Amplitude modulation (AM): Modulation factor, Analysis, Advantages, Limitations

Modulation

In radio broadcasting, it is necessary to send audio frequency signal (eg. music, speech etc.) from a broadcasting station over great distances to a receiver. The music, speech etc., are converted into audio signals using a microphone. The energy of a wave increases with frequency. So, the audio frequency (20 - 20000 Hz) is not having large amount of energy and cannot be sent over long distances. The radiation of electrical energy is practicable only at high frequencies e.g. above 20 kHz. The high frequency signals can be sent through thousands of kilometres with comparatively small power.

Therefore, if audio signal is to be transmitted properly, the audio signal must be superimposed on high frequency wave called carrier. The resultant waves are known as modulated waves and this process is called as modulation. This high frequency wave (Radio frequency wave) is transmitted in space through antenna. At the receiver end, the audio signal is extracted from the modulated wave by the process called demodulation. The audio signal is then amplified and reproduced into sound by the loud speaker.

A high frequency radio wave is used to carry the audio signal. On adding the audio signal to carrier, any one of the characteristics namely amplitude or frequency or phase of the carrier wave is changed in accordance with the intensity of the audio signal. This process is known as modulation and may be defined as the process of changing amplitude or frequency or phase of the carrier wave in accordance with the intensity of the signal. Some of the modulation process namely,

(i) amplitude modulation,

(ii) frequency modulation and

(iii) phase modulation

 Amplitude modulation (AM)

When the amplitude of high frequency carrier wave is changed in accordance with the intensity of the signal, the process is called amplitude modulation.

In the amplitude modulation, only the amplitude of the carrier wave is changed. The frequency and the phase of the carrier wave remains constant. Fig  shows the principle of amplitude modulation.

Fig a shows the audio electrical signal of frequency f_s. Fig b shows a carrier wave of constant amplitude with frequency f_c. Fig c is the amplitude modulated wave. It is to be noted that the amplitudes of both positive and negative half cycles of carrier wave are changed in accordance with the signal. Thus the amplitude of the modulated wave possesses the frequency of the audio signal wave.

Modulation factor

An important term in amplitude modulation is modulation factor which describes the extent to which the amplitude of the carrier wave is changed by the audio signal. It is defined as the ratio of the change of amplitude in carrier wave after modulation to the amplitude of the unmodulated carrier wave.

i.e.   modulation factor, m = Amplitude change of carrier wave after modulation / Amplitude of carrier wave before modulation

^{m = Signal amplitude / Carrier amplitude}

Modulation factor determines the strength and quality of the transmitted signal. When the modulation factor m < 1, the amount of carrier amplitude varia-tion is small (Fig a). Consequently, the audio signal being transmitted will not be very strong. When the modulation factor m > 1, distortion is produced in the transmitted wave as shown in Fig  b.

Hence, the signal wave is not exactly reproduced. For effective modulation, the degree of modulation should never exceed 100 %.

Analysis of amplitude modulated wave

A carrier wave may be represented as,

e_c = E_c cos ω_ct   ……………… (1)

where e_c , E_c and ω_c represent the instantaneous voltage, amplitude and angular frequency of the carrier wave respectively.

In amplitude modulation, the amplitude E_c of the carrier wave is varied in accordance with the intensity of the audio signal as shown in Fig . The modulating signal may be represented as,

e_s = E_s cosω_st  ……….(2)

where e_s, E_s and ω_s represent instantaneous voltage, amplitude and angular frequency of the signal respectively.

Amplitude modulated wave is obtained by varying E_c of equation (1) in accordance with E_s. Thus, amplitude modulated wave is,

e = (E_c + E_s cosω_st ) cosω_ct

e = Ec[ 1+(E_s/E_c) cosω_st] cosω_ct = E_c[1+m cosω_st] cosω_ct

where m is the modulation factor which is equal to E_s/E_c

∴ e = E_ccos ω_ct + mE_ccos ω_ct . cosω_st  ……………(3)

= E_ccos ω_ct + (mE_c/2)( ω_{c +} ω_s)t + + (mE_c/2)( ω_{c -} ω_s)t   ……..(4)

This expression shows that the modulated wave contains three components:

1.     E_c cos ω_ct  : This component is same as the carrier wave.

2.     ^mE₂^c cos (ω_c + ω_s)t : This component has a frequency greater than that of the carrier and is called as the Upper Side Band (USB).

3.     ^mE₂^c cos (ω_c - ω_s)t : This component has a frequency lesser than that of the carrier and is called as the Lower Side Band (LSB).

Frequency spectrum

The lower side band term and upper side band term are located in the frequency spectrum on either side of the carrier at a frequency interval of ω_s as shown in Fig . The magnitude of both the upper

and lower side bands is ^m₂ times the carrier amplitude E_c. If the modulation factor m is equal to unity, then each side band has amplitude equal to half of the carrier amplitude.

Bandwidth

However, in a broadcasting station, the modulating signal is the human voice or music which contains waves     with a frequency range of 300 - 3000 Hz. Each of these waves has its own side bands. The upper side band (USB), in fact, contains all sum components of the signal and carrier frequency whereas lower side band (LSB) contains the difference components, as shown in Fig .

The channel width is given by the difference between extreme frequencies i.e. between maximum frequency of USB and minimum frequency of LSB.

 Channel width = 2 × maximum frequency of the modulating signal = 2 × (f_s)_max

Advantages

(i) Easy  transmission and reception

(ii)Lesser bandwidth requirements

(iii)              Low cost

Limitations

(i)                   Noisy reception : In an AM wave, the signal appears in the amplitude variations of the carrier. Practically, all the natural and man made noises consists of electrical amplitude disturbances. As a radio receiver cannot distinguish between amplitude variation that represent noise and those that contain the desired signal, the reception is generally noisy.

(ii)                 Low efficiency : In AM, useful power is available in the side bands, since they contain signals. The sideband power for an AM wave is low. Hence the efficiency of AM is low.

_(iii)                   Small operating range : Due to low efficiency of amplitude modulation, transmitters employing this method have a small operating range i.e. the messages cannot be transmitted over long distances.