What will be the total modulation index if a wave is amplitude modulated by three sine waves with modulation indices of 25%, 50% and 75%?

Concept:

When a carrier is modulated by different waves having different modulation indexes, the effective (total) modulation index is given by:

\({{\rm{μ }}_{{\rm{eff}}}} = \sqrt {{\rm{μ }}_1^2 + {\rm{μ }}_2^2+μ_3^2+...}\)

Calculation:

With μ₁ = 0.25, μ2 = 0.50, μ3 = 0.75, the effective modulation index will be:

\({{\rm{μ }}_{{\rm{eff}}}} = \sqrt {(0.25)^2 + (0.50)^2+(0.75)^2}\)

μ_eff = 0.935

Important Note:

The total power of the modulated signal for the given effective modulation index is given by:

\({P_t} = {P_c}\left( {1 + \frac{{{μ_{eff}^2}}}{2}} \right)\)

Pc = Carrier Power

μeff = Effective modulation Index