Noise Notes

8/2/2019 Noise Notes

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AnalCommunic

Suresh P. Nair [AIE, ME, (PhD)] MIEEEProfessor & Head

Department of Electronics and Communication EngineeringRoyal College of Engineering and Technology

Chiramanangad PO, Akkikkavu, Thrissur, Kerala, India



Module 4

NOISE

P. Suresh Venugopal 2Analog Communication - NOISE



Topics to be covered• Noise

– Sources of noise • Thermal Noise, Shot Noise, Flicker noise and White noise

• Noise Parameters – Signal to noise ratio – Noise factor – Noise equivalent band width – Effective noise temperature






Noise Sources•

Introduction to Noise• Shot Noise• Thermal Noise•

Flicker Noise• White Noise




Noise - Introduction

• Noise – Unwanted Signals that tend to disturb theTransmission and Processing of Signals inCommunication System and over which we haveincomplete 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.




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.P. Suresh Venugopal 7Analog Communication - NOISE



Sources of Noise

• Noise performance by external sources is shownbelow.



Sources of Noise• Internal Noise is an important type of noise that

arises from the SPONTANEOUS FLUCTUATIONSof Current or Voltage in Electrical Circuits.

• This type of noise is the basic limiting factor of employing more complex Electrical Circuits inCommunication System.

• Most Common Internal Noises are: – Shot Noise –

Thermal NoiseP. Suresh Venugopal 9Analog Communication - NOISE



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 cathodewhen light falls on it.• The circuit generates a current pulse when an

electron is emitted.P. Suresh Venugopal 10Analog Communication - NOISE



Shot Noise• The electrons are emitted at Random times, k

where -∞ < k < ∞ and assume this randomemission have been gone for a long time.

• Thus the Total Current flowing through thePhotodiode may be modeled as the sum of theseCurrent Pulses.

• This process X(t) is Stationary and is called SHOT

NOISEP. Suresh Venugopal 11Analog Communication - NOISE



Thermal Noise

• Thermal Noise is the name given to the Electrical Noise arisingfrom the Random motion of electrons n a conductor.

• It is also called Jonson Noise or Nyquist Noise.

• Let VTN is the Thermal Noise Voltage appearing across the twoterminals of a resistor.

• Let the applied voltage have a bandwidth or frequency), ∆f .

• Then the Mean Square value of VTN is given by:




Thermal Noise

• Wherek = Boltzmann’s constant = 1.38 x 10 -23 Joules per oKT = absolute temperature in oK

R = resistance in ohms




Jonson Noise or Nyquist Noise




Thermal Noise• We can model a noisy resistor using the Thevenin and

Norton Equivalent Circuit as shown below:



Thermal Noise

• The number of electrons inside a resistor is verylarge and their random motions inside theresistors are statistically independent.

•

The Central Limiting Theorem indicates thatthermal Noise is a Gaussian Distribution with Zeromean.




Low Frequency or Flicker Noise• Active devices, integrated circuit, diodes, transistors etc also

exhibits a low frequency noise, which is frequencydependent (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 anddefects in the crystal structure in semiconductors, and inthe oxide coating on the cathode of vacuum tube devices




Low Frequency or Flicker Noise• Flicker Noise is found in many natural phenomena such as

nuclear radiation, electron flow through a conductor, oreven in the environment.

• The noise power is proportional to the bias current , and,unlike Thermal and Shot Noise, Flicker Noise decreases withfrequency.

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

• However, the inverse proportionality with frequency isalmost exactly 1/f for low frequencies, whereas forfrequencies above a few kilohertz, the noise power is weakbut essentially flat.




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 isconcentrated 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 lownoise applications is due to their tendency to produce flicker noisewhen carrying a direct current.

• In this connection, metal film resistors are a better choice for low

frequency, low noise applications.P. Suresh Venugopal 19Analog Communication - NOISE



White Noise• The Noise Analysis of Communication System is

done on the basis of an idealized form of noisecalled WHITE NOISE.

• Its power spectral density is independent onoperating frequency.

• White – White light contain equal amount of allfrequencies in visible spectrum.




White Noise• Power spectral density is given by:

The 1/2 here emphasizes that thespectrum extends to both positive

and negative frequencies.




Power Spectral Density of WhiteNoise

• A random process W(t) is called white noise if ithas a flat power spectral density , i.e., SW(f) is aconstant c for all f .




