In amplitude modulation (AM), the power of the modulated signal is directly related to the modulation index, which is a measure of the extent of modulation applied to the carrier signal. The modulation index is defined as the ratio of the peak amplitude of the modulating signal to the peak amplitude of the carrier signal.
Let's consider an unmodulated carrier signal with a power of P_c and a modulating signal with a peak amplitude that results in 100% modulation. In this case, the peak amplitude of the modulating signal is equal to the peak amplitude of the carrier signal.
Without modulation, the total power of the carrier signal is P_c. When the modulation index is 100%, the peak amplitude of the modulating signal matches the peak amplitude of the carrier signal, causing the amplitude of the carrier to vary between zero and twice its unmodulated peak amplitude.
The power of a signal is proportional to the square of its amplitude. Therefore, the power of the modulated signal will vary between zero and four times the power of the unmodulated carrier signal.
Mathematically, we can express this relationship as:
P_m = 4 * P_c
where P_m is the power of the modulated signal and P_c is the power of the unmodulated carrier signal.
Comparing the power of the modulated signal with the unmodulated carrier signal, we find:
P_m = 4 * P_c
The increase in power due to 100% amplitude modulation can be calculated as follows:
Increase in power = P_m - P_c = 4 * P_c - P_c = 3 * P_c
Hence, a 100% amplitude modulation results in a power increase of three times (or 300%) compared to the unmodulated carrier signal, not 50% as initially stated.
Apologies for the confusion in the earlier response.