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Chapter 20: Problem 2720

A transmitter transmit a power of \(10 \mathrm{KW}\) when modulation is \(50 \%\). What is the power of carrier wave? (A) \(12 \mathrm{KW}\) (B) \(7.0 \mathrm{KW}\) (C) \(8.89 \mathrm{KW}\) (D) \(5.0 \mathrm{KW}\)

Short Answer

Expert verified
The power of the carrier wave is (B) \(7.0 \mathrm{KW}\).

Step by step solution

01

Understanding modulation in Amplitude Modulation

Amplitude Modulation (AM) is a modulation technique where the amplitude of the carrier wave is varied in proportion to the amplitude of the modulating (information) signal. The radio frequency carrier wave has a much higher frequency than that of the modulating (information) signal, and the modulation index is a measure of how much the amplitude of the carrier wave is varied by the modulating signal.
02

Apply the modulation index formula

In Amplitude Modulation, the total power Pt of the modulated signal is given by the formula: \(Pt = Pc(1 + \dfrac{m^2}{2})\), where Pt is the total transmitted power, Pc is the power of the carrier wave, m is the modulation index. The modulation index 'm' is expressed in percentage, and in this case, it is given as 50% (0.5 in decimal). Having this formula and the necessary values, we can then solve for the power of the carrier wave, Pc.
03

Determine the carrier wave power

Given the total transmitted power Pt = 10 KW and modulation index m = 0.5, we can now solve for the carrier wave power Pc: \(10 = Pc(1 + \dfrac{(0.5)^2}{2})\) After solving for Pc, we get: Pc = \(7.0 KW\) Answer: The power of the carrier wave is (B) \(7.0 \mathrm{KW}\).

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