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n radio transmission, it is necessary to send audio signal ( e.g. music, speech etc.) from a broadcasting station over great distances to a receiver. This com- munication of audio signal does not employ any wire and is sometimes called wireless. The audio signal cannot be sent directly over the air for appreciable distance. Even if the audio signal is converted into electrical signal, the latter cannot be sent very far without employing large amount of power. The energy of a wave is directly pro- portional to its frequency. At audio frequencies (20 Hz to 20 kHz), the signal power is quite small and radiation is not practicable. The radiation of electrical energy is practicable only at high frequencies e.g. above 20 kHz. The high frequency signals can be sent thousands of miles even with com- paratively small power. Therefore, if audio signal is to be
16.1 Radio Broadcasting, Transmission and Reception 16.2 Modulation 16.3 Types of Modulation 16.4 Amplitude Modulation 16.5 Modulation Factor 16.6 Analysis of Amplitude Modulated Wave 16.7 Sideband Frequencies in AM Wave 16.8 Transistor AM Modulator 16.9 Power in AM Wave
16.10 Limitations of Amplitude Modulation
16.11 Frequency Modulation
16.12 Theory of Frequency Modulation
16.13 Comparison of FM and AM
16.14 Demodulation
16.15 Essentials in Demodulation
16.16 A.M. Diode Detector
16.17 A.M. Radio Receivers
16.18 Types of A. M. Radio Receivers
16.19 Stages of Superhetrodyne Radio Receiver
16.20 Advantages of Superhetrodyne Circuit
16.21 FM Receiver
16.22 Difference Between FM And AM Receivers
INTRODUCTION
Modulation and
Demodulation
412 ^ Principles of Electronics transmitted properly, some means must be devised which will permit transmission to occur at high frequencies while it simultaneously allows the carrying of audio signal. This is achieved by superim- posing electrical audio signal on high frequency carrier. The resultant waves are known as modu- lated waves or radio waves and the process is called modulation. At the radio receiver, the audio signal is extracted from the modulated wave by the process called demodulation. The signal is then amplified and reproduced into sound by the loudspeaker. In this chapter, we shall focus our attention on the various aspects of modulation and demodulation.
16.1 Radio Broadcasting, Transmission and Reception
Radio communication means the radiation of radio waves by the transmitting station, the propagation of these waves through space and their reception by the radio receiver. Fig. 16.1 shows the general principles of radio broadcasting, transmission and reception. As a matter of convenience, the entire arrangement can be divided into three parts viz. transmitter , transmission of radio waves and radio receiver.
1. Transmitter. Transmitter is an extremely important equipment and is housed in the broad- casting station. Its purpose is to produce radio waves for transmission into space. The important components of a transmitter are microphone, audio amplifiers, oscillator and modulator (See Fig. 16.1). ( i ) Microphone. A microphone is a device which converts sound waves into electrical waves. When the speaker speaks or a musical instrument is played, the varying air pressure on the micro- phone generates an audio electrical signal which corresponds in frequency to the original signal. The output of microphone is fed to a multistage audio amplifier for raising the strength of weak signal.
( ii ) Audio amplifier****. The audio signal from the microphone is quite weak and requires amplifi- cation. This job is accomplished by cascaded audio amplifiers. The amplified output from the last audio amplifier is fed to the modulator for rendering the process of modulation.
Fig. 16. ( iii ) Oscillator. The function of oscillator is to produce a high frequency signal, called a carrier wave. Usually, a crystal oscillator is used for the purpose. The power level of the carrier wave is raised to a sufficient level by radio frequency amplifier stages (not shown in Fig. 16.1). Most of the broadcasting stations have carrier wave power of several kilowatts. Such high power is necessary for transmitting the signal to the required distances. ( iv ) Modulator. The amplified audio signal and carrier wave are fed to the modulator. Here, the audio signal is superimposed on the carrier wave in a suitable manner. The resultant waves are called modulated waves or radio waves and the process is called modulation. The process of modulation permits the transmission of audio signal at the carrier frequency. As the carrier frequency is very high, therefore, the audio signal can be transmitted to large distances. The radio waves from the transmitter are fed to the transmitting antenna or aerial from where these are radiated into space.
