A carrier wave with a peak voltage of 100 V and power of 100 kW is amplitude modulated simultaneously by two sinusoidal message signals. The first message signal produces a modulation index of 0.6, an

Question

A carrier wave with a peak voltage of 100 V and power of 100 kW is amplitude modulated simultaneously by two sinusoidal message signals. The first message signal produces a modulation index of 0.6, and the second message signal produces a modulation index of 0.8. Assuming the modulating signals are independent, calculate the total power (in kW) of the amplitude modulated wave.

TestHub · Accepted Answer

When a carrier wave is modulated by multiple independent sinusoidal message signals, the effective or total modulation index $m_{t}$ is given by $m_{t} = m_{1}^{2} + m_{2}^{2} + ...$ . Given $m_{1} = 0.6$ and $m_{2} = 0.8$ . The total modulation index $m_{t} = (0.6)^{2} + (0.8)^{2} = 0.36 + 0.64 = 1.0 = 1$ .

The total power $P_{t}$ of an AM wave is related to the carrier power $P_{c}$ and the total modulation index $m_{t}$ by the formula $P_{t} = P_{c} (1 + \frac{m _{t}^{2}}{2})$ . Given carrier power $P_{c} = 100 kW$ . $P_{t} = 100 kW (1 + \frac{1 ^{2}}{2}) = 100 kW (1 + 0.5) = 100 kW \times 1.5 = 150 kW$ . The peak voltage of the carrier wave (100 V) is extraneous information for this calculation.

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