Question

1. A modulated carrier is given by S(t) = 25 Cos[ 628 * 10⁶t + 3 Sin 31.4 * 10³t].
Determine 3 upper and lower sideband frequency components, bandwidth of the
signal, carrier deviation and the average power of the above signal​

Answer 1

Answer:

formulas, we can find the respective parameter values. In this chapter, let us solve a few problems based on the concept of amplitude modulation.

Problem 1

A modulating signal m(t)=10cos(2π×103t) is amplitude modulated with a carrier signal c(t)=50cos(2π×105t). Find the modulation index, the carrier power, and the power required for transmitting AM wave.

Solution

Given, the equation of modulating signal as

m(t)=10cos(2π×103t)

We know the standard equation of modulating signal as

m(t)=Amcos(2πfmt)

By comparing the above two equations, we will get

Amplitude of modulating signal as Am=10volts

and Frequency of modulating signal as

fm=103Hz=1KHz

Given, the equation of carrier signal is

c(t)=50cos(2π×105t)

The standard equation of carrier signal is

c(t)=Accos(2πfct)

By comparing these two equations, we will get

Amplitude of carrier signal as Ac=50volts

and Frequency of carrier signal as fc=105Hz=100KHz

We know the formula for modulation index as

μ=AmAc

Substitute, Am and Ac values in the above formula.

μ=1050=0.2

Therefore, the value of modulation index is 0.2 and percentage of modulation is 20%.

The formula for Carrier power, Pc= is

Pc=Ac22R

Assume R=1Ω and substitute Ac value in the above formula.

Pc=(50)22(1)=1250W

Therefore, the Carrier power, Pc is 1250 watts.

We know the formula for power required for transmitting AM wave is

⇒Pt=Pc(1+μ22)

Substitute Pc and μ values in the above formula.

Pt=1250(1+(0.2)22)=1275W