analog communication unit7 vtu

ANALOG COMMUNICATION (VTU) - 10EC53

UNIT-7:

NOISE: Introduction, shot noise, thermal noise, white noise, Noise equivalent bandwidth,

Narrow bandwidth, Noise Figure, Equivalent noise temperature, cascade connection of two-port

networks.

TEXT BOOKS:

1. Communication Systems, Simon Haykins, 5thEdition, John Willey, India Pvt. Ltd, 2009.

2. An Introduction to Analog and Digital Communication, Simon Haykins, John Wiley India

Pvt. Ltd., 2008.

Special Thanks To:

Faculty(Chronological): Ravitej B (GMIT).

BY:

RAGHUDATHESH G P

Asst Prof

ECE Dept, GMIT

Davangere 577004

Cell: +917411459249

Mail: [email protected]

Quotes:

If you want something you never had then you have to do something you never done.

Real stupidity beats artificial intelligence every time.

Think before you speak. Read before you think.

Music is the wine that fills the cup of silence.

In my experience, there is only one motivation, and that is desire. No reasons or principle

contain it or stand against it.

Neither in this world nor elsewhere is there any happiness in store for him who always

doubts.

Noise Raghudathesh G P Asst Professor

ECE Dept, GMIT [email protected] Page No - 1

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NOISE

Introduction:

Why to study Noise: 1. Noise is one of the two principle limiting factors in the performance of

communication systems.

2. Electrical noise is any undesired voltages or currents that end up appearing at the receiver output. An example is static that is commonly encountered on broadcast

AM radio.

Definitions: 1. Noise is any undesirable voltages or a current that ends up appearing in the

receiver output.

2. Noise is any unwanted form of disturbance of signal or energy tending to interfere with the proper and easy reception and reproduction of desired signal.

3. Noise is a random energy that corrupts and distorts the desired signal. 4. Noise is an unwanted electrical disturbance which gives rise to audible or visual

disturbances in the communication systems, and errors in the digital

communication.

Noise is strong when the signal is weak. Example of noise in communication system:

1. Noise heard when tuning AM or FM receiver. 2. Hiss or static heard in the speaker. 3. Noise shows up in TV pictures as snow, known as confetti. 4. Noise that occurs in the transmission of digital data manifests itself as bit error.

Noise can affect the communication system performance in three areas: 1. Noise can cause listener to misunderstand the original signal or be unable to

understand it at all.

2. Noise can cause the receiver to malfunction. Noise can cause the receivers circuitry to function incorrectly, erratically or improperly.

3. Noise can also result in a less efficient system. Figure represents the communication system with associated noise at various stages.



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Classification of Noise:

Noise can be divided into two general categories:

1. Uncorrelated Noise: noise present regardless of whether there is a signal present or not. 2. Correlated Noise: noise present as a direct result of a signal. Mutually related to the

signal and cannot be present in circuit unless there is an input signal and is produced by

non-linear amplification. No signal, no noise.

Types of Uncorrelated Noise:

1. External Noise:

Noise present in the received radio signal that has been introduced in the communication medium.

Noise generated outside the device or outside the receiver.

2. Internal Noise:

Noise produced by active and passive devices in the receiver. Noise generated within the device or within the receiver.



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Types of External Noise:

1. Man-Made / Industrial Noise:

Produced by spark-producing mechanism such as commutators in electric motors, automobile ignition system, power switching equipment, fluorescent and gas filled

lamps.

Produced by any equipment that causes high voltages or currents to be abruptly switched. This noise is called impulse noise.

Noise in DC power supply such as AC ripple. Noise in AC power line such as surges of currents and voltage. Noise introduced by nearby communication system. In general, Man-made/Industrial noises are form of electromagnetic interference that

can be traces to non-natural causes.

Industrial noise frequency is between 15 to 160MHz, and it can extend to 500MHz.

