Mobile Communications Systems

Angle MODULATION

1 What is the difference between amplitude modulation and angle modulation ?

1 Amplitude of the modulated carrier is held constant

2 Phase or the Time Derivative of the phase of the carrier is varied

linearly with the message signal m(t).

3 The general angle-modulated signal is given by

x(t ) = Ac cos [2fct + (t) ]

4 (2fc t + (t)) = i(t) is called the instantaneous phase of x(t),

5 (t) is called the phase deviation of x(t).

1 What is the difference between amplitude modulation and angle modulation ?

6 instantaneous angular frequency of x(t) is

7 The instantaneous frequency fi(t), of x(t) is accordingly given by

8 The quantity d/dt is called the angular frequency deviation.

dttd

cfdtttcfd

dtidti

)(2))(2()(

dttd

cftit

if

i

)(21

2)(

)(

2 what are the two types of angle modulation methods ?

1 PHASE MODULATION (PM)

2 FREQUENCY MODULATION (FM)

2 what are the two types of angle modulation methods ?

PHASE MODULATION

1 Phase modulation implies that (t) is proportional to the

modulating signal. Thus

)(2)( tmpkt

where kp is the deviation constant, with unit volt-1.

FREQUENCY MODULATION

1 Frequency modulation implies that d/dt is proportional to the

modulating signal.

)(2 tmf

kdtd

2 in FM the instantaneous frequency varies linearly with the

message signal.

fi fc k f m t ( )

3 Derive an expression that describes the Frequency modulated output signal When the modulating signal is S m (t) = Am cos( m t ) and

the carrier signal is S c(t) = Ac cos( c t ).

FREQUENCY DEVIATION 1 Consider a sinusoidal modulating information signal

m t Am fmt( ) cos( ) 22 The instantaneous frequency of the resulting FM signal

equalsfi t fc k f Am fmt( ) cos( ) 2

3 The maximum change in instantaneous frequency f i from

the carrier frequency fc, is known as frequency deviation

f. f k f Am

• The ratio of the frequency deviation to the modulation

frequency fm is called the modulation index of the FM

signal.

PHASE DEVIATION

We denote it by f

fm

is measured in radians. It represents the phase deviation

of the FM signal. In other words represents the maximum

departure of the angle (t) from the angle “2fc t” of the

carrier The FM signal is thus given by x t Ac fct fmt( ) cos( sin( )) 2 2

• Depending on the value of the modulation index , we may

distinguish two cases of frequency modulation - Narrow-

Band FM and Wide-Band FM.

1 Narrow-band frequency modulation

2 Wide-band frequency modulation

4 How the frequency spectrum of a FM modulated signal varies with modulation index.

4 How the frequency spectrum of a FM modulated signal varies with modulation index.

• With the increase in the modulation index, the carrier

amplitude decreases while the amplitude of the various side

bands increases. With some values of modulation index,

the carrier can disappear completely.

5 What is the power in an angle-modulated signal ?

5 What is the power in an angle-modulated signal ?

• The power in an angle-modulated signal is easily computed

2

2

)(2221

cA

n

nnJcAP

Thus the power contained in the FM signal is independent of the message signal. This is an important difference between FM and AM.

6 Calculate the bandwidth occupied by a FM signal with a modulation index of 2 and a highest modulating frequency of 2.5 kHz.

6 Calculate the bandwidth occupied by a FM signal with a modulation index of 2 and a highest modulating frequency of 2.5 kHz.

Theoretically, a FM signal contains an infinite number of side frequencies so that the bandwidth required to transmit such signal is infinite.

• Referring to the table, we can see that this produces six

significant pairs of sidebands. The bandwidth can then be

determined with the simple formula

max2. NfWB

where N is the number of significant sidebands. • Using the example above and assuming a highest

modulating frequency of 2.5 kHz, the bandwidth of the FM signal is

kHzWB

305.262..

using Carson's Rule

• Carson's rule is given by the expression

BT BW f fm 2 2

f is the maximum frequency deviation, and fm is the

maximum modulating frequency.

• We may thus define an approximate rule for the

transmission bandwidth of an FM signal generated by a

single of frequency fm as follows:

BT BW f fm f 2 2 2 1 1 ( )

Example: Assuming a maximum frequency deviation of 5

kHz and a maximum modulating frequency of 2.5 kHz, the

bandwidth would be

kHzkHz

kHzkHzWB

155.72

)55.2(2..

7 Briefly explain DIRECT FM generation method

fi fc k f m t ( )

• In a direct FM system the instantaneous frequency is

directly varied with the information signal.

• To vary the frequency of the carrier is to use an Oscillator

whose resonant frequency is determined by components

that can be varied. The oscillator frequency is thus changed

by the modulating signal amplitude.

• For example, an electronic Oscillator has an output

frequency that depends on energy-storage devices.

• There are a wide variety of oscillators whose frequencies

depend on a particular capacitor value.

• By varying the capacitor value, the frequency of oscillation

varies. If the capacitor variations are controlled by m(t),

the result is an FM waveform

• To perform frequency demodulation we require a two-port

device that produces an output signal with amplitude

directly proportional to the instantaneous frequency of a

frequency modulated wave used as the input signal.

• They are two methods of designing a frequency

demodulator

(1) Indirect

(2) Direct.

8 What are the FM demodulation methods ?

• The phase-locked loop (PLL) is a negative feedback system, which can be used for indirect frequency demodulation. This important circuit finds application both in analog and digital communication systems.

1. Phase-Locked Loop

2. DISCRIMINATOR

• Noise is essentially amplitude variations. An FM signal,

on the other hand, has a constant carrier amplitude.

• Because of this, FM receivers contain limiter circuits that

restrict the amplitude of the received signal.Any amplitude

variations occurring on the FM signal are effectively

clipped off.

• Because of the clipping action of the limiter circuits, noise

is almost completely eliminated.

NOISE in FM Signals

• Despite the fact that FM has superior noise rejection

qualities, noise still interferes with an FM signal. This is

particularly true for the high-frequency components in the

modulating signal.

• These high frequencies can at times be larger in amplitude

than the high-frequency content of the modulating signal.

This causes a form of frequency distortion that can make

the signal unintelligible.

• To overcome this problem Most FM system use a

technique known as Pre-emphasis and De-emphasis.

• At the transmitter the modulating signal is passing

through a simple network which amplifies the high

frequency component more the low-frequency component.

• The simplest form of such circuit is a simple high pass

filter.

• This improves the signal-to-noise ratio.

• To return the frequency response to its normal level, a de-

emphasis circuit is used at the receiver.

• This is a simple low-pass filter

• The de-emphasis circuit provides a normal frequency

response.

• The combined effect of pre-emphasis and de-emphasis is to

increase the high-frequency components during the

transmission so that they will be stronger and not masked

by noise