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CHAPTER-1

NETWORK NOISE

AND

INTERMODULATION DISTORTION

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Basic Communication Model

Main purpose of an electronic communications system is totransfer information from one place to another.

Electronic communications can be viewed as the transmission,reception and processing of information between two or

more locations using electronic circuit/device.

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What are we going to discuss ? Types of Noise

Sources of noise

Parameters related to noise

Signal to Noise Ratio

Noise Figure Noise Factor

Noise Temperature

Friss formula

Designing of Low noise amplifiers Intermodulation Distortion

- Different terms related to intermodulation distortion

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How do you characterize a receiver performance?

Sensitivity : (Minimum detectable signal)

That is the minimum power level at the point of transmission

that will ensure a final receiver output signal with acceptable

SNR

Signal-to-Noise Ratio

S/N ratio : average signal power

average noise power

The signal-to-noise (S/N) ratio indicates the relative

strengths of the signal and the noise in a communication

system.

The stronger the signal and the weaker the noise, the

higher the S/N ratio.

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Why should we study noise?


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NoiseRepresentation, types & source

5

Noise is an unwanted electrical signal that gets added to the

information signal as it is transmitted from one place to another.

It is notthe same as interference from other information signals.

It modifies the electrical nature of the transmitted signal

Noise produces Hiss in the loudspeakers when you tune any AM or

FM receiver to any position between stations.It is also the snow or confetti that is visible on a TV screen.

In pulse communication it may produce unwanted pulse which may

perhaps cancel out the wanted ones or which may cause some

serious mathematical errors


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Effects of Noise?

Limits the range of communication

6

Places a limit on the weakest signal that can be

received and amplified by the receiver( affects the sensitivity of the receiver)

Introduction of noise may also lead to reduction

of bandwidth of the system.


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Classification of Noise

Depends upon the sources producing it

External noise

Internal noise

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External noise

a. Atmospheric noise

b. Extraterrestrial noise

c. Industrial noise

Internal noise

a. Thermal noise

b. Shot noise


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External Noise :Noise created outside the receiver/ the communication

system

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External noise comes from sources over which we have little or

no control, such as:

Atmospheric sources

The naturally occurring electrical disturbances in the

earths atmosphere tends to interfere with the reception

program

Example: Lighting discharges in the thunderstorms or

other electrical disturbances occurring in nature

These spurious signals induces voltages in antenna.


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10

Extraterrestrial noisealso called as SPACE NOISE

-consists of electrical signal that originate from outside earths

atmosphere and therefore also known as deep-space noise.-2 categories of extraterrestrial noise.isolar noisenoise that generated directly from the suns heat.iicosmic noise noise that is distributed throughout the galaxies.

The sun , stars, and other planets in the galaxy are at high

temperature and hence radiate RF noise which interferes with thereceived signal. (GLACTIC NOISE)

Industrial noise (Man made noise)source : automobile, aircraft ignition system.

Electric motors

Switching equipmentsLeakage from high voltage linesHeavy electric machines/motorsFluorescent light


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Frequency Ranges:

Atmospheric noise becomes less severe above about 30 MHz

Space noise is observable in the range from about 8MHz to

somewhat above 1.43 MHz

Industrial noise between 1 to 600 MHz.

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Internal Noise

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Electronic components in a receiver such as resistors,

diodes, and transistors are major sources ofinternal

noise.

Noise that generated within the device or circuit.

Types of internal noise include:

Thermal noise

Semiconductor noise(Shot Noise)


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Thermal Noise / Resistor Noise

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The noise created due to random motion of the electrons in a

conductor due to heat ( i.e. at any temperature above absolute

zero i.e. 0 Kelvin or -273 o C.

Noise arises due to thermal cause hence called as THERMAL

NOISE


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The rms value of the thermal noise generated in an impedance

Z(f) is given as

Thermal Noise / Resistor Noise Formula

Instantaneous Value is unpredictable.


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Representation of Resistor Noise

16

Equivalent circuit of a noisy resistor


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Available Thermal noise Power

KTB

R

V

R

VP

NN

4

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How much amount of noise power will be given to the

load the noisy resistor


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Analysis of a noisy resistor connected

to a linear network with frequency

dependent transfer function G(f)

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G(f) is the transfer function of the network

It is the magnitude squared of the frequency dependent transfer

function between the input and the output voltages.

