Antenna & Wave Propagation
ANTENNAS AND WAVE PROPAGATION
TWO MARK QUESTIONS
1. Define an antenna.
Antenna is a transition device or a
transducer between a guided wave and a free space wave
or vice versa. Antenna is also said to be an impedance
transforming device.
2. What is meant by radiation pattern?
Radiation pattern is the relative distribution
of radiated power as a function of distance in space .It is a
graph which shows the variation in actual field strength of
the EM wave at all points which are at equal distance from
the antenna. The energy radiated in a particular direction by
an antenna is measured in terms of FIELD STRENGTH.(E
Volts/m)
3. Define Radiation intensity?
The power radiated from an antenna per unit
solid angle is called the radiation intensity U (watts per
steradian or per square degree). The radiation intensity is
independent of distance.
4. Define Beam efficiency?
The total beam area ( WA) consists of the
main beam area ( WM ) plus the minor lobe area ( Wm) .
Thus WA = WM+ Wm .
The ratio of the main beam area to the total
beam area is called beam efficiency.
Beam efficiency = SM = WM / WA.
5.Define Directivity?
The directivity of an antenna is equal to the
ratio of the maximum power density P(q,f)max to its
average value over a sphere as observed in the far field
of an antenna.
D = P(q,f)max / P(q,f)av. Directivity from
Pattern.
D = 4p / WA. . Directivity from beam
area(WA ).
6.What are the different types of aperture.?
i) Effective aperture.
ii). Scattering aperture.
iii) Loss aperture.
iv) collecting aperture.
v). Physical aperture.
7.Define different types of aperture.?
Effective aperture(Ae).
It is the area over which the power is
extrated from the incident wave and delivered to the
load is called effective aperture.
Scattering aperture(As.)
It is the ratio of the reradiated power to
the power density of the incident wave.
Loss aperture. (Ae).
It is the area of the antenna which
dissipates power as heat.
Collecting aperture. (Ae).
It is the addition of above three
apertures.
Physical aperture. (Ap).
This aperture is a measure of the
physical size of the antenna.
8. Define Aperture efficiency?
The ratio of the effective aperture to
the physical aperture is the aperture efficiency. i.e
Aperture efficiency = hap = Ae / Ap
(dimensionless).
9. What is meant by effective height?
The effective height h of an antenna is the
parameter related to the aperture.It may be defined as
the ratio of the induced voltage to the incident field.i.e
H= V / E.
10. What are the field zone?
The fields around an antenna ay be divided into
two principal regions.
i. Near field zone (Fresnel zone)
ii. Far field zone (Fraunhofer zone)
11.What is meant by Polarization.?
The polarization of the radio wave can be defined by
direction in which the electric vector E is aligned during
the passage of atleast one full cycle.Also polarization can
also be defined the physical orientation of the radiated
electromagnetic waves in space.
The polarization are three types. They are
Elliptical polarization ,circular polarization and linear
polarization.
12. What is meant by front to back ratio.?
It is defined as the ratio of the power radiated in
desired direction to the power radiated in the opposite
direction. i.e
FBR = Power radiated in desired direction / power
radiated in the opposite direction.
13. Define antenna efficiency.?
The efficiency of an antenna is defined as the ratio
of power radiated to the total input power supplied to the
antenna.
Antenna efficiency = Power radiated / Total input
power
14. What is radiation resistance ?
The antenna is a radiating device in which power
is radiated into space in the form of electromagnetic
wave.
W’ = I2 R
Rr = W’/ I2
Where Rr is a fictitious resistance called called as
radiation resistance.
15 What is meant by antenna beam width?
Antenna beamwidth is a measure of directivity
of an antenna. Antenna beam width is an angular width in
degrees, measured on the radiation pattern (major lobe)
between points where the radiated power has fallen to
half its maximum value .This is called as “beam width”
between half power points or half power beam
width.(HPBW).
16. What is meant by reciprocity Theorem.?
If an e.m.f is applied to the terminals of an antenna
no.1 and the current measured at the terminals of the
another antenna no.2, then an equal current both in
amplitude and phase will be obtained at the terminal of
the antenna no.1 if the same emf is applied to the
terminals of antenna no.2.