2. Atmospheric Noise:

Noise caused by naturally occurring disturbances in the Earths atmosphere, such as static caused by lightning and thunderstorm.

It has a great impact on signals at frequencies less than 30MHz. Form of interference caused by rain, hail or snow is called precipitation static.

3. Extraterrestrial / Space Noise:

Noise coming from outer space due to sun, stars, distant planet and other celestial bodies.

Noise caused by the sun is called solar noise. It is cyclical and reaches a very annoying peak every 11 years.

Noise caused by stars, distant planet and other celestial objects is called cosmic noise. It has great impact on signals with frequencies beginning at approximately 8 MHz

and extends out to 1.43 GHz and beyond.

Types of Correlated Noise:

1. Harmonic Distortion: Unwanted multiples of a single frequency sine wave that are created

when sine wave is amplified in a non-linear device, such as large signal amplifier.

2. Intermodulation Interference: Unwanted cross-product (sum & difference) frequencies

created when two or more signals are amplified in non- linear device.



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Types of Internal Noise:

Shot Noise:

Shot noise is produced by random movement of electrons or holes across a amplifying

device due to discontinuities.

The shot noise is produced due to shot effect. Due to the shot effect, shot noise is

produced in all the amplifying devices rather in all the active devices.

It appears as a randomly varying noise current superimposed on the output.

The shot noise "sounds" like a shower of lead shots falling on a metal sheet.

The shot noise has a uniform spectral density like thermal noise. The exact formula for

the shot noise can be obtained only for diodes.

For all other devices an approximate equation is stated. The mean square shot noise

current for a diode is given as,

-------- (1)

Here,

I = direct current across the junction (in amp)

Io = reverse saturation current (in amp)

q = electron charge = 1.6 x 10-19

C.

B = effective noise bandwidth in Hz.

For the amplifying devices the shot noise is:

1. Inversely proportional to the transconductance of the device.

2. Directly proportional to the output current.

Low Frequency or Flicker Noise:

The flicker noise will appear at frequencies below a few kilohertz. It is sometimes called

as 1/f noise.

The power spectral density of this noise increases as the frequency decreases.

In the semiconductor devices, the flicker noise is generated due to the fluctuations in the

carrier density. These fluctuations in the carrier density will cause the fluctuations in the

conductivity of the material.

This will produce a fluctuating voltage drop when a direct current flows through a device.

This fluctuating voltage is called as flicker noise voltage.

The mean square value of flicker noise voltage is proportional to the square of direct

current flowing through the device.



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It is proportional to emitter current and junction temperature, inversely proportional to

frequency.

High Frequency or Transit Time Noise:

If the time taken by an electron to travel from the emitter to the collector of a transistor

becomes comparable to the period of the signal which is being amplified then the transit

time effect takes place.

This effect is observed at very high frequencies. Due to the transit time effect some of the

carriers may diffuse back to the emitter. This gives rise to an input admittance, the

conductance component of which increases with frequency.

The minute currents induced in the input of the device by the random fluctuations in the

output current, will create random noise at high frequencies.

This process gives rise to an admittance in which the conductance component increases

with frequency. This conductance has a noise current source which is associated with it in

parallel.

This conductance increases with frequency, the power spectral density increase.

Once this noise appears, it goes on increasing with frequency at a rate of 6 dB per octave.

Partition Noise:

This noise is generated when the current gets divided between two or more paths.

It is generated due to the random fluctuation in the current divisions.

This type of noise is higher in transistor as compared to the diode.

Thermal Noise or Johnson Noise:

Also known as White noise or Johnson noise.

It is a random noise which is generated in a resistor or the resistive component of the

complex impedance due to the rapid and random motion of the molecules, atoms and

electrons.

The free electrons within a conductor are always in random motion. This random motion

is due to the thermal energy received by them. The distribution of these free electrons

within a conductor at a given instant of time is not uniform.