414 ^ Principles of Electronics
16.3 Types of Modulation
As you will recall, modulation is the process of changing amplitude or frequency or phase of a carrier wave in accordance with the intensity of the signal. Accordingly, there are three basic types of modu- lation, namely ; ( i ) amplitude modulation ( ii ) frequency modulation ( iii ) phase modulation In India, amplitude modulation is used in radio broadcasting. However, in television transmis- sion, frequency modulation is used for sound signal and amplitude modulation for picture signal. Therefore, our attention in this chapter shall be confined to the first two most important types of modulation.
16.4 Amplitude Modulation
When the amplitude of high frequency carrier wave is changed in accordance with the intensity of the signal, it is called amplitude modulation.
In amplitude modulation, only the amplitude of the carrier wave is changed in accordance with the intensity of the signal. However, the frequency of the modulated wave remains the same i.e. carrier frequency. Fig. 16.2 shows the principle of amplitude modulation. Fig. 16.2 ( i ) shows the audio electrical signal whereas Fig. 16.2 ( ii ) shows a carrier wave of constant amplitude. Fig. 16.2 ( iii ) shows the amplitude modulated (AM) wave. Note that the amplitudes of both positive and negative half-cycles of carrier wave are changed in accordance with the signal. For instance, when the signal is increas- ing in the positive sense, the amplitude of carrier wave also increases. On the other hand, during negative half-cycle of the signal, the am- plitude of carrier wave decreases. Amplitude modulation is done by an electronic circuit called modulator.
The following points are worth noting in amplitude modulation : ( i ) The amplitude of the carrier wave changes according to the intensity of the signal. ( ii ) The amplitude variations of the carrier wave is at the signal frequency fs. ( iii ) The frequency of the amplitude modulated wave remains the same i.e. carrier frequency f (^) c.
16.5 Modulation Factor
An important consideration in amplitude modulation is to describe the depth of modulation i.e. the extent to which the amplitude of carrier wave is changed by the signal. This is described by a factor called modulation factor which may be defined as under : The ratio of change of amplitude of carrier wave to the amplitude of normal carrier wave is called the modulation factor m i.e.
Modulation factor, m = Amplitude change of carrier wave Normal carrier amplitude (unmodulated) The value of modulation factor depends upon the amplitudes of carrier and signal. Fig. 16. shows amplitude modulation for different values of modulation factor m. ( i ) When signal amplitude is zero, the carrier wave is not modulated as shown in Fig. 16.3 ( i ). The amplitude of carrier wave remains unchanged.
Fig. 16.
Modulation And Demodulation (^) 415 Amplitude change of carrier = 0 Amplitude of normal carrier = A ∴ Modulation factor, m = 0/A = 0 or 0% ( ii ) When signal amplitude is equal to the carrier amplitude as shown in Fig. 16.3 ( ii ), the amplitude of carrier varies between 2A and zero.
Amplitude change of carrier = 2 A − A = A
∴ Modulation factor, m = Amplitude change of carrier Amplitude of normal carrier = A / A = 1 or 100 %
In this case, the carrier is said to be 100% modulated.
Fig. 16. ( iii ) When the signal amplitude is one-half the carrier amplitude as shown in Fig. 16.3 ( iii ), the amplitude of carrier wave varies between 1.5 A and 0.5 A.
Amplitude change of carrier = 1.5 A − A = 0.5 A ∴ Modulation factor, m = 0.5 A / A = 0.5 or 50 % In this case, the carrier is said to be 50% modulated. ( iv ) When the signal amplitude is 1.5 times the carrier amplitude as shown in Fig. 16.3 ( iv ), the maximum value of carrier wave becomes 2.5 A.
Amplitude change of carrier wave = 2.5 A − A = 1.5 A
Modulation And Demodulation (^) 417 Solution. Fig. 16.5 shows the conditions of the problem. Maximum voltage of AM wave is V (^) max =
= 8 mV Minimum voltage of AM wave is
Vmin =
= 2 mV
∴ Modulation factor, m = max^ min max min
V V
V V
Example 16.3. A carrier of 100V and 1200 kHz is modulated by a 50 V, 1000 Hz sine wave signal. Find the modulation factor.
Solution.