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The total noise at the output of the network will begiven as.

Where, Is referred to as the

noise bandwidth Bn of the

system


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Problem: Find the total output noise for the parallel

combination of R and C given below

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Hints:

21

Find:

(1)

(2)

We get :

Substituting in (2) we get

Since standard form of noise voltage

is


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Shot Noise / Active Device Noise

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Is a phenomenon associated with the flow of current across asemiconductor junction.

If Id is the average current, then the total diode

current i(t) will be given asi(t) = Id + in (t)

Where, in (t) represents the noise/ fluctuating

component of the current.


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Representation of shot noise in a diode

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Represented by a appropriate current source in parallel with the

dynamic resistance of the barrier across which the noiseoriginated


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Shot Noise Formula

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Shot noise current spectral density :

Where, q is the charge on electron = 1.6 x 10 -12 C

Io is the direct current

k is a constant which varies from device to device

and also depends on how the junction is biased.For junction transistor k=2

For junction diode/ transistor :

Total noise current over the given bandwidth :

Where, f is the bandwidth

N i i T i t A lifi


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Noise in Transistor Amplifiers

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Transistor Amplifier

in1 is the shot noise current density due to the i/p bias currentin2 is the shot noise current density due to the bias current on the

o/p of the device.

en is the noise due to the load resistor RL

in1 = 2qIB A2/Hz , in2 = 2qIc A2/Hz, en = 4kTRL V2/Hz


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Representation model of transistor amplifier with

the noise sources referenced to the input side of the

amplifer

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Values of e2, e3

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Derivation

Assuming RL is much less than the transistor output impedance

Amplifier Voltage Gain is

(1) (2)


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Model or transistor amplifier with all

noise sources on the input side

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Noise Parameters

Signal to Noise Ratio

Noise Figure

Noise Factor

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Noise Parameters

1. Signal-to-noise Power Ratio

signal-to-noise power ratio (S/N) is the ratio of the average signal

power level to the average noise power level and can be expressedas

in logarithmic function

in terms of voltages and resistance

30

n

s

P

P

N

S

n

s

P

PdB

N

Slog10)(

RVRVdB

NS

n

s

//log10)(

2

2

n

s

V

VdB

N

Slog20)(


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2. Noise Factor

Noise factoris the ratio of input signal-to-

noise ratio to output signal-to-noise ratio

Receiver noise figure is a measure of how

much noise is added by the system

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out

in

NS

NSF

)/(

)/(

A low noise figure is always desirable.


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out

in

NS

NSFNF)/()/(log10log10

Noise figure is the noise factor stated in dB and is a

parameter to indicate the quality of a receiver.

3. Noise Figure


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Noise Factor IEEE definition of noise factor

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Noiseless Network

Minimum value of Noise factor ,F =1 (noiseless n/w)

i.e. No=Ni

The noise figure of a ideal noise less network = 0 db.

However, F is always greater than unity

A low noise figure is always desirable.


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Noise added by the amplifier in terms

of noise factor ( F )

If Ni is the input noise ( noise due to source resistance)

If Si is the input signal (i/p s/g power due to source voltage)

If No is the noise at the o/p of the amplifier

If So is the signal at the output of the amplifier

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Formula for Noise added by amplifier

Na = (F-1)KTB

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Derivation ?

Noise factor of the amplifier

Gain of the amplifier


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Value of

Substituting in Pno we get


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It is seen that the noise power at the output of the

amplifier is increased by F over what it would have

been if the amplifier was noiseless


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Noise added by the amplifier (referred to the i/p)

Noise added by the amplifier as

referred on the i/p side.

Noise Factor and Noise Figure of cascade Amplifier


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Noise Factor and Noise Figure of cascade Amplifier

- when two or more amplifiers are cascaded as shown in the following figure,

the total noise factor is the accumulation of the individual noise factors.

- Friss formula is used to calculate the total noise factor of several cascade

amplifiers

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N

N

T

AAA

F

AA

F

A

FFF

...

1...

11

2121

3

1

21

Derivation?


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Derivation

Pno = G2 [ G1 F1 KTB + ( F21)KTB] ?

