Unit 5

Noise

Prepared by
Dr.P.Sunitha,M.Tech,Ph.D,
Associate Professor,
Dept.of ECE,
 OBJECTIVE: By studying this chapter the students will
learn Noise Characteristics of Amplitude & Frequency
modulation Techniques

 OUTCOME: Upon successful completion of the chapter,

the student will be able to Analyze Noise Characteristics of
Amplitude & Frequency modulation Techniques
Contents
 Noise in Analog communication Systems
 Noise in AM-SC System
 Noise in AM-FC system
 Noise in Frequency Modulation System
 Threshold effect in Frequency
Modulation System
 Pre-emphasis & de-emphasis
 Noise - Introduction

• Noise – Unwanted Signals that tend to disturb the

Transmission and Processing of Signals in
Communication System and over which we have
incomplete control.

• Noise is a general term which is used to describe

an unwanted signal which affects a wanted signal.

• These unwanted signals arise from a variety of

sources.

4
 Sources of Noise
• Sources of noise may be:
– External
– Internal
• Naturally occurring external noise sources include:
– Atmosphere disturbance (e.g. electric storms, lighting,
ionospheric effect etc), so called ‘Sky Noise’
– Cosmic noise which includes noise from galaxy, solar
noise
– ‘Hot spot’ due to oxygen and water vapour resonance in
the earth’s atmosphere.
5
 Sources of Noise
• Internal Noise is an important type of noise that arises
from the SPONTANEOUS FLUCTUATIONS of Current or
Voltage in Electrical Circuits.
• This type of noise is the basic limiting factor of employing
more complex Electrical Circuits in Communication System.
• Most Common Internal Noises are:
– Shot Noise
– Thermal Noise

6
 Shot Noise
• Shot Noise arises in Electronic Components like
Diodes and Transistors.
• Due to the discrete nature of Current flow In
these components.
• Take an example of Photodiode circuit.
• Photodiode emits electrons from the cathode
when light falls on it.
• The circuit generates a current pulse when an
electron is emitted.
7
 Thermal Noise
• Thermal Noise is the name given to the Electrical Noise arising
from the Random motion of electrons in a conductor.
• It is also called Jonson Noise or Nyquist Noise.
• Let VTN is the Thermal Noise Voltage appearing across the two
terminals of a resistor.
• Let the applied voltage have a bandwidth or frequency, ∆f.
• Then the Mean Square value of VTN is given by:

8
 Thermal Noise

• Where
k = Boltzmann’s constant = 1.38 x 10-23 Joules per oK
T = absolute temperature in oK
R = resistance in ohms

9
 Low Frequency or Flicker Noise
• Active devices, integrated circuit, diodes, transistors etc also
exhibits a low frequency noise, which is frequency
dependent (i.e. non uniform) known as flicker noise .
• It is also called ‘one – over – f’ noise or 1/f noise because
of its low-frequency variation.
• Its origin is believed to be attributable to contaminants and
defects in the crystal structure in semiconductors, and in
the oxide coating on the cathode of vacuum tube devices
10
 Low Frequency or Flicker Noise
• Flicker Noise is found in many natural phenomena such as nuclear
radiation, electron flow through a conductor, or even in the
environment.

• The noise power is proportional to the bias current, and, unlike

Thermal and Shot Noise, Flicker Noise decreases with frequency.

• An exact mathematical model does not exist for flicker noise because it
is so device-specific.

• However, the inverse proportionality with frequency is almost exactly

1/f for low frequencies, whereas for frequencies above a few kilohertz,
the noise power is weak but essentially flat. 11
 Low Frequency or Flicker Noise
• Flicker Noise is essentially random, but because its frequency spectrum is
not flat, it is not a white noise.

• It is often referred to as pink noise because most of the power is

concentrated at the lower end of the frequency spectrum.

• Flicker Noise is more prominent in FETs (smaller the channel length,

greater the Flicker Noise), and in bulky carbon resistors.

• The objection to carbon resistors mentioned earlier for critical low noise
applications is due to their tendency to produce flicker noise when
carrying a direct current.

• In this connection, metal film resistors are a better choice 12for low
frequency, low noise applications.
 White Noise

• The Noise Analysis of Communication System is

done on the basis of an idealized form of noise
called WHITE NOISE.

• Its power spectral density is independent on

operating frequency.

• White – White light contain equal amount of all

frequencies in visible spectrum.
13
 White Noise
• Power spectral density is given by:
The 1/2 here emphasizes that
the spectrum extends to both
positive and negative
frequencies.

