JEE Main & Advanced Physics Communication System / संचार तंत्र Amplitude Modulation (AM)

The process of changing the amplitude of a carrier wave in accordance with the amplitude of the audio frequency (AF) signal is known as amplitude modulation (AM).

In AM frequency of the carrier wave remains unchanged.

The amplitude of modulated wave is varied in accordance with the amplitude of modulating wave.

(1) Modulation index : The ratio of change of amplitude of carrier wave to the amplitude of original carrier wave is called the modulation factor or degree of modulation or modulation index \[({{m}_{a}})\].

\[{{m}_{a}}=\frac{\text{Change in amplitude of carrier wave}}{\text{Amplitude of original carrier wave}}=\frac{k{{E}_{m}}}{{{E}_{c}}}\]

where k = A factor which determines the maximum change in the amplitude for a given amplitude \[{{E}_{m}}\]of the modulating signal. If k = 1 then \[{{m}_{a}}=\frac{{{E}_{m}}}{{{E}_{c}}}=\frac{{{E}_{\max }}-{{E}_{\min }}}{{{E}_{\max }}+{{E}_{\min }}}\]

If a carrier wave is modulated by several sine waves the total modulated index \[{{m}_{t}}\] is given by \[{{m}_{t}}=\sqrt{m_{1}^{2}+m_{2}^{2}+m_{3}^{2}+........}\]

(2) Voltage equation for AM wave : Suppose voltage equations for carrier wave and modulating wave are  \[{{e}_{c}}={{E}_{c}}\cos {{\omega }_{c}}t\] and \[{{e}_{m}}={{E}_{m}}\sin {{\omega }_{m}}t=m{{E}_{c}}\sin {{\omega }_{m}}t\]

where \[{{e}_{c}}=\] Instantaneous voltage of carrier wave, \[{{E}_{c}}=\] Amplitude of carrier wave, \[{{\omega }_{c}}=2\pi \,{{f}_{c}}=\] Angular velocity at carrier frequency \[{{f}_{c}}\], \[{{e}_{m}}=\] Instantaneous voltage of modulating, \[{{E}_{m}}=\] Amplitude of modulating wave, \[{{\omega }_{m}}=2\pi \,{{f}_{m}}=\]Angular velocity of modulating frequency \[{{f}_{m}}\]

Voltage equation for AM wave is

\[e=E\sin {{\omega }_{c}}t=({{E}_{c}}+{{e}_{m}})\sin {{\omega }_{c}}t\]\[=({{E}_{c}}+{{e}_{m}}\sin {{\omega }_{m}}t)\sin {{\omega }_{c}}t\] \[={{E}_{c}}\sin {{\omega }_{c}}t+\frac{{{m}_{a}}{{E}_{c}}}{2}\cos ({{\omega }_{c}}-{{\omega }_{m}})t-\frac{{{m}_{a}}{{E}_{c}}}{2}\cos \,({{\omega }_{c}}+{{\omega }_{m}})t\]

The above AM wave indicated that the AM wave is equivalent to summation of three sinusoidal wave, one having amplitude \[{{E}_{c}}\]and the other two having amplitude \[\frac{{{m}_{a}}{{E}_{c}}}{2}\].

(3) Side band frequencies and band width in AM wave

(i) Side band frequencies : The AM wave contains three frequencies \[{{f}_{c}},\,({{f}_{c}}+{{f}_{m}})\] and \[({{f}_{c}}-{{f}_{m}}),\] \[{{f}_{c}}\] is called carrier frequency, \[({{f}_{c}}+{{f}_{m}})\] and \[({{f}_{c}}-{{f}_{m}})\] are called side band frequencies.

\[({{f}_{c}}+{{f}_{m}}):\] Upper side band (USB) frequency

\[({{f}_{c}}-{{f}_{m}}):\] Lower side band (LSB) frequency

Side band frequencies are generally close to the carrier frequency.

(ii) Band width : The two side bands lie on either side of the carrier frequency at equal frequency interval \[{{f}_{m}}\]. So, band width \[=({{f}_{c}}+{{f}_{m}})-\,({{f}_{c}}-{{f}_{m}})=2{{f}_{m}}\]

(4) Power in AM waves : Power dissipated in any circuit \[P=\frac{V_{rms}^{2}}{R}\]. Hence (i) carrier power \[{{P}_{c}}=\frac{{{\left( \frac{{{E}_{c}}}{\sqrt{2}} \right)}^{2}}}{R}=\frac{E_{c}^{2}}{2R}\]

(ii) Total power of side bands \[{{P}_{sb}}=\frac{{{\left( \frac{{{m}_{a}}{{E}_{c}}}{2\sqrt{2}} \right)}^{2}}}{R}+\frac{\left( \frac{{{m}_{a}}{{E}_{c}}}{2\sqrt{2}} \right)}{R}\]\[=\frac{m_{a}^{2}E_{c}^{2}}{4R}\]

(iii) Total power of AM wave \[{{P}_{Total}}={{P}_{c}}+{{P}_{sb}}\]\[=\frac{E_{c}^{2}}{2R}\left( 1+\frac{m_{a}^{2}}{2} \right)\]

(iv) \[\frac{{{P}_{t}}}{{{P}_{c}}}=\left( 1+\frac{m_{a}^{2}}{2} \right)\] and \[\frac{{{P}_{sb}}}{{{P}_{t}}}=\frac{m_{a}^{2}/2}{\left( 1+\frac{m_{a}^{2}}{2} \right)}\]

(v) Maximum power in the AM (without distortion) will occur when \[{{m}_{a}}=1\] i.e. \[{{P}_{t}}=1.5P=3{{P}_{sb}}\]

(vi) If \[{{l}_{c}}=\] Unmodulated current and \[{{l}_{t}}=\] total or modulated current  \[\Rightarrow \]\[\frac{{{P}_{t}}}{{{P}_{c}}}=\frac{I_{t}^{2}}{I_{c}^{2}}\]\[\Rightarrow \]\[\frac{{{I}_{t}}}{{{I}_{c}}}=\sqrt{\left( 1+\frac{m_{a}^{2}}{2} \right)}\]

(5) Limitation of amplitude modulation

(i) Noisy reception          

(ii) Low efficiency

(iii) Small operating range    

(iv) Poor audio quality