17.What is meant by isotropic radiator?
A isotropic radiator is a fictitious radiator and is
defined as a radiator which radiates fields uniformly in all
directions. It is also called as isotropic source or omni
directional radiator or simply unipole.
18. Define gain
The ratio of maximum radiation intensity in
given direction to the maximum radiation intensity from a
reference antenna produced in the same direction with
same input power. i.e
Maximum radiation intensity
from test antenna
Gain (G) = --------------------------------------------------------
-----------------------
Maximum radiation intensity from the reference antenna
with same input power
19. Define self impedance
Self impedance of an antenna is defined as its
input impedance with all other antennas are completely
removed i.e away from it.
20 . Define mutual impedance
The presence of near by antenna no.2 induces a
current in the antenna no.1 indicates that presence of
antenna no.2 changes the impedance of the antenna
no.1.This effect is called mutual coupling and results in
mutual impedance.
21. What is meant by cross field.?
Normally the electric field E is perpendicular to the
direction of wave propagation. In some situation the
electric field E is parallel to the wave propagation that
condition is called Cross field.
22.Define axial ratio
The ratio of the major to the minor axes of the
polarization ellipse is called the Axial Ratio. (AR).
23. What is meant by Beam Area.?
The beam area or beam solid angle or WA of an
antenna is given by the normalized power pattern over a
sphere.
WA = ò ò4p Pn ( q,f ) dW
Where dW = Sin q d q .df
24. What is duality of antenna.?
It is defined as an antenna is a circuit device with
a resistance and temperature on the one hand and the
space device on the other with radiation patterns, beam
angle ,directivity gain and aperture.
25.State Poynting theorem.
It states that the vector product of electric field
intensity vector E and the magnetic filed intensity vector
H at any point is a measure of the rate of energy flow per
unit area at that point.The direction of power flow is
perpendicular to both the electric field and magnetic field
components.
26.What is point source?
It is the waves originate at a fictitious volumeless
emitter source at the center ‘O’ of the observation circle.
27.What is meant by array.?
An antenna is a system of similar antennas oriented
similarly to get greater directivity in a desired direction.
28.What is meant by uniform linear array.?
An array is linear when the elements of the array are
spaced equally along the straight line. If the elements are
fed with currents of equal magnitude and having a uniform
progressive phase shift along the line, then it is called
uniform linear array .
29.What are the types of array.?
a. Broad side array.
b. End fire array
c. Collinear array.
d. Parasitic array.
30.What is Broad side array.?
Broad side array is defined as an arrangement in
which the principal direction of radiation is perpendicular
to the array axis and also the plane containing the array
element. For Broad side array the phase difference EHWZHHQ DGMDFHQW HOHPHQW LV
31.Define End fire array.?
End fire array is defined as an arrangement in
which the principal direction of radiation is coincides with
the array axis. )RU HQG )LUH DUUD\ - G :KHUH $QG G GLVWDQFH EHWZHHQ WKH HOHPHQWV
32. What is collinear array.?
In this array the antenna elements are arranged
coaxially by mounting the elements end to end in straight
line or stacking them one over the other with radiation
pattern circular symmetry. Eg. Omnidirectional antenna.
33. What is Parasitic array.?
In this array the elements are fed parasitically to
reduce the problem of feed line. The power is given to one
element from that other elements get by electro magnetic
coupling.
Eg. Yagi uda antenna.
34. What is the condition on phase for the end fire array
with increased directivity.?
:KHQ - G SURGXFHV PD[LPXP ILHOG LQ WKH GLUHFWLRQ
= 0 but does not give the maximum directivity. It has
been shown by Hansen and woodyard that a large
directivity is obtained by increasing the phase change EHWZHHQ WKH VRXUFHV VR WKDW - G Q
This condition will be referred to as the condition for
increased directivity.
35.Define array factor.
The normalized value of the total field is given by, ( Q VLQ Q VLQ
The field is given by the expression E will be
referred to as array factor.
36. Define beam width of major lobe?
It is defined the angle between the first nulls (or) it
is defined as twice the angle between the first null and the
major lobe maximum direction.
