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:

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  1. \(\sqrt{0.54}\)
  2. \(\sqrt{1.2}\)
  3. 1.2
  4. \(\sqrt{0.9}\)

Answer (Detailed Solution Below)

Option 1 : \(\sqrt{0.54}\)
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Detailed Solution

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Concept:

When a carrier is amplitude modulated by multiple independent modulating signals, the effective modulation index is calculated using the square root of the sum of the squares of individual modulation indices.

Effective modulation index, \( m_{eff} = \sqrt{m_1^2 + m_2^2 + m_3^2} \)

Given:

Modulation percentages are 50%, 50%, and 20%.

So, \( m_1 = 0.5, \; m_2 = 0.5, \; m_3 = 0.2 \)

Calculation:

\( m_{eff} = \sqrt{(0.5)^2 + (0.5)^2 + (0.2)^2} = \sqrt{0.25 + 0.25 + 0.04} = \sqrt{0.54} \)

 

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