UNIT III – NOISE THEORY
PART-A
1. Define Shot noise. NOV/DEC 2005PART-A
The noise caused by random fluctuations in the motion of charge carriers in a conductor.
2. What is White noise? NOV/DEC 2007, 2010
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.
3. Define Noise equivalent Bandwidth. MAY/JUNE 2008
The noise equivalent bandwidth of the filter is defined as the bandwidth of an ideal filter at which the noise power passed by real filter and ideal filter is same.
4. Define Thermal noise. NOV/DEC 2006, 2008, 2009
Thermal noise is the name given to the electrical noise arising from the random motion of Electrons in a conductor.
5. Define Noise Figure. NOV/DEC 2003
It is defined as the ratio of input signal to noise ratio to the output signal to noise ratio.
F = Input (s/n) / output (s/n).
6. Define Noise Temperature. NOV/DEC 2010
The available noise power is directly proportional to temperature and it is independent of value of resistance. This power specified in terms of temperatures is called as noise temperature.
7. Give the expression for noise voltage in a resistor. NOV/DEC 2006, 2008
The mean –square value of thermal noise voltage is given by
Vn2 = 4 K T B R
K – Boltz man constant
R – resistance
T – absolute temperature
B – Bandwidth
8. What is partition Noise? APRIL / MAY 2008
In an electron tube having one or more positive grids, this noise is caused by irratic partition of the cathode current among the positive electrodes. In a transistor, the partition noise is created. From the random fluctuation in the division of current between the collector and base.
9. Define a random variable? NOV / DEC 2012
Random variable is defined as a rule or mapping from the original sample space to a numerical sample space subjected to certain constraints. Random variable is also defined as a function where domain is the set of outcomes ωεs and whose range is R, is the real line.
10. What is meant by figure of merit of a receiver? NOV / DEC 2006
The ratios of output signal to noise ratio to channel signal to noise ratio is called figure of merit.
Figure of Merit = (SNR) o / (SNR) c = (So/No) / (Si/nNi)
11. Find the thermal noise voltage developed across a resistor of 700Ω. The bandwidth of the measuring instrument is 7MHz and the ambient temperature is 27oC. NOV /DEC 2005
Here R = 700Ω, B = 7 MHz
T = 27 + 273 = 300oK , k = 1.38 x 10-23 J/K
En =
En=
En = 9µV
12. Define Noise factor. NOV /DEC 2008
Noise factor is defined as the ratio of signal to noise power ratio at the input to signal to noise power ratio at the output i.e.
F =
13. Mention the characteristics of white noise. NOV /DEC 2009
• White noise contains all frequency components in equal proportion.
• White noise contains frequencies from -∞ to +∞
• Any two samples of white noise are totally uncorrelated.
14. Give the definitions of noise equivalent temperature. MAY / JUNE 2012
Noise equivalent temperature 0 is the amount of incident signal temperature that would be needed to match the internal noise of the detector such that signal to noise ratio equal to one.
15. When a random process is called deterministic? APRIL / MAY 2010
A process is called deterministic, if the future values of any sample function can be predicted from past values.
Example: consider the random process x(t) = A cos ( t). 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.
16. A receiver connected with an antenna of resistance of 50Ω has an equivalent noise of 30Ω. Find the receiver noise figure. APRIL / MAY 2010
Ra = 50Ω R’eq = 30Ω
Noise figure F = 1 +
F = 1 + = 1.6
17. Two resistors of 20 kΩ, 50 kΩ are at room temperature (290k), for a bandwidth of 100 KHz, calculate the thermal noise voltage generated by the two resistors in series. NOV / DEC 2011
= 4kT∆fReq
= 4 x 1.38 x 10-23 x 290 x 100 x 103 x 70 x 103 = 10.58 µV
Req = R1 + R2
18. What is narrow band noise? NOV / DEC 2009
In most communication systems we are often dealing with band-pass filtering of Signals. The bandpass filters have narrow bandwidths in the sense that bandwidth is small as compared to center frequency. We refer output of this kind of band pass filter as narrow band noise.
19. Draw the Autocorrelation function and power spectral density of white noise. APRIL / MAY 2010
Power spectral density Autocorrelation function
20. Write the Rayleigh probability density function. APRIL / MAY 2011
fR(r). fψ(ψ) = e – r2 / 2 .