14
 Power Spectral Density of
White Noise
• A random process W(t) is called white noise if it
has a flat power spectral density, i.e., SW(f) is a
constant c for all f.

15
Receiver Model

Receiver model
 Receiver Model
◊ s(t) denotes the incoming modulated signal.
◊ w(t) denotes front-end receiver noise. The power
spectral density of the noise w(t) is denoted by N0/2,
defined for both positive and negative frequencies. N0
is the average noise power per unit bandwidth
measured at the front end of the receiver.
◊ The bandwidth of this band-pass filter is just wide
enough to pass the modulated signal without
distortion.
◊ Assume the band-pass filter is ideal, having a bandwidth
equal to the transmission bandwidth BT of the modulated
signal s(t) , and a mid- band frequency equal to the
carrier frequency fc , fc >> BT .
 Receiver Model

Fig. Idealized characteristic of band-pass filtered noise

◊ The filtered noise n(t) may be treated as a narrow band noise
represented in the canonical form:
n t   nI t cos 2πf ct   nQ t sin 2πf ct 
where nI(t) is the in-phase noise component and nQ(t) is the
quadrature noise component, both measured with respect to the
carrier wave Accos(2πfct).
 Power spectral density (PSD) of
band- pass filtered noise

• The average noise power may be calculated from the power

spectral density.
• The average power N of filtered Gaussian white noise is:
 Signal to Noise Ratio
(SNR)
• A measure of the degree to which a signal is
contaminated with additive noise is the signal-
to-noise ratio (SNR)
 Figure of Merit Of CW
Modulation Schemes
• Goal: Compare the performance of different CW modulation
schemes.
• Signal-to-noise ratio (SNR) is a measure of the degree to which
a signal is contaminated by noise.
• Assume that the only source of degradation in message signal
quality is the additive noise w(t).
• Noisy receiver model:
 Figure of Merit Of CW
Modulation Schemes
• The signal-to-noise ratio at the demodulator input:

• The signal-to-noise ratio at the demodulator output:

 Figure of Merit Of CW
Modulation Schemes
• (SNR)O is well defined only if the recovered message signal
and noise appear additively at demodulator output. This
condition is:
– Always valid for coherent demodulators
– But is valid for noncoherent demodulators only if the input signal
to- noise ratio (SNR)I is high enough

• Output signal-to-noise ratio (SNR)O depends on:

– Modulation scheme
– Type of demodulator
 Figure of Merit Of CW
Modulation Schemes
 Conditions of comparison
• To get a fair comparison of CW modulation schemes
and receiver configurations, it must be made on an equal
basis.
– Modulated signal s(t) transmitted by each modulation scheme has the
same average power
– Channel and receiver noise w(t) has the same average power measured
in the message bandwidth W
• According to the equal basis, the channel signal-to-
noise ratio is defined as:
 Figure of Merit Of CW
Modulation Schemes
• Noise performance of a given CW modulation scheme and a
given type of demodulator is characterized by the figure of merit.

• By definition, the figure of merit is:

• The higher the value of the figure of merit, the better the noise
performance
SNRs & Figure of Merit
Noise in AM Receivers
Noise in AM Receivers

 SNR Calculations in AM System

 Consider the following receiver model of AM system to
analyze noise.
Noise in AM Receivers
 Noise in AM Receivers

P is the power of the message signal, W is the message bandwidth

 Assume the band pass noise is mixed with AM wave in the channel as
shown in the above figure. This combination is applied at the input of
AM demodulator. Hence, the input of AM demodulator is.
v(t)=s(t)+n(t)
Noise in AM Receivers
Noise in AM Receivers
Noise in AM Receivers
 Noise in AM Receivers

◊ Ex: Single-Tone Modulation

◊ Consider a sinusoidal wave of frequency fm and amplitude Am
as the modulating wave, as shown by
m(t) = Amcos(2πfmt)
◊ The corresponding AM wave is

s(t) = Ac [1+ μcos(2πfmt)] cos(2πfct)

modulation factor : μ = kaAm

◊ The average power of the modulation wave m(t) is (assuming a

1 A2
P m
2
 Noise in AM Receivers

◊ We obtain the figure of merit

◊ When μ = 1 (100% modulation using envelope detection), we get a

figure of merit = 1/3.

