ANALOG

COMMUNICATIONS

(19EC0408)
 UNIT-I
AMPLITUDE MODULATION-I

Introduction to Communication System

Communication is the process by which information is exchanged between individuals

through a medium.

Communication can also be defined as the transfer of information from one point in space
and time to another point.

The basic block diagram of a communication system is as follows.

 Transmitter: Couples the message into the channel using high frequency signals.
 Channel: The medium used for transmission of signals
 Modulation: It is the process of shifting the frequency spectrum of a signal to a
frequency range in which more efficient transmission can be achieved.
 Receiver: Restores the signal to its original form.
 Demodulation: It is the process of shifting the frequency spectrum back to the
original baseband frequency range and reconstructing the original form.

Modulation:

Modulation is a process that causes a shift in the range of frequencies in a signal.

• Signals that occupy the same range of frequencies can be separated.

• Modulation helps in noise immunity, attenuation - depends on the physical

medium. The below figure shows the different kinds of analog modulation schemes that are

available
Modulation is operation performed at the transmitter to achieve efficient and reliable
information transmission.

For analog modulation, it is frequency translation method caused by changing the appropriate
quantity in a carrier signal.

It involves two waveforms:

 A modulating signal/baseband signal – represents the message.

 A carrier signal – depends on type of modulation.

•Once this information is received, the low frequency information must be removed from the
high frequency carrier. •This process is known as “Demodulation”.

Need for Modulation:

 Baseband signals are incompatible for direct transmission over the medium so,
modulation is used to convey (baseband) signals from one place to another.
 Allows frequency translation:
o Frequency Multiplexing
o Reduce the antenna height
o Avoids mixing of signals
o Narrowbanding
 Efficient transmission
 Reduced noise and interference

Types of Modulation:

Three main types of modulations:

Analog Modulation

 Amplitude modulation
Example: Double sideband with carrier (DSB-WC), Double- sideband
suppressed carrier (DSB-SC), Single sideband suppressed carrier (SSB-SC), vestigial
sideband (VSB)
  Angle modulation (frequency modulation & phase modulation)
Example: Narrow band frequency modulation (NBFM), Wideband frequency
modulation (WBFM), Narrowband phase modulation (NBPM), Wideband phase
modulation (NBPM)

Pulse Modulation

 Carrier is a train of pulses

 Example: Pulse Amplitude Modulation (PAM), Pulse width modulation (PWM) ,
Pulse Position Modulation (PPM)

Digital Modulation

 Modulating signal is analog

o Example: Pulse Code Modulation (PCM), Delta Modulation (DM), Adaptive
Delta Modulation (ADM), Differential Pulse Code Modulation (DPCM),
Adaptive Differential Pulse Code Modulation (ADPCM) etc.
 Modulating signal is digital (binary modulation)
o Example: Amplitude shift keying (ASK), frequency Shift Keying (FSK),
Phase Shift Keying (PSK) etc

Amplitude Modulation (AM)

Amplitude Modulation is the process of changing the amplitude of a relatively high

frequency carrier signal in accordance with the amplitude of the modulating signal
(Information).

The carrier amplitude varied linearly by the modulating signal which usually consists of a
range of audio frequencies. The frequency of the carrier is not affected.
 Application of AM - Radio broadcasting, TV pictures (video), facsimile transmission
 Frequency range for AM - 535 kHz – 1600 kHz
 Bandwidth - 10 kHz

Various forms of Amplitude Modulation

• Conventional Amplitude Modulation (Alternatively known as Full AM or Double

Sideband Large carrier modulation (DSBLC) /Double Sideband Full Carrier (DSBFC)

• Double Sideband Suppressed carrier (DSBSC) modulation

• Single Sideband (SSB) modulation

• Vestigial Sideband (VSB) modulation

Time Domain and Frequency Domain Description

It is the process where, the amplitude of the carrier is varied proportional to that of the
message signal.

Let m (t) be the base-band signal, m (t) ←→ M (ω) and c (t) be the carrier, c(t) = A c
cos(ωct). fc is chosen such that fc >> W, where W is the maximum frequency component of
m(t). The amplitude modulated signal is given by

s(t) = Ac [1 + kam(t)] cos(ωct)

Fourier Transform on both sides of the above equation

S(ω) = π Ac/2 (δ(ω − ωc) + δ(ω + ωc)) + kaAc/ 2 (M(ω − ωc) + M(ω + ωc))

ka is a constant called amplitude sensitivity.

kam(t) < 1 and it indicates percentage modulation.

Fig.2. Amplitude modulation in time and frequency domain

Power relations in AM waves:

Consider the expression for single tone/sinusoidal AM wave

The ratio of total side band power to the total power in the modulated wave is given by

This ratio is called the efficiency of AM system

Single Tone Modulation:
Consider a modulating wave m(t ) that consists of a single tone or single frequency
component given by

Expanding the equation (2), we get

 Fig.3. Frequency Domain characteristics of single tone AM
Generation of AM waves:

Two basic amplitude modulation principles are discussed. They are square law modulation
and switching modulator.

Square Law Modulator

When the output of a device is not directly proportional to input throughout the
operation, the device is said to be non-linear. The Input-Output relation of a non-linear device
can be expressed as

When the output is considered up to square of the input, the device is called a square law
device and the square law modulator is as shown in the figure 4

Fig.4. Square Law Modulator

Consider a non-linear device to which a carrier c(t)=A ccos(2πfct) and an information

signal m(t) are fed simultaneously as shown in figure 4. The total input to the device
at any instant is
Therefore the square law device output 0 V consists of the dc component at f = 0.
The information signal ranging from 0 to W Hz and its second harmonics are signal at
fc and 2fc.
 Switching Modulator

Fig.5. Switching Modulator

The total input for the diode at any instant is given by

When the peak amplitude of c(t) is maintained more than that of information signal, the
operation is assumed to be dependent on only c(t) irrespective of m(t).
When c(t) is positive, v2=v1since the diode is forward biased. Similarly, when c(t) is
negative, v2=0 since diode is reverse biased. Based upon above operation, switching response
of the diode is periodic rectangular wave with an amplitude unity and is given by
 The required AM signal centred at fc can be separated using band pass filter.
The lower cut off-frequency for the band pass filter should be between w and fc-w
and the upper cut-off frequency between fc+w and 2fc. The filter output is given by
the equation

Detection of AM waves

Demodulation is the process of recovering the information signal (base band) from
the incoming modulated signal at the receiver. There are two methods, they are Square law
Detector and Envelope Detector

Square Law Detector

Consider a non-linear device to which the AM signal s(t) is applied. When the level of s(t) is
very small, output can be considered upto square of the input.
The device output consists of a dc component at f =0, information signal ranging from 0-W
Hz and its second harmonics and frequency bands centered at fc and 2fc. The required
information can be separated using low pass filter with cut off frequency ranging between W
and fc-w. The filter output is given by

When the information level is very low, the noise effect increases at the receiver, hence the
system clarity is very low using square law demodulator.
Envelope Detector

It is a simple and highly effective system. This method is used in most of the commercial AM
radio receivers. An envelope detector is as shown below.

Fig.7. Envelope Detector

During the positive half cycles of the input signals, the diode D is forward biased and
the capacitor C charges up rapidly to the peak of the input signal. When the input signal falls
below this value, the diode becomes reverse biased and the capacitor C discharges through
the load resistor RL.

The discharge process continues until the next positive half cycle. When the input
signal becomes greater than the voltage across the capacitor, the diode conducts again and the
process is repeated.

The charge time constant (rf+Rs)C must be short compared with the carrier period,
the capacitor charges rapidly and there by follows the applied voltage up to the positive peak
when the diode is conducting.That is the charging time constant shall satisfy the condition,

Where ‘W’ is band width of the message signal. The

result is that the capacitor voltage or detector output is nearly the same as the envelope of
AM wave.
Advantages and Disadvantages of AM:

Advantages of AM:

 Generation and demodulation of AM wave are easy.

 AM systems are cost effective and easy to build.

Disadvantages:
 AM contains unwanted carrier component, hence it requires more transmission
power.
 The transmission bandwidth is equal to twice the message bandwidth.

Radio Transmitters

There are two approaches in generating an AM signal. These are known as low and
high level modulation. They're easy to identify: A low level AM transmitter performs the
process of modulation near the beginning of the transmitter. A high level transmitter
performs the modulation step last, at the last or "final" amplifier stage in the transmitter. Each
method has advantages and disadvantages, and both are in common use.