37. List out the expression of beam width for broad side
array and end fire array.
For broad side array the expression for beam width
between the first nulls is given by,
BWFN = ((+/ - Q G
For End fire array the expression for beam width
between the first nulls is given by,
BWFN = ((+/ - Q G 1/ 2.
38. Differentiate broad side and End fire array.?
Broad side
array
End fire
array
1. Antennas fed in Phase
2. Maximum Radiation is
perpendicular
to the direction of array
axis.
3. Beam width of major
lobe is twice the
Antenna elements are fed of
out of Phase - G
Maximum Radiation is
directed along the array axis.
Beam width is greater than
that for a broad side array of
same length.
BW = ((+/ - Q G 1/
2
reciprocal of the array
length.
BW = ((+/ - Q G
2.
39.What is the need for the Binomial array.?
The need for a binomial array is
i). In uniform linear array as the array length is
increased to increase the directivity, the secondary lobes
also occurs.
ii) For certain applications, it is highly desirable
that secondary lobes should be eliminated completely or
reduced to minimum desirable level compared to main
lobes.
40. Define power pattern.?
Graphical representation of the radial
component of the pointing vector Sr at a constant radius as
a function of angle is called power density pattern or
power pattern.
41. What is meant by similar Point sources.?
Whenever the variation of the amplitude and the
phase of the field with respect to the absolute angle for any
two sources are same then they are called similar point
sources.
The maximum amplitudes of the individual
sources may be unequal.
42. What is meant by identical Point sources.?
Similar point sources with equal maximum
amplitudes are called identical point sources.
43. What is the principle of the pattern multiplication?
The total field pattern of an array of non
isotropic but similar sources is the product of the
i) individual source pattern and
ii) The array pattern of isotropic point sources each
located at the phase center of the individual
source having the same amplitude and phase.
While the total phase pattern is the sum of the phase
patterns of the individual source pattern and array pattern.0
44.What is the advantage of pattern multiplication? ™ Useful tool in designing antenna ™ It approximates the pattern of a complicated array
without making lengthy computations
45.What is tapering of arrays?
Tapering of array is a technique used for reduction
of unwanted side lobes .The amplitude of currents in the
linear array source is non-uniform; hence the central source
radiates more energy than the ends. Tapering is done from
center to end.
46.What is a binomial array?
It is an array in which the amplitudes of the
antenna elements in the array are arranged according to the
coefficients of the binomial series.
47.What are the advantages of binomial array?
Advantage: ™ No minor lobes
Disadvantages: ™ Increased beam width ™ Maintaining the large ratio of current
amplitude in large arrays is difficult
48.What is the difference between isotropic and nonisotropic
source ™ Isotropic source radiates energy in all
directions but non-isotropic source radiates
energy only in some desired directions. ™ Isotropic source is not physically realizable
but non-isotropic source is
physically realizable.
49.Define Side Lobe Ratio
Side Lobe Ratio is defined as the ratio of
power density in the principal or main lobe to the power
density of the longest minor lobe.
50. List the arrays used for array tapering ™ Binomial Array:Tapering follows the
coefficient of binomial series
™ Dolph Tchebycheff Array: Tapering follows
the coefficient of Tchebycheff polynomial
51.What is a Short Dipole?
Ans: A short dipole is one in which the field is
oscillating because of the oscillating voltage and current.It
is called so, because the length of the dipole is short and
the current is almost constant throughtout the entire length
of the dipole.It is also called as Hertzian Dipole which is a
hypothetical antenna and is defined as a short isolated
conductor carrying uniform alternating current.
52.How radiations are created from a short Dipole?
Ans:The dipole has two equal charges of
opposite sign oscillating up and down in a harmonic
motion.The charges will move towards each other and
electric filed lines were created.When the charges meet at
the midpoint, the field lines cut each other and new field
are created.This process is spontaneous and so more fields
are created around the antenna.This is how radiations are
obtained from a short dipole.(See Figure from John. D
.Kraus Book)
53.Why a short dipole is also called an elemental dipole?
A short dipole that does have a
uniform current will be known as the elemental dipole.Such
a dipole will generally be considerably shorter than the
tenth wave length maximum specified for a short
dipole.Elemental dipole is also called as elementary
dipole,elementary doublet and hertzian dipole.
