Consider the following statements Statement (I): In AM systems the modulation index (0 < m < 1) should be high.

Question

Consider the following statements:

Statement (I): In AM systems the modulation index (0 < m < 1) should be high.

Statement (II): The higher the value of m, the greater the power in the sidebands.

Choose the correct option.

1. A. Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I). (Correct answer)
2. B. Both Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I).
3. C. Statement (I) is true but Statement (II) is false.
4. D. Statement (I) is false but Statement (II) is true.

Correct Answer

Option A — Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I).

Detailed Solution & Explanation

The correct answer is Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I).

Key Points

• Statement (I) is true: the modulation index should be kept high (close to 1 without exceeding it) for efficient AM transmission.
• Statement (II) is true: sideband power is given by P_SB = P_c x m² / 2, so it rises with the square of the modulation index.
• (II) genuinely explains (I): because only the sidebands carry information, a higher m puts more of the transmitted power into the useful part of the signal.

Additional Information

• Total transmitted power is P_t = P_c (1 + m²/2). Even at m = 1 the sidebands hold only 33.3% of the total, with the carrier taking the remaining two-thirds.
• If m > 1 the signal becomes overmodulated, producing envelope distortion and spurious sidebands — which is why m is held just below unity.