Ideal Low Pass Filtered WhiteNoise

• Let – w(t) = White Gaussian Noise applied to the LPF – B = Bandwidth of LPF – n(t) = noise appearing at the output of LPF – SN(f) = Power Spectral Density of n(t) – RN( ) = Auto Correlation function of n(t)




Ideal Low Pass filtered WhiteNoise




Noise Parameters•

Signal to noise ratio• Noise factor• Noise equivalent band width• Effective noise temperature




Signal to Noise Ratio (SNR)

where: P S is the signal power in wattsPN is the noise power in watts

• Hartley-Shannon Theorem (also called Shannon’s Limit)states that the maximum data rate for a communicationschannel is determined by a channel’s bandwidth and SNR.

• A SNR of zero dB means that noise power equals thesignal power.

N

S10 P

P log10dBSNR








Noise equivalent band width




Effective noise temperature

• T = environmental temperature (Kelvin)•

N = noise power (watts) • K = Boltzmann’s constant (1.38 10 -23 J/K)

• B = total noise factor (hertz)

• T e = equivalent noise temperature• F = noise factor (unitless)


N T

KB

1eT T F 1 eT F T



NarrowbandNoise• Introduction to Narrowband Noise

• Representation of narrowband noise in terms of

In phase and Quadrature Components




Narrow band noise

• Preprocessing of received signals

• Preprocessing done by a Narrowband Filter

• Narrowband Filter – Bandwidth large enough topass the modulated signal.

•

Noise also pass through this filter.• The noise appearing at the output of this NB filter

is called NARROWBAND NOISE.P. Suresh Venugopal 32Analog Communication - NOISE



Narrow band noise

• Fig (a) – spectral components of NB Noise concentrates about +f c • Fig (b) – shows that a sample function n(t) of such process appears

somewhat similar to a sinusoidal wave of frequency f c



Narrow band noise• We need a mathematical representation to analyze the

effect of this NB Noise.• There are 2 specific representation of NB Noise

(depending on the application)


Representation of narrowband noise in



Representation of narrowband noise interms of In phase and Quadrature

Components• Let n(t) is the Narrowband Noise with Bandwidth

2B centered at f c

• We can represent n(t) in canonical (standard) formas:

• We can extract n I(t) (In Phase Component) andnQ (t) (Quadrature Component) from n(t).


f f



Extraction of n I(t) and nQ (t) from n(t)

• Each LPF have bandwidth ‘B’ • This is known as NARROWBAND NOISE ANALYSER

f ( ) f ( ) d



Generation of n(t) from n I(t) and nQ (t)

• This is known as NARROWBAND NOISE SYNTHESISERP. Suresh Venugopal 37Analog Communication - NOISE

i f ( ) d



Important properties of n I(t) and nQ (t)

I i f ( ) d



Important properties of n I(t) and nQ (t)




Noise in CW modulationSystems

• Noise in linear Receivers using Coherent detection•

Noise in AM Receivers using Envelope detection• Noise in FM Receivers




Gaussian process• Let X(t) denote a random process for an interval that starts at

time t = 0 and lasts until t = T.• The random variable Y is a linear functional of the random

process X(t) if:

where g(t) is an arbitrary function

• By definition:

The random process X(t) is a Gaussian process if every linear functional of X(t) is a Gaussian random variable.




Main virtues of the Gaussian process:

• Gaussian process has many properties that make results possible in analytic form

• Random processes produced by physical phenomena (seethermal noise as an example) are often such that theymay be modeled by the Gaussian process

• If the input to a linear time invariant (LTI) system isGaussian then its output is also Gaussian




Thermal noise

• Is generated by each resistor.

• Used to model channel noise in analysis the of communication systems.

• It is an ergodic, Gaussian process with themean of zero.




Power spectral density (PSD) of a



Power spectral density (PSD) of arandom process

• By definition, the power spectral density S X

(t) and autocorrelation function R X ( ) of an ergodic random process X(t) form a Fourier transform pair with and f as the variables of interest.

• The power of an ergodic random process X(t) is equal to the total area under the graph of power spectral density.

• The power spectral density is that characteristic of a randomprocess which is easy to measure and which is used in

communication engineering to characterize noise. 45



White Gaussian Noise• Gaussian means Gaussian process.

A measurable consequence: Measured instantaneous values of athermal noise give a Gaussian distribution.

• White means that the autocorrelation function consists of a deltafunction weighted by the factor N0=2 and occurring a = 0.