54.What is a Infinitesimal Dipole?
When the length of the short dipole is
vanishingly small,then such a dipole is called a
infinitesimal dipole.If dl be the infinitesimally small length
and I be the current,then Idl is called as the current element.
55.Why a short dipole is called a oscillating dipole?
A short dipole is initially in neutral condition
and the moment a current starts to flow in one direction,one
half of the dipole require an excess of charge and the other
a deficit because a current is a flow of electrical
charge.Then ,there will be a voltage between the two halves
of the dipole.When the current changes its direction this
charge unbalance will cause oscillations.Hence an
oscillating current will result in an oscillating
voltage.Since,in such dipole,electric charge oscillates ,it
may be called as Oscilllating electric dipole.
56.What do you understand by retarded current?
Since,the short electric dipole is so
short,the current which is flowing through the dipole is
assumed to be constant throughtout its length.The effect of
this current is not felt instantaneous at a distance point only
after an interval equal to the time required for the wave to
propagate over the distance r is called the retardation time.
The retarded current [I]=Io exp(j W-r/c))
Where U F LV WKH SKDVH UHWDUGDWLRQ
57.Define induction field
The induction field will predominate at points
close to the current element ,where the distance from the
centre of the dipole to the particular point is less.This field
is more effective in the vicinity of the current element
only.It represents the energy stored in the magnetic field
surrounding the current element or conductor.This field is
also known as near field.
58.Define Radiation field
The radiation field will be produced at a larger
distance from the the current element ,where the distance
from the centre of the dipole to the particular point is very
large.It is also called as distant field or far field.
59.At what distance from the dipole is the induction field
equal to the radiation field?
As the distance from the current element or the
short dipole increases ,both induction and radiation fields
emerge and start decreasing .However,a distance reaches
from the conductor at which both the induction and
radiation field becomes equal and the particular distance
depends upon the wavelength.The two fields will thus have
equal amplitude at that particular distance.This distance is
given by
U
60.Define Radiation Resistance
It is defined as the fictitious resistance which when
inserted in series with the antenna will consume the same
amount of power as it is actually radiated.The antenna
appears to the transmission line as a resistive component
and this is known as the radiation resistance.
61.Give the expression for the effective aperture of a short
dipole
The effective aperture of a short dipole is
given by
$H 2
62.What is a dipole antenna?
A dipole antenna may be defined as a symmetrical antenna in which the two ends are
at equal potential relative to the midpoint.
63.What is a half wave dipole?
A half wave antenna is the fundamental radio antenna of metal rod or tubing or thin
wire which has a physical length of half wavelength in free space at the frequency of
operation
64.Give the expression for the effective aperture of a Half
wave Dipole
The effective aperture of a half wave dipole is
given by
Ae=0 2
65.What is the radiation resistance of a half wave dipole
The radiation resistance of a half wave dipole is given by
Rr=73 ohm
66.What is a loop antenna?
A loop antenna is a radiating coil of any convenient cross-section of one or more
turns carrying radio frequency current.it may assume any shape (e.g.
rectangular,square,triangular and hexagonal)
67.Give an expression of radiation resistance of a small loop
Radiation resistance of a small loop is given by
Rr=31,200 (A/ 2)2
68.How to increase the radiation resistance of a loop antenna
The radiation resistance of a loop antenna can be increased by:
1. increasing the number of turns
2. inserting a ferrite core of very high permeability with loop antenna’ s
circumference which will rise the magnetic field intensity called ferrite
loop.
69.What are the types of loop antennas?
Loop antennas are classified into:
1. (OHFWULFDOO\ 6PDOO &LUFXPIHUHQFH
2. (OHFWULFDOO\ /DUJH 'LPHQVLRQ FRPSDUDEOH WR
70.What are Electrically Small loop antennas?
Electrically Small loop antennas is one in which the overall length of the loop is less
than one-tenth of the wavelength. Electrically Small loop antennas have small radiation
resistances that are usually smaller than their loop resistances.They are very poor radiators
and seldom employed for transmission in radio communication.
71.What are Electrically large loop antennas?
