Modulation

1. The carrier wave of a signal is given by

<math>c(t) = 3\sin(8\pi t)</math> volt

The modulating signal is a square wave as shown. Find modulation index. [Delhi 2014]

m(t) in volt 2

t in second

Ans.

According to the diagram,

Amplitude of modulating signal <math>A_m = 1V</math>

Amplitude of carrier wave <math>A_c = 2 \text{ V}</math>

Modulation index, <math>\mu = \frac{A_m}{A} = \frac{1}{2} = 0.5</math> (1)

1. Why do we need a higher bandwidth for transmission of music compared to that for commercial telephonic communication? [Delhi 2009]

Ans. The range of frequencies of music is higher than commercial telephone conversation and therefore, greater bandwidth is needed for music. Also, it is free from noise.

3.Identify the part X and Y in the following block diagram of a generalised communication system. [Delhi 2008C]

Transmitter Receiver

Ans. According to question figure,

1. Information source.
2. Communication channel

2 Marks Questions

4.Define the term modulation. Draw a block diagram of a simple modulator for obtaining AM signal. [Foreign 2014]

Ans. Modulation is the process in which low frequency message signal is superimposed on high frequency carrier wave so that they can be trasmitted over long distances. The block diagram for a simple modulator for obtaining AM signal is shown as below:

Square law | y(t) Bandpass Modulating device AΜ filter Signal wave m(t) Carrier wave

5.A message signal of frequency 10 kHz and peak voltage 10 V is used to modulate a carrier of frequency 1 MHz and peak voltage 20 V. Determine

the modulation index

the side bands produced. [Delhi 2013C]

Ans.

(i) Modulation index:, <math>\frac{E_m}{E_c} = \frac{10}{20} = 0.5</math>

(1)

1. Side band frequencies = <math>f_c \pm f_m</math>

<math>f_m = 10 \text{ kHz}</math> <math>f_c = 1 \text{MHz} = 1000 \text{ kHz}</math> <math>\therefore</math> Side band frequencies = 1000 ± 10 <math>=1010 \text{ kHz}, 990 \text{ kHz}</math> (1) 6.In the block diagram of a simple modulator for obtaining an AM signal shown in the figure, identify the boxes A and B. Write their function. AΜ Modulating В wave Signal Carrier wave [All India 2013]

Ans.

In the block diagram of modulator, a is square law device and b is bandpass filter. Bandpass filter rejects low and high frequencies and allows a band of frequencies to pass thorough. Square law device is a non-linear device. It produces a non-linear output of message and carrier signals. The output from square (1) law device is <math>y(t) = Bx(t) + Cx^2(t)</math>.

where, B and C are constants and

<math>x(t) = \text{message signal } (A_m \sin \omega_m t) + \text{carrier}</math>

signal <math>(A_c \sin \omega_c t)</math> (1)

1. Block diagram of a receiver is shown in the figure below:

Receiving antenna

Receiving signal Amplifier Detector Output

1. Identify X and Y.
2. Write their functions. [Delhi 2013; All India 2012]

Ans. From the given block diagram of demodulation of a typical receiver, we can conclude the following,

1. X represents Intermediate Frequency (IF) stage while Y represents an amplifier.