It is possible that an excess number of electrons may appear at one end or the other of the

conductor. The average voltage resulting from this non-uniform distribution is zero but

the average power is not zero. As this power results from the thermal energy, it is called

as the "thermal noise power".



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According to the kinetic theory of thermodynamics, the temperature of a particle denotes its internal kinetic energy. This means that the temperature of a body expresses the rms

value of the velocity of motion of the particles in body.

As per this kinetic theory, the kinetic energy of these particles becomes approximately zero (i.e. velocity) at absolute zero.

Therefore, the noise power produced in a resistor is proportional to its absolute temperature. Also the noise power is proportional to the bandwidth over which the noise

is measured.

Therefore the expression for maximum noise power output of a resistor may be given as

----------------- (1)

Here, k = Boltzmanns constant = 1.38 X 10-23 Joule/Kelvin

T = Temperature of the conductor in o Kelvin

B = Bandwidth of interest in Hz.

Equation (1) indicates that a conductor operated at a finite temperature can work as a generator of electrical energy.

The thermal noise power Pn is proportional to the noise BW and conductor temperature.

Voltage and Current Models of a Noisy Resistor:

If we connect a DC voltmeter across any given resistor at room temperature i.e. 27oC (or 300K), then no voltage is displayed by the dc voltmeter. However, if a sensitive

electronic voltmeter is used, then it displays some reading.

This happens because of the fact that every resistor may be treated as a noise generator so a sufficiently large voltage may develop across it.

The noise voltage generated is always random and thus it has zero dc value but a definite RMS value. Therefore only an AC meter across the resistor would register a value. This

noise voltage is produced by the random movement of electrons within the resistor

constituting a current.

When measured over a long period of a time, as many electrons arrive at one end of the resistor as at the other. But, at any particular instant of time, this principle does not hold

good i.e. more electrons arrive at one end than at the other due to their random

movement. This means that the rate of arrival of electrons at either end of the resistor will



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vary randomly and there the potential difference between the two ends will also vary

randomly.

This random voltage across the resistor can be both measured and calculated. The random noise voltage is always expressed in terms of RMS value rather than instantaneous value.

Now, we can draw an equivalent circuit of a resistor as a noise voltage genera as shown in figure below. This equivalent circuit is also called as voltage model of a Noisy

resistor.

From this equivalent circuit, we can compute the resistor's equivalent noise voltage Vn. Let us consider that a noiseless load resistor RL, is connected across the noise generator

as shown in figure.

According to maximum power transfer theorem, for maximum transfer of power from noise voltage source Vn to load resistor RL, we must have

----------- (1)

Then the maximum noise power so transferred will be given as

Applying voltage-divider method in figure, we get

Thus,



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------------ (2)

But, , thus

----------- (3)

We may conclude that the square of the RMS noise voltage associated with a resistor is proportional to the absolute temperature T of resistor, value R of the resistor and the

bandwidth B over which noise is being measured.

At this point, it may be noted that the noise voltage is independent of the frequency at which it is measured. This happens because of the fact that this noise is random and so on

an average is evenly distributed over the frequency spectrum.

Norton's theorem may be used to find an equivalent current generator as shown in figure below. This equivalent current generator is called as current model of a noisy resistor.

Using conductance G = 1/R , the RMS noise current In for current model of a noisy resistor will be expressed as

------------- (4)



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Thermal Noise Due to Several Sources (Resistors):

Resistors in Series:

The resistors act as the sources of thermal noise. We shall see the effect of connecting two noise sources i.e. two resistors in series with

each other. The situation is as shown in Figures (a) and (b) as shown above. The two

resistances R1 and R2 are replaced by the voltage source equivalent circuits.

Since the two resistors are in series they can be replaced by a resistance R = R1 + R2. The noise voltage generated by the resistor R is given by,

------------- (1)

---------- (2)

Using the same logic if a number of resistors are connected in series then the resultant noise voltage is given by

----------- (3)

Thus, the effective resistance R is given as,

------------- (4)



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Resistors in Parallel:

For the parallel connection of the resistors R1 and R2 the current (Norton) equivalent circuits should be used. The equivalent circuits are as shown in the Figures (a) and (b)

below.

