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AE_Lecture 9_revised_Noise(Untitled)

Module by: Bijay_Kumar Sharma. E-mail the author

Summary: AE_Lecture 9_Noise has been revised. In the previous version there were some conceptual mistakes.

Lecture no-9 Noise sources and theoretical formulation of noise parameters.

Internal Noise Sources

  • Resistors
  • Vacuum Tubes
  • BJT & Other Solid State Devices

External Noise Sources

  • Atmospheric
  • Man Made Electric DC Machines
  • Extraterrestrial sources
  • Multiple Transmission Paths
  • Random Changes in attenuation within the transmission medium.

1.ATMOSPHERIC NOISES

Due to electric discharge in thunder clouds spurious radio waves are produced.

In time domain, electric discharge is a SPIKE (or a Dirac Delta Function). In frequency domain we have uniformly distributed RF waves in MW region 540kHz to1.6 MHz. Below 100MHz field strength of the radiations from the electric discharges are significant in Medium Wave Range of RF and not in Short Wave Range. This is why during thunder storms maximum static is produced in MW Range of radio reception.

2.MAN MADE SOURCES

  • High voltage powerline corona discharge.
  • Commutator-generated noise in DC electric motors..
  • Switching gear noise.
  • EM Interference by high intensity radio transmitters in neighbourhood.

3.EXTRATERRESTRIAL NOISE SOURCES

  1. Periodic increase in Solar Activities(The period is 11 years) in the form of increased sun-spots and furious sun-flares lead to major disruptions in power transmissions and communication systems. The surface of the Sun is a roiling mass of plasma- charged high-energy particles- some of which escape from the surface and travel through the space as the solar wind. During a sun storm solar wind carries billion-tonne glob of plasma, a fireball known as coronal mass ejection(CME). If the CME hits the Earth, it changes the configuration of Earth’s Magnetic field leading to severe Electro-Magnetic Induction in the long lines of Power Grids. This will cause increased dc currents leading to saturation of the magnetic core of the transformers. The saturation of magnetic cores will limit the opposing e.m.f. leading to runaway currents in the secondary coil. This leads to rapid heating, melting of the transformer. One such event in March 1989 in Quebec, Canada, left 6 million people without electricity for 9 hours.
  2. Global Radio Broadcast at short wave RF gets seriously affected due to disruptions of ionosphere surrounding the Earth.
  3. QUASERS-Quasi-Stellar Radio Sources are important Radio Noise Sources in frequency range from MHz to GHz.
  4. Pulsars RF interference- Pulsars are Neutron Stars which are rapidly spinning and which have the magnetic field axis inclined to geo-graphical polar axis of spin. Due to this inclination, there is synchrotron radiation covering the entire span of spectrum. It emits radio waves, optical waves, X-Rays and Gamma Rays. This is emitted from the polar ends of the magnetic axis. Hence a beam of EM radiation are sweeping the entire space around the spinning Neutron Star at the same rate as that at which it is spinning. If our Earth falls in its line of sight, it receives periodic burst of EM radiations hence they are called pulsars. This is generally very weak hence does not cause much disturbance on Earth.

4.MULTIPLE TRANSMISSION PATHS-This occurs due to reflection off buildings, earth, airplanes & ships or from refraction from stratification in the transmission medium.

  1. Diffused Noise Source-received signals are numerous reflected components.
  2. Specular Noise Source-Received signals are one or two reflected strong rays.

5.RANDOM CHANGES IN ATTENNUATION IN THE ATMOSPHERE -this leads to fading.

INTERNAL NOISE SOURCES

Thermal Noise :- Random Motion of electrons in the conductor leading to fluctuations in the conducting semi free electron density(n) in the metallic lattice. This leads to fluctuating dipole leading to thermal voltages. This directly depends on the absolute temperature of the conductor.

Shot Noise:- Statistical fluctuations in the thermionic emissions from the cathode or the fluctuations in the forward current in the forward biased pn junction diode.

Partition Noise:- Statistical fluctuations in the current division or current merger in Vacuum tubes or in solid state devices.

Flicker Noise:-The number of free electrons or holes present in the channel decide the conductivity of the channel in FET devices. But due to interface states at the Gate Oxide in MOS the channel conductivity fluctuates due to random capture of majority carriers from the channel. This noise is inversely proportional to frequency. Hence it is also known as [

Figure 1
Figure 1 (graphics1.png)
noise.

Thermal Noise in Resistors(R)

Figure 2
Figure 2 (graphics2.png)

Random motion of electrons due to thermal energy(

Figure 3
Figure 3 (graphics3.png)
)leads to fluctuating dipole in the metallic lattice. This leads to random voltage fluctuation at the terminals.