Low-Level AM Transmitter:

Fig.8. Low-Level AM Transmitter Block Diagram

There are two signal paths in the transmitter, audio frequency (AF) and radio
frequency (RF). The RF signal is created in the RF carrier oscillator. At test point A the
oscillator's output signal is present. The output of the carrier oscillator is a fairly small AC
voltage, perhaps 200 to 400 mV RMS. The oscillator is a critical stage in any transmitter. It
must produce an accurate and steady frequency. Every radio station is assigned a different
carrier frequency. The dial (or display) of a receiver displays the carrier frequency.
If the oscillator drifts off frequency, the receiver will be unable to receive the
transmitted signal without being readjusted. Worse yet, if the oscillator drifts onto the
frequency being used by another radio station, interference will occur. Two circuit techniques
are commonly used to stabilize the oscillator, buffering and voltage regulation.
 The buffer amplifier has something to do with buffering or protecting the oscillator.
An oscillator is a little like an engine (with the speed of the engine being similar to the
oscillator's frequency). If the load on the engine is increased (the engine is asked to do more
work), the engine will respond by slowing down. An oscillator acts in a very similar fashion.
If the current drawn from the oscillator's output is increased or decreased, the oscillator may
speed up or slow down slightly.

Buffer amplifier is a relatively low-gain amplifier that follows the oscillator. It has a
constant input impedance (resistance). Therefore, it always draws the same amount of current
from the oscillator. This helps to prevent "pulling" of the oscillator frequency. The buffer
amplifier is needed because of what's happening "downstream" of the oscillator. Right after
this stage is the modulator. Because the modulator is a nonlinear amplifier, it may not have a
constant input resistance -- especially when information is passing into it. But since there is a
buffer amplifier between the oscillator and modulator, the oscillator sees a steady load
resistance, regardless of what the modulator stage is doing.

Voltage Regulation: An oscillator can also be pulled off frequency if its power
supply voltage isn't held constant. In most transmitters, the supply voltage to the oscillator is
regulated at a constant value. The regulated voltage value is often between 5 and 9 volts;
zener diodes and three-terminal regulator ICs are commonly used voltage regulators. Voltage
regulation is especially important when a transmitter is being powered by batteries or an
automobile's electrical system. As a battery discharges, its terminal voltage falls. The DC
supply voltage in a car can be anywhere between 12 and 16 volts, depending on engine RPM
and other electrical load conditions within the vehicle.

Modulator: The stabilized RF carrier signal feeds one input of the modulator stage.
The modulator is a variable-gain (nonlinear) amplifier. To work, it must have an RF carrier
signal and an AF information signal. In a low-level transmitter, the power levels are low in
the oscillator, buffer, and modulator stages; typically, the modulator output is around 10 mW
(700 mV RMS into 50 ohms) or less.

AF Voltage Amplifier: In order for the modulator to function, it needs an

information signal. A microphone is one way of developing the intelligence signal, however,
it only produces a few millivolts of signal. This simply isn't enough to operate the modulator,
so a voltage amplifier is used to boost the microphone's signal. The signal level at the output
of the AF voltage amplifier is usually at least 1 volt RMS; it is highly dependent upon the
transmitter's design. Notice that the AF amplifier in the transmitter is only providing a
voltage gain, and not necessarily a current gain for the microphone's signal. The power levels
are quite small at the output of this amplifier; a few mW at best.
 RF Power Amplifier: At test point D the modulator has created an AM signal by
impressing the information signal from test point C onto the stabilized carrier signal from test
point B at the buffer amplifier output. This signal (test point D) is a complete AM signal, but
has only a few milliwatts of power. The RF power amplifier is normally built with several
stages. These stages increase both the voltage and current of the AM signal. We say that
power amplification occurs when a circuit provides a current gain. In order to accurately
amplify the tiny AM signal from the modulator, the RF power amplifier stages must be
linear. You might recall that amplifiers are divided up into "classes," according to the
conduction angle of the active device within. Class A and class B amplifiers are considered to
be linear amplifiers, so the RF power amplifier stages will normally be constructed using one
or both of these type of amplifiers. Therefore, the signal at test point E looks just like that of
test point D; it's just much bigger in voltage and current.

Antenna Coupler: The antenna coupler is usually part of the last or final RF power
amplifier, and as such, is not really a separate active stage. It performs no amplification, and
has no active devices. It performs two important jobs: Impedance matching and filtering. For
an RF power amplifier to function correctly, it must be supplied with a load resistance equal
to that for which it was designed.

The antenna coupler also acts as a low-pass filter. This filtering reduces the amplitude
of harmonic energies that may be present in the power amplifier's output. (All amplifiers
generate harmonic distortion, even "linear" ones.) For example, the transmitter may be tuned
to operate on 1000 kHz. Because of small nonlinearities in the amplifiers of the transmitter,
the transmitter will also produce harmonic energies on 2000 kHz (2nd harmonic), 3000 kHz
(3rd harmonic), and so on. Because a low-pass filter passes the fundamental frequency (1000
kHz) and rejects the harmonics, we say that harmonic attenuation has taken place.

High-Level AM Transmitter:

Fig.9. Low-Level AM Transmitter Block Diagram

The high-level transmitter of Figure 9 is very similar to the low-level unit. The RF
section begins just like the low-level transmitter; there is an oscillator and buffer amplifier.
The difference in the high level transmitter is where the modulation takes place. Instead of
adding modulation immediately after buffering, this type of transmitter amplifies the
unmodulated RF carrier signal first. Thus, the signals at points A, B, and D in Figure 9 all
look like unmodulated RF carrier waves. The only difference is that they become bigger
in voltage and current as they approach test point D.

The modulation process in a high-level transmitter takes place in the last or final
power amplifier. Because of this, an additional audio amplifier section is needed. In order
to modulate an amplifier that is running at power levels of several watts (or more),
comparable power levels of information are required. Thus, an audio power amplifier is
required. The final power amplifier does double-duty in a high-level transmitter. First, it
provides power gain for the RF carrier signal, just like the RF power amplifier did in the
low-level transmitter. In addition to providing power gain, the final PA also performs the
task of modulation. The final power amplifier in a high-level transmitter usually operates
in class C, which is a highly nonlinear amplifier class.

Comparison:

Low Level Transmitters

 Can produce any kind of modulation; AM, FM, or PM.

 Require linear RF power amplifiers, which reduce DC efficiency and increases
production costs.

High Level Transmitters

 Have better DC efficiency than low-level transmitters, and are very well suited
for battery operation.
 Are restricted to generating AM modulation only.
 UNIT-II
AMPLITUDE MODULATION-II

To overcome these limitations, the conventional AM system is modified at the

cost of increased system complexity. Therefore, three types of modified AM systems are
discussed.

DSBSC (DoubleSide Band Suppressed Carrier) modulation: In

DSBC modulation, the modulated wave consists of only the upper and lower side bands.
Transmitted power is saved through the suppression of the carrier wave, but the channel
bandwidth requirement is the same as before.

SSBSC (Single Side Band Suppressed Carrier) modulation: The SSBSC

modulated wave consists of only the upper side band or lower side band. SSBSC is suited
for transmission of voice signals. It is an optimum form of
modulation in that it requires the minimum transmission power and minimum channel
band width. Disadvantage is increased cost and complexity.

VSB (Vestigial Side Band) modulation: In VSB, one side band is completely
passed and just a trace or vestige of the other side band is retained. The required channel
bandwidth is therefore in excess of the message bandwidth by an amount equal to the
width of the vestigial side band. This method is suitable for the transmission of wide
band signals.
DSB-SC Time domain and Frequency domain Description:

DSBSC modulators make use of the multiplying action in which the modulating
signal multiplies the carrier wave. In this system, the carrier component is eliminated and
both upper and lower side bands are transmitted. As the carrier component is suppressed,
the power required for transmission is less than that of AM.

Consequently, the modulated signal s(t) under goes a phase reversal , whenever the
message signal m(t) crosses zero as shown below.
 Fig.1. (a) DSB-SC waveform (b) DSB-SC Frequency Spectrum

The envelope of a DSBSC modulated signal is therefore different from the

message signal and the Fourier transform of s(t) is given by
Generation of DSBSC Waves:

Balanced Modulator (Product Modulator)

A balanced modulator consists of two standard amplitude modulators

arranged in a balanced configuration so as to suppress the carrier wave as shown in
the following block diagram. It is assumed that the AM modulators are identical, except
for the sign reversal of the modulating wave applied to the input of one of them. Thus,
the output of the two modulators may be expressed as,

Hence, except for the scaling factor 2ka, the balanced modulator output is equal
to the product of the modulating wave and the carrier.