F1 is the noise factor of amplifier A1

G1 is the Gain of amplifier A1

F2 is the noise factor of amplifier A2

G2 is the Gain of amplifier A2


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We shall first see the derivation for Pno

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Total Noise referred the input of the amp A2 = O/p noise of amp. A1 + noise added by amp A2

Pni2 = G1 F1 KTB + ( F21)KTB

Output noise of Amplifier A2 will be

Pno = G2 [ G1 F1 KTB + ( F21)KTB]

O ll N i F t f th d d


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Overall Noise Factor of the cascaded

Network F

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Overall Noise Factor

Overall Gain

Where.

Therefore


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Where,

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Pno

= G2

[ G1

F1

KTB + ( F2

1)KTB]

And Pni = KTB , G= G1 G2

Substituting all in

We get, the total noise factor of two cascaded

amplifiers as :


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This argument can be extended to any number of amplifiers in

cascade which gives a total noise factor of :

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N

N

T

GGG

F

GG

F

G

FFF

...

1...

11

2121

3

1

21

FRISS Formula


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Note:

- the Total Noise Figure

where,

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TT FNF log10

N

N

T

AAA

F

AA

F

A

FFF

...

1...

11

2121

3

1

21

When using Friss formula, the noise figures mustbe converted to noise factors !!!


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Problem 1

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Ans:

Noise Factor F = 1.779

Noise Figure NF = 2.5dB


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Problem 2

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For problem 1 what will be the total noisepower of the cascaded system in a 3-kHz

bandwidth? The opeating temperature is

290o

K

Ans:

Total output noise power = 337 x 10 -17 W

N i T t


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Noise Temperature

50

Noise added by amplifier is considered to be the

noise added by a resistor which is as a fictious

temperature Tr, and the amplifier is now

considered to be noiseless.


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4. Noise Temperature

Noise added by amplifier is

given by

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Where T is the reference noise temperature

Tr is referre to as system noise temperature

Formula

Derivation

Pn a =(F1)KTB

Where the resistor noise equation is Pn = KTB

Resistor now being at fictious temp. Tr the eqn is Pn = KTrB

Therefore, KTrB =(F1)KTB

Tr =(F-1)KT

O ll N i T t f d d


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Overall Noise Temperature of cascaded

network

Friss Formula can be expressed in terms of

equivalent temp. Tr

Overall noise temp. of a cascaded network is

given by :

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Problem What is the variation in noise temperature as

the noise factor varies from 1 to 1.6 ( I,e NF

caries from 0 to 2 dB)? Assume the reference

temperature is 290K

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Ans:Tr= ( 1.6 -1) 290 = 174K

Note: The change is noise temperature is much greater than thechange in noise factor. This is the prime reason why noise

temperature is used to describe the system noise

5. Sensitivity


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5. SensitivityDenoted as Si and is also called as MINIMUM DETECTABLE SIGNAL/ SYSTEM SENSITIVITY

/ NOISE FLOOR

Definition:

For a given output Signal to Noise ratio (S/N)o ,the available input signal level is

referred to as system sensitivity

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Formula:

where, No is the total noise power at the output

So is the total signal power at the output

Note:

Sensitivity is always specified for a given signal-to-noise ratio


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Derivation for Sensitivity

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Problem:

What minimum input signal will give an output signalto noise ratio of 0dB in a system that has an input

impedance equal to 50 , a noise figure (NF) of 8 dB,

and a bandwidth of 2.1kHz?

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Ans:

10 log Si = NF -144+10 log B+10log(S/N)o

Si = -133 dBm

Si= (Ei2

/ 4 Rs) =5.02 x 10-17

WEi=0.10V

That is, for the specifications given the noise floor for

an output signal to noise ratio of 1 is 0.10V.


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Problem: What is the minimum detectable signal or the

noise floor of the system in the previousexample for a output signal to noise ratio of10 dB

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Ans:Given data: (S/N)o= 10 dB

B=2.1kHz

10 log Si = NF -144+10 log B+10log(S/N)o

Si = -123dBmSi= (Ei2 / 4 Rs)

Ei=0.32V


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Problem What is the minimum detectable signal level

of a communication receiver with a 50 inputimpedance, ofB of 3 kHz, and a 4dB noisefigure at an output signal to noise ratio of 10

dB

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Ans:

Si = -125dBm = 3 x 10-16 W

Ei=0.245V

That is an input signal of 0.245 V will produce a 10 dB

output signal to noise ratio.