This random voltage

Figure 4
Figure 4 (graphics4.png)

Mean Square Noise Power Spectral density=

Figure 5
Figure 5 (graphics5.png)

In double sided representation

Figure 6
Figure 6 (graphics6.png)

Figure 2. Noise Power Spectral Density Distribution w.r.t. frequency in a double sided spectrum.

We have almost uniform Noise Power Spectral Density over the entire frequency spectrum. Therefore Thermal noise(Johnson Noise) is also known as White Noise. Just as WHITE LIGHT has all the seven colours in equal magnitude, in the same way WHITE NOISE has equal spectral components over the entire frequency spectrum.

The actual Noise Power measured will depend on the Bandwidth B Hz.

Therefore Mean Square Noise Power in a resistance over B Hz.

Figure 7
Figure 7 (graphics7.png)
watts= available noise power;

Figure 8
Figure 8 (graphics8.png)

At 300K,

Figure 9
Figure 9 (graphics9.png)
=
Figure 10
Figure 10 (graphics10.png)

Let BW=1MHz

Figure 11
Figure 11 (graphics11.png)

This is the noise available from the resistance under consideration.

Figure 12
Figure 12 (graphics12.png)

Figure 3. Equivalent circuit of a noisy resistance connected to load. The noisy Resistor has been represented as a noise voltage source of v n delivering noise voltage to the load and with an internal resistance R having no noise.

Figure 13
Figure 13 (graphics13.png)

If R=RL, then

Figure 14
Figure 14 (graphics14.png)

Maximum power transferred to RL =Available noise power from the resistance to the load

=

Figure 15
Figure 15 (graphics15.png)
= kTB

Figure 16
Figure 16 (graphics16.png)
Figure 17
Figure 17 (graphics17.png)

Mean Square Noise Voltage= <vn2> =

Figure 18
Figure 18 (graphics18.png)

RMS Value of Noise Voltage=√<vn2> =

Figure 19
Figure 19 (graphics19.png)

If R=1k, B=1MHz, T=300K

Figure 20
Figure 20 (graphics20.png)

Figure 21
Figure 21 (graphics21.png)

The signals received at the antenna of a receiver is of comparable amount and hence the intelligent signal can easily be swamped by the thermal noise at the front end of a communication receiver. In deep space communication the problem is further compounded due to the fact that received signal from PIONEER or VOYAGER from the very edge of heliosphere is one or two orders of magnitude fainter than 4µV.

CALCULATION OF EFFECTIVE NOISE TEMPERATURE and DEFINITION of NOISE FIGURE.

Figure 22
Figure 22 (graphics22.png)

Figure 4. A two port network with SNR at the input and output.

SNR=Signal to Noise Ratio=

Figure 23
Figure 23 (graphics23.png)

Figure 24
Figure 24 (graphics24.png)
Figure 25
Figure 25 (graphics25.png)

So, ratio

Figure 26
Figure 26 (graphics26.png)

But actually it is not so because there is some internally generated noise in the amplifier.

Thus

Figure 27
Figure 27 (graphics27.png)

It is actually:

Figure 28
Figure 28 (graphics28.png)

Thus:

Figure 29
Figure 29 (graphics29.png)
Figure 30
Figure 30 (graphics30.png)

Therefore:

Noise Figure=

Figure 31
Figure 31 (graphics31.png)

An Ideal Noise Figure for an amplifier should be 0dB but it is never 0dB in actual practice. In actual practice the noise figure can be 0.1dB/ 0.2dB/0.5dB/1 dB or more.

EFFECTIVE NOISE TEMPERATURE

At the input:

Figure 32
Figure 32 (graphics32.png)

There is a thermal noise generator of equivalent temperature=

Figure 33
Figure 33 (graphics33.png)

This is the noise picked up by the antenna .

The noise power at the o/p:

Figure 34
Figure 34 (graphics34.png)

Here

Figure 35
Figure 35 (graphics35.png)

Therefore:

Figure 36
Figure 36 (graphics36.png)

Thus:

Figure 37
Figure 37 (graphics37.png)

Where:

Figure 38
Figure 38 (graphics38.png)
=
Figure 39
Figure 39 (graphics39.png)

Figure 40
Figure 40 (graphics40.png)
Figure 41
Figure 41 (graphics41.png)
Figure 42
Figure 42 (graphics42.png)

While the signal is passing through an amplifier the signal to noise ratio deterioration is defined by

Figure 43
Figure 43 (graphics43.png)
. If by cryogenic cooling effective noise temperature of the front end amplifier is minimized to zero then we achieve the ideal N.F. of 1 or 0dB.

