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Transcript of MAHALAKSHMI · o Shot noise consists of random fluctuations of the electric ... calculate the...
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 1
MAHALAKSHMI ENGINEERING COLLEGE
QUESTION BANK
DEPARTMENT: ECE SEMESTER: IV
SUBJECT CODE / Name: EC2252 – COMMUNICATION THEORY
UNIT-III NOISE THEORY
PART-A
1. What is the classification of random process? give one example for each
(AUC MAY 2006)
Stationary and Nonstationary random process
A random process whose statistical characteristics do not change with time
Random process X(t) and X(t+ε) have the same statistical properties In other words, time
translation of a sample function results in another sample function of the random process having
the same probability Example of stationary random process: noise If the statistical
characteristics depend on time, it is called nonstationary random processExample of
nonstationary random process: temperature
2. Define random process? (AUC NOV 2006)
An RV that is a function of time (or any other variable) is called a random process or stochastic
process. The collection of all possible waveform is known as ensemble of the random process
x(t).A waveform in the collection is called a sample function. Sample function amplitudes at
some instant are the values taken by the RV in various trials
3. Define noise figure (AUC MAY 2008)
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 2
It is simply defined as the ratio between input signal to noise ratio and output signal to noise
ratio. Noise figure of amplifier is defined as the ratio of the total noise density in
the load to the noise power density delivered to the load due to the source
4. What is white noise? (AUC MAY 2011) (AUC DEC 2010) (AUC MAY 2008)
Many types of noise sources are Gaussian and have flat spectral density over a wide
frequency range. Such spectrum has all frequency components in equal portion, and is
therefore called white noise. The power spectral density of white noise is independent of
the operating frequency.
And it is also defined as noise in idealized form is known as white noise. This means that
in a communication system, the noise analysis is based on an idealized form of noise, is
white noise.
5. Define noise equivalent bandwidth (AUC MAY 2008)
6. What is partition noise? (AUC MAY 2008)
It is generated whenever a current has to divide between two or more electrodes and
result from random fluctuation in the division. It would be expected therefore that a diode
would be less noisy than a transistor, if the third electrode draws current. For this
reason, the input stage of microwave receiver is often a diode circuit which has been
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 3
developed for low noise microwave amplification. The spectrum of the partition noise is
flat
7. Draw the auto correlation function and power spectral density of white noise.
(AUC MAY 2008)
8. Define noise factor (AUC NOV 2008)
S/ N at the input
Noise Factor F = _________________
S/ N at the output
S/N = Signal power / Noise Power
9. Define noise temperature (AUC MAY 2004)(AUC NOV 2008)
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 4
10. Calculate noise figure and equivalent noise temperature for a receiver connected to an
antenna whose resistance is 100Ω and equivalent noise resistance is 50Ω?
(AUC NOV 2008)
11. State central limit theorem. (AUC NOV 2008)
12. Give the characteristic of shot noise (AUC MAY 2009)
o Shot noise consists of random fluctuations of the electric current in electrical
conductors, which are caused by the fact that the current is carried by discrete
charges (electrons).
o The strength of this noise increases for growing magnitude of the average
current flowing through the conductor.
o Shot noise is to be distinguished from current fluctuations in equilibrium, which
happen without any applied voltage and without any average current flowing.
o These equilibrium current fluctuations are known as Johnson-Nyquist noise.
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 5
o Shot noise is important in electronics, telecommunication, and fundamental
physics.
o The strength of the current fluctuations can be expressed by giving the variance
of the current I, where <I> is the average ("macroscopic") current.
o However, the value measured in this way depends on the frequency range of
fluctuations
13. Define shot noise and thermal noise?(AUC MAY 2010)(AUC MAY 2009)
Shot noises arise in active devices due to random behaviour of charge carriers. In
electron tubes, shot noise is generated due to random emission of electrons from
cathodes, whereas in semiconductor devices shot noise is generated due to random
diffusion of minority carriers or simply random generation and recombination of electron-
hole pairs.