As the two conductances G1 and G2 are in parallel, the effective value of conductance is given by Gp = G1+G2.

The noise current generated by the conductance Gp is given as,

---------- (1)

---------- (2)

Using the same logic if a number of resistors are connected in parallel then the resultant noise voltage is given by

----------- (3)

If it is required to obtain the voltage generator equivalent circuit for parallel connection of the resistors then the equivalent parallel resistance Rp is given as,

------- (4)

Thus,

------- (5)



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White Noise:

Noise in an idealized form is known as white noise. Thus, in a communication system, the noise analysis is based on an idealized form of noise, i.e., white noise.

As white light consists of all colure frequencies, in the same manner, white noise contains all frequencies in equal amount.

The power density spectrum of a white noise is independent of frequency. This means that white noise consists of all the frequency components in equal amount.

If the probability of occurrence of a white noise is specified by a Gaussian distribution function, it is called as white Gaussian Noise.

Since the power density spectrum of thermal and shot noise is independent of the operating frequencies, therefore, shot noise and thermal noise can be treated as white

Gaussian Noise for all practical purposes.

The power spectrum density of white noise is expressed as,

-------- (1)

Here, the factor 1/2 has been included to show that half of the power is associated with the positive frequencies and remaining half with the negative frequencies. This has been

shown in figure below.

The power spectrum density of white noise shown in figure above reveals the fact that it has no dc power, i.e., the mean or average value of white noise is zero. In addition to this,

the auto-correlation function of the power spectrum density of white noise may be

obtained by simply taking the inverse Fourier transform of both sides of expression

The power spectral density and auto correlation function form a Fourier transform pair,



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Above is the expression for the auto correlation function of white noise. The auto correlation function can is plotted below

Noise Equivalent Bandwidth:

Consider a white noise present at the input of a receiver. Let the filter have a transfer function H(f) as shown in Figure below.

The filter above is being used to reduce the noise power actually passed on to the receiver. Now consider an ideal (rectangular) filter as shown by the dotted plot in Figure

above. The center frequency of this ideal filter also is fo.

Let the bandwidth "BN" of the ideal filler be adjusted in such a way that the noise output power of the ideal filter is exactly equal to the noise output power of a real R-C filter.

Then BN is called as the noise bandwidth of the real filter.



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Noise bandwidth "BN" is defined as the bandwidth of an ideal (rectangular) filter which passes the same noise power as does the real filter.

Consider a passive filter having voltage-ratio transfer function H() as shown in the figure below,

The input noise spectral density is give as,

------ (1)

Then output noise spectral density Sno is given as,

-------- (2)

Scenario: Consider a passive RC low pass filter shown below for this we shall fine: 1. Total noise power at output

2. Effective noise bandwidth

3. RMS noise voltage

The transfer function foe this LPF is given below,

------- (3)



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-------- (4)

Here,

Substituting in equation (2) we get,

--------- (5)

The total noise power at the output is obtained by integrating Sno over the complete frequency spectrum, i.e., from 0 to ,

Substituting then thus,



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Thus, total noise power at the output is,

------- (6)

Maximum noise power at the output is,

-------- (7)

Comparing equations (6) and (7) effective noise bandwidth is given as,

------- (8)

RMS noise voltage is given as,

--------- (9)

The capacitance C will not contribute to the noise and will limit the RMS noise voltage.

Narrowband Noise:

Definition: When in a narrow bandpass filters centre frequency is much greater than the

bandwidth. The noise process appearing at the output of such a filter is called narrowband

noise.

