The antenna current of an AM transmitter is 8 A when only the carrier is sent, but it increases to 8.93 A when the carrier is modulated by a single sine wave. Find the percentage modulation.

Question

The antenna current of an AM transmitter is 8 A when only the carrier is sent, but it increases to 8.93 A when the carrier is modulated by a single sine wave. Find the percentage modulation. (A) 60.1 % (B) 70.1 % (C) 80.1 % (D) 50.1 %

Tardigrade Admin · Accepted Answer

The power dissipated in any circuit is a function of the square of voltage across the circuit and the effective resistance of the circuit. Equation of AM wave reveals that it has three components of amplitude

E_{c}, m E_{c} /2

and

m E_{c} /2.

Clearly, power output must be distributed among these components.
Carrier Power,

P_{C} = \frac{( E _{c} / 2 ) ^{2}}{R} = \frac{E _{c}^{2}}{2 R}

Total power of side bands,

P_{S} = \frac{( m E _{c} /2 2 ) ^{2}}{R} + \frac{( m E _{c} /2 2 ) ^{2}}{R}

= \frac{m ^{2} E _{c}^{2}}{4 R}

∴ \frac{P _{S}}{P _{C}} = \frac{1}{2} m^{2}

and

P_{T} = P_{C} + P_{S} = P_{C} (1 + \frac{m ^{2}}{2})

∴ \frac{P _{T}}{P _{C}} = 1 + \frac{m ^{2}}{2}

or

(\frac{I _{T}}{I _{C}})^{2} = 1 + \frac{m ^{2}}{2}

Given that,

I_{T} = 8.93 A, I_{C} = 8 A, m =

?

∴ (\frac{8.93}{8})^{2} = 1 + \frac{m ^{2}}{2}

or

1.246 = 1 + \frac{m ^{2}}{2}

or

\frac{m ^{2}}{2} = 0.246

or

m = 2 \times 0.246 = 0.701

= 70.1%

The situation is summarised in figure.

BC = A D = 3 c m, A B = D C = 4 c m,

so

A C = 5 c m

Q. The antenna current of an AM transmitter is 8A when only the carrier is sent, but it increases to 8.93A when the carrier is modulated by a single sine wave. Find the percentage modulation.

60.1 %

70.1 %

80.1 %

50.1 %

Q. The antenna current of an $A M$ transmitter is $8 A$ when only the carrier is sent, but it increases to $8.93 A$ when the carrier is modulated by a single sine wave. Find the percentage modulation.