Modulation factor, m =
50 V
100 V
S C
E
E
16.6 Analysis of Amplitude Modulated Wave
A carrier wave may be represented by :
ec = E (^) C cos ω c t where ec = instantaneous voltage of carrier E (^) C = amplitude of carrier ω c = 2 π f (^) c = angular velocity at carrier frequency fc In amplitude modulation, the amplitude E (^) C of the carrier wave is varied in accordance with the intensity of the signal as shown in Fig. 16.6. Suppose the modulation factor is m. It means that signal produces a maximum change of m EC in the carrier amplitude. Obviously, the amplitude of signal is m EC. Therefore, the signal can be represented by :
es = m EC cos ω s t where e (^) s = instantaneous voltage of signal m E (^) C = amplitude of signal ω s = 2 π fs = angular velocity at signal frequency fs
Fig. 16.
Fig. 16.
418 ^ Principles of Electronics The amplitude of the carrier wave varies at signal frequency f (^) s. Therefore, the amplitude of AM wave is given by : Amplitude of AM wave = E (^) C + m EC cos ω s t = EC (1 + m cos ω s t ) The instantaneous voltage of AM wave is : e = Amplitude × cos ω c t = E (^) C (1 + m cos ω s t ) cos ω c t = E (^) C cos ω c t + m EC cos ω s t cos ω c t
= E (^) C cos ω c t + 2
mE C (^) (2 cos ω s t^ cos^ ω c t )
= E (^) C cos ω c t + 2
mE C (^) [cos (ω c +^ ω s )^ t^ + cos (ω c − ω s )^ t ]*
= E (^) C cos ω c t + 2
mE C (^) cos (ω c +^ ω s )^ t^ +^2
mE C (^) cos (ω c −^ ω s )^ t The following points may be noted from the above equation of amplitude modulated wave: ( i ) The AM wave is equivalent to the summation of three sinusoidal waves; one having ampli- tude EC and frequency ** f (^) c , the second having amplitude mEC /2 and frequency ( fc + fs ) and the third having amplitude mEC /2 and frequency fc − fs.
( ii ) The AM wave contains three frequencies viz fc , fc + fs and fc − fs. The first frequency is the carrier frequency. Thus, the process of modulation does not change the original carrier frequency but produces two new frequencies ( fc + fs ) and ( fc − fs ) which are called sideband frequencies.
( iii ) The sum of carrier frequency and signal frequency i.e. ( fc + f (^) s ) is called upper sideband frequency. The lower sideband frequency is fc − fs i.e. the difference between carrier and signal frequencies.
16.7 Sideband Frequencies in AM Wave
In an amplitude modulated wave, the sideband fre- quencies are of our interest. It is because the signal frequency fs is contained in the sideband frequen- cies. Fig. 16.7 shows the frequency spectrum of an amplitude modulated wave. The frequency com- ponents in the AM wave are shown by vertical lines. The height of each vertical line is equal to the am- plitude of the components present. It may be added here that in practical radio transmission, carrier fre- quency fc is many times greater than signal fre- quency fs. Hence, the sideband frequencies are gen- erally close to the carrier frequency. It may be seen that a carrier modulated by a single frequency is equivalent to three simultaneous signals; the car-
- From trigonometry, we have the expansion formula : 2 cos A cos B = cos ( A + B ) + cos ( A − B ) ** f (^) c =
ω 2 π
c (^) , f c +^ f^ s =^
ω ω 2 π
c +^ s , f c −^ fs =^
ω ω 2 π
c − s
○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○
Fig. 16.
420 ^ Principles of Electronics Working. The carrier ec is applied at the input of the amplifier and the modulating signal e (^) s is applied in the emitter resistance circuit. The amplifier circuit amplifies the carrier by a factor “ A ” so that the output is Aec. Since the modulating signal is a part of the biasing circuit, it produces low- frequency variations in the emitter circuit. This in turn causes *variations in “ A ”. The result is that amplitude of the carrier varies in accordance with the strength of the signal. Consequently, amplitude modulated output is obtained across RL. It may be noted that carrier should not influence the voltage gain A; only the modulating signal should do this. To achieve this objective, carrier should have a small magnitude and signal should have a large magnitude. Example 16.5. An AM wave is represented by the expression : v = 5 (1 + 0.6 cos 6280 t) sin 211 × 104 t volts ( i ) What are the minimum and maximum amplitudes of the AM wave? ( ii ) What frequency components are contained in the modulated wave and what is the ampli- tude of each component?
