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Communication System — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsCommunication System5 Marks
Question
What do you mean by modulation ? Define modulation index. For an amplitude modulated wave the maximum and minimum amplitude is ' $a$ ' and ' $b$ '. Calculate modulation index for it.
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Answer

Modulation : The process of changing some characteristic e.g. amplitude, frequency of phase of a carrier wave in accordance with the intensity of the signal to be transmitted is known as modulation.
Modulation Index : The extent to which the amplitude of carrier wave is changed is determined by modulation index.
The ratio of change of amplitude of carrier waves to the amplitude of the original carrier wave i.e., unmodulated wave is called modulation index and is denoted by $m_{a}$.
$m_{a}=\frac{\Delta E_{c}}{E_{c}}$.
It is also defined as the ratio of amplitude of modulated wave to amplitude of carrier wave
i.e., $m_{a}=\frac{E_{m}}{E_{c}}$ ... (1)
The value of $m_{a}$ kept less than one because if $m_{a}$ is greater than one then modulating signal is deformed.
Image
In adjacent fig. a amplitude modulated wave is shown. From fig. it is obvious that maximum and minimum amplitude are as follows :
$E _{\max }= E _c+ E _m$ ...(2)
$E _{\max }= E _c- E _m$ ...(3)
Solving these equations, we get
$E _c=\frac{ E _{\max }- E _{\min }}{2}$
$E _m=\frac{ E _{\max }+ E _{\min }}{2}$
∴ From eq. (1): $m_\alpha=\frac{ E _m}{ E _c}=\frac{\left( E _{\max }+ E _{\min }\right) / 2}{\left( E _{\max }- E _{\min }\right) / 2}$
$\Rightarrow \quad m_\alpha=\frac{ E _{\max }+ E _{\min }}{ E _{\max }- E _{\min }}$
Here, $E _{\max }=a$ and $E _{\min }=b$
$\therefore \quad m_a=$
$\frac{E_{\max }+E_{\min }}{E_{\max }-E_{\min }}=\frac{a+b}{a-b}$

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