◊ This means that, other factors being equal, an AM system (using

envelope detection) must transmit three times as much average power
as a suppressed-carrier system (using coherent detection) in order to
achieve the same quality of noise performance.
Noise in DSBSC Receivers
Noise in DSBSC Receivers
Noise in DSBSC Receivers
 Assume the band pass noise is mixed with DSBSC
modulated wave in the channel as shown in the above
figure.
 This combination is applied as one of the input to the
product modulator. Hence, the input of this product
modulator is
 Noise in DSBSC Receivers
 Local oscillator generates the carrier signal c(t)=cos(2πfct).
 This signal is applied as another input to the product modulator.
 Therefore, the product modulator produces an output, which is the
product of v1(t) and c(t).
Noise in DSBSC Receivers
Noise in DSBSC Receivers
 Noise in AM Receivers

◊ Comparison of figure of merit ( AM, DSB-SC, SSB )

◊ The figure of merit of a DSB-SC receiver or that of an SSB

receiver using coherent detection is always unity.
◊ The corresponding figure of merit of an AM receiver using
envelope detection is always less than unity.
◊ In other words, the noise performance of an AM receiver is always
inferior to that a DSB-SC receiver. This is due to the
wastage of transmitter power, which results from transmitting the carrier
as a component of AM wave.
Noise in SSBSC Receiver
 SNR Calculations in SSBSC System
 Assume the band pass noise is mixed with SSBSC
modulated wave in the channel as shown in the above
figure.
 This combination is applied as one of the input to the
product modulator. Hence, the input of this product
modulator is
 The local oscillator generates the carrier
signal c(t)=cos(2πfct).This signal is applied as another
input to the product modulator.

 Therefore, the product modulator produces an output,

which is the product of v1(t) and c(t).

v2(t)=v1(t)c(t)
 Noise in FM Receivers
◊ The receiver model is given
by:

◊ The noise w(t) is modeled as white Gaussian noise of zero mean and
power spectral density N0/2.
◊ The received FM signal s(t) has a carrier frequency fc and transmission
bandwidth BT, such that only a negligible amount of power lies outside
the frequency band fc ± BT /2 for positivefrequencies.
◊ The band-pass filter has a mid-band frequency fc and bandwidth BT and
therefore passes the FM signal essentially without distortion.
◊ Ordinary, BT is small compared with the mid-band frequency fc so that
we may use the narrowband representation for n(t), the filtered version
of receiver noise w(t), in terms of its in-phase and quadrature
components. 28
 Noise in FM Receivers
◊ In an FM system, the message information is transmitted by
variations of the instantaneous frequency of a sinusoidal
carrier wave, and its amplitude is maintained constant.
◊ Any variations of the carrier amplitude at the receiver input
must
result from noise or interference.

◊ The limiter is used to remove amplitude variations by

clipping the modulated wave at the filter output almost to the
zero axis.
◊ The resulting rectangular wave is rounded off by another

bandpass filter that is an integral part of the limiter,

thereby suppressing harmonics of the carrier frequency.
◊ The filter output is again sinusoidal, with an amplitude that

is practically independent29 of the carrier amplitude at the

receiver input.
 Noise in FM Receivers
◊ The discriminator consists of two components:
◊ A slope network or differentiator with a purely imaginary transfer
function that varies linearly with frequency. It produces a hybrid-
modulated wave in which both amplitude and frequency vary in
accordance with the message signal.
◊ An envelope detector that recovers the amplitude variation and
thus reproduces the message signal.
◊ The slope network and envelope detector are usually
implemented as integral parts of a single physical unit.
◊ The post-detection filter, labeled “baseband low-pass filter,” has
a bandwidth that is just large enough to accommodate the
highest frequency component of the message signal.
◊ This filter removes the out-of-band components of the noise

at the discriminator output and thereby keeps the effect of

the output noise to a minimum.
30
 Noise in FM Receivers
◊ The filtered noise at the band-pass filter output is defined
as:

◊ The incoming FM signal s(t) is given by

 t   2πk f 0 m  d
 Noise in FM Receivers
◊ The noisy signal at the band-pass filter output
is:

◊ The envelope of x(t) is of no interest to us, because any

envelope variations at the band-pass output are removed by the
limiter.
◊ Our motivation is to determine the error in the instantaneous
frequency of the carrier wave caused by the presence of the
filtered noise n(t).
Noise in FM Receivers

(31
)
 Noise in FM Receivers

◊ This means that the additive noise nd(t) appearing at the

discriminator output is determined effectively by the
carrier amplitude Ac and the quadrature component nQ(t) of
the narrowband noise n(t).
36
 Noise in FM Receivers
◊ The output signal-to-noise ratio is defined as the ratio of the
average output signal power to the average output noise power.

