 

Fig. 13. Range of ground waves. 


     In right angled triangle OAT

                      OT² = OA² + AT²

     Here        OT = R + h, OA = R and AT = d

Where R is the radius of earth and 'd' is the distance up to which the waves can reach. 

     ∴                     (R + h)² = R² + d²

or              R² + h² + 2Rh = R² + d²

     ∴                              d² = h² + 2Rh

or                                   d = √h(2R + h) 

     It is clear from this expression that 'd' increases with an increase in h. 

     In order to reach still greater distances, we can make use of following methods :

     (a) Relay stations. Waves transmitted from a place are received by a number of intermediate stations called relay stations. At these stations, the waves are reprocessed and transmitted further. In this way, we can reach from one point to any other point on earth. 

     (b) Geostationary satellite. A satellite revolving around the surface of earth with a time period of 24 hours is called geostationary satellite. It always appears to be stationed directly above a particular station on earth. Any transmission done from that station is received by the satellite and is retransmitted towards the earth. These retransmitted waves will be able to reach a vast area of the surface. 

Satellite Communication

For transmitting audio information, we make use of low frequency radio waves which can be reflected back to the surface of earth by the ionosphere surrounding the earth. Thus, one transmitting station can be send messages all over the world. To transmit video messages, we require carrier waves of high frequency (>300 MHz). Ionosphere is transperent for these frequencies. Therefore, we can receive these waves only as ground waves. To receive them around the curve of the surface we shall require very high antennaes which is simply impracticable. Development of artificial satellites has given us a mode if transmission of high frequency waves from one place to all over the world around the globe. 

     Signals to be transmitted are aired by the transmitter [Fig. 14]. These signals are received by geostationary satellites S₁ and S₂ situated on the teo sides of the transmitter. Satellites retransmit the signals after processing them. The retransmitted signals can be received at all the places around the globe. 

     In early days of development of satellites we did not have geostationary satellites. The satellites used to cover a certain region for a specified duration only. Therefore, constant reception of signal at a particular place was not possible. Now with the development of geostationary satellites, this problem has been overcome. Any place on the surface of earth receive the signals round the clock. 

Fig. 14. Communication through satellites. 

Application of satellite in communication

     1. Cable network. Distribution of information all around the world through cable network is one of the most common applications of satellites. 

     A simple cable network is shown in Fig. 15. Transmission from the satellite is received by the 'head end' through a dish antenna. After proper processing it is distributed to different homes through co-axial cables. Due to attenuation of signal during propagation amplifiers (A) have to be installed at different places. These amplifiers boost the signals to provide quality reception. 

Fig. 15. Cable network. 

     Band-width capacity plays an increasingly significant role in cable industry. The original cable systems built in 1950s had a band-width of 170 MHz and supported 12 to 22 channels. As of 1996, new urban systems are being built with a single cable providing a band-width of 450 MHz to 760 MHz and the ability to support 108 to 120 channels. 

     2. Direct to Home (DTH) Services. Originally satellites were not meant for transmitting directly to homes. Till 1972 when satellite industry was privatised, satellite operators were content to distribute programming between television networks and stations. Two portions of the Fixed Satellite Services (FSS) frequency bands were assigned for these relay services. (i) Low power C-band (3.7 GHz to 4.2 GHz) (ii) Medium power Ku band (11.7 GHz to 13.2 GHz). 

     In the 1980s, a few entrepreneurs saw the possibility of using existing medium power Ku band satellites for DTH services. Because of higher frequencies and higher power (as compared to C-band) there was less interference from other frequency transmission. It was possible to obtain strong signals with a smaller three foot home receiving dishes. Direct to home (DTH) transmission has not gained much popularity because of higher cost and significant signal interference from rain and snow. 

      3. Direct Broadcast Satellites (DBS) services. In 1979, the World Administrative Radio Conference (WARC) of International Telecommunication Union (ITU) allocated a  higher power Ku band (13.2 GHz to 13.7 GHz) for multichannel transmission. These services were to be called Direct Broadcast Satellite (DBS) services. Specific DBS frequency assignments for each country as well as satellite orbital slits to transmit these high power frequencies were allocated at ITU regional conference in 1983.

