A 2KW carrier is an amplitude modulated by a sinusoidal signal to adepth of 70%. Calculate the power at the lower sideband and determinethe percentage of the total power
Question
A 2KW carrier is an amplitude modulated by a sinusoidal signal to adepth of 70%. Calculate the power at the lower sideband and determinethe percentage of the total power
Solution
The total power in an AM system is given by the formula:
P_total = P_c(1 + (m^2)/2)
where: P_c = carrier power = 2KW = 2000W m = modulation index = 70% = 0.7
First, let's calculate the total power:
P_total = 2000(1 + (0.7^2)/2) = 2000(1 + 0.245) = 2000 * 1.245 = 2490W
The power in each sideband is given by the formula:
P_sb = P_c * (m^2)/4
So, the power at the lower sideband is:
P_lsb = 2000 * (0.7^2)/4 = 2000 * 0.1225 = 245W
The percentage of the total power in the lower sideband is:
%P_lsb = (P_lsb / P_total) * 100 = (245 / 2490) * 100 = 9.84%
So, the power at the lower sideband is 245W and it represents 9.84% of the total power.
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