Electrically Large loop antennas is one in which the overall length of the loop
approaches the wavelength.
72.List out the uses of loop antenna
Various uses of loop antenna are:
™ It is used as receiving antenna in portable radio and pagers
™ It is used as probes for field measurements and as directional antennas for radio
wave navigation
™ It is used to estimate the direction of radio wave propagation
73.What are the parameters to be considered for the design of an helical antenna?
The parameters to be considered for the design of an helical antenna are:
1. Bandwidth
2. Gain
3. Impedance
4. Axial Ratio
74.What are the types of radiation modes of operation for an helical antenna
The two types of radiation modes of operation possible for an helical antenna are:
1. Normal mode of operation
2. Axial mode of operation
75.Which antenna will produce circularly polarized waves
Helical antenna radiates circularly polarized wave.
76.List the applications of helical antenna
The applications of helical antenna are:
™ It became thw workhouse of space communications for telephone,television and
data,being employed both on satellites and at ground stations
™ Many satellites including weather satellites,data relay satellites all have helical
antennas
™ It is on many othe probes of planets and comets,including moon and mars,being used
alone,in arrays or as feeds for parabolic reflectors,its circular polarization and high
gain and simplicity making it effective for space application
77.Define Sky wave.
Waves that arrive at the receiver after reflection in
the ionosphere is called sky wave.
78.Define Tropospheric wave.
Waves that arrive at the receiver after reflection from
the troposphere
region is called Tropospheric wave.(ie 10 Km from Earth
surface).
79. Define Ground wave.
Waves propagated over other paths near the earth
surface is called ground wave propagation.
80.What are the type of Ground wave.
Ground wave classified into two types.
i. Space wave
ii. Surface wave.
81 What is meant by Space Wave.?
It is made up of direct wave and ground
reflected wave. Also includes the portion of energy
received as a result of diffraction around the earth surface
and the reflection from the upper atmosphere.
82. What is meant by Surface Wave.?
Wave that is guided along the earth’ s surface like
an EM wave is guided by a transmission is called surface
wave. Attenuation of this wave is directly affected by the
constant of earth along which it travels.
83. What is meant by fading.?
Variation of signal strength occur on line of sight
paths as a result of the atmospheric conditions and it is
called .It can not be predicted properly.
84. What are the type of fading.?
Two types. i. Inverse bending.
iii. Multi path fading.
85. What is inverse and multi path fading.?
Inverse bending may transform line of sight
path into an obstructed one.
Multi path fading is caused by interference
between the direct and ground reflected waves as well as
interference between two are more paths in the atmosphere.
86.What is meant by diversity reception.?
To minimize the fading and to avoid the multi
path interference the technique used are diversity
reception. It is obtained by two ways.
i. Space diversity reception.
ii. Frequency diversity reception.
iii. Polarization diversity.
87. Define Space diversity Reception.
This method exploits the fact that signals
received at different locations do not fade together. It UHTXLUHV DQWHQQDV VSDFHG DW OHDVW DSDUW DUH SUHIHUUHG
and the antenna which high signal strength at the moment
dominates.
88 .Define frequency diversity Reception.
This method takes advantage of the fact that
signals of slightly different frequencies do not fade
synchronously. This fact is utilized to minimize fading in
radio telegraph circuits.
89. Define polarization diversity reception.
It is used in normally in microwave links, and it
is found that signal transmitted over the same path in two
polarizations have independent fading patterns.in broad
band dish antenna system, Polarization diversity combined
with frequency diversity reception achieve excellent
results.
90. What is meant by Faraday’ s rotation.?
Due to the earth’ s magnetic fields, the
ionosheric medium becomes anisotropic and the incident
plane wave entering the ionosphere will split into ordinary
and extra ordinary waves/modes.
When these modes re-emerge from the
ionosphere they recombine into a single plane wave again.
Finally the plane of polarization will usually
have changed, this phenomenon is known as Faraday’ s
rotation.
91. What are the factors that affect the propagation of radio
waves.?
i. Curvature of earth.
ii. Earth’ s magnetic field.
iii. Frequency of the signal.
iv. Plane earth reflection.