The spectral component of the narrowband noise concentrated about some midband

frequency fc as in the figure (a) below, the sample function n(t) of such a process

appears somewhat similar to a sine wave f frequency fc, undulates (Move in a wavy

pattern or with a rising and falling motion) slowly in both amplitude and phase as shown

in figure (b) below.



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To analyze the effect of narrowband noise on the performance of a communication system based on the application there are two specific representation of narrowband

noise:

1. The narrowband noise is defined in terms of a pair of components called in-phase and quadrature components.

2. The narrowband noise is defined in terms of a pair of components called the envelope and phase.

Representation of Narrowband Noise in Terms of In-Phase and Quadrature Components:

Consider a narrowband noise n(t) of bandwidth 2B centered on frequency f, as shown in Figure below,

Narrowband noise n(t) represented in canonical form as,

------- (1)

Here, = in-phase component of n(t)

= quadrature component of n(t).



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Both nI(t) and nQ(t) are low-pass signals. Given the narrowband noise n(t), we may extract its in-phase and quadrature components

using the scheme shown in Figure below. It is assumed that the two low-pass filters used

in this scheme are ideal, each having a bandwidth equal to B (i.e., one-half the bandwidth

of the narrowband noise n(t)).

This Scheme is known as narrowband noise analyzer.

We can directly generate the narrowband noise n(t), given its in-phase and quadrature components, as shown in Figure below.

This scheme is known as narrowband noise synthesizer.



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Properties of Inphase and Quadrature components of a Narrowband Noise:

1. The in-phase component nI(t) and quadrature component nQ(t) of narrowband noise n(t) have zero mean.

2. If the narrowband noise n(t) is Gaussian, then its in-phase component nI(t) and quadrature component nQ(t) are jointly Gaussian.

3. If the narrowband noise n(t) is stationary, then its in-phase component nI(t) and quadrature component nQ(t) are jointly stationary.

4. Both the in-phase component nI(t) and quadrature component nQ(t) have the same power spectral density.

5. The in-phase component nI(t) and quadrature component nQ(t) have the same variance as the narrowband noise n(t).

6. The cross-spectral density of the in-phase and quadrature components of narrow-band noise n(t) is purely imaginary.

7. If the narrowband noise n(t) is Gaussian and its power spectral density Sn(t) is symmetric about the mid-band frequency fc, then the in-phase component nI(t) and quadrature

component nQ(t) are statistically independent.

Noise Factor:

It is defined as the ratio of the signal to noise power ratio supplied to the input terminals of a receiver or amplifier to the signal to noise power ratio supplied to the output or load

resistor.

It is denoted by F and is given as,

------------- (1)

Here, Psi and Pni = Signal and noise power at the input

Pso and Pno = Signal and noise power at the output.



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The temperature to calculate the noise power is assumed to be the room temperature. The S/N at the input will always be greater than that at the output. This is due to the noise

added by the amplifier. Therefore the noise factor is the means to measure the amount of

noise added and it will always be greater than one. The ideal value of the noise factor is

unity.

The noise factor F is sometimes frequency dependent. Then its value determined at one frequency is known as the spot nose factor and the frequency must be stated along with

the spot noise factor.

Noise Output Power in Terms of F:

Noise factor is given as,

---------- (1)

The available power gain is defined as,

---------- (2)

Substituting equation (2) in (1)

Thus noise power at the amplifier output is given by,

--------- (4)

But and noise factor is determined at room temperature. Therefore substitute To in the equation for Pni.

Thus, ------------ (3)

Thus with increase in the noise factor F, the noise power at the output will increase. Higher the noise factor value is more will be noise contributed by the amplifier.



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Noise Figure:

Often the noise factor is expressed in decibels. When noise factor is expressed in decibels it is called noise figure.

-------- (1)

The ideal value of noise figure is 0 dB.

Noise Temperature:

The equivalent noise temperature is another way of measuring noise alternative to noise figure or noise factor.

The equivalent noise temperature is used in dealing with the UHF and microwave low noise antennas, receivers or devices.