IN COMMUNAICATION RECEIVER SYSTEMS

Figure 44
Figure 44 (graphics44.png)

Figure 5. A Communication Receiver in RF range. Different stages of the receiver are shown. In the first stage we have series resonance circuit tuned to a given station or tuned to a given communication frequency. At resonance frequency maximum electromagnetic induction takes place and maximum current is introduced in the primary coil of RF Transformer. The first stage is a RF tuned amplifier. After amplification, picked up radio frequency is downward frequency translated to intermediate frequency (IF). IF is 455kHz in AM Radio Receivers or 10.7MHz in TV or FM Radio.IF signal is amplified and then second detection or demodulation takes place. In the second detection it is again downward frequency translated to base band signals. This base band signal is voltage amplified by pre-amplifier and power amplified by Complementary Symmetry Amplifier. The power amplified is fed to the Speaker or Video Monitor.

The first downward frequencytranslation is known as 1st detection or 1st demodulation. This is also known as superhetrodyne mixing of tuned frequency f0 and fLo and fLo –f0 = Intermediate Frequency (I.F.).

FRISS FORMULA will have to be utilized to calculate the overall noise figure.

FRISS FORMULA

What is the overall noise figure of 2 cascaded stages ?

Figure 45
Figure 45 (graphics45.png)

Figure 6: Two Stage Cascaded Amplifier

We have a matched network for maximum power transfer.

Overall Noise Figure

Figure 46
Figure 46 (graphics46.png)

For n Stage cascade system:

Figure 47
Figure 47 (graphics47.png)

This formula implies that the overall Noise Figure is dominated by the noise figure of the first stage.

Figure 48
Figure 48 (graphics48.png)

Figure 49
Figure 49 (graphics49.png)

Front end amplifier is referred to as Low Noise Amplifier.

With a good front-end having cryogenic cooling, we achieve a good amplification with no deterioration in SNR as we proceed along the cascade chain.

Table 1. Typical Noise Figure

Table 1
Amplifier NF(abs) NF(dB) Te (K) Gain(dB) fop(GHz)
Parametric Amplifier(uncooled) 1.45 1.61 130 10-20 9
Parametric Amplifier(77K) 1.17 0.69 50 10-20 3&6
Parametric Amplifier(4K) 1.03 0.13 9 10-20 4
Travelling Wave Tube(TWT) 1.59 2.00 170 20-30 2.66
  1.86 2.7 250   3
  2.69 4.3 490   9
Tunel Diode Amplifier-Ge 2.38 3.77 400 20-40 ?
Tunnel Diode Amplifier-GaAs 1.69 2.28 200 20-40 ?
Low Noise Heterodyne Receiver 2.38 3.77 400 20-40 500kHz-30MHz
IC BJT IF Amplifier for TV 5.01 7 1163 50 10.7MHz
GaAs MESFET Amplifier ? ? ? ? ?

(1)Mumford & Scheibe,Noise Performance Factors in Communication Systems,Horizon House-Microwace,Inc,Dedham,Massachusets(1968),pp 36,39

(2)Linear Integrated Circuits Data Book,Motorola Inc.,(1974).

References:

1.Ziemer & Tranter,Principles of Communications-System,Modulation and Noise,Wiley India,5th Edition,2002.

2. Shanmugam,Digital and Analog Communication Systems, Wiley-India,Reprint 2007.

APPENDIX-1. Derivation Of The FRISS FORMULA (Refer to figure 6)

Noise at the output of the second stage is:

Figure 50
Figure 50 (graphics50.png)
______(1)

Similarly the output of the first stage is:

Figure 51
Figure 51 (graphics51.png)
______(2)

Available Noise power Input at the First stage is:

Figure 52
Figure 52 (graphics52.png)
________(3)

Substituting (3) into (2), we get,

Figure 53
Figure 53 (graphics53.png)
____(4)

Substituting (4)in (1),we get,

Figure 54
Figure 54 (graphics54.png)

Further Simplifying it,

Figure 55
Figure 55 (graphics55.png)
______(5)

But

Figure 56
Figure 56 (graphics56.png)
__(6)

And

Figure 57
Figure 57 (graphics57.png)
___(7)

Also,

Figure 58
Figure 58 (graphics58.png)
and
Figure 59
Figure 59 (graphics59.png)
_______(8)

From Eq(8), we have

Figure 60
Figure 60 (graphics60.png)
_______(9)

From Eq(9)and(7),

Figure 61
Figure 61 (graphics61.png)
_____(10)

Using relations(6) ,(8) and(10),

Eq(5) can be re-written as:

Figure 62
Figure 62 (graphics62.png)
Figure 63
Figure 63 (graphics63.png)

Simplifying:

Figure 64
Figure 64 (graphics64.png)
______(11)

But,

Figure 65
Figure 65 (graphics65.png)
_____(12)

[this is arrived at by induction logic recognizing the Na1=g1kBF1T0]

Where F is the overall noise figure.

Hence dividing(11)by (12), we get,

Figure 66
Figure 66 (graphics66.png)
______(13)

For 3 stages:

Figure 67
Figure 67 (graphics67.png)
_______(14)

For n stages:

Figure 68
Figure 68 (graphics68.png)
____(15) FRISS FORMULA.

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