ANALOG MODULATION

By
R. N. Akol
 Introduction
• Questions process by which characteristics of carrier signal are varied in
accordance to the intelligent signal
– What is modulation?
– Why do we modulate?
To ease signal processing, the range of frequencies of signals to be processed may not match the processing equiptment.

To reduce noise and optimize signal to noise ratio. This is done t the expense of band width.

To reduce attenuation of base band signals by certain channels that absorb a given range of frequencies

To reduce size of antenna

To allow for multi plexing

 Introduction cont...
• Modulation is a process by which the
characteristics of the carrier wave are varied in
accordance to the intelligent signal
• The resulting signal is referred to as the
modulated signal
• The intelligent signal is the modulating signal
• The different characteristics of the carrier are
modified by the modulating signal so that it can
carry information.
• Modulation is carried out at the transmitter by
use of a modulator
 Introduction cont...
• These characteristics of the carrier to be
varied include:
– Amplitude, hence amplitude modulation (AM)
– Angle , hence angle modulation
• Frequency –Frequency Modulation (FM)
• Phase-Phase Modulation (PM)
 Amplitude Modulation
• This is where the amplitude of the carrier wave is
varied in a accordance to the baseband or (
modulating or intelligent) signal
• Consider a sinusoid carrier wave (a) being modulated
by sinusoid baseband signal (b), the resultant
modulated signal (is as shown in C)
• Reference Chapter 2, Communications Systems, 4th
Edition by Simon Haykin
Amplitude Modulation
An AM wave is given as

The AM signal has the same shape as the baseband

signal if
 Note
• The AM wave is a signal at a carrier frequency but
with amplitude changing at the same rate as the
baseband signal
– The rate of change is dependent of the AM envelope
is dependent on the frequency of the modulating
signal
– The AM wave reaches a maximum when the
modulating signal is maximum and minimum when
the modulating signal is minimum
– The AM wave does not include any frequency
component of the modulating signals
 AM Cont...
• Recall the definition of AM..
• Suppose the baseband signal is defined as
• ei (t )  A i sin(i t ) where A is the amplitude
i

and ω is the frequency

i

• From trigonometry we can write the AM

signal as
S (t )   A c +A i sin(i t )  cos c t
 A c cos c t  A i sin(i t ) cos c t
Ai
 A c cos c t   cos(c  i )t  cos(c  i )t 
2
 AM cont....
• The AM signal contain:
– The carrier signal f c
– Upper frequency fc  fi
– Lower frequency fc  fi
– Harmonics of the above frequencies
• Therefore AM signal is wasteful of :
– Power since it contains the carrier which consumes much
of the power
– Bandwidth as it contains of the same information in the
lower and upper frequencies
• In practise, the modulating signal consist of a range of
frequencies hence range of side frequencies above &
bellow the carrier frequency.
– Referred to as upper sideband and lower sideband
 Variants of the AM
• In order to maximize the efficiency of AM i.e.
Utilize the bandwidth & power
– Double side band suppressed carrier (DSBSC)
– Single sideband (SSB)
– Vestigial sideband (VSB)
• Qn. Discuss the merits and demerits of the
different AM formats. Where do they find
application? ??
 AM Modulation Index
• AM modulation is measured in terms of the
relative amplitude of the carrier and the
modulating signal
• % modulation is the extent to which a carrier
voltage is varied by the modulating signal
• Modulation index/factor (m)
Ai
m 100
Ac
 AM modulation index Vs. Power
• The transmitted power for an AM signal is
given as  m2 
PT  Pc  1  
 2 
– where P is the power of the carrier signal
c

– It is desirable to have % modulation close to 100%

– Care must be taken not to exceed 100% as this
will lead to over modulation
– over modulation leads to other stations picking
up un dersired signal (noise)
 Angle Modulation
• Modulation in which the angle of the carrier
wave is varied in accordance to the modulating
signal
– Frequency modulation (FM) is the angle modulation in
which the carrier frequency is varied linearly with the
massage signal
– Phase modulation (PM) is the angle modulation in
which the phase of the carrier is varied linearly with
the message signal
– The difference between PM and FM is in the amount
of phase change is proportional to the amplitude of
the intelligence signal while in FM the frequency
change is proportional to the amplitude of the
intelligence signal
– PM is not directly used to transmit signals but does
help in the generation and study of FM
• For the carrier signal c(t )  Ac cos[c (t )] and  (t )  2 f t   ,
c c c

• PM the phase is directly proportional to the

modulating signal
– s(t )  Ac cos  2 fc t  k p m(t )  therefore c  k p m(t ) , k p is the
proportionality constant known as the phase sensitivity
of the modulator with units radian/volt
• FM the frequency is directly proportional to the
modulating signal t

f  f c  k f m(t ),  (t )  2 f c t  2 k f  m( )d

0
 t

s (t )  Ac cos  2 f c t  2 k f  m( )d 
 0 
• Note that PM can generated from FM by
differentiating the modulating signal vice versa
 FM
• Consider a monotone modulation, then the
instantaneous frequency of the resulting FM
signal is f  fc  k f m(t ) where m(t )  Ai cos(2 fi t )
f  f c  k f Ai cos(2 fi t )
• f  k f Ai
is the frequency deviation and
represents the maximum deviation of the
instantaneous frequency of the carrier
– It is proportional to the amplitude of the
modulating signal
• The modulation index of FM signal is defined
as m f  f / fi
 FM cont...