Definition: The temperature at which the noisy resistor has to be maintained so that by connecting this resistor to the input of a noiseless version of the system, it will produce

the same amount of noise power at the system output as that produced by the actual

system.

Equivalent Noise Temperature Teq at Amplifier Input:

The noise at the input of the amplifier input is given as,

---------- (1)

If Teq represent the equivalent noise temperature representing the noise power then,

--------- (2)

Substituting equation (2) in (1) we get,



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--------- (3)

Cascade Connection of Two Port Networks:

In practice the filters or amplifiers are not used in isolated manner. They are used in the cascaded manner.

Noise Factor of Amplifiers in Cascade(Friiss Formula):

In the communication systems many a times the amplifiers or other stages are connected in the cascade connection.

The overall noise factor of such cascade connection can be determined as follows the figure below shows two amplifiers connected in cascade.

Let the power gains of the two amplifiers be G1 and G2 respectively and let their noise factors be F1 and F2 respectively.

The total noise power at the input of the first amplifier is given as,

----------- (1)

The total noise power at the output of amplifier 1 will be the addition of two terms. i.e,

The first term represents the amplified noise power (by G1) and the second term represents the noise contributed by the second amplifier.



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The noise power at the output of the second amplifier is G2 times the input noise power to amplifier 2.

--------- (2)

The overall gain of the cascade connection is given by,

--------- (3)

The overall noise factor F is defined as follows:

------------- (4)

Here Thus,

------------ (5)

The same logic can be extended for more number of amplifiers connected in cascade. Then the expression for overall noise factor F would be,

-------- (6)

This formula is known as the Friiss formula.

Equivalent Noise Temperature of Amplifiers in Cascade:

The Friiss formula derived for the overall noise factor can be written in terms of the overall noise temperature as follows:

Friiss formula is give by,

------- (1)



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Subtracting 1 on both sides of the equation we get,

------ (2)

But

, thus

------- (3)

Here Teq1, Teq2 etc are the noise temperatures of amplifiers 1, 2 etc.

Noise Factor of a Lossy Network:

Connecting cable is a good example of a lossy network. When a signal source is matched through such a connecting cable (lossy network), the

signal power reduces due to insertion loss of the network.

But the output noise remains constant equal to kTB because the noise power does not depend on the source resistance.

Thus a network attenuates the source noise and adds its own noise. The signal to noise ratio at the output is therefore lower than that at the input of the network. The noise factor

of such a network is given by,

--------- (1)

Consider a lossy network such as a connecting cable is connected to an amplifier as shown in Figuere below,



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The power gain of a lossy network is (1 / L). The noise factor of the overall combination is given by,

------- (2)

Here, Fnw = Noise factor of the lossy network

Fa = Noise factor of the amplifier

Gnw = Gain of the lossy network.

But Gnw = 1 / L and Fnw = L, Substituting these values in (2) we get,

------- (3)

If the lossy network is connected after the amplifier as shown in Figure (b), then the overall noise figure at the input is given by

As Fnw = L, Substituting these value in above equation we get,

---------- (4)

In this expression, we can neglect the second term if the amplifier power gain Ga is very large. Then,

------ (5)

That means the overall noise factor is equal to the noise factor of the high gain amplifier.



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Problems:

1. A noise generator using diode is required to produce 15V noise voltage in a receiver which

has an input impedance of 75. The receiver has a noise power bandwidth of 200 kHz. Find the

current through the diode.

Solution:

Given: Vn=15V, R=75, B=200 kHz

Current through the diode is given by,

Neglecting Io in above equation we get

------- (1)

Calculating the noise current

Now substituting In in equation (1)

2. A receiver has a noise power bandwidth of 12 kHz. A resistor which matches with the receiver

input impedance is connected across the antennas terminals. What is the noise power contributed

by this receiver bandwidth? Assume temperature to be 300 C.