The thermal noise or white noise or Johnson noise is the random noise which is
generated in a resistor or the resistive component of complex impedance due to rapid
and random motion of the molecules, atoms and electrons.
14. A receiver connected to an antenna resistance of 50Ω has an equivalent noise
resistance of 30Ω. Find the receiver noise figure.(AUC MAY 2010)
Ra=50Ω,Req=30Ω
Noise Figure=1+req/Ra =1+30/15= 16
15. Define a random variable. Specify the sample space and the random variable for a
coin tossing experiment.(AUC DEC 2010)
Eg:Sample space-Head, Tail
Random variable : 1 for w=Head
0 for w=Tail
16. Write the Rayleigh and Rician probability density functions(AUC MAY 2011)
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 6
Let R is the random variable and r to represent the value assumed by the random
variable
The Rayleigh probability density function is defined by
: fR(r) = (r/σ2) e^ (-r2/2 σ2)
The raician distribution is useful for nalysis of carrier sinusoidal signal passing through
narrowband noisy channel.The Rician Distribution expressed as
17. When i s a random process called deterministic?(AUC DEC 2011) (AUC MAY 2010)
A process is called deterministic, if the futures value of any sample function can be
predicted from past values.
Eg: considered the random process x(t)=Acos (wt).In this the knowledge of the sample
function prior to any time instant automatically allows prediction of the future values of
the sample function since its form is known.
18. Two resistors of 20 KΩ, 50 KΩ are at room temperature (290 K). For a bandwidth
of 100 KHz, calculate the thermal noise voltage generated by the two resistors in series
E02=4KTΔfReq
=4*1.38*10-23*290*100*103*70*103
=10.58µV
19. Define random variable. Specify the sample space and the random variable for a coin
tossing experiment(AUC MAY 2012)
The functional relationship which is assigas a real number x(λ) to each possible
outcomes λ of a random experiment is called random variable.
Sample space =Head,Tail
20. Give the definition of the noise equivalent temperature(AUC MAY 2012)
It is the amount of incident signal temperature that would needed to match the internal
noise of the detector such that signal to noise ration is equal to one.
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 7
PART-B
1. Explain the following terms(i)Random variable (ii)Gaussian process(iii) Shot noise
(iv) Noise temperature (AUC NOV 2006)ii) Write a short note on shot noise and also
explain about power spectral density of shot noise. (8)(AUC MAY 2010) Discuss the type’s
causes and effects of various forms of noise created within a receiver? (AUC NOV
2008)
- In probability theory and statistics, a Gaussian process is a stochastic process whose
realizations consist of random values associated with every point in a range of times (or of space) such that each such random variable has a normal distribution.
- Moreover, every finite collection of those random variables has a multivariate normal distribution.
Gaussian processes are important in statistical modeling because of properties inherited from the normal distribution.
- For example, if a random process is modeled as a Gaussian process, the distributions of various derived quantities can be obtained explicitly.
- Such quantities include: the average value of the process over a range of times; the error in estimating the average using sample values at a small set of times.
A process is Gaussian if and only if for every finite set of indices t1, ..., tk in the index
set Tis a vector-valued Gaussian random variable. Using characteristic functions of
random variables, the Gaussian property can be formulated as follows: Xt ; t ∈ T is
Gaussian if and only if, for every finite set of indices t1, ..., tk, there are reals σl j with σi
i > 0 and reals μj
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 8
2. Explain the following terms (i)Thermal noise(ii)White noise(ii)Narrow band noise
(iv) Random noise (AUC NOV 2006) (ii) Write short notes on shot noise (6) (AUC MAY
2012) (ii)What causes thermal noise in a material? Write the expression for RMS values
of the noise.(AUC MAY 2012) What is thermal noise in communication? What are the
different types of noise? Explain. (ii) Write short notes on shot noise. (6)(AUC DEC
2010) (AUC MAY 2009)
THERMAL NOISE:
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 9
WHITE NOISE
Narrow band noise
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 11
3. Explain in detail about the white noise and filtered noise (AUC NOV 2008)
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 12
Flicker noise is the one appearing in transistors operating at low audio frequencies. Flicker noise is produced at low frequencies (below few KHz).This noise is also called as flicker noise (1/f noise).