Ring Modulator

Ring modulator is the most widely used product modulator for generating DSBSC wave
and is shown below.

The four diodes form a ring in which they all point in the same direction. The
diodes are controlled by square wave carrier c(t) of frequency fc, which is applied
longitudinally by means of two center-tapped transformers.
Assuming the diodes are ideal, when the carrier is positive, the outer diodes D1 and
D2 are forward biased where as the inner diodes D3 and D4 are reverse biased, so
that the modulator multiplies the base band signal m(t) by c(t). When the carrier is
negative, the diodes D1 and D2 are reverse biased and D3 and D4 are forward, and the
modulator multiplies the base band signal –m(t) by c(t).

Thus the ring modulator in its ideal form is a product modulator for
square wave carrier and the base band signal m(t). The square wave carrier can be
expanded using Fourier series as

From the above equation it is clear that output from the modulator consists
entirely of modulation products. If the message signal m(t) is band limited to the
frequency band − w < f < w, the output spectrum consists of side bands centered at fc.
Detection of DSB-SC waves:

Coherent Detection:

The message signal m(t) can be uniquely recovered from a DSBSC wave s(t)
by first multiplying s(t) with a locally generated sinusoidal wave and then low pass
filtering the product as shown.

It is assumed that the local oscillator signal is exactly coherent or synchronized, in

both frequency and phase, with the carrier wave c(t) used in the product modulator to
generate s(t). This method of demodulation is known as coherent detection or
synchronous detection.
 Fig.6.Spectrum of output of the product modulator

From the spectrum, it is clear that the unwanted component (first term in the
expression) can be removed by the low-pass filter, provided that the cut-off frequency
of the filter is greater than W but less than 2fc-W. The filter output is given by

The demodulated signal vo(t) is therefore proportional to m(t) when the phase error ϕ
is constant.

Introduction of SSB-SC

Standard AM and DSBSC require transmission bandwidth equal to twice the

message bandwidth. In both the cases spectrum contains two side bands of
width W Hz, each. But the upper and lower sides are uniquely related to each other
by the virtue of their symmetry about the carrier frequency. That is, given the
amplitude and phase spectra of either side band, the other can be uniquely determined.
Thus if only one side band is transmitted, and if both the carrier and the other side band
are suppressed at the transmitter, no information is lost. This kind of modulation is called
SSBSC and spectral comparison between DSBSC and SSBSC is shown in the figures 1
and 2.
Frequency Domain Description
side band is transmitted; the resulting SSB modulated wave has the spectrum shown in figure
1. Similarly, the lower side band is represented in duplicate by the frequencies
below fc and those above -fc and when only the lower side band is transmitted, the
spectrum of the corresponding SSB modulated wave shown in figure 5.Thus the
essential function of the SSB modulation is to translate the spectrum of the modulating
wave, either with or without inversion, to a new location in the frequency domain.
The advantage of SSB modulation is reduced bandwidth and the elimination of
high power carrier wave. The main disadvantage is the cost and complexity of its
implementation.

Generation of SSB wave:

Frequency discrimination method

Consider the generation of SSB modulated signal containing the upper side band
only. From a practical point of view, the most severe requirement of SSB generation
arises from the unwanted sideband, the nearest component of which is separated from the
desired side band by twice the lowest frequency component of the message signal. It
implies that, for the generation of an SSB wave to be possible, the message spectrum
must have an energy gap centered at the origin as shown in figure 7. This requirement
is naturally satisfied by voice signals, whose energy gap is about 600Hz wide.
 The frequency discrimination or filter method of SSB generation consists of a
product modulator, which produces DSBSC signal and a band-pass filter to extract the
desired side band and reject the other and is shown in the figure 8.

Application of this method requires that the message signal satisfies two conditions:
1. The message signal m(t) has no low-frequency content. Example: speech, audio, music.
2. The highest frequency component W of the message signal m(t) is much less than the
carrier frequency fc.

Then, under these conditions, the desired side band will appear in a non-overlapping
interval in the spectrum in such a way that it may be selected by an appropriate filter.

In designing the band pass filter, the following requirements should be satisfied:
1.The pass band of the filter occupies the same frequency range as the spectrum of the
desired SSB modulated wave.

2. The width of the guard band of the filter, separating the pass band from the stop
band, where the unwanted sideband of the filter input lies, is twice the lowest frequency
component of the message signal.

When it is necessary to generate an SSB modulated wave occupying a frequency band

that is much higher than that of the message signal, it becomes very difficult to design an
appropriate filter that will pass the desired side band and reject the other. In such a situation
it is necessary to resort to a multiple-modulation process so as to ease the filtering
requirement. This approach is illustrated in the following figure 9 involving two stages of
modulation.

The SSB modulated wave at the first filter output is used as the modulating wave
for the second product modulator, which produces a DSBSC modulated wave with a
spectrum that is symmetrically spaced about the second carrier frequency f2. The
frequency separation between the side bands of this DSBSC modulated wave is
effectively twice the first carrier frequency f1, thereby permitting the second filter to
remove the unwanted side band.

Hilbert Transform & its Properties:

The Fourier transform is useful for evaluating the frequency content of an energy signal, or in
a limiting case that of a power signal. It provides mathematical basis for analyzing and
designing the frequency selective filters for the separation of signals on the basis of their
frequency content.Another method of separating the signals is based on phase selectivity,
which uses phase shifts between the appropriate signals (components)
to achieve the desired separation.
o
In case of a sinusoidal signal, the simplest phase shift of 180 is obtained by “Ideal
transformer” (polarity reversal). When the phase angles of all the components of a given
signal are shifted by 90o, the resulting function of time is called the “Hilbert transform” of the
signal.
Consider an LTI system with transfer function defined by equation 1
 The device which possesses such a property is called Hilbert transformer. Whenever a
signal is applied to the Hilbert transformer, the amplitudes of all frequency components of the
input signal remain unaffected. It produces a phase shift of -90o for all positive frequencies,
while a phase shifts of 90o for all negative frequencies of the signal.

If x(t) is an input signal, then its Hilbert transformer is denoted by xˆ(t ) and shown in
the following diagram.
Now consider any input x(t) to the Hilbert transformer, which is an LTI system. Let the
impulse response of the Hilbert transformer is obtained by convolving the input x(t) and
impulse response h(t) of the system.
Properties:

Time Domain Description:

The time domain description of an SSB wave s(t) in the canonical form is given
by the equation 1.
 Following the same procedure, we can find the canonical representation for an SSB
wave
s(t) obtained by transmitting only the lower side band is given by

Phase discrimination method for generating SSB wave:

Time domain description of SSB modulation leads to another method of SSB

generation using the equations 9 or 10. The block diagram of phase discriminator
is as shown in figure 15.
 The phase discriminator consists of two product modulators I and Q, supplied
with carrier waves in-phase quadrature to each other. The incoming base band signal m(t)
is applied to product modulator I, producing a DSBSC modulated wave that contains
reference phase sidebands symmetrically spaced about carrier frequency fc.

The Hilbert transform mˆ (t) of m (t) is applied to product modulator Q, producing a

DSBSC modulated that contains side bands having identical amplitude spectra to those of
modulator I, but with phase spectra such that vector addition or subtraction of the two
modulator outputs results in cancellation of one set of side bands and reinforcement of
the other set.

The use of a plus sign at the summing junction yields an SSB wave with
only the lower side band, whereas the use of a minus sign yields an SSB wave with only
the upper side band. This modulator circuit is called Hartley modulator.

Demodulation of SSB Waves:

Introduction to Vestigial Side Band Modulation

Vestigial sideband is a type of Amplitude modulation in which one side band is

completely passed along with trace or tail or vestige of the other side band. VSB is a
compromise between SSB and DSBSC modulation. In SSB, we send only one side
band, the Bandwidth required to send SSB wave is w. SSB is not appropriate way of
modulation when the message signal contains significant components at extremely low
frequencies. To overcome this VSB is used.

Frequency Domain Description

The following Fig illustrates the spectrum of VSB modulated wave s (t) with respect to the
message m (t) (band limited)

Assume that the Lower side band is modified into the vestigial side band. The
vestige of the lower sideband compensates for the amount removed from the
upper sideband. The bandwidth required to send VSB wave is
 The vestige of the Upper sideband compensates for the amount removed from
the Lower sideband. The bandwidth required to send VSB wave is B = w+fv, where fv is
the width of the vestigial side band.