21. Calculate noise figure and equivalent noise temperature for a receiver connected to an antenna whose resistance is 100Ω and equivalent noise resistance is 50Ω.
F = (1 + (Req / Ra)) = ( 1 + ( 50 / 100) ) = 1.5.
22. What is a random process?
A Random process X (s,t) is a function that maps each element of a samples space into a time function called sample function. Random process is a collection of time functions.
23. What is a stationary random process?
When the statistical properties of a process do not change with time, it is called Stationary process.
24. A receiver connected to an antenna of resistance of 15 Ω has an equivalent noise resistance of 30Ω. Find the receiver noise figure.
F = (1 + (Req / Ra)) = ( 1 + ( 30 / 15) ) = 3
25. Define probability.
The probability of occurrence of an event A is defined as,
P(A)= number of possible favorable outcomes
Total number of equal likely outcomes
26. What are mutually exclusive events?
Two possible outcomes of an experiment are defined as being mutually exclusive if the occurrence of one outcome precludes the occurrence of the other.
27. Define probability density function.
Probability density function is defined as fx(x) is defined in terms of cumulative distribution function Fx (x) as
fx(x) = d Fx (x)
dx
28. Define noise.
Noise is defined as any unwanted form of energy, which tends to interfere with proper reception and reproduction of wanted signal.
29. Give the classification of noise.
Noise is broadly classified into two types. They are External noise and internal noise.
30. What are the types of External noise?
External noise can be classified into
1. Atmospheric noise
2. Extraterrestrial noises
3. Man –made noises or industrial noises
31. What are types of internal noise?
Internal noise can be classified into
1. Thermal noise
2. Shot noise
3. Transit time noise
4. Miscellaneous internal noise
32. What are the types of extraterrestrial noise and write their origin?
o The two type of extraterrestrial noise are solar noise and cosmic noise
o Solar noise is the electrical noise emanating from the sun.
o Cosmic noise is the noise received from the center part of our galaxy, other distant galaxies and other virtual point sources.
33. Define transit time of a transistor.
Transit time is defined as the time taken by the electron to travel from emitter to the collector.
34. Define flicker noise.
Flicker noise is the one appearing in transistors operating at low audio frequencies. Flicker noise is proportional to the emitter current and junction temperature and inversely proportional to the frequency.
35. State the reasons for higher noise in mixers.
1. Conversion transconductance of mixers is much lower than the transconductance of amplifiers.
2. If image frequency rejection is inadequate, the noise associated with the image frequency Also gets accepted.
36. What is intermediate frequency?
Intermediate frequency (IF) is defined as the difference between the signal
frequency and the oscillator frequency.
IF = fs – fo when fs > fo (or)
IF = fo –fs when fo > fs
37. Give the expression for equivalent noise temperature in terms of hypothetical temperature.
The expression for equivalent noise temperature in terms of hypothetical
Temperature is Te = (F- 1) T0
Where, F is the noise figure and T0 absolute temperature.
38. Give the expression for noise voltage when several sources are cascaded.
Enr = Sqrt (4 KTB (R1 + R2 + …..))
Where R1, R2 --- are the resistances of the noise resistors.
K – Boltz man constant
T – Absolute temperature
B – Bandwidth
39. Define ensemble average.
The ensemble average of a random process X(t) are averages across the process.
Example: The mean of a random process X(t) at four fixed time tk is the expectation of the random variable X(tk).
40. Give the characteristics of shot noise.
• Shot noise is generated due to fluctuations in the number of electrons or holes.
• Shot noise has uniform spectral density
• Shot noise depends upon operating conditions of the device.
• Mean square noise current depends upon direct component of current.
41. What is the figure of merit of DSB-SC system?
The figure of merit of a DSB-SC system is 2.
42. What is the figure of merit of SSB-SC system?
The figure of merit of an SSB-SC system is 1
43. Write an expression for thermal noise generated in a resistor.
The expression for maximum noise power output of a resistor may be given as
Pn = KTnB
Where, Pn is the power, B is the total bandwidth is the Boltzmann constant,
Tn is the noise temperature.
44. Define atmospheric noise.
Atmospheric noise, which is also called static, is produced by lighting discharges in thunderstorms and other natural electrical disturbances which occur in the atmosphere.
45. Define Industrial noise
The industrial noise or manmade noise is that type of which is produced by such sources as automobiles and aircraft ignition, electrical motors, switch gears and leakages from high voltage transmission lines and several other heavy electrical equipments.