• Power spectral density of white noise is:




White Gaussian Noise




White Gaussian Noise• Thermal noise is a white Gaussian noise.

• It is an ergodic Gaussian process with mean of zero, its power isgiven by the variance σ2.

• Its power spectral density is:

where k is the Boltzmann’s constant and Te is the equivalent noisetemperature.

• Note:

Power of white noise is infinite. Only the bandlimited whitenoise has a finite power!




Noisy Receiver Model

• where the receiver noise is included in N0 given by:

the bandwidth and center frequency of ideal band-pass channelfilter are identical to the transmission bandwidth BT and thecenter frequency of modulated waveform, respectively.




Noisy Receiver Model

• The filtered noisy received signal x(t) available for demodulation

is defined by:

• Note: Noise n(t) is the band-pass filtered version of w(t)


l d ( ) f b d



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 iscontaminated with additive noise is the signal-to-noise ratio (SNR)


Fi f M i Of CW M d l i



Figure of Merit Of CW ModulationSchemes

• Goal: Compare the performance of different CW modulationschemes.

• Signal-to-noise ratio (SNR) is a measure of the degree to which asignal is contaminated by noise.

• Assume that the only source of degradation in message signalquality is the additive noise w(t).

• Noisy receiver model:

53







• (SNR)O is well defined only if the recovered message signal and noise appear additively at demodulator output. Thiscondition 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






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:

56





• Noise performance of a given CW modulation scheme and a giventype 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 noiseperformance




SNRs & Figure of Merit


N i i AM DSB FC R i



Noise in AM DSB-FC Receivers

t)f π(t)sin(2n-t)f π(t)]cos(2nm(t)k A[A

n(t)s(t)x(t)

signal -

N2P)k (1A (SNR)

)2

N(2W ← NpowernoiseAverage -

2P)k (1ApowersignalAverage -

t)f πm(t)]cos(2k [1As(t)

-

CQCIaCC

0

2a2CAMC,

00

2a

2C

CaC

Filtered

W

W

signal AM

59



Noise in AM DSB-FC Receivers

1Pk 1

Pk )()(

meritof Figure

1 ≤k

powernoiseAvgpowercarrierAvg

N2Pk A

(SNR) -

(t)nm(t)k AAy(t)

(t)n(t),n m(t)]k 1[A (t)n(t)]nm(t)k A[A

x(t)of envelop)(

2a

2a

a

0

2a

2C

AMO,

IaCC

QIaC

21

2

Q

2

IaCC

AM C

O

SNRSNR

W

Assume

t y




Threshold effect

• The threshold is a value of carrier-to-noise ratio below which the noise performance of a demodulatordeteriorates much more rapidly than proportionately tothe carrier-to-noise ratio.

• Every noncoherent detector exhibits a threshold effect,

below the threshold the restored message signalbecomes practically useless.


N i i AM DSB FC R i



Noise in AM DSB-FC Receivers• Figure of merit for DSB modulation:

where P denotes the average power of message signal m(t)and ka is the amplitude sensitivity of AM modulator.

• The best figure of merit is achieved if the modulation factor is µ = k a Am = 1

• DSB system using envelope detection must transmit threetimes as much average power as a suppressed-carrier system




Threshold effect

Physical explanation:

• If the carrier-to-noise ratio is high enough then the signaldominates and the noise causes only a small unwanted

AM and PM.

• However, if the carrier-to-noise ratio is small then thenoise dominates which results in a complete loss of

information.• As a result, the demodulator output does not contain the

message signal at all.P. Suresh Venugopal 63Analog Communication - NOISE

Th h ld ff t



Threshold effect

Threshold Effect : loss of message in an envelope detector thatoperates at a low CNR. 64

N i i AM DSB SC R i



Noise in AM DSB-SC Receivers




N i i AM DSB SC R i




Finding (SNR) O

)t(n

2

1)t(mCA

2

1y(t)

)tf4sin()t(nA21)tf4cos()t(n)t(mCA

21)t(n

21)t(mCA

21

)tf2cos()t(x)t(v -

)tf2sin()t(n)tf2cos()t(n)t(m)tf2cos(CA

)t(n)t(s)t(x -

IC

CQCCICIC

C

CQCICC

ππ

π

πππ


N i i AM DSB SC R i




Finding (SNR) O

1

)SNR(

)SNR(

meritofFigure NW2

PAC2NW4PAC

)SNR( -

NW2n(t)noisefilteredpassbandofPower(t))Power(n

(passband) NW21(2W)N

41 powernoiseAverage-

4PAC

powersignalAverage-

SCDSBC

O

0

2C

2

0

2C

2

O

0I

00

2C

2




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 athreshold effect . Coherent AM detectors have no threshold effect!