Therefore, VSB has the virtue of conserving bandwidth almost as efficiently as SSB
modulation, while retaining the excellent low-frequency base band characteristics of DSBSC
and it is standard for the transmission of TV signals.

Generation of VSB Modulated Wave

VSB modulated wave is obtained by passing DSBSC through a sideband shaping filter as
shown in fig below.

Fig.17. Block Diagram of VSB Modulator

The exact design of this filter depends on the spectrum of the VSB waves. The
relation between filter transfer function H (f) and the spectrum of VSB waves is given by

S(f) = Ac /2 [M (f - fc) + M(f + fc)]H(f)-------------------------(1)

Where M(f) is the spectrum of Message Signal. Now, we have to determine the
specification for the filter transfer function H(f) It can be obtained by passing s(t) to a
coherent detector and determining the necessary condition for undistorted version of the
message signal m(t). Thus, s (t) is multiplied by a locally generated sinusoidal wave cos
(2πfct) which is synchronous with the carrier wave A ccos(2πfct) in both frequency and phase,
as in fig below,
 The spectrum of Vo (f) is in fig below,

Similarly, the transfer function H (f) of the filter for sending Lower sideband along with the
vestige of the Upper sideband is shown in fig below,
Time Domain Description:

Time domain representation of VSB modulated wave, procedure is similar to SSB

Modulated waves. Let s(t) denote a VSB modulated wave and assuming that s(t) containing
Upper sideband along with the Vestige of the Lower sideband. VSB modulated wave s(t) is
the output from Sideband shaping filter, whose input is DSBSC wave. The filter transfer
function H(f) is of the form as in fig below,

Fig (2) Low pass equivalent to H(f)

Note:
1. If vestigial side band is increased to full side band, VSB becomes DSCSB ,i.e., mQ(t) = 0.
Envelope detection of a VSB Wave plus Carrier
Comparison of AM Techniques:

Applications of different AM systems:

 Amplitude Modulation: AM radio, Short wave radio broadcast

 DSB-SC: Data Modems, Color TV’s color signals.
 SSB: Telephone
 VSB: TV picture signals
 UNIT III
ANGLE MODULATION
 Basic concepts
 Frequency Modulation
 Single tone frequency modulation
 Spectrum Analysis of Sinusoidal FM Wave
 Narrow band FM, Wide band FM, Constant Average Power
 Transmission bandwidth of FM Wave
 Generation of FM Waves:
o Indirect FM, Direct FM: Varactor Diode and
Reactance Modulator
 Detection of FM Waves:
o Balanced Frequency discriminator, Zero crossing detector,
Phase locked loop
 Comparison of FM & AM
 Pre-emphasis & de-emphasis
 FM Transmitter block diagram and explanation of each block
Instantaneous Frequency

The frequency of a cosine function x(t) that is given by

x(t)  cosct 0 

is equal to c since it is a constant with respect to t, and the phase of the cosine is the

constant 0. The angle of the cosine (t) = ct +0 is a linear relationship with respect to t

(a straight line with slope of c and y–intercept of 0). However, for other sinusoidal
functions, the frequency may itself be a function of time, and therefore, we should not think
in terms of the constant frequency of the sinusoid but in terms of the INSTANTANEOUS
frequency of the sinusoid since it is not constant for all t. Consider for example the
following sinusoid
y(t)  cos (t),

where (t) is a function of time. The frequency of y(t) in this case depends on the function
of (t) and may itself be a function of time. The instantaneous frequency of y(t) given above
is defined as
d (t)
 (t)  .
i
dt

As a checkup for this definition, we know that the instantaneous frequency of x(t) is equal to
its frequency at all times (since the instantaneous frequency for that function is constant) and
is equal to c. Clearly this satisfies the definition of the instantaneous frequency since (t) =
ct +0 and therefore i(t) = c.
If we know the instantaneous frequency of some sinusoid from – to sometime t, we can find
the angle of that sinusoid at time t using
t

 (t)  i ( )d.



Changing the angle (t) of some sinusoid is the bases for the two types of angle modulation:
Phase and Frequency modulation techniques.

Phase Modulation (PM)

In this type of modulation, the phase of the carrier signal is directly changed by the message
signal. The phase modulated signal will have the form
 g PM (t )  A  cos c t  k p m (t )  ,

where A is a constant, c is the carrier frequency, m(t) is the message signal, and kp is a
parameter that specifies how much change in the angle occurs for every unit of change of
m(t). The phase and instantaneous frequency of this signal are

PM (t )  ct  k p m (t ),
 (t )   
k dm (t )  k m (t ).
 
i c p c p
dt

So, the frequency of a PM signal is proportional to the derivative of the message signal.

Frequency Modulation (FM)

This type of modulation changes the frequency of the carrier (not the phase as in PM) directly
with the message signal. The FM modulated signal is
 t

g FM (t )  A cos ct  k f  m ( )d   ,
  

where kf is a parameter that specifies how much change in the frequency occurs for every
unit change of m(t). The phase and instantaneous frequency of this FM are

FM (t )  ct  k t

f
 m ( )d  ,

d t 
i (t )  c  k
dt 
f  m (  )d    c  k f m (t ).
 

Relation between PM and FM

PM and FM are tightly related to each other. We see from the phase and frequency
t

relations for PM and FM given above that replacing m(t) in the PM signal with
 m ( )d 


gives an FM signal and replacing m(t) in the FM signal with dm (t

)
gives a PM signal. This
is illustrated in the following block diagrams.
dt
 Frequency Modulator (FM)

t
 m (t )d

Phase
gFM (t)
 ()d
m(t) Modulator
 (PM)

Phase Modulator (PM)

dm (t )
d () Frequency
dt Modulator
m(t) dt gPM(t)
(FM)

Frequency Modulation

In Frequency Modulation (FM) the instantaneous value of the information signal

controls the frequency of the carrier wave. This is illustrated in the following diagrams.

Notice that as the information signal increases, the frequency of the carrier increases,
and as the information signal decreases, the frequency of the carrier decreases.
 The frequency fi of the information signal controls the rate at which the carrier
frequency increases and decreases. As with AM, fi must be less than fc. The amplitude of the
carrier remains constant throughout this process.
When the information voltage reaches its maximum value then the change in
frequency of the carrier will have also reached its maximum deviation above the nominal
value. Similarly when the information reaches a minimum the carrier will be at its lowest
frequency below the nominal carrier frequency value. When the information signal is zero,
then no deviation of the carrier will occur.
The maximum change that can occur to the carrier from its base value f c is called the
frequency deviation, and is given the symbol fc. This sets the dynamic range (i.e. voltage
range) of the transmission. The dynamic range is the ratio of the largest and smallest
analogue information signals that can be transmitted.
Bandwidth of FM and PM Signals
The bandwidth of the different AM modulation techniques ranges from the bandwidth
of the message signal (for SSB) to twice the bandwidth of the message signal (for DSBSC
and Full AM). When FM signals were first proposed, it was thought that their bandwidth can
be reduced to an arbitrarily small value. Compared to the bandwidth of different AM
modulation techniques, this would in theory be a big advantage. It was assumed that a signal
with an instantaneous frequency that changes over of range of f Hz would have a
bandwidth of f Hz. When experiments were done, it was discovered that this was not the
case. It was discovered that the bandwidth of FM signals for a specific message signal was at
least equal to the bandwidth of the corresponding AM signal. In fact, FM signals can be
classified into two types: Narrowband and Wideband FM signals depending on the
bandwidth of each of these signals
Narrowband FM and PM

The general form of an FM signal that results when modulating a signals m(t) is
 t

g FM (t )  A cos ct  k f  m ( )d   .
  

A narrow band FM or PM signal satisfies the condition

k f a(t ) 1

For FM and
 k p  m (t )

1
For PM, where
t

a(t )   m ( )d  ,


such that a change in the message signal does not results in a lot of change in the
instantaneous frequency of the FM signal.

Now, we can write the above as

g FM (t )  A cos ct  k f a(t ) .