46. Define Transit time noise or high frequency noise.
• It is generally observed in semiconductor devices, when transit time of charge carriers crossing a junction is comparable with time period of the signal.
• Some charge carriers diffuse back the source, this process gives rise to the input admittance and it affects the conductance with increases in frequency. This conductance produces transit time noise.
47. Define Avalanche noise.
• The reverse bias characteristic of a diode shows a region where the reverse current increases rapidly with a slight increase in magnitude of the reverse bias voltage. This is voltage increase current also increases.
• This is because the holes and electrons in the depletion region gain sufficient energy from reverse bias to ionize atoms by collision. This collision provides spikes in current in avalanche region. This noise is called as avalanche noise.
48. Explain why thermal noise is also called as Johnson noise?
Thermal noise is also called as Johnson noise after the scientist J.B.Johnson who presented a detailed investigation of it.
49. What are the advantages of Gaussian process?
• Modeling as a Gaussian process makes analysis easier.
• Gaussian modeling is most suitable for random processes which are generated from physical phenomena.
• Experiments have confirmed the suitability of Gaussian model for random processes that are produced by physical phenomena.
50. Define Gaussian process.
The random process X(t) is said to be Gaussian distributed if every linear functional of X(t) is a Gaussian random variable.
51. Write the properties of Gaussian process.
• If input is Gaussian, output is also Gaussian
• Set of random variables obtained by sampling Gaussian process is jointly Gaussian
• Stationary Gaussian process is strictly stationary.
• Uncorrelated sample of Gaussian process are statistically independent.
52. Why thermal noise is sometimes called white noise?
The spectral density of the thermal noise is independent of frequency. Hence it is referred to as white noise. Hence it is referred to as white noise. If a noise contains all frequency components in equal proportion in 15 spectrums it is called white noise.
53. Define Random noise.
Random noise varies randomly with time. Identification of message signal at the receiver depends upon the amount of noise accompanied by the message during the process of communication. The presence of noise complicates the system of communication. The amount of noise power present in the received signal decides the minimum power level of the desired message signal at the transmitter.
54. Define narrowband noise.
Narrowband noise is defined as the output of a bandpass filters whose bandwidth B is very small compared to the center frequency fc, when B/fc approaches zero.
55. State the characteristics of narrowband noise.
When the ratio of bandwidth to center frequency is small but finite, narrow band noise looks very much like a wave but with slow and random amplitude and phase variations. The power spectrum of narrow band noise will have the same shape as the band pass filter.
56. What is meant by random experiment?
The mathematical technique for dealing with the result of an experiment, whose outcomes are not known in advance, is called random experiment i.e., an experiment whose outcome is not known in advance.
57. What is meant by sample space?
The set of all possible outcome of a random experiment is called sample space and is represented by an alphabet‘s’.
58. Define probability theory.
The chance of occurrence of something is probability. It occurs when we consider the possible outcome of an experiment whose result is not always same. If N times an experiment is repeated and the result A occurs N times then the relative chance of occurrence of A is NA/N.
PART – B
8 MARKS:
1. Write Short note on i) Shot Noise ii) Thermal Noise iii) white noise 8 MARKS:
(APRIL/MAY2006)
2. Derive the Friis Formula.
3. Write Notes on noise temperature, noise factor and noise figure. (MAY/JUNE 2006)
4. Discuss the Noise power spectral Density. (MAY/JUNE 2007)
5. What is meant by noise equivalent bandwidth? Illustrate it with a diagram.(NOV/DEC 2006)
6. Obtain the expression for the envelope and phase of the narrow band noise. (MAY/JUNE 2008)
7. How sine wave pulse noise is represented. Obtain the joint pdf of such noise component. (NOV/DEC 2007)
16 MARKS:
1. Explain how the various noises are generated and the method of representing them. (APRIL/MAY2004)
2. Derive the noise figure and equivalent noise temperature of cascaded stages. (NOV/DEC 2004)
3. Define Narrow band noise. List the properties of narrow band noise and give a brief explanation of each of them. (MAY/JUNE 2009)
4. Discuss the properties of the in-phase and quadrature components of narrow band noise. (MAY/JUNE 2008)
5. State and prove properties of a Gaussian process and central limit theorem (APRIL/MAY2011)
6. Derive the expression for RC low pass filter and ideal LPF.
7. Refer Class note - Problems
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