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in Electronics by (53.2k points)

The rms value of a carrier voltage is 80V. After amplitude modulation by a sinusoidal audio signal, rms value of the carrier voltage becomes 96V. Determine modulation factor.

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VC(rms) = 80V, VT(rms) = 96V

VT = VC(1 + \(\frac{m_a^2}{2}\))

96 = 80[1 + \(\frac{m_a^2}{2}\)]

\(\frac{96}{80}\) = 1 + \(\frac{m_a^2}{2}\)

1.2 = 1 + \(\frac{m_a^2}{2}\)

1.2 - 1 = \(\frac{m_a^2}{2}\)

\(m_a^2\) = 0.4

ma \(\sqrt{0.4}\)

= 0.6324

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