Starting with FM, to evaluate the bandwidth of this signal, we need to expand it using a
power series expansion. So, we will define a slightly different signal

j ct kf a(t )

gˆF (t )  A e  A e j  t e jk f a(t ) .
c

Remember that

 ct kf a (t )
gˆFM (t )  A e j  A cosc t  k f a(t )   jA sinc t  k a(t ) ,
f

so

g FM (t )  Re gˆ FM (t ) .

a (t )
Now we can expand the term e jk f
gˆ FM (t ) , which gives
in

t
 j 2k 2a2 (t ) j 3k f3a3 (t ) j 4k f4a4 (t ) 
gˆ (t )  A e j c  1 jk a(t )  f    
FM
 2! 3! 4! 
f

 k 2a2 (t jk 3a3 (t k 4a4 (t ) 
) )
t t t t t
 A  e j c  jk a(t )e j c  f e j c  f e j c  f e j c  
f
 2! 3! 4! 

Since kf and a(t) are real (a(t) is real because it is the integral of a real function m(t)), and
since Re{ejct} = cos(ct) and Re{ jejct} = –sin(ct), then

g FM (t )  Re gˆ FM
(t ) k 2a2 (t ) k 3a3(t ) k 4a4 (t ) 

 A  cos( t )  k a(t ) sin( t )  f
cos( t )  f
sin( t )  f
cos( t )  
c
 c f c c
 2! 3! c
4! 

The assumption we made for narrowband FM is ( k f a(t ) 1). This assumption will result in

making all the terms with powers of k a(t greater than 1 to be small compared to the first
f
)
two terms. So, the following is a reasonable approximation
for g FM (t )

gFM (Narrowband ) (t )  A cos(ct )  k f a(t ) when k f a(t ) 1.

sin(ct ) ,
It must be stressed that the above approximation is only valid for narrowband FM signals that
satisfy the condition ( k f a(t ) 1). The above signal is simply the addition (or actually the
subtraction) of a cosine (the carrier) with a DSBSC signal (but using a sine as the carrier).
The message signal that modulates the DSBSC signal is not m(t) but its integration a(t). One
of the properties of the Fourier transform informs us that the bandwidth of a signal m(t) and
its integration a(t) (and its derivative too) are the same (verify this). Therefore, the bandwidth
of the narrowband FM signal is

BW FM (Narrowband )  BW DSBSC  2  BW m (t )
 .

We will see later that when the condition (kf << 1) is not satisfied, the bandwidth of the FM
signal becomes higher that twice the bandwidth of the message signal. Similar relationships
hold for PM signals. That is

g PM (Narrowband ) (t )  A  cos(ct )  k p m (t ) when k  m (t ) 1,

p
sin(ct ) ,
and

BW PM (Narrowband )  BW DSBSC  2  BW m (t )
 .

Construction of Narrowband Frequency and Phase Modulators

The above approximations for narrowband FM and PM can be easily used to construct
modulators for both types of signals
kf<<1
t
a(t)
m(t)  ()d X kf


sin(ct)

–/2
 A gFM (NarrowBand)(t)
 cos(ct)

Narrowband FM Modulator

kp<<1

m(t) X kp

sin(ct)

–/2
 A gPM (NarrowBand)(t)

cos(ct)

Narrowband PM Modulator

Generation of Wideband FM Signals

Consider the following block diagram

m(t)
Narrowband ( . )P
FM gFM (WB) (t)
Modulator

gFM (NB) (t)

Assume a BPF is included in this
block to pass the signal with the
highest carrier freuqnecy and
reject all others

A narrowband FM signal can be generated easily using the block diagram of the narrowband
FM modulator that was described in a previous lecture. The narrowband FM modulator
generates a narrowband FM signal using simple components such as an integrator (an
OpAmp), oscillators, multipliers, and adders. The generated narrowband FM signal can be
converted to a wideband FM signal by simply passing it through a non–linear device with
power P. Both the carrier frequency and the frequency deviation f of the narrowband signal
are increased by a factor P. Sometimes, the desired increase in the carrier frequency and the
desired increase in f are different. In this case, we increase f to the desired value and use a
frequency shifter (multiplication by a sinusoid followed by a BPF) to change the carrier
frequency to the desired value.

SINGLE-TONE FREQUENCY MODULATION

Time-Domain Expression

Since the FM wave is a nonlinear function of the modulating wave, the frequency
modulation is a nonlinear process. The analysis of nonlinear process is the difficult
task. In this section, we will study single-tone frequency modulation in detail to
simplify the analysis and to get thorough understanding about FM.

Let us consider a single-tone sinusoidal message signal defined by

n(t) = An cos(2nƒnt) (5.13)

The instantaneous frequency from Eq. (5.8) is then

ƒ(t) = ƒc + kƒAn cos(2nƒnt) = ƒc+ ∆ƒcos(2nƒnt) (5.14)

where

∆ƒ = kƒAn
 is the modulation index of the FM wave. Therefore, the single-tone FM wave is
expressed by

sFM(t) = Ac cos[2nƒct + þƒ sin(2nƒnt)] (5.18)

This is the desired time-domain expression of the single-tone FM wave

Similarly, single-tone phase modulated wave may be determined from Eq.as

sPM(t) = Ac cos[2nƒct + kpAn cos(2nƒnt)]

or, sPM(t) = Ac cos[2nƒct + þp cos(2nƒnt)] (5.19)

where
þp = kpAn (5.20)
 is the modulation index of the single-tone phase modulated wave.
The frequency deviation of the single-tone PM wave is

Spectral Analysis of Single-Tone FM Wave

The above Eq. can be rewritten as
sFM(t) = Re{Acej2nƒctejþ sin(2nƒnt)}

For simplicity, the modulation index of FM has been considered as þ instead

of þƒ afterward. Since sin(2nƒnt) is periodic with fundamental period T =
sin(2nƒnt)
1⁄ƒn, the complex expontial ejþ is also periodic with the same
fundamental period. Therefore, this complex exponential can be expanded in
Fourier series representation as

where the Fourier series coefficients cn are obtained as

 TRANSMISSION BANDWIDTH OF FM WAVE

The transmission bandwidth of an FM wave depends on the modulation index þ. The

modulation index, on the other hand, depends on the modulating amplitude and modulating
frequency. It is almost impossible to determine the exact bandwidth of the FM wave. Rather,
we use a rule-of-thumb expression for determining the FM bandwidth.

For single-tone frequency modulation, the approximated bandwidth is determined by

the expression

This expression is regarded as the Carson’s rule. The FM bandwidth determined by

this rule accommodates at least 98 % of the total power.

For an arbitrary message signal n(t) with bandwidth or maximum frequency W, the
bandwidth of the corresponding FM wave may be determined by Carson’s rule as

GENERATION OF FM WAVES
FM waves are normally generated by two methods: indirect method and direct method.

Indirect Method (Armstrong Method) of FM Generation

In this method, narrow-band FM wave is generated first by using phase modulator and
then the wideband FM with desired frequency deviation is obtained by using
frequency multipliers.
The above eq is the expression for narrow band FM wave

In this case

Fig: Narrowband FM Generator

The frequency deviation ∆ƒ is very small in narrow-band FM wave. To produce

wideband FM, we have to increase the value of ∆ƒ to a desired level. This is achieved by
means of one or multiple frequency multipliers. A frequency multiplier consists of a nonlinear

device and a bandpass filter. The nth order nonlinear device produces a dc component and n
number of frequency modulated waves with carrier frequencies ƒc, 2ƒc, … nƒc and frequency
deviations ∆ƒ, 2∆ƒ, … n∆ƒ, respectively. If we want an FM wave with frequency deviation

of 6∆ƒ, then we may use a 6th order nonlinear device or one 2nd order and one 3rd order
nonlinear devices in cascade followed by a bandpass filter centered at 6ƒ c. Normally, we may
require very high value of frequency deviation. This automatically increases the carrier
frequency by the same factor which may be higher than the required carrier frequency. We
may shift the carrier frequency to the desired level by using mixer which does not change the
frequency deviation.