Solution:

Given: B=12 kHz, T=300 C=30+273=303

0K

Noise power contributed by the receiver is,

3. A 600 resistor is connected across a 600 antenna input of a radio receiver. The bandwidth

of the radio receiver is 20 kHz and the resistor is at room temperature of 270 C. Calculate the

noise power and the noise voltage applied at the input of the receiver.

Solution:



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Given: R1=600 , R2=600 , B=20 kHz, T=270 C=27+273=3000K

As two resistors are in series thus,

Noise power is given as,

Noise voltage applied at the input of the receiver:

4. Two resistors 28 k and 51 k are at room temperature T = 290o Kelvin. Calculate for a

bandwidth of 100 kHz, the mean square value and RMS value of thermal noise voltage:

a. For each resistor b. For two resistors in series and c. For two resistors in parallel

Solution:

Given: R1=28 k, R2=51 k, T=290o Kelvin, B=100 kHz

a. the mean square value of thermal noise voltage for each resistors

R1=28 k

R2=51 k



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RMS value of thermal noise voltage for each resistor:

R1=28 k

R2=51 k

b. For two resistors in series the mean square value of thermal noise voltage:

or two resistors in series the RMS value of thermal noise voltage:

c. For two resistors in parallel the Resistance is:

For two resistors in parallel the mean square value of thermal noise voltage:



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For two resistors in parallel the RMS value of thermal noise voltage:

5. An amplifier is fed from a 100 , 15 V RMS sinusoidal signal source. Its equivalent input

noise resistance and equivalent input current are 250 and 6 A, respectively. Calculate the

individual noise voltages at the input and the input SNR. Assume noise bandwidth is 10MHz and

temperature is 30oC.

Solution:

Given: Rs=100 , Vs=15 V, Ran=250 , Ia=6 A, B=10MHz, T=273+30=303oK

Noise voltage due signal source:

Noise voltage due Amplifier noise:

Noise voltage due input shot noise current:

Expression for shot noise current is:



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Shot noise voltage is given as:

Total noise voltage at the input of the amplifier:

The Signal-to-noise ratio in desibles is:

6. The signal power and noise power measured at the input of an amplifier are 150 W and 1.5

W respectively. If the signal power at the output 1.5 W and noise power is 40 mW, Calculate

the amplifier noise factor and noise figure.

Solution:

Given: Psi= 150 W, Pni=1.5 W, Pso= 1.5 W, Pno=40 mW



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7. An Amplifier has a noise figure of 3 dB. Calculate its equivalent noise temperature.

Solution:

Equivalent noise temperature is,

8. A mixer stage has a noise figure of 20 dB and it is preceded by another amplifier with a noise

figure of 9 dB and an available power gain of 15 dB. Calculate the overall noise figure referred

to the input.

Solution:

The system can be represented as below

Input Output

Expression for overall noise figure for two stage cascade is,

------ (1)

First we shall convert dB into equivalent power ratios,

F1= 9 dB 9=10 log F1 F1=Antilog (0.9) F1=7.94 F2= 20 dB 20 =10 log F2 F2= Antilog (2) F2=100 G1=15 dB 15=10 log G1 G1= Antilog (1.5) G1=31.62

Thus Over all noise factor is,

Mixer

F1= 9 dB, G1= 15 dB

Amplifier

F2= 20 dB



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Overall noise figure is,

9. An amplifier with 10 dB noise figure and 4 dB power gain is cascaded with a second amplifier

which has a 10 dB power gain. What is the overall noise figure and power gain?

