The ratio of modulating power to total power at 100% modulation will be:

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UPRVUNL AE EC 2014 Official Paper

Option 3 : 1 : 3

CT 3: Building Materials

2962

10 Questions
20 Marks
12 Mins

**Concept:**

The general expression for an amplitude modulated signal, with single tone modulating signal, is defined as:

\(S\left( t \right) = {A_c}\left[ {1 + \cos 2\pi fm\left( t \right)} \right]\cos 2\pi fct\)

\(= {A_c}\cos 2\pi \;f_ct + {A_c}u\cos 2\pi f_mt\cos 2\pi f_ct\)

\(= {A_c}\cos 2\pi f_ct + \frac{{{A_c}u}}{2}\cos 2\pi \left( {f_c + f_m} \right)t\) + \(\frac{{{A_c}u}}{2}\cos 2\pi \left( {fc - fm} \right)t\)

Also, the modulation efficiency of an AM signal is defined as the ratio of the power with the sidebands to the total power i.e.

\(η = \frac{{{P_{sb}}}}{{{P_t}}} \times 100\)

\({η } = \frac{{{μ ^2}}}{{2 + {μ ^2}}}\)

**Calculation:**

Given: μ = 1

\({η } = \frac{{{μ ^2}}}{{2 + {μ ^2}}}\)

η = 1/3