The narrowband FM has some distortion due to the approximation made in deriving
the expression of narrowband FM from the general expression. This produces some amplitude
modulation in the narrowband FM which is removed by using a limiter in frequency
multiplier.
Direct Method of FM Generation

In this method, the instantaneous frequency ƒ(t) of the carrier signal c(t) is varied directly
with the instantaneous value of the modulating signal n(t). For this, an oscillator is used in
which any one of the reactive components (either C or L) of the resonant network of the
oscillator is varied linearly with n(t). We can use a varactor diode or a varicap as a voltage-
variable capacitor whose capacitance solely depends on the reverse-bias voltage applied
across it. To vary such capacitance linearly with n(t), we have to reverse-bias the diode by
the fixed DC voltage and operate within a small linear portion of the capacitance-voltage
characteristic curve. The unmodulated fixed capacitance C0 is linearly varied by n(t) such that
the resultant capacitance becomes

C(t) = C0 − kn(t)

where the constant k is the sensitivity of the varactor diode (measured in

capacitance per volt).

fig: Hartley oscillator for FM generation

The above figure shows the simplified diagram of the Hartley oscillator in
which is implemented the above discussed scheme. The frequency of oscillation for
such an oscillator is given
is the frequency sensitivity of the modulator. The Eq. (5.42) is the required expression for the
instantaneous frequency of an FM wave. In this way, we can generate an FM wave by direct
method.
Direct FM may be generated also by a device in which the inductance of the resonant
circuit is linearly varied by a modulating signal n(t); in this case the modulating signal being
the current.
The main advantage of the direct method is that it produces sufficiently high
frequency deviation, thus requiring little frequency multiplication. But, it has poor frequency
stability. A feedback scheme is used to stabilize the frequency in which the output frequency
is compared with the constant frequency generated by highly stable crystal oscillator and the
error signal is feedback to stabilize the frequency.

DEMODULATION OF FM WAVES
The process to extract the message signal from a frequency modulated wave is known
as frequency demodulation. As the information in an FM wave is contained in its
instantaneous frequency, the frequency demodulator has the task of changing frequency
variations to amplitude variations. Frequency demodulation method is generally categorized
into two types: direct method and indirect method. Under direct method category, we will
discuss about limiter discriminator method and under indirect method, phase-locked loop
(PLL) will be discussed.
Limiter Discriminator Method

Recalling the expression of FM signal,

t

s(t) = Ac cos [2nƒct + 2nkƒ ƒ n(t)dt]

0

In this method, extraction of n(t) from the above equation involves the three steps:
amplitude limit, discrimination, and envelope detection.
A. Amplitude Limit

During propagation of the FM signal from transmitter to receiver the

amplitude of the FM wave (supposed to be constant) may undergo changes due to
fading and noise. Therefore, before further processing, the amplitude of the FM
signal is limited to reduce the effect of fading and noise by using limiter as discussed
in the section 5.9. The amplitude limitation will not affect the message signal as the
amplitude of FM does not carry any information of the message signal.

B. Discrimination/ Differentiation

In this step we differentiate the FM signal as given by

Here both the amplitude and frequency of this signal are modulated.
In this case, the differentiator is nothing but a circuit that converts change in
frequency into corresponding change in voltage or current as shown in Fig. 5.11. The
ideal differentiator has transfer function

H(jw) = j2nƒ
 Figure : Transfer function of ideal differentiator.

Instead of ideal differentiator, any circuit can be used whose frequency

response is linear for some band in positive slope. This method is known as slope
detection. For this, linear segment with positive slope of RC high pass filter or LC
tank circuit can be used. Figure 5.13 shows the use of an LC circuit as a
differentiator. The drawback is the limited linear portion in the

slope of the tank circuit. This is not suitable for wideband FM where the peak
frequency deviation is high.

Figure : Use of LC tank circuit as a differentiator.

A better solution is the ratio or balanced slope detector in which two tank
circuits tuned at ƒc + ∆ƒ and ƒc− ∆ƒ are used to extend the linear portion as shown in
below figure.
 Figure : Frequency response of balanced slope detector.

Another detector called Foster-seely discriminator eliminates two tank circuits but still
offer the same linear as the ratio detector.

C. Envelope Detection

The third step is to send the differentiated signal to the envelope detector to recover the
message signal.

Phase-Locked Loop (PLL) as FM Demodulator

A PLL consists of a multiplier, a loop filter, and a VCO connected together to form a
feedback loop as shown in Fig. 5.15. Let the input signal be an FM wave as defined
by

s(t) = Ac cos[2nƒct + ∅1(t)]

Fig: PLL Demodulator

Let the VCO output be defined by

vVCO(t) = Av sin[2nƒct + ∅2(t)]

where
t

∅2(t) = 2nkv ƒ v(t)dt

0

The high-frequency component is removed by the low-pass filtering of the loop

filter. Therefore, the input signal to the loop filter can be considered as

The difference ∅2(t) − ∅1(t) = ∅e(t) constitutes the phase error. Let us assume that
the PLL is in phase lock so that the phase error is very small. Then,
Since the control voltage of the VCO is proportional to the message signal, v(t) is
the demodulated signal.
We observe that the output of the loop filter with frequency response H(ƒ) is the
desired message signal. Hence the bandwidth of H(ƒ) should be the same as the bandwidth W
of the message signal. Consequently, the noise at the output of the loop filter is also limited to
the bandwidth W. On the other hand, the output from the VCO is a wideband FM signal with
an instantaneous frequency that follows the instantaneous frequency of the received FM
signal.

PREEMPHASIS AND DEEMPHASIS NETWORKS

In FM, the noise increases linearly with frequency. By this, the higher frequency
components of message signal are badly affected by the noise. To solve this problem, we
can use a preemphasis filter of transfer function H p(ƒ) at the transmitter to boost the higher
frequency components before modulation. Similarly, at the receiver, the deemphasis filter
of transfer function Hd(ƒ)can be used after demodulator to attenuate the higher frequency
components thereby restoring the original message signal.
The preemphasis network and its frequency response are shown in Figure 5.19
(a) and (b) respectively. Similarly, the counter part for deemphasis network is shown
in Figure 5.20.

Figure ;(a) Preemphasis network. (b) Frequency response of preemphasis network.

 Figure (a) Deemphasis network. (b) Frequency response of Deemphasis network.

In FM broadcasting, ƒ1 and ƒ2 are normally chosen to be 2.1 kHz and 30 kHz

respectively.

The frequency response of preemphasis network is

Comparison of AM and FM:
S.NO AMPLITUDE MODULATION FREQUENCY MODULATION
1. Band width is very small which is one of It requires much wider channel ( 7 to 15
the biggest advantage times ) as compared to AM.
2. The amplitude of AM signal varies The amplitude of FM signal is constant
depending on modulation index. and independent of depth of the
modulation.
3. Area of reception is large The are of reception is small since it is
limited to line of sight.
4. Transmitters are relatively simple & Transmitters are complex and hence
cheap. expensive.
5. The average power in modulated wave is The average power in frequency
greater than carrier power. This added modulated wave is same as contained
power is provided by modulating source. in un-modulated wave.
6. More susceptible to noise interference and Noise can be easily minimized amplitude
has low signal to noise ratio, it is more variations can be eliminated by using
difficult to eliminate effects of noise. limiter.
7. it is not possible to operate it is possible to operate several
without interference. independent transmitters on same
frequency.
8. The maximum value of modulation index No restriction is placed on modulation
= 1, other wise over-modulation would index.
result in distortions.

FM Transmitter
The FM transmitter is a single transistor circuit. In the telecommunication,
the frequency modulation (FM)transfers the information by varying the frequency of carrier
wave according to the message signal. Generally, the FM transmitter uses VHF radio
frequencies of 87.5 to 108.0 MHz to transmit & receive the FM signal. This transmitter
accomplishes the most excellent range with less power. The performance and working of the
wireless audio transmitter circuit is depends on the induction coil & variable capacitor. This
article will explain about the working of the FM transmitter circuit with its applications.
The FM transmitter is a low power transmitter and it uses FM waves for transmitting
the sound, this transmitter transmits the audio signals through the carrier wave by the
difference of frequency. The carrier wave frequency is equivalent to the audio signal of the
amplitude and the FM transmitter produce VHF band of 88 to 108MHZ.Plese follow the
below link for: Know all About Power Amplifiers for FM Transmitter
 Block Diagram of FM Transmitter

Working of FM Transmitter Circuit

The following circuit diagram shows the FM transmitter circuit and the required electrical
and electronic components for this circuit is the power supply of 9V, resistor, capacitor,
trimmer capacitor, inductor, mic, transmitter, and antenna. Let us consider the microphone to
understand the sound signals and inside the mic there is a presence of capacitive sensor. It
produces according to the vibration to the change of air pressure and the AC signal.

FM Transmitter circuit

The formation of the oscillating tank circuit can be done through the transistor of 2N3904 by
using the inductor and variable capacitor. The transistor used in this circuit is an NPN
transistor used for general purpose amplification. If the current is passed at the inductor L1
and variable capacitor then the tank circuit will oscillate at the resonant carrier frequency of
the FM modulation. The negative feedback will be the capacitor C2 to the oscillating tank
circuit.