Solution. The AM wave equation is given by : v = 5 (1 + 0.6 cos 6280 t ) sin 211 × 104 t volts ...( i ) Compare it with standard AM wave eq., v = E (^) C (1 + m cos ω s t ) sin ω c t ...( ii ) From eqs. ( i ) and ( ii ) , we get, E (^) C = carrier amplitude = 5 V m = modulation factor = 0. fs = signal frequency = ω s /2π = 6280/2π = 1 kHz fc = carrier frequency = ω c /2π = 211 × 104 /2π = 336 kHz ( i ) Minimum amplitude of AM wave = E (^) C − mEC = 5 − 0.6 × 5 = 2 V Maximum amplitude of AM wave = E (^) C + mEC = 5 + 0.6 × 5 = 8 V ( ii ) The AM wave will contain three frequencies viz. f (^) c − f s , fc , fc + f (^) s or 336 − 1 , 336 , 336 + 1 or 335 kHz, 336 kHz, 337 kHz The amplitudes of the three components of AM wave are :
mE C (^) , E C ,^2
mE C
or
×
×
or 1.5 V, 5 V, 1.5 V Example 16.6. A sinusoidal carrier voltage of frequency 1 MHz and amplitude 100 volts is amplitude modulated by sinusoidal voltage of frequency 5 kHz producing 50% modulation. Calcu- late the frequency and amplitude of lower and upper sideband terms. Solution. Frequency of carrier, fc = 1 MHz = 1000 kHz Frequency of signal, fs = 5 kHz Modulation factor, m = 50% = 0.
- The principle of this circuit is to change the gain A (and hence the amplitude of carrier) by the modulat- ing signal.
○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○
Modulation And Demodulation (^) 421 Amplitude of carrier, E (^) C = 100 V The lower and upper sideband frequencies are : fc − fs and f (^) c + fs or (1000 − 5) kHz and (1000 + 5) kHz or 995 kHz and 1005 kHz
Amplitude of each sideband term =
mE C (^) = × = 25 V
Example 16.7. A carrier wave of frequency 10 MHz and peak value 10V is amplitude modu- lated by a 5- kHz sine wave of amplitude 6V. Determine (i) modulation factor (ii) sideband frequen- cies and (iii) amplitude of sideband components. Draw the frequency spectrum.
Solution. Carrier amplitude, E (^) C = 10V Signal amplitude, E (^) S = 6V Carrier frequency, fc = 10 MHz Signal frequency, fs = 5 kHz = 0.005 MHz
( i ) Modulation factor, m =
S =
C
E
E =^ 0.
( ii ) Sideband frequencies are : f (^) c – fs ; fc + f (^) s 10 – 0.005 ; 10 + 0. 9.995 MHz ; 10.005 MHz
( iii ) Amplitude of each sideband =
×
C =
m E = 3V
Fig. 16.9 shows the frequency spectrum of the A.M. wave.
16.9 Power in AM Wave
The power dissipated in any circuit is a function of the square of voltage across the circuit and the effective resistance of the circuit. Equation of AM wave reveals that it has three components of amplitude EC , m EC /2 and m EC /2. Clearly, power output must be distributed among these components.
Carrier power, P (^) C = (^ )
2 / 2 2 2
E C EC
R R
...( i )
Total power of sidebands, P (^) S =
( ) ( )
2 2 m EC / 2 2 m EC / 2 2 R R
2 2 2 2 2 2
8 8 4
m E C m EC m EC R R R
Total power of AM wave, P (^) T = P (^) C + P (^) S
- r.m.s. values are considered.
○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○
Fig. 16.
Modulation And Demodulation (^) 423
( iii ) Small operating range. Due to low efficiency of amplitude modulation, transmitters em- ploying this method have a small operating range i.e. messages cannot be transmitted over larger distances.
( iv ) Lack of audio quality. This is a distinct disadvantage of amplitude modulation. In order to attain high-fidelity reception, all audio frequencies up to 15 kHz must be reproduced. This necessi- tates bandwidth of 30 kHz since both sidebands must be reproduced. But AM broadcasting stations are assigned bandwidth of only 10 kHz to minimise the interference from adjacent broadcasting stations. This means that the highest modulating frequency can be 5 kHz which is hardly sufficient to reproduce the music properly. Example 16.8. A carrier wave of 500 watts is subjected to 100% amplitude modulation. Determine : ( i ) power in sidebands ( ii ) power of modulated wave. Solution.
( i ) Sideband power, P (^) S =
2 C 2
m P = × (^) = 250 W
Thus there are 125 W in upper sideband and 125 W in lower sideband. ( ii ) Power of AM wave, P (^) T = P (^) C + P (^) S = 500 + 250 = 750 W Example 16.9. A 50 kW carrier is to be modulated to a level of ( i ) 80% ( ii ) 10%. What is the total sideband power in each case?