92. Define gyro frequency.
Frequency whose period is equal to the
period of an electron in its orbit under the influence of the
earths magnetic flux density B.
93. Define critical frequency.
For any layer , the highest frequency that will
be reflected back for vertical incidence is
fcr = 9¥1max
94. Define Magneto-Ions Splitting.
The phenomenon of splitting the wave into
two different components (ordinary and extra-ordinary) by
the earths magnetic field is called Magneto-Ions Splitting.
95.Define LUHF.
The lowest useful HF for a given distance
and transmitter power is defined as the lowest frequency
that will give satisfactory reception for that distance and
power.
It depends on
i. The effective radiated power
ii. Absorption character of ionosphere for the
paths between transmitter and receiver.
iii. The required field strength which in turn
depends upon the radio noise at the
receiving location and type of service
involved .
96. Define Refractive index.
It is defined as n = c / vp
Velocity of light
in vacua
n =
Phase velocity in
the medium
n = ¥ r
97Define maximum Usable Frequency.
The maximum Frequency that can be
reflected back for a given distance of transmission is called
the maximum usable frequency (MUF) for that distance.
MUF = fcr VHF i
98. Define skip distance.
The distance with in which a signal of
given frequency fails to be reflected back is the skip
distance for that frequency.The higher the frequency the
greater the skip distance.
99. Define Optimum frequency.?
Otimum frequency for transmitting between
any two points is therefore selected as some frequency
lying between about 50 and 85 percent of the predicted
maximum usable frequency between those points.
100. What is wave impedance.?
0 /¥ - (fc / f)
LH ¥ - (fc / f)
101. Define wave velocity and Group velocity.?
wave velocity vp = c / ¥ - (fc / f)2
Group velocity, vp vg = c2
vg = c2 / vp
16 MARK QUESTIONS
1. Write the potential function in different form.
2. Explain in detail about the aperture Concept
Aperture represents the area of the antenna
confining the effective radiations
The various types of antenna apertures are
i) Effective aperture.
ii). Scattering aperture.
iii) Loss aperture.
iv) collecting aperture.
v). Physical aperture.
Effective aperture(Ae).
It is the area over which the power
is extrated from the incident
wave and delivered to the load is called
effective aperture.
Scattering aperture(As.)
It is the ratio of the reradiated
power to the power density of the
incident wave.
Loss aperture. (Ae).
It is the area of the antenna which
dissipates power as heat.
Collecting aperture. (Ae).
It is the addition of above three
apertures.
Physical aperture. (Ap).
This aperture is a measure of the
physical size of the antenna.
The ratio of the effective aperture to the
physical aperture is the aperture efficiency. i.e
Aperture efficiency = hap = Ae / Ap (dimensionless).
Antenna matching:
When the antenna is receiving with a load
resistance matched to the antenna radiation resistance ,
maximum power is transferred to the load and the power
is also reradiated from the dipole.This is called antenna
matching( Give detailed explanation )
3.Briefly explain the radiation from a short dipole
Defn: A short dipole is one in which the field is
oscillating because of the oscillating voltage and current.It
is called so, because the length of the dipole is short and
the current is almost constant throughtout the entire length
of the dipole.
Fields from Oscillating Dipole: The dipole has two
equal charges of opposite sign oscillating up and down in
a harmonic motion.The charges will move towards each
other and electric filed lines were created.when the
charges meet at the midpoint, the field lines cut each other
and new field are created.This process is spontaneous and
so more filed are created around the antenna.This is how
radiations are obtained from a short dipole.(See Figure
from John. D .Kraus Book)
Antenna Field Zones:The regions containing the
radiations that are present around the antenna are called
Zones.The fields around an antenna ay be divided into
two principal regions.
a)Near field zone (Fresnel zone)
b)Far field zone (Fraunhofer zone)
Electric and Magnetic field components of short
Dipole: Write the derivations by referring The
Book,K.D.Prasad.
4.Gives notes on the antenna impedances. Find the
effective aperture and Directivity of a short dipole
antenna.
Self Impedance:
Defn:Self impedance of an antenna is defined as its
input impedance with all other antennas are
completely removed i.e away from it.