To generate the radio frequency carrier waves the FM transmitter circuit requires an
oscillator. The tank circuit is derived from the LC circuit to store the energy for
oscillations.
The input audio signal from the mic penetrated to the base of the transistor, which modulates
the LC tank circuit carrier frequency in FM format. The variable capacitor is used to change
the resonant frequency for fine modification to the FM frequency band. The modulated signal
from the antenna is radiated as radio waves at the FM frequency band and the antenna is
nothing but copper wire of 20cm long and 24 gauge. In this circuit the length of the antenna
should be significant and here you can use the 25-27 inches long copper wire of the antenna.

Application of Fm Transmitter
 The FM transmitters are used in the homes like sound systems in halls to fill the sound
with the audio source.
 These are also used in the cars and fitness centers.
 The correctional facilities have used in the FM transmitters to reduce the prison noise in
common areas.
Advantages of the FM Transmitters

 The FM transmitters are easy to use and the price is low

 The efficiency of the transmitter is very high
 It has a large operating range
 This transmitter will reject the noise signal from an amplitude variation.
 UNIT IV
NOISE
 Noise in communication System,
 White Noise
 Narrowband Noise –In phase and Quadrature phase components
 Noise Bandwidth
 Noise Figure
 Noise Temperature
 Noise in DSB& SSB System
 Noise in AM System
 Noise in Angle Modulation System
 Threshold effect in Angle Modulation System
Noise in communication system

 Noise is unwanted signal that affects wanted signal

 Noise is random signal that exists in communication
systems Effect of noise

 Degrades system performance (Analog and digital)

 Receiver cannot distinguish signal from noise
 Efficiency of communication system
reduces Types of noise

 Thermal noise/white noise/Johnson noise or fluctuation noise

 Shot noise
 Noise temperature
 Quantization noise

Noise temperature
Equivalent noise temperature is not the physical temperature of amplifier, but a theoretical
construct, that is an equivalent temperature that produces that amount of noise power

𝑇𝑒 = (𝐹 − 1)

White noise
One of the very important random processes is the white noise process. Noises in
many practical situations are approximated by the white noise process. Most importantly, the
white noise plays an important role in modelling of WSS signals.

A white noise process is a random process that has constant power spectral density at
all frequencies. Thus
where is a real constant and called the intensity of the white noise. The
corresponding autocorrelation function is given by

where is the Dirac delta.

The average power of white noise

The autocorrelation function and the PSD of a white noise process is shown in Figure 1
below.

fig: auto correlation and psd of white noise

NARROWBAND NOISE (NBN)

In most communication systems, we are often dealing with band-pass filtering of signals.
Wideband noise will be shaped into band limited noise. If the bandwidth of the band limited
noise is relatively small compared to the carrier frequency, we refer to this as narrowband
noise.

the narrowband noise is expressed as as

where fc is the carrier frequency within the band occupied by the noise. x(t) and y(t)
are known as the quadrature components of the noise n(t). The Hibert transform of
 n(t) is
Proof.
The Fourier transform of n(t) is

^ ^
Let N ( f ) be the Fourier transform of n^ ( t). In the frequency domain, N
(f) = N(f)[-j sgn(f)]. We simply multiply all positive frequency components of N(f)
by -j and all negative frequency components of N(f) by j. Thus

The quadrature components x(t) and y(t) can now be derived from equations

x(t) = n(t)co2fct + n^(t)sin 2fct \

and
y(t) = n(t)cos 2fct - n^(t)sin 2fct

Fig: generation of narrow band noise

 Fig: Generation of quadrature components of n(t).

Filters at the receiver have enough bandwidth to pass the

desired signal but not too big to pass excess noise.
Narrowband (NB) fc center frequency is much bigger that the bandwidth.
Noise at the output of such filters is called narrowband noise (NBN).
NBN has spectral concentrated about some mid-band frequency fc
The sample function of such NBN n(t) appears as a sine wave of frequency fc which
modulates slowly in amplitude and phase
Noise figure
The Noise figure is the amount of noise power added by the electronic circuitry in the
receiver to the thermal noise power from the input of the receiver. The thermal noise at the
input to the receiver passes through to the demodulator. This noise is present in the receive
channel and cannot be removed. The noise figure of circuits in the receiver such as amplifiers
and mixers, adds additional noise to the receive channel. This raises the noise floor at the
demodulator.

Noise Bandwidth

A filter’s equivalent noise bandwidth (ENBW) is defined as the bandwidth of a perfect

rectangular filter that passes the same amount of power as the cumulative bandwidth of the
channel selective filters in the receiver. At this point we would like to know the noise floor in
our receiver, i.e. the noise power in the receiver intermediate frequency (IF) filter bandwidth
that comes from kTB. Since the units of kTB are Watts/ Hz, calculate the noise floor in the
channel bandwidth by multiplying the noise power in a 1 Hz bandwidth by the overall
equivalent noise bandwidth in Hz.

NOISE IN DSB-SC SYSTEM:

Let the transmitted signal is

The received signal at the output of the receiver noise- limiting filter : Sum of this signal and
filtered noise .A filtered noise process can be expressed in terms of its in-phase and quadrature
components as

where n (t) is in-phase component and n (t) is quadrature component

c s
Received signal (Adding the filtered noise to the modulated signal)

Demodulate the received signal by first multiplying r(t) by a locally generated sinusoid

cos(2 f t + ), where is the phase of the sinusoid.Then passing the product signal through
c
an ideal lowpass filter having a bandwidth W.

The low pass filter rejects the double frequency components and passes only the low pass
components.

the effect of a phase difference between the received carrier and a locally generated carrier at
2
the receiver is a drop equal to os
c ) in the received signal
(
power. Phase-locked loop

The effect of a phase-locked loop is to generate phase of the received carrier at the receiver.

If a phase-locked loop is employed, then = 0 and the demodulator is

called a coherent or synchronous demodulator.

In our analysis in this section, we assume that we are employing a coherent demodulator.

With this assumption, we assume that =0

Therefore, at the receiver output, the message signal and the noise components are additive
and we are able to define a meaningful SNR. The message signal power is given by
Power PM is the content of the messagesignal

The noise power is given by

The power content of n(t) can be found by noting that it is the result of passing n (t) through
w
a filter with bandwidth B .Therefore, the power spectral density of n(t) is given by
c

which is identical to baseband SNR.

In DSB-SC AM, the output SNR is the same as the SNR for a baseband system. DSB-SC
AM does not provide any SNR improvement over a simple baseband communication system.

NOISE IN SSB-SC SYSTEM:

Let SSB modulated signal is

Input to the demodulator

Assumption : Demodulation with an ideal phase reference.

Hence, the output of the lowpass filter is the in-phase component (with a
coefficient of ½) of the precedingsignal.

The signal-to-noise ratio in an SSB system is equivalent to that of a DSB system.

Noise in Conventional AM

Where a is the modulation index

mn(t) is normalized so that its minimum value is -1

If a synchronous demodulator is employed, the situation is basically similar to the

DSB case, except that we have 1 + amn(t) instead of m(t).
  In practical applications, the modulation index a is in the range of 0.8-0.9.

 Power content of the normalized message process depends on the message source.

 Speech signals : Large dynamic range, PM is about 0.1.

 The overall loss in SNR, when compared to a baseband system, is a

factor of 0.075 or equivalent to a loss of 11 dB.

The reason for this loss is that a large part of the transmitter power is used to send the
carrier component of the modulated signal and not the desired signal. To analyze the
envelope-detector performance in the presence of noise, we must use certain
approximations.

This is a result of the nonlinear structure of an envelope detector, which makes an exact
analysis difficult

In this case, the demodulator detects the envelope of the received signal and the noise
process.
The input to the envelope detector is

Therefore, the envelope of r ( t ) is given by

Now we assume that the signal component in r ( t ) is much stronger than the noise
component. Then

Therefore, we have a high probability that

After removing the DC component, we obtain

which is basically the same as y(t) for the synchronous demodulation without the ½
coefficient.
This coefficient, of course, has no effect on the final SNR. So we conclude that, under the
assumption of high SNR at the receiver input, the performance of synchronous and envelope
demodulators is the same.