Comparison of noise performance of



p pAM modulation schemes

Remarks• Curve I: DSB modulation

and envelope detector with modulation factor

µ = 1• Curve II: DSB– SC and

SSB with coherent demodulator

• Note the threshold effect that appears at about 10 dB


Noise in FM Receivers




•

w(t): zero mean white Gaussian noise with PSD = No/2• s(t): carrier = f c, BW = BT

• BPF: [f C - BT/2 - f C + BT/2]

• Amplitude limiter: remove amplitude variation.• Discriminator

» Slope network : varies linearly with frequency» Envelope detector






•

FM signal:

• Filtered noise n(t):)]t(tf2cos[A)t(s

dt)t(mk2)t(]dt)t(mk2tf2cos[A)t(s

CC

t0f

t0fCC

φπ

πφππ

∫∫

)t(n

)t(ntan)t(

))t(n())t(n(r(t) where

)]t(tf2r(t)cos[

)tf2sin()t(n)tf2cos()t(n)t(n

I

Q1

2Q

2I

C

CQCI

ψ

ψπ

ππ





Noise in FM Receivers• Phasor diagram interpretation of noisy demodulator input:

• Due to the PM generated by the noise, noise appears at thedemodulator output.

• But the FM demodulator is sensitive to the instantaneousfrequency of the input signal.

• The instantaneous frequency is the first derivative of thephase of input signal.





Noise in FM Receivers• The instantaneous frequency is the first derivative of the

phase of input signal.

• Derivation in the time domain corresponds to multiplication by (j2 π f) in the frequency domain.

• Multiplication by (j2 π f) means that the frequency response of derivation is:

• Recall, power spectral density of the output process equals tothe PSD of the input process multiplied by the squared magnitude of the frequency response H(f) of the LTI two-port.





Noise in FM Receivers• Recall, power spectral density of the output process equals to

the PSD of the input process multiplied by the squared magnitude of the frequency response H(f) of the LTI two-port.

• Therefore, the PSD SN 0 (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





Noise in FM ReceiversDiscriminator output

dt)t(dn

πA21

)t(n

)]}t(sin[)t(r{dt

d

πA2

1

)]}t()t(sin[)t(r{dtd

πA21

)t(n

where

)t(n)t(mkdt

d21)t(v

Q

Cd

C

Cd

df

ψ

φψ

θ(t)π





P. Suresh Venugopal Analog Communication - NOISE 77


















Noise in FM ReceiversFigure of merit for frequency modulation

• we obtain by substituting:

where β is the Modulation Index.

• Note: An increase in the transmission bandwidth BT provides acorresponding quadratic increase in the output signal-to-noise ratio(or in the figure of merit) of the FM system.


FM h h ld ff



FM threshold effect

• The figure of merit discussed above is valid only if thecarrier-to-noise ratio (SNR)C is high compared with unity .

•

It has been found experimentally that as (SNR)C isdecreased 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



FM threshold effectA qualitative explanation

• If (SNR)C is small then the noise becomes dominant and the phasor representation and the decomposition of noise into aPM and AM are not valid any more.

• The phase of noise is a random variable and it may take anyvalue.

• Recall, the FM demodulator is sensitive to the derivate of

phase.• When the phase of demodulator input varies suddenly by 2 π

due to the noise then an impulse, i.e., click appears at thereceiver output.


Pre-emphasis and de-emphasis in FM



Pre emphasis and de emphasis in FMsystems

• Recall: The power spectral density SN 0 (f) of noise at an FM receiveroutput has a square law dependence on the operating frequency.

• The high-frequency noise is dominant at the output of an FMreceiver.

• The power spectral density of message signals usually fallsoff 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 noiseperformance of FM systems





Pre emphasis and de emphasis in FMsystems

• 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.





e e p as s a d de e p as ssystems

•

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



p p pin an FM system


Comparison of noise performance of



CW systems

• Note: Threshold problem is more serious in FM modulation than inAM. The higher the β , the better the FM noise performance. But the

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Noise Notes