In an amplitude modulation system, the total power is $P_t=600\text{ W}$. If the modulation index is $\mu =0.5$, what is the power of the carrier wave $P_c$?

Solution

1. The total power $P_t$ in an amplitude modulation system is given by the formula $P_t=P_c(1+\frac{{\mu }^2}{2})$, where $P_c$ is the carrier power and $\mu$ is the modulation index.
2. Substitute the given values $P_t=540\text{ W}$ and $\mu =0.5$ into the equation: $540=P_c(1+\frac{0.5^2}{2})$.
3. Simplify the expression inside the parentheses: $$\begin{array}{rl}540& =P_c(1+\frac{0.25}{2})\\ & =P_c(1+0.125)\\ & =1.125P_c\end{array}$$.
4. Solve for the carrier power: $$\begin{array}{rl}{P}_c& =\frac{540}{1.125}\\ & =480\text{ W}\end{array}$$.
5. Hence the answer is (B).