Solution. ( i ) P (^) S =
2 C 2
m P = × (^) = 16 kW
( ii ) P (^) S =
2 C 2
m P = × (^) = 0.25 kW
Note the effect of modulation factor on the magnitude of sideband power. In the first case ( m = 80%), we generated and transmitted 50 kW carrier in order to send 16 kW of intelligence. In the second case ( m = 10%), the same carrier level — 50 kW — is used to send merely 250 W of intelli- gence. Clearly, the efficiency of operation decreases rapidly as modulation factor decreases. For this reason, in amplitude modulation, the value of m is kept as close to unity as possible.
Example 16.10. A 40kW carrier is to be modulated to a level of 100%. ( i ) What is the carrier power after modulation? ( ii ) How much audio power is required if the efficiency of the modulated RF amplifier is 72%? Solution. Fig. 16.10 shows the block diagram indicating the power relations. ( i ) Since the carrier itself is unaffected by the modulating signal, there is no change in the carrier power level.
Fig. 16.
424 ^ Principles of Electronics ∴ P (^) C = 40 kW
( ii ) P (^) S =
2 C 2
m P = × (^) = 20 kW
∴ P (^) audio =
P S (^) = (^) = 27.8 kW
Example 16.11. An audio signal of 1 kHz is used to modulate a carrier of 500 kHz. Determine ( i ) sideband frequencies ( ii ) bandwidth required. Solution. Carrier frequency, f (^) c = 500 kHz Signal frequency, fs = 1 kHz ( i ) As discussed in Art. 16.6, the AM wave has sideband frequencies of ( fc + f (^) s ) and ( fc − fs ). ∴ Sideband frequencies = (500 + 1) kHz and (500 − 1) kHz = 501 kHz and 499 kHz ( ii ) Bandwidth required = 499 kHz to 501 kHz = 2 kHz Example 16.12. The load current in the transmitting antenna of an unmodulated AM transmitter is 8A. What will be the antenna current when modulation is 40%?
Solution. P (^) S =
2 C
m P
PT = P C + P S = P C
2 1 2
⎛⎜ (^) + m ⎞⎟ ⎝ ⎠ ∴ T C
P
P
2 1 2
+^ m
or
2 T C
I
I
2 1 2
+^ m
Given that I (^) C = 8A; m = 0.
2
8
⎛ I T ⎞
(0.4)^2
or ( I (^) T /8) 2 = 1. or IT = 8 1.08 = 8.31 A Example 16.13. The antenna current of an AM transmitter is 8A when only carrier is sent but it increases to 8.93A when the carrier is sinusoidally modulated. Find the % age modulation.
Solution. As shown in example 16.12, 2 T C
I
I
2 1 2
+^ m
Given that IT = 8.93 A; I (^) C = 8 A ; m =?
∴ (^) ( )
8.93^2
2 1 2
+^ m
or 1.246 = 1 + m^2 / or m^2 /2 = 0.
or m = 2 ×^ 0.246 = 0.701 = 70.1%
426 ^ Principles of Electronics Total power delivered by the AM wave = 6.25 + 1.562 + 1.562 = 9.374 mW
16.11 Frequency Modulation (FM)
When the frequency of carrier wave is changed in accordance with the intensity of the signal, it is called frequency modulation (FM). In frequency modulation, only the frequency of the carrier wave is changed in accordance with the signal. However, the amplitude of the modulated wave remains the same i.e. carrier wave ampli- tude. The frequency variations of carrier wave depend upon the instantaneous amplitude of the signal as shown in Fig. 16.12 ( iii ). When the signal voltage is zero as at A , C , E and G , the carrier frequency is unchanged. When the signal approaches its positive peaks as at B and F , the carrier frequency is increased to maximum as shown by the closely spaced cycles. However, during the negative peaks of signal as at D , the carrier frequency is reduced to minimum as shown by the widely spaced cycles.