     According to ITU specification, a direct broadcast satellite would be located in the geo-stationary orbit, 35888 km above the equator. It would receive signals from earth and retransmit them for reception by small, inexpensive receiving antennas installed at individual residences. The receiver package for DBS system will probably consist of a parabolic dish antenna, a down converter and any auxiliary equipment necessary for encoding , channel selection, etc. 

     4. Remote sensing. Remote sensing is the term associated with observing the earth from space. Since satellites revolve around the earth in space, they can be used for remote sensing. Satellites are made to revolve in polar orbits at a height laying between 250 km to 1000 km. These satellites probe the earth resources and its environment from space. Their working is based on sensors data processing, data analysis and data interpretation. The sensors placed in the satellite receive radiation reflected/emitted/radiated from earth's surface. They record, interpret and transmit this information back to base laboratories. Remote sensing can provide valued information about land and sea. A microwave transmitter in satellite sends microwave pulses towards sea. They reflected pulses are received back by the sensors. By noting the time taken by the wave to come back and a knowledge of its intensity provides us information about sea surface elevation and deep features of sea. 

     There are two types of sensors in remote sensing satellites : Passive and active sensors. Passive sensors like TV or photographic camera do not emit any radiation, but only act as devices for analysis of received radiation. They contain seven sensors each sensitive to different wave lengths ranging from visible to far infrared. By noting the percentage crops can be detected. Passive sensors become ineffective in cloudy days. Active sensors send radio pulses towards the earth and study the reflected waves. The extent of moisture in soil and plants can be estimated by studying reflected infrared rays from them. 

     Super computers, in combination with satellite, are used for remote sensing to locate crude oil and other natural resources inside rocks, sea and desert inside the mother earth. Dur to their unique scanning and encoding techniques as well as modular construction, they can monitor a single remote site or they can be used for complete control and supervision of a large system. 

Conceptual questions with answers

1. What is meant by a channel ? 

Ans. It is a medium through which a signal is propagated from one place to another. It may be a wire link, co-axial cable, optical fiber or radio link. 

2. What is noise ? 

Ans. A distortion in the shape of a signal, due to internal and/or external factor is called distortion. 

3. What is band width ? 

Ans. The carrying capacity of a channel which limits the amount of information the channel can handle is called band width. 

4. What are carrier wave ? 

Ans. These are high frequency electromagnetic waves whose amplitude/frequency gets varied according to the amplitude/frequency of imposed signal. 

5. What is ozone layer ? 

Ans. It is a region of atmosphere at the upper end of stratosphere and is responsible for protecting life on earth from harmful radiations from sun. 

Key words

Analog (signal). Electrically oscillating signal which is similar to the original signal. 

Band width. A range of frequencies. 

Binary signal. A signal having variations only. 

Channel capacity. The amount of information a channel can handle. 

Channel. A medium through which a signal propagates. 

DBS services. Direct Broadcasting Satellite services. 

Demodulation. Process of separating the information from modulated wave. 

Digital signal. A signal which is discrete in nature. 

DTH services. Direct to home services. 

E-layer. A region of ionosphere capable of reflecting comparatively lower frequencies. 

F-layer. A region of ionosphere capable of reflecting higher frequencies. 

Geostationary satellite. A satellite having a time period of rotation of 24 hours. 

Ground waves. Radio waves which travel directly from transmission to receiving station. 

Ionosphere. A region of earth's atmosphere composed of ions. 

Mesopause. A region separating mesosphere and ionosphere. 

Mesosphere. A region of earth's atmosphere between 50 km to 80 km. 

Modulation. Process of mixing signal with carrier waves. 

Noise. A distortion produced in the signal due to external factors. 

Ozone layer. A region of earth's atmosphere in between stratosphere and mesosphere capable of absorbing harmful radiations from sun. 

Remote sensing. Process of observing the earth from the atmosphere. 

Satellite. A body going round the surface of earth in a stable orbit. 

Signal. Information to be transmitted. 

Sky waves. Radio waves reflected back to the surface of earth by the ionosphere. 

Stratopause. Region of earth's atmosphere at the bottom of mesosphere. 

Stratosphere. Region of earth's atmosphere between 12 km to 50 km height. 

Tropopause. Region of earth's atmosphere separating troposphere and stratosphere. 

Troposphere. Lowermost part of earth's atmosphere (upto a height of 12 km). 

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