Write the formula required
Mutual Impedance:
Defn:The presence of near by antenna no.2
induces a current in the antenna no.1 indicates that
presence of antenna no.2 changes the impedance of the
antenna no.1.This effect is called mutual coupling and
results in mutual impedance.
State Reciprocity theorem
Formula required
Effective aperture and Directivity of a short dipole
antenna.
Consider a plane wave incident on a short
dipole.The wave is assumed to be linearly polarized with
electric field in the y direction. The current in the dipole is
assumed constant and in the same phase over its entire
length,and the terminating resistance is assumed equal to
the dipole radiation resistance.
The effective aperture of this dipole is given by $H
The directivity is found to be
' $H VT
5.Define Polarization? Explain the different types of
polarization in detail.
Polarization is defined as the orientation of
electric field as a function of direction. The polarization
of the radio wave can be defined by direction in which the
electric vector E is aligned during the passage of atleast
one full cycle.Also polarization can also be defined the
physical orientation of the radiated electromagnetic waves
in space.The polarization are of three types. They are:
Elliptical polarization
Circular polarization
Linear polarization.
Linear Polarisation:
A linearly polarized wave is one in which the
electric field remains in only one direction.For a linearly
polarized wave,the axial ratio is infinity.
Elliptical polarization
The electric field vector rotates and form a
ellipse called polarization ellipse. The ratio of the major to
the minor axes of the polarization ellipse is called the
Axial Ratio. (AR). AR is greater than 1 .
Circular polarization
The electric filed vector rotates and form a
circle and this wave is called circularly polarized
wave.AR is unity.
6.Explain in detail the different cases of the array
containing two isotropic sources
™ Case 1: Arrays of two isotropic sources fed with
currents of equal amplitude and in phase ™ Case 2: Arrays of two isotropic sources fed with
currents of equal amplitude and opposite phase ™ Case 3: Arrays of two isotropic sources fed with
currents of unequal amplitude and any phase ™ Case 1: Arrays of two isotropic sources fed with
currents of equal amplitude and in phase
quadrature.
Write about the following:
· Field pattern of the individual cases
· Find the maxima ,minima direction and half
power point direction
· Draw the radiation pattern.
7. What is broadside array? Derive the maxima ,null
directions and also the beamwidth of a broadside array.
Broad side array is defined as an arrangement in
which the principal direction of radiation is perpendicular
to the array axis and also the plane containing the array
element. For Broad side array the phase difference EHWZHHQ DGMDFHQW HOHPHQW LV
· Field pattern of a linear array with n isotropic
sources
· Determine the maxima ,minima direction and
half power point direction
· Draw the radiation pattern.
8.What is End Fire array? Derive the maxima ,null
directions and also the beamwidth of a Endfire array.
End fire array is defined as an arrangement in
which the principal direction of radiation is coincides with
the array axis. )RU HQG )LUH DUUD\ - G :KHUH $QG G GLVWDQFH EHWZHHQ WKH HOHPHQWV
· Field pattern of a linear array with n isotropic
sources
· Determine the maxima ,minima direction and
half power point direction
· Draw the radiation pattern.
9.Explain the principle of pattern multiplication with some
examples.
Principle of pattern multiplication:
The total field pattern of an array of non
isotropic but similar sources is the product of the
iii) individual source pattern and
iv) The array pattern of isotropic point sources each
located at the phase center of the individual
source having the same amplitude and phase.
While the total phase pattern is the sum of the phase
patterns of the individual source pattern and array pattern.0
™ Situation 1: Array of two point sources fed in
phase with the amplitude of the individual
source to be Eo=Eo1 Sin (theta) ™ Situation 2: Array of two point sources fed in
phase with the amplitude of the individual
source to be Eo=Eo1 Cos (theta) ™ Situation 3: Array of four point sources fed in
phase with the amplitude of the individual
source to be Eo=Eo1 Sin (theta)
10.Explain the different techniques used for tapering of
arrays
Array Tapering:
Tapering of array is a technique used for
reduction of unwanted side lobes .The amplitude of
currents in the linear array source is non-uniform; hence the
central source radiates more energy than the ends. Tapering
is done from center to end.