• Therefore the FM signal can be written as

 t

s (t )  A c cos  2 f c t  2 k f  A i cos(2 f i  ) d 
 0 
 f 
 A c cos  2 f c t  sin 2 f i t 
 fi 
 A c cos  2 f c t  m f sin 2 f i t 
 Narrow band FM
• Occurs when the modulation index is very
small compared to one radian m f 1
• Using trigonometry expand
s(t )  Ac cos 2 fc t  m f sin 2 fi t 

• Draw some conclusions from the expansion

......
 Wideband FM
• Also known as broadband FM
– The modulation index is much greater than one
radians/volt
– The FM signal can be written in complex form as
 
s(t )  re Ac exp  j 2 fc t  jm f sin(2 fi t ) 
– The complex envelope of the FM signal is periodic
with the fundamental frequency equal to the
intelligent frequency Ac exp  jmf sin(2 fi t ) 
– From Fourier series & using Bessel function J (m ) ofn f

the 1st kind, the FM signal can be written as


s(t )  Ac  J n (m f ) cos[2 ( f c  nf i )t ]
n
 Wideband cont....

• For small values of the modulation index, the FM

signal has f c , f c  f i and the situation
corresponds to narrowband FM
• The spectrum of wideband FM contains a carrier
frequency and infinite set of side frequencies
symmetric about f at fi , 2 fi , 3 fi
c

• The amplitude of carrier varies with modulation

index
 Bandwidth of FM signals
• Carson rule
BW  2(f  f i )
• Transmission bandwidth
BWT  2nmax f i
– is the separation between two frequencies
beyond which non of the side frequencies is
greater than 1% of the carrier amplitude
– i.e. nmax is a largest value that satisfies J n (mf )  0.01
 Power of FM signal
• Recall from the definition of FM signal

s(t )  Ac  J n (m f ) cos[2 ( f c  nf i )t ]
n

• Therefore, the average power of an FM signal

is

Ac2 A 2

PT 
2
 n f
n
J 2
( m ) 
2
c
 AM Reception
Antenna
RF Amplifier Detector Audio Amp Out put

• Tuned radio receiver

• Radio Frequency (RF) Amplifier
– RF signal is received through the antenna is usually
very small, therefore requiring amplification
– This stage should have low noise characteristics (
tuned to receive only the carrier and side frequencies)
• The detector extracts intelligence signal from the
RF signal
• Audio amplifier
• Output (might be a speaker)
 Envelope Detector

• Consist of a diode connected to a resistor & a

capacitor
• The diode charges and discharges the capacitor
during the positive and negative half of the cycle
respectively
• RC time constant is chosen such that the
1
BW fc
2 RC
 Envelope Detector cont..

• Advantages of the envelope detector:

– Relatively simple to construct; Can handle relatively
high power; They develop a readily usable dc
voltage for AGC; Distortions are acceptable for most
AM
• Disadvantages:
– No amplification; Power is absorbed in the circuit
which reduces the selectivity (tuning);Requires
constant tuning every time the frequency is change
Superheterodyne Receiver
 Superheterodyne Receiver
• Superhet recever
– Offers amplification through the use of Automatic
gain control hence improved sensitivity
– improved carrier frequency tuning and selectivity
• Done by the radio frequency and intermediate stages
– Improved filtering of the message signal from the
carrier frequency
– Remove the necessity of having continuous tuning
 Receiver characteristics
• Sensitivity
– The ability to drive the output to desired level
– Minimum input signal required to produce a specified
output
– Therefore the sensitivity is determined by an amount
of gain provided by the receiver and the noise
characteristics
– i.e. the signal input must be greater than the noise
floor of the receiver
• Selectivity
– To what extent the receiver is capable of
distinguishing between the desired signal and the
unwanted frequencies (interference from other
stations and AWGN)
 Recall from a Noise
• Narrowband noise can be represented in
– In phase and quadrature form as
n(t )  nI (t ) cos c t  nQ (t ) sin c t
• Where nI (t ), nQ (t ) are zero mean, jointly Gaussian
in phase & quadrature components of the noise signal
• With the same PSD and variance
– Complex envelop form
n(t )  r (t )cos c t   (t )
1/2
r (t )  n (t )  n (t )  and  (t )  tan nQ (t ) / nI (t ) 
 2
I
2
Q
 1
 Noise Characteristics of FM
Resultant
r(t)
Ѳ(t) Ac Ф(t)

• Since noise affects the angle

t
 r (t ) sin  (t ) 
 (t )  2 k f  m( )d  tan
1
 
0  A c  r (t ) cos  (t ) 
t
 r (t ) sin  (t ) 
 2 k f  m( )d  tan
1
 
0  Ac 
• The FM detector needs to be followed by
differentiator and therefore the noise term
1 d  r (t ) sin  (t ) 
v (t )  k m(t ) 
2 A c
f
dt
1 d  r (t ) sin  (t )  jfnQ (t )
noise  
2 A c dt Ac
 FM Noise Characteristics
• Hence the power spectral density and the
average power output of the noise signal in
FM systems is f 2 N f 2
S nose ( f )  Sn ( f )  o

A c2 Q
A c2
W 2
No f 2 N oW 3
Pnoise  
W A c2
df 
3A c2
 FM Noise characteristics
• Note that
– The average noise power is inversely proportional
to average carrier power
– The noise power increase with increasing
frequency
– The signal components are usually weaker at
higher frequencies
 Cont...
• Pre-emphasis
• De-emphasis
 FM cont..
• Note that FM receivers are similar to AM receiver
 Other related topics
• Frequency division multiplexing
• FM threshold effect