###### Advertisements

###### Advertisements

A modulating signal is a square wave, as shown

The carrier wave is given by `c(t) = 2 sin (8pit) "volts"`

**(i)** Sketch the amplitude modulated waveform

**(ii) **What is the modulation index?

###### Advertisements

#### Solution

It can be observed from the given modulating signal that the amplitude of the modulating signal, *A*_{m} = 1 V

It is given that the carrier wave *c* (*t*) = 2 sin (8π*t*)

∴Amplitude of the carrier wave, *A*_{c} = 2 V

Time period of the modulating signal *T*_{m} = 1 s

The angular frequency of the modulating signal is calculated as:

`omega_m = 2pi/T_m`

`= 2pi "rad" s^(-1)` ... (1)

The angular frequency of the carrier signal is calculated as:

`omega_c = 8pi "rad" s^(-1)` ... (ii)

From equations (*i*) and (*ii*), we get:

`mega_c = 4omega_m`

The amplitude modulated waveform of the modulating signal is shown in the following figure.

**(ii)**Modulation index, `m = A_m/A_c = 1/2 = 0.5`

#### APPEARS IN

#### RELATED QUESTIONS

For an amplitude modulated wave, the maximum amplitude is found to be 10 V while the minimum amplitude is found to be 2 V. Determine the modulation index *μ*. What would be the value of *μ* if the minimum amplitude is zero volt?

How is amplitude modulation achieved?

The frequencies of two side bands in an AM wave are 640 kHz and 660 kHz respectively. Find the frequencies of carrier and modulating signal. What is the bandwidth required for amplitude modulation?

Define the term 'amplitude modulation'

Explain any two factors which justify the need for modulating a low frequency base-band signal.

Draw a schematic sketch showing how amplitude modulated signal is obtained by superposing a modulating signal over a sinusoidal carrier wave.

What is meant by term ‘modulation’? Draw a block diagram of a simple modulator for obtaining an AM signal.

Why is frequency modulation preferred over amplitude modulation for transmission of music?

In amplitude modulation ______.

A message signal of frequency ω_{m} is superposed on a carrier wave of frequency ω_{c} to get an amplitude modulated wave (AM). The frequency of the AM wave will be ______.

Identify the mathematical expression for amplitude modulated wave ______.

In amplitude modulation, the modulation index m, is kept less than or equal to 1 because ______.

- m > 1, will result in interference between carrier frequency and message frequency, resulting into distortion.
- m > 1 will result in overlapping of both side bands resulting into loss of information.
- m > 1 will result in change in phase between carrier signal and message signal.
- m > 1 indicates amplitude of message signal greater than amplitude of carrier signal resulting into distortion.

Compute the LC product of a tuned amplifier circuit required to generate a carrier wave of 1 MHz for amplitude modulation.

Why is a AM signal likely to be more noisy than a FM signal upon transmission through a channel?

Draw the plot of amplitude versus ‘ω’ for an amplitude modulated wave whose carrier wave (ω_{c}) is carrying two modulating signals, ω_{1} and ω_{2} (ω_{2} > ω_{1}).

- Is the plot symmetrical about ωc? Comment especially about plot in region ω < ωc.
- Extrapolate and predict the problems one can expect if more waves are to be modulated.
- Suggest solutions to the above problem. In the process can one understand another advantage of modulation in terms of bandwidth?

An audio signal v_{m }= 20sin2π(1500t) amplitude modulates a carrier v_{c} = 80 sin 2π (100,000t). The value of percent modulation is ______.

An amplitude-modulated wave is represented by C_{m}(t) = 10(1 + 0.2 cos 12560t) × sin (111 × 10^{4}t) volts. The modulating frequency in kHz will be ______.

The maximum and minimum voltage of an amplitude modulated signal are 60 V and 20 V respectively. The percentage modulation index will be ______.

The maximum amplitude for an amplitude modulated wave is found to be 12V while the minimum amplitude is found to be 3V. The modulation index is 0.6x where x is ______.

A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal are ______.