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Design of Low Noise Network

59

Transistor amplifier

noise model.

Transistor amplifier

noise model with voltage source

D i D i ti


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Design Derivation

60

Total Noise referred to the input side in a unit bandwidth B=1, is

N = en2 + in2Rs2 + 4KTRs (1)

Na = en2 + in

2Rs2 (2)

Noise added by the network/amplifier

Amplifier equivalent

noise voltage sources


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Design Derivation

Overall noise Factor of the network

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F = Available input noise power + noise added

available input noise power

Network noise factor depends upon the source resistance Rs

Value of Rs that minimizes the noise factor can be found as


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Contd:

62

Rs is chosen to minimize the spot noise factor at a specified

frequency.


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Problem:

63

What will be the minimum noise figure for 741 operational

amplifier with a 10 kHz source resistance at 1kHz , the inputnoise voltages are en

2 = 8 x 10-16 V2/Hz, in2 = 9 x 10-25 A2/Hz

Formula:

Minimum noise factor F = 4.35

Minimum noise figure NF = 6.4 dB

Ans:


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Problem

64

Find the noise factor for an 741 operational amplifier with a

10 kHz source resistance at 1kHz , the input noise voltages areen

2 = 8 x 10-16 V2/Hz, in2 = 9 x 10-25 A2/Hz

Formula:

Ans: F = 6.6


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For Rs = 30 K, Minimum noise factor F = 4.35

For Rs = 10 K, F = 6.6

Noise Factor minimizes when the Rs increases

from 10K to 30 K

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Another aspect of low noise design

Noise Factor

Signal to Noise ratio

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By selecting high Rs

F is minimized (which is desirable)S/N also has minimized(which is undesirable)


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There fore ,

Minimizing the noise factor does not necessarilymaximize the S/N ratio

Solution:

Value of Rs should be such that it

simultaneously

1. minimizes noise factor and2. maximizes the S/N ratio


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Design

68

Source is transformer coupled to the amplifier i/p

In this case, Reflected source resistance

Equivalent source voltage

Output Signal to Noise Ratio

Contd:


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The resistor value Rs which maximizes the S/N ratio and

minimizes the noise factor is found as follows:

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gives:

This is the value of source resistance Rs which minimizes

the noise factor as well as maximizes the signal to noise

ratio Noiseless transformer coupling can be used to match the

source to amplifier input, then the turn ratio that

minimizes the noise factor will also maximize the o/p s/n

ratio


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Intermodulation Distortion

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Effects of nonlinearity?

Harmonic distortion

Intermodulation distortion

Gain Compression

Terms related to IMD

IMR (Intermodulation Distortion Ratio)

Intercept point Dynamic Range

SINAD


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Explanation for IMD A network nonlinearity can be described by the following

expression

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f(x) is the input signal to the circuit

y(x) is the output signal to the circuitLet the inputf(x) consist of two sinusoids

Then the output y(x) will be

Ignoring the higher order terms


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Contd.Expanding the given eqn.

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Contd: Effects of Nonlinearity


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y Amplitude ofcos1tterm which wasA1 now becomes

73

Gain Compression ?

Normally K3 will be negative

If A2cos

2t is of large amplitude

1.It will mask a smaller signalA1cos1t

2. It results in a reduced gain because of the third order

term coefficient K3.( This effect is known as GAIN

COMPRESSION)

How to avoid Gain Compression ?

The third order coefficient K3 must be reduced.

Multiple signals at the input must be avoided as it leads to

further reduction of gain

1 dB Compression Point


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1 dB Compression Point

The K3 term causes gain to deviate

from the idealized linear curve

The point at which the power gain is

down by 1dB from the ideal is

referred to as 1-dB compression

point.

Significance

Receivers must be operated below

their gain compression point if the

nonlinear gain region is to beavoided


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If only one signal is present at the input the

reduction in gain from amplitudeA1 to A1 is known

as the SINGLE TONE GAIN COMPRESSION FACTOR

given by

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Single Tone Gain Compression Factor


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Harmonic Distortion

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Harmonic Distortion occurs when unwanted harmonics of

signal are produced through nonlinear amplification.Harmonics are integer multiples of the original signal.