Techniques used for array tapering: ™ Binomial Array:Tapering follows the
coefficient of binomial series ™ Dolph Tchebycheff Array: Tapering follows
the coefficient of Tchebycheff polynomial.
1. Binomial Array:
It is an array in which the amplitudes of the
antenna elements in the array are arranged according to the
coefficients of the binomial series.
The need for a binomial array is
i). In uniform linear array as the array length is
increased to increase the directivity, the secondary lobes
also occurs.
ii) For certain applications, it is highly desirable
that secondary lobes should be eliminated completely or
reduced to minimum desirable level compared to main
lobes.
Advantage: ™ No minor lobes
Disadvantages: ™ Increased beam width ™ Maintaining the large ratio of current
amplitude in large arrays is difficult
2. Dolph Tchebycheff Array: ™ Tapering follows the coefficient of
Tchebycheff polynomial.
11.Derive the fields radiated from a short electric dipole.List the far field
components.Determine its radiation resistance and directivity.
™ Fields radiated from the short dipole and radiation resistance(Refer
Antennas & propagation By K.D.Prasad,Page No.210 to 227)
™ Directivity is 1.5(Refer Antennas & propagation By K.D.Prasad,Page
No.251 to 252)
12.Derive the expressions for the fields and power radiated from a half wave dipole
antenna.Find its radiation resistance and directivity.
™ Fields radiated from the short dipole and radiation resistance(Refer
Antennas & propagation By K.D.Prasad,Page No.229 to 234)
™ Directivity is 1.5(Refer Antennas & propagation By K.D.Prasad,Page
No.252 to 253)
13.Derive the field radiated from a small loop antenna
™ Small loop radiated fields(Refer “Antennas” By John.D.Kraus,Page
No.200 to 208)
14.Explain in detail about the helical antenna
™ Definition of helical antenna
™ Helical Geometry
™ Radiated fields of helical antenna
™ Types of helix
Refer “Antennas” By John.D.Kraus
15.Explain the different modes of operation of helical antenna
™ Normal mode of operation
™ Axial mode of operation.
16. Explain Ground wave Propagation.
Sky wave.
Waves that arrive at the receiver after reflection in
the ionosphere is called sky wave.
Tropospheric wave.
Waves that arrive at the receiver after reflection from
the troposphere
region is called Tropospheric wave.(ie 10 Km from Earth
surface).
Ground wave.
Waves propagated over other paths near the earth
surface is called ground wave propagation.
Type of Ground wave.
Ground wave classified into two types.
iv. Space wave
v. Surface wave.
Space Wave.
It is made up of direct wave and ground
reflected wave. Also includes the portion of energy
received as a result of diffraction around the earth surface
and the reflection from the upper atmosphere.
Surface Wave.
Wave that is guided along the earth’ s surface like
an EM wave is guided by a transmission is called surface
wave. Attenuation of this wave is directly affected by the
constant of earth along which it travels.
17.Explain diversity reception.?
To minimize the fading and to avoid the
multi path interference the technique used are
diversity reception. It is obtained by two ways.
1. Space diversity reception
2. Frequency diversity reception.
3. Polarization diversity.
Space diversity Reception.
This method exploits the fact that signals
received at different locations do not fade together. It UHTXLUHV DQWHQQDV VSDFHG DW OHDVW DSDUW DUH SUHIHUUHG
and the antenna which high signal strength at the moment
dominates.
Frequency diversity Reception.
This method takes advantage of the fact that
signals of slightly different frequencies do not fade
synchronously. This fact is utilized to minimize fading in
radio telegraph circuits.
Polarization diversity reception.
It is used in normally in microwave links, and
it is found that signal transmitted over the same path in
two polarizations have independent fading patterns.in
broad band dish antenna system, Polarization diversity
combined with frequency diversity reception achieve
excellent results.
18. Explain in detail ionospheric propagation.
Waves that arrive at the receiver after the
propagation through ionosphere is ionospheric
propagation..
The ionosphere is that region of the
earths atmosphere in which the constituent gases are
ionized by radiation from the outer space.
The region is 50 Km to 400 Km.
· Effective Dielectric and conductivity of an ionized
gas.
· Reflection