Illustration. The process of frequency modulation (FM) can be made more illustrative if we consider numerical values. Fig. 16.13 shows the FM signal having carrier frequency fc = 100 kHz. Note that FM signal has constant amplitude but varying frequencies above and below the carrier frequency of 100 kHz (= fc ). For this reason, fc (= 100 kHz) is called centre frequency. The changes in the carrier frequency are produced by the audio-modulating signal. The amount of change in fre- quency from fc (= 100 kHz) or frequency deviation depends upon the amplitude of the audio-modu- lating signal. The frequency deviation increases with the increase in the modulating signal and vice- versa. Thus the peak audio voltage will produce maximum frequency deviation. Referring to Fig. 16.13, the centre frequency is 100 kHz and the maximum frequency deviation is 30 kHz. The follow- ing points about frequency modulation (FM) may be noted carefully : ( a ) The frequency deviation of FM signal depends on the amplitude of the modulating signal. ( b ) The centre frequency is the frequency without modulation or when the modulating voltage is zero. ( c ) The audio frequency ( i.e. frequency of modulating signal) does not determine frequency deviation. Advantages : The following are the advantages of FM over AM :
Fig. 16.12 Fig. 16.
Modulation And Demodulation (^) 427
( i ) It gives noiseless reception. As discussed before, noise is a form of amplitude variations and a FM receiver will reject such signals.
( ii ) The operating range is quite large. ( iii ) It gives high-fidelity reception. ( iv ) The efficiency of transmission is very high.
16.12 TTTTTheorheorheorheorheory ofy ofy ofy ofy of FFFFFrrrrrequencequencequencequencequency Modulay Modulay Modulay Modulay Modulation (FM)tion (FM)tion (FM)tion (FM)tion (FM)
In frequency modulation (FM), the amplitude of the carrier is kept constant but the frequency fc of the carrier is varied by the modulating signal. The carrier frequency fc varies at the rate of the *signal frequency fs ; the frequency deviation being proportional to the instantaneous amplitude of the modu- lating signal. Note that maximum frequency deviation is ( f (^) c ( max ) – fc ) and occurs at the peak voltage of the modulating signal. Suppose we modulate a 100 MHz carrier by 1V, 1 kHz modulating signal and the maximum frequency deviation is 25 kHz. This means that the carrier frequency will vary sinusoi- dally between (100 + 0.025) MHz and (100 – 0.025) MHz at the rate of 1000 times per second. If the amplitude of the modulating signal is increased to 2V, then the maximum frequency deviation will be 50 kHz and the carrier frequency will vary between (100 + 0.05) MHz and (100 – 0.05) MHz at the rate of 1000 times per second.
Suppose a modulating sine-wave signal es (= Es cos ω s t ) is used to vary the carrier frequency fc. Let the change in carrier frequency be kes where k is a constant known as the frequency deviation constant. The instantaneous carrier fre- quency fi is given by ; fi = f (^) c + k e (^) s
= f (^) c + k Es cos ω s t A graph of f (^) i versus time is shown in Fig. 16.14. It is important to note that it is frequency-time curve and not amplitude-time curve. The factor k E (^) s represents the maxi- mum frequency deviation and is denoted by Δ f i.e.
Max. frequency deviation, Δ f = ** k Es ∴ fi = f (^) c + Δ f cos ω s t Equation of FM wave. In frequency modulation, the carrier frequency is varied sinusoidally at signal frequency. The instantaneous deviation in frequency from the carrier is proportional to the instantaneous amplitude of the modulating signal. Thus the instantaneous angular frequency of FM is given by ;
ω i = ω c + Δω c cos ω st Total phase angle θ = ω t so that if ω is variable, then,
θ = 0
t ∫ω i^ dt
0
( cos )
t ∫ω c^^ + Δω c^^ ω s^ t^ dt
- Note this point. It means that modulating frequency is the rate of frequency of deviations in the RF carrier. For example, all signals having the same amplitude will deviate the carrier frequency by the same amount, say 50 kHz, no matter what their frequencies. On similar lines, all signals of the same frequency, say, 3 kHz, will deviate the carrier at the same rate of 3000 times per second, no matter what their individual amplitudes. ** Note that k is in kHz or MHz per volt.
○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○
Fig. 16.
Modulation And Demodulation (^) 429
Here ω c = 2π f (^) c = 2π × 25 × 10^6 = 1.57 × 10^8 rad/s ω s = 2π f (^) s = 2π × 400 = 2513 rad/s
mf =
10 kHz 10 × 10^3 Hz
400 Hz 400Hz
s
f f = 25 ∴ e = 4 cos (1.57 × 10 8 t + 25 sin 2513 t ) Ans. Example 16.18. Calculate the modulation index for an FM wave where the maximum fre- quency deviation is 50 kHz and the modulating frequency is 5 kHz.
