Topic: Analog Communications
When a carrier is AM modulated by three single tone signals of modulation percentages 50%, 50% and 20%, then the effective modulation index of the resulting signal is:
- A. $\sqrt{0.54}$
- B. $\sqrt{1.2}$
- C. 1.2
- D. $\sqrt{0.9}$
Answer: A. $\sqrt{0.54}$
Explanation: The effective modulation index $m_t$ for a multi-tone AM signal is given by $m_t = \sqrt{m_1^2 + m_2^2 + m_3^2}$.
Given $m_1 = 0.5$, $m_2 = 0.5$, and $m_3 = 0.2$.
$m_t = \sqrt{0.5^2 + 0.5^2 + 0.2^2} = \sqrt{0.25 + 0.25 + 0.04} = \sqrt{0.54}$.