The original signal is thefirst harmonic (fundamental

harmonic), a frequency two times the fundamental

frequency is thesecond harmonic, three times is the third

harmonic and so on.


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Second Harmonic Distortion

The receiver output due to k2term

If a single signal is present at the receiverinput, then the amplitude of the second

harmonic is

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Distortion caused due to cubic term

Cubic term creates INTERMODULATION FREQUENCIES

78

The frequencies which lie within the system

passband and appear at the output as signal

distortion are

Intermodulation Distortion Ratio (IMR)


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Intermodulation Distortion Ratio (IMR)

Desired Output: K1A1

Intermodulation distortion terms are

79

Amplitude of Intermodulation distortion terms are

Definition:

IMR is defined as the ratio of the amplitude of one of the

intermodulation terms to the amplitude of the desiredoutput signal


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Intercept Point Intermodulation Power

(IMD):

80

Rearranging,

Intermodulation Power Pd:


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Therefore

IMD power varies as cube of the input power.

i.e. for every 1 dB increase in the input power there

is a 3 dB increase in the power of the

intermodulation terms

On Log scale the IMD power increases 3 times as fast

as the expected output power.

Intermodulation Distortion Power is given as

Pi is the power in one signal component

Kd is called the scale factor where, Kd = (3/4 ) (K3/K1)

Significance

IMD P i i


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IMD Power is given as

Out put Power contributed by

linear term is given as

Plot of outputpower

v/s

input power


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What is INTERCEPT POINT(Pi )?

The value of input power for which the IMDpower Pd is equal to the output power Po

contributed by the linear term

83

At intercept point Pi,Pd = Po

Significance ofINTERCEPT POINT(Pi )?

A measure of the distortion created in the receiver.

Ability to reject large amplitude signals that lie in the

close frequency proximity to a weak signal targeted

for reception.

Formula for INTERCEPT POINT(Pi )?


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( i )

84

IMD power (PIMR ) is defined as

Substituting PdandPo

We get ,

At Pi, Pd=Po and PIMR= 1

That is,

Since, At this signal level

Where,Ki = (Kd / K12) and Kd = (3/4 ) (K3/K1)

Problem :


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Problem :

If the intercept point of a system is +20dBm, whatis the IMR for an input signal power of 0dBm?

85

Formula :

In dB : PIMR =2 x (Pi dB PI dB)

Ans : PIMR = - 40 dBm

Dynamic Range:


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Dynamic Range:

86

SINAD:


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SINAD:

Equivalent Noise Bandwidth, Bn


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n

88

When noise is passed through a filter having a frequency

response, some of the noise power is rejected by the filter and

some is passed through to the output

The noise bandwidth of a non-ideal filter is defined as the

bandwidth of an ideal (rectangular) filter which will pass

the same noise power as the non-ideal filter.

Definition

Equivalent Noise Bandwidth f


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Equivalent Noise Bandwidth f

89

The relationship between f and f3dB, the 3dB

frequency of the system,

The NBW is the frequency such that a rectangle defined by

H(max)2 and Bn has an area equal to the area under|H()|2.

D i ti f N i B d idth


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Derivation of Noise Bandwidth

90

The relationship between f and f3dB, the 3dBfrequency of the system, depends on the number of

poles in the transfer function.

The noise bandwidth for a single pole filter


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The noise bandwidth for a single pole filterExample: A RC filter

Questions:


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Q

Define noise factor, noise figure, and sensitivity. State and explain the sources of noise.

Explain the concept of equivalent noise bandwidth

What is intermodulation distortion? Discuss in detail the different

parameters that are related with intermodulation distortion.

Explain the noises that occur in active devices.

Derive the expression of the noise factor of n cascaded stages. What is the

significance of the first stage.

Explain the significance of 1dB compression point.

A receiver has 10 dB noise figure, 50 input impedance, a 5dBm two toneintercept point (PI), and a 3.5 KHz bandwidth. What is the minimum

detectable signal for a 0 dB output signal to noise ratio? What is the

receivers dynamic range.

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