◊ From Eq. (31), the message component in the discriminator

output, and therefore the low-pass filter output, is kf m(t).
◊ The average output signal power is equal to kf 2P, where P is the
average power of the message signal m(t).
◊ To determine the average output noise power, we note that the noise
nd(t) at the discriminator output is proportional to the time derivative
of the quadrature noise component nQ(t).
◊ The differentiation of a function respect to time corresponds to
multiplication of its Fourier transform by j2πf. We may obtain the
noise nd(t) by passing nQ(t) though a linear filter with a transfer
Noise in FM Receivers
 Noise in FM Receivers
◊ In FM system, increasing the carrier power has a noise-
quieting

◊ The average power in the modulated signal s(t) is A2c /2, and the
average noise power in the message bandwidth is WNo. The
channel signal to noise ratio (SNR)C,FM is

◊ Figure of merit for frequency modulation:

 Noise in FM Receivers
◊ Ex: Single-Tone Modulation

◊ A sinusoidal wave of frequency fm as the modulating signal, and

assume a peak frequency deviation ∆f . The FM signal is
defineby

◊ Therefore, we may
write

◊ Differentiating both sides with respect to time and solving for

m(t)
 Noise in FM Receivers
◊ The average power of message signal
m(t)

P

◊ We get output signal-to-noise ratio

◊ Where β = ∆f /W is the modulation index and we get the figure

of merit

◊ It is important to note that the modulation index β = ∆f /W is

determined by the bandwidth W of the postdetection low-pass
filter and is related to the sinusoidal message frequency fm.
 Threshold effect

• The threshold is a value of carrier-to-noise ratio below

which the noise performance of a demodulator
deteriorates much more rapidly than proportionately to
the carrier-to-noise ratio.
• Every noncoherent detector exhibits a threshold effect,
below the threshold the restored message signal
becomes practically useless.
 Threshold effect
Physical explanation:

• If the carrier-to-noise ratio is high enough then the

signal dominates and the noise causes only a small
unwanted AM and PM.

• However, if the carrier-to-noise ratio is small then the

noise dominates which results in a complete loss of
information.

• As a result, the demodulator output does not contain

the message signal at all.
 Threshold effect

Threshold Effect : loss of message in an envelope detector

that operates at a low CNR.
 Noise performance of AM receivers

Note: For high value of (SNR)C, the noise performance of coherent and
noncoherent DSB are identical. But noncoherent DSB has a
threshold effect. Coherent AM detectors have no threshold effect!
 FM threshold effect
• The figure of merit discussed above is valid only if the
carrier-to-noise ratio (SNR)C is high compared with unity.

• It has been found experimentally that as (SNR)C is

decreased below a threshold, each FM demodulator,
either coherent or noncoherent, breaks:

– At first isolated clicks are heard and if the (SNR)C is decreased

further, the clicks rapidly merge into a crackling. sound
 FM threshold effect
A qualitative explanation
• If (SNR)C is small then the noise becomes dominant and the
phasor representation and the decomposition of noise into a
PM and AM are not valid any more.
• The phase of noise is a random variable and it may take any
value.
• Recall, the FM demodulator is sensitive to the derivate of
phase.
• When the phase of demodulator input varies suddenly by 2π
due to the noise then an impulse, i.e., click appears at the
receiver output.
 Pre-emphasis and de-emphasis in
FM systems
• Recall: The power spectral density SN0(f) of noise at an FM receiver
output has a square law dependence on the operating frequency.
• The high-frequency noise is dominant at the output of an FM
receiver.
• The power spectral density of
message signals usually falls
off at higher frequencies.
• Generally, the most part of a
message signal is in the low-
frequency region.
• These facts may be exploited
to improve the noise
performance of FM systems
 Pre-emphasis and de-emphasis in
FM systems
• Basic idea
– Apply a filter at the demodulator output which reduces the high
frequency content of the output spectrum.
– To compensate this attenuation, a pre-emphasis must be
applied to the high-frequency signals at the transmitter

• Pre-emphasis at the transmitter:

– A filter that artificially emphasize the high-frequency
components of the message signal prior to the modulation.
 Pre-emphasis and de-emphasis in
FM systems
• De-emphasis at the receiver:
– An inverse operation performed by a filter placed after the
demodulation.
– The de-emphasis filter restores the original signal by de-
emphasizing the high-frequency components.

• Effects of pre-emphasis and de-emphasis filters cancel each other:

Use of pre-emphasis and de-emphasis in
an FM system
Comparison of noise performance of
CW systems

• Note: Threshold problem is more serious in FM modulation than in

AM. The higher the β, the better the FM noise performance. But
the price to be paid is the wider transmission bandwidth