4. Explain the following terms 1Statistical average, correlation, covariance and ergodicity?
ERGODICITY
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 14
5. Discuss the properties of Gaussian process? (AUC MAY 2008) State and prove four
properties of Gaussian process(AUC MAY 2011)
ergodicity
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 17
6. i) Determine the overall noise figure of a three stage cascade amplifier; each stage
having a power gain of 10dB and noise figure of 6dB?
7. i)Give a random process, X (t) = A cos(ωt+ θ), where Aandω a re constants and θ is a
uniform random variable. Show that X (t) is ergodic in both mean and autocorrelation. (8
8. (i) A mixer stage has a noise figure of 20 dB and this i s preceded by an amplifier that
has a noise figure of 9 dB and an available power gain of 15 dB. Calculate the overall
noise figure referred to the input. (8)
Noise figure of an amplifier F1=9dB
Noise figure of mixer F2=20dB
Available power gain of an amplifer A1=15db
F1= in ratio =Antilog10(9/10)=7.94
F2= in ratio =Antilog10(20/10)=100
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 18
A1= in ratio =Antilog10(15/10)=31.62
F=F1+f2-1/A1
F=7.99+100-1/31.62
=11.07
F= in dB= 10 log 10(Fratio)= 10 log 10(11.07)=1044dB
(ii) A receiver has a noise figure of 12 dB and it is fed by a low noise amplifier that has a
gain of 50 dB and a noise temperature of 90 K. Calculate the noise temperature of the
receiver and the overall noise temperature of the receiving system. Take room
temperature as 290 K. (8)(AUC DEC 2010)
Receiver noise figure F2=12dB
Amplifier gain G1=50dB
Amplifer noise figure Te1=900l
F2 in db = 10 log F1=12 =15.84
Similarly G1 in db = 50 db =100000
Noise temperature related to noise factor
Te2=(F2-1)T0
T0=290 0K
9. Consider two amplifiers are connected in cascade. First stage amplifier has gain and
noise figure as 10 dB and 2 dB. Second stage has noise figure of 3 dB.
(AUC MAY 2011)
Noise figure of first stage amplifier F1=2dB
Noise figure of second stage amplifier F2=3dB
Noise figure of first stage amplifier Ga=10dB
F=F1-F2-1/Ga =2+3-1/10 =2.2
10. State any 5 properties of autocorrelation function(10)
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 19
11. When is a random process said to be strict stationary (SSS), wide sense stationary(WSS)
and ergodicprocess (6)(AUC DEC 2011) (i)List the different type of random process and
give the definitions(10)
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 21
12. Explain Narrowband Noise. Show that a narrow band noise n(t) can be represented in
terms of its in phase and qudrature phase components. Write t he details about narrow
band noise and t he properties of quadrature components of narrowband noise.
(16)(AUC MAY 2010) ii) Discuss the properties of narrow band noise. (AUC MAY 2008)
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 23
13. Thermal noise from a measured as 4*10-17 W at a temperature of 200 C for a given
bandwidth. What will be the Noise power when temperature is changed to 500
(AUC DEC 2011)
Average noise power Pn=kTB
4*10-17=k(200)B---1
X= k(500)B---2
Divide eqn 1&2
X=10-16W
14. Write the definition, power spectral density and autocorrelation function for white noise and
narrow band noise(filtered white noise)(10)
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 24
15. (i)Derive the representation of narrow band noise in terms of envelop and phase
component and list out its properties (i)Derive the representation of narrow band noise in
terms of envelop and phase component and list out its properties
EC2252 – COMMUNICATION THEORY IV Sem ECE – R.Vanitha Asst.Prof./ECE Page 26
16. Explain in detail about Noise Equivalent Bandwidth