Question
The total power contained in an AM signal is 1000W. Determine the power transmitted on the carrier frequency and on each of the side panels when the percentage modulation is 100%.
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Answer to a math question The total power contained in an AM signal is 1000W. Determine the power transmitted on the carrier frequency and on each of the side panels when the percentage modulation is 100%.
Sigrid
4.5119 Answers
Given that the total power contained in the AM signal is 1000W and the percentage modulation is 100%.
LetP_c P_s
The total power in an AM signal can be expressed as:
P_{\text{total}} = P_c + P_s + P_s
Since the percentage modulation is 100%, the maximum amplitude of the modulated signal is twice the carrier amplitude. Therefore, the power transmitted on each sideband is half the total power in the modulated signal.
Thus, the total power can be expressed as:
1000 = P_c + \frac{1}{2}P_{\text{total}} + \frac{1}{2}P_{\text{total}}
1000 = P_c + 2\left(\frac{1}{2}P_{\text{total}}\right)
Solving forP_c
1000 = P_c + P_{\text{total}}
P_c = 1000 - 500 = 500W
Solving forP_s
P_s = \frac{1}{2}P_{\text{total}} = \frac{1}{2}(1000) = 500W
Therefore, the power transmitted on the carrier frequency is500W 500W
\boxed{P_c = 500W, \, P_s = 500W}
Let
The total power in an AM signal can be expressed as:
Since the percentage modulation is 100%, the maximum amplitude of the modulated signal is twice the carrier amplitude. Therefore, the power transmitted on each sideband is half the total power in the modulated signal.
Thus, the total power can be expressed as:
Solving for
Solving for
Therefore, the power transmitted on the carrier frequency is
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