Question

A certain am transmitter radiates 9kw with carrier unmodulated and 10.125kw when carrier is sinusoidally modulated. find

a.modulation index

b.if another sine wave corresponding to 40% modulation is transmitted simultaneously determine total radiated power.

Answer 1

We have , $\bold{\frac{P_f}{P_c}=1+\frac{m^2}{2}}$
Here Pt is modulated or total power
Pc is unmodulated or Carrier power
m is modulation index

Given, Pt = 10.125 kW , Pc = 9kW
∴ 10.125/9 = 1 + m²/2
⇒ 10.125/9 - 1 = m²/2
⇒ m²/2 = 1.125/9
⇒m² = 2.25/9
⇒ m = 1.5/3 = 0.5


We know, in case of modulation by two sinsudal waves , the total modulation index is given by $\bold{m_t=\sqrt{m_1^2+m_2^2}}$
Here m₁ = m = 0.5 and m₂ = 0.4 [ because 40% modulation]
so, mt = √{0.5² + 0.4²} = 0.64

Now, again apply , Pt/Pc = 1 + mt²/2
Pt = Pc(1 + mt²/2)
= 9(1 + 0.64²/2)
= 9(1.205) = 10.84kW