Solution:

The system can be represented as below

Input Output

Expression for overall noise figure for two stage cascade is,

------ (1)

First we shall convert dB into equivalent power ratios,

F1= 10 dB 10=10 log F1 F1=Antilog (1) F1=10 F2= 10 dB 10 =10 log F2 F2= Antilog (1) F2=10 G1=4 dB 4=10 log G1 G1= Antilog (0.4) G1=2.5 G2=10 dB 4=10 log G2 G2= Antilog (0.4) G2=10

Thus Over all noise factor is,

1st Amplifier

F1=10 dB, G1=4 dB

1st Amplifier

F2=10 dB, G2=10 dB



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h G P

Overall noise figure is,

Overall power gain,

10. Figure below shows a typical microwave receiver used in satellite communication.

Determine:

a. The overall noise figure of the receiver. b. The overall equivalent temperature of the receiver.

Assume the ambient temperature T = 17 C.

Solution:

To=17+273=290o K

Evaluation of master amplifiers noise figure:

The overall noise figure of the receiver:

Expression for noise factor is,



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dathes

h G P

a. Expression for noise figure is,

b. The overall equivalent temperature of the receiver is,

11. In TV receiver, the antenna is often mounted on a tall mast and a long loss-cable is used to

connect the antenna to the receiver. To overcome the effect of lossy-cable, a pre-amplifier is

mounted on the antenna as shown in Figure below.

a. Find the overall noise figure of the system. b. Find the overall noise figure of the system if the pre-amplifier is omitted and the gain of

the front-end is increased by 20 dB [Assume, F = 16 dB for the front end].

Solution:

First we shall convert Noise figures into equivalent noise factors,

F1= 6 dB 6=10 log F1 F1=Antilog (0.6) F1=3.981 F2=L2= 3 dB 3 =10 log F2 F2= Antilog (0.3) F2= L2=2 F3=16 dB 16=10 log F3 F3= Antilog (1.6) F3=39.81 G1=20 dB 20=10 log G1 G1= Antilog (2) G1=100 G3=60 dB 60=10 log G3 G3= Antilog (6) G1=1x106

a. Overall noise factor of the system:

------- (1)

As



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dathes

h G P

Thus Substituting F2 in equation (2) we get,

Overall noise figure of the system:

b. overall noise figure of the system if the pre-amplifier is omitted and the gain of the front-

end is increased by 20 dB,

Overall noise figure of the system:

12. A satellite receiving system consists of a Low Noise Amplifier (LNA) that has a gain of 47

dB and a noise temperature of 120o K, a cable with a loss of 6.5 dB and the main receiver with a

noise factor of 7 dB. Calculate the equivalent noise temperature of the overall system referred to

the input for the following system connections.

a. LNA at the input followed by the cable connecting to the main receiver. b. The input direct to the cable which then connected to the LNA, which in turn is

connected to the main receiver.

Solution:

The system setup for (a) can be represented as below,

F2 = Lcable

LNA

G1 = 47 dB, Te1 = 120o K

Main Receiver

F3 = 7 dB



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L = 6.5 dB

First we shall convert Noise figures into equivalent noise factors,

L= 6.5 dB 6.5 =10 log L L = Antilog (0.65) L =4.4668 F3=7 dB 7=10 log F3 F3= Antilog (0.7) F3=5.0118 G1=47 dB 47=10 log G1 G1= Antilog (4.7) G1=50.118x103

Given Te1 = 120o K and assuming T0= 17

o C=290

o K

We know that,

Noise Factor of a Lossy Network is,

Overall noise factor of the system:

The overall equivalent temperature is,

The system setup for (b) can be represented as below,

Input Cable

Overall LNA

G1 = 47 dB, Te1 = 120o K

Main Receiver

F3 = 7 dB



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h G P

L = 6.5 dB Amplifier

The LNA and main receiver can be considered to be equivalent of Single amplifier.

The overall factor at the system input due to lossy nature is given as,

-------- (1)

Here Fa=Noise factor of overall amplifier Thus,

-------- (2)

But F1 is unknown is determined as,

Substituting F1 in (2) we get,

Thus, Substituting Fa in (1) we get,

The overall equivalent temperature is,



Raghu

dathes

h G P



Raghu

dathes

h G P



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h GP

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