# An AM signal is represented by x(t)={20+4sin(500t)}cos(5000t). What will be the transmission efficiency? Express the answer in percentage.

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An AM signal is represented by x(t)={20+4sin(500t)}cos(5000t).

What will be the transmission efficiency? Express the answer in percentage.

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Step 1

The general expression of am amplitude modulated waveform can be expressed as

The transmission efficiency of an amplitude modulated (AM) waveform is expressed as

Step 2

In this case, the expression of the amplitude modulated waveform is given as

The waveform expressed by equation (2) can be rewritten as

Step 3

Comparing equation (1) and (3), it can be concluded that the value of the modulation index will be

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