However, if the preceding assumption is not true, that is, if we assume that, at the receiver
input, the noise power is much stronger than the signal power, Then
We observe that, at the demodulator output, the signal and the noise components are no
longer additive. In fact, the signal component is multiplied by noise and is no longer
distinguishable. In this case, no meaningful SNR can be defined. We say that this system is
operating below the threshold. The subject of threshold and its effect on the performance of
a communication system will be covered in more detail when we discuss the noise
performance in angle modulation.

Effect of threshold in angle modulation system:

FM THRESHOLD EFFECT FM threshold is usually defined as a Carrier-to-Noise ratio at

which demodulated Signal-to-Noise ratio falls 1dB below the linear relationship . This is the
effect produced in an FM receiver when noise limits the desired information signal. It occurs
at about 10 dB, as earlier stated in 5 the introduction, which is at a point where the FM signal-
to-Noise improvement is measured. Below the FM threshold point, the noise signal (whose
amplitude and phase are randomly varying) may instantaneously have amplitude greater than
that of the wanted signal. When this happens, the noise will produce a sudden change in the
phase of the FM demodulator output. In an audio system, this sudden phase change makes a
“click”. In video applications the term “click noise” is used to describe short horizontal black
and white lines that appear randomly over a picture

An important aspect of analogue FM satellite systems is FM threshold effect. In FM systems

where the signal level is well above noise received carrier-to-noise ratio and demodulated
signal-to-noise ratio are related by:

The expression however does not apply when the carrier-to-noise ratio decreases below a
certain point. Below this critical point the signal-to-noise ratio decreases significantly. This is
known as the FM threshold effect (FM threshold is usually defined as the carrier-to-noise
ratio at which the demodulated signal-to-noise ratio fall 1 dB below the linear relationship
given in Eqn 9. It generally is considered to occur at about 10 dB).

Below the FM threshold point the noise signal (whose amplitude and phase are randomly
varying), may instantaneously have an amplitude greater than that of the wanted signal.
When this happens the noise will produce a sudden change in the phase of the FM
demodulator output. In an audio system this sudden phase change makes a "click". In video
applications the term "click noise" is used to describe short horizontal black and white lines
that appear randomly over a picture, because satellite communications systems are power
limited they usually operate with only a small design margin above the FM threshold point
(perhaps a few dB). Because of this circuit designers have tried to devise techniques to delay
the onset of the FM threshold effect. These devices are generally known as FM threshold
extension demodulators. Techniques such as FM feedback, phase locked loops and frequency
locked loops are used to achieve this effect. By such techniques the onset of FM threshold
effects can be delayed till the C/N ratio is around 7 dB.

Noise in Angle Modulated Systems

Like AM, noise performance of angle modulated systems is characterized by parameter γ

Note: if bandwidth ratio is increased by a factor 2.Then increases by a factor 4

This exchange of bandwidth and noise performance is an important feature of FM

 UNIT-V
Receivers
Introduction to Radio Receivers:

In radio communications, a radio receiver (receiver or simply radio) is an electronic

device that receives radio waves and converts the information carried by them to a usable
form.

Types of Receivers:

Tuned Radio Frequency Receiver:

Fig.1. TRF Receiver
Problems in TRF Receivers:
Fig.2. Block diagram of Super heterodyne Receiver.
Characteristics of Radio Receiver:
Fig.3. Typical Fidelity curve
Blocks in Super heterodyne Receiver:

 Basic principle
o Mixing
o Intermediate frequency of 455 KHz
o Ganged tuning
 RF section
o Tuning circuits – reject interference and reduce noise figure
o Wide band RF amplifier
 Local Oscillator
o 995 KHz to 2105 KHz
o Tracking
 IF amplifier
o Very narrow band width Class A amplifier – selects 455 KHz only
o Provides much of the gain
o Double tuned circuits
 Detector
o RF is filtered to ground
1. RF Amplifier:
 2. Mixer

Separately Excited Mixer:

Fig.5 Separately Excited FET Mixer

Self Excited Mixer:

Fig.6. Self Excited Mixer

3. Tracking
4. Local Oscillator

5. IF Amplifier

Fig.7 Two Stage IF Amplifier

Choice of Intermediate Frequency:

6. Automatic Gain Control

Fig.8. Simple AGC circuit

 Fig.9. Delayed AGC circuit

Fig.10. Response of receiver with various AGC circuits.

FM Receiver:

Fig.11. FM Receiver Block diagram

Comparisons with AM Receivers
Amplitude Limiter:
 PULSE MODULATION

Introduction:

Pulse Modulation

 Carrier is a train of pulses

 Example: Pulse Amplitude Modulation (PAM), Pulse width modulation (PWM) ,
Pulse Position Modulation (PPM)

Types of Pulse Modulation:

 The immediate result of sampling is a pulse-amplitude modulation (PAM) signal

 PAM is an analog scheme in which the amplitude of the pulse is proportional to

the amplitude of the signal at the instant of sampling

 Another analog pulse-forming technique is known as pulse-duration modulation

(PDM). This is also known as pulse-width modulation (PWM)

 Pulse-position modulation is closely related to PDM

Pulse Amplitude Modulation:

In PAM, amplitude of pulses is varied in accordance with instantaneous value of

modulating signal.

PAM Generation:

The carrier is in the form of narrow pulses having frequency fc. The uniform
sampling takes place in multiplier to generate PAM signal. Samples are placed Ts sec
away from each other.
 Fig.12. PAM Modulator

 The circuit is simple emitter follower.

 In the absence of the clock signal, the output follows input.
 The modulating signal is applied as the input signal.
 Another input to the base of the transistor is the clock signal.
 The frequency of the clock signal is made equal to the desired carrier pulse train
frequency.
 The amplitude of the clock signal is chosen the high level is at ground level(0v) and
low level at some negative voltage sufficient to bring the transistor in cutoff region.
 When clock is high, circuit operates as emitter follower and the output follows in the
input modulating signal.
 When clock signal is low, transistor is cutoff and output is zero.
 Thus the output is the desired PAM signal.

PAM Demodulator:
 The PAM demodulator circuit which is just an envelope detector followed by a
second order op-amp low pass filter (to have good filtering characteristics) is as
shown below

Fig.13. PAM Demodulator

Pulse Width Modulation:
 In this type, the amplitude is maintained constant but the width of each pulse is varied
in accordance with instantaneous value of the analog signal.

 In PWM information is contained in width variation. This is similar to FM.

 In pulse width modulation (PWM), the width of each pulse is made directly
proportional to the amplitude of the information signal.

Pulse Position Modulation:

 In this type, the sampled waveform has fixed amplitude and width whereas the
position of each pulse is varied as per instantaneous value of the analog signal.

 PPM signal is further modification of a PWM signal.

PPM & PWM Modulator:

Fig.14. PWM & PPM Modulator

• The PPM signal can be generated from PWM signal.

• The PWM pulses obtained at the comparator output are applied to a mono stable multi
vibrator which is negative edge triggered.
 • Hence for each trailing edge of PWM signal, the monostable output goes high.
It remains high for a fixed time decided by its RC components.

• Thus as the trailing edges of the PWM signal keeps shifting in proportion with
the modulating signal, the PPM pulses also keep shifting.

• Therefore all the PPM pulses have the same amplitude and width. The information
is conveyed via changing position of pulses.

Fig.15. PWM & PPM Modulation waveforms

PWM Demodulator:

Fig.16. PWM Demodulator

  Transistor T1 works as an inverter.

 During time interval A-B when the PWM signal is high the input to transistor T2 is
low.

 Therefore, during this time interval T2 is cut-off and capacitor C is charged through
an R-C combination.

 During time interval B-C when PWM signal is low, the input to transistor T2 is high,
and it gets saturated.

 The capacitor C discharges rapidly through T2.The collector voltage of T2 during B-

C is low.

 Thus, the waveform at the collector of T2is similar to saw-tooth waveform whose
envelope is the modulating signal.

 Passing it through 2nd order op-amp Low Pass Filter, gives demodulated signal.

PPM Demodulator:

Fig.17. PPM Demodulator

 The gaps between the pulses of a PPM signal contain the information regarding the
modulating signal.

 During gap A-B between the pulses the transistor is cut-off and the capacitor C gets
charged through R-C combination.

 During the pulse duration B-C the capacitor discharges through transistor and the
collector voltage becomes low.

 Thus, waveform across collector is saw-tooth waveform whose envelope is the

modulating signal.

 Passing it through 2nd order op-amp Low Pass Filter, gives demodulated signal.