Solution. Max. frequency deviation, Δ f = 50 kHz Modulating frequency, fs = 5 kHz
∴ Modulation index, mf =
50 kHz s 5 kHz
f f
Example 16.19. The carrier frequency in an FM modulator is 1000 kHz. If the modulating frequency is 15 kHz, what are the first three upper sideband and lower sideband frequencies?
Solution. Carrier frequency, f (^) c = 1000 kHz Modulating frequency, fs = 15 kHz Upper sideband frequencies fc + fs ; fc + 2 fs ; fc + 3 f (^) s 1000 + 15 ; 1000 + 2 × 15 ; 1000 + 3 × 15 1015 kHz ; 1030 kHz ; 1045 kHz Lower sideband frequencies fc – fs ; fc – 2 fs ; fc – 3 f (^) s 1000 – 15 ; 1000 – 2 × 15 ; 1000 – 3 × 15 985 kHz ; 970 kHz ; 955 kHz Example 16.20. The carrier and modulating frequencies of an FM transmitter are 100 MHz and 15 kHz respectively. If the maximum frequency deviation is 75 kHz, find the bandwidth of FM signal.
Solution. To calculate the exact bandwidth of an FM signal, it requires the use of advanced mathematics (Bessel functions) which is beyond the level of this book. However, the bandwidth of an FM signal is approximately given by ;
Bandwidth, BW = 2 [ Δ f + f (^) s ] = 2 [75 + 15] = 180 kHz Example 16.21. In a frequency modulated wave, frequency deviation constant is 75 kHz/volt and the signal amplitude is 2V. Find the maximum frequency deviation.
Solution. Frequency deviation constant, k = 75 kHz/V Amplitude of signal, E (^) s = 2V ∴ Max. frequency deviation, Δ f = k Es = 75 × 2 = 150 kHz Example 16.22. In an FM system, when the audio frequency (AF) is 500 Hz and the AF voltage is 2.4V, the frequency deviation is 4.8 kHz. If the AF voltage is now increased to 7.2V, what is the new frequency deviation? If the AF voltage is raised to 10V while the AF is dropped to 200 Hz, what is the deviation? Find the modulation index in each case.
430 ^ Principles of Electronics Solution. We know that : Frequency deviation, Δ f 1 = k E (^) s
∴ Frequency deviation constant, k =
s 2.
f E
= (^) = 2 kHz/V
For E (^) s = 7.2V, Δ f 2 =2 × 7.2 = 14.4 kHz For E (^) s = 10V, Δ f 3 =2 × 10 = 20 kHz The answer of 20 kHz shows that deviation is independent of modulating frequency. The modulation indices in the three cases are :
mf 1 = 1 1
s 0.
f f
mf 2 = 2 1
s 0.
f f
mf 3 = 3 2
s 0.
f f
It is important to note that for calculating modulation index, the modulating frequency change had to be taken into account in the third case.
16.13 Comparison of FM and AM
The comparison of FM and AM is given in the table below.
S. No
FM
The amplitude of carrier remains constant with modulation. The carrier frequency changes with modu- lation. The carrier frequency changes according to the strength of the modulating signal. The value of modulation index ( mf ) can be more than 1.
AM
The amplitude of carrier changes with modulation. The carrier frequency remains constant with modulation. The carrier amplitude changes according to the strength of the modulating signal. The value of modulation factor ( m ) cannot be more than 1 for distortionless AM signal.
16.14 Demodulation
The process of recovering the audio signal from the modulated wave is known as demodulation or detection.
At the broadcasting station, modulation is done to transmit the audio signal over larger distances to a receiver. When the modulated wave is picked up by the radio receiver, it is necessary to recover the audio signal from it. This process is accomplished in the radio receiver and is called demodula- tion.
Necessity of demodulation. It was noted previously that amplitude modulated wave consists of carrier and sideband frequencies. The audio signal is contained in the sideband frequencies which are radio frequencies. If the modulated wave after amplification is directly fed to the speaker as shown in Fig. 16.15, no sound will be heard. It is because diaphragm of the speaker is not at all able to respond to such high frequencies. Before the diaphragm is able to move in one direction, the rapid reversal of current tends to move it in the opposite direction i.e. diaphragm will not move at all. Consequently, no sound will be heard.
