Question

A 10 kW carrier is sinusoidally modulated by two carriers corresponding to a modulation index of 30% and 40%, respectively. The total radiated power is

• A. 11.25 kW
• B. 12.50 kW
• C. 15 kW
• D. 17 kW

Hint:

When dealing with multiple modulating tones in AM, don't add the modulation indices directly. The total power depends on the sum of the squares of the individual indices.

Answer 1

The Correct Option is A

Step 1: Recall the formula for total power in AM with multiple modulating signals. For a carrier with power \(P_c\) modulated by multiple sine waves with modulation indices \(m_1, m_2, \ldots, m_n\), the total transmitted power \(P_t\) is given by: \[ P_t = P_c \left( 1 + \frac{m_{eff}^2}{2} \right) \] where the effective modulation index \(m_{eff}\) is given by: \[ m_{eff}^2 = m_1^2 + m_2^2 + \ldots + m_n^2 \]
Step 2: Identify the given values. Carrier Power, \(P_c = 10 \text{ kW}\). Modulation index 1, \(m_1 = 30% = 0.3\). Modulation index 2, \(m_2 = 40% = 0.4\).
Step 3: Calculate the square of the effective modulation index. \[ m_{eff}^2 = (0.3)^2 + (0.4)^2 = 0.09 + 0.16 = 0.25 \]
Step 4: Calculate the total power. \[ P_t = 10 \text{ kW} \left( 1 + \frac{0.25}{2} \right) \] \[ P_t = 10 \left( 1 + 0.125 \right) \] \[ P_t = 10 \times 1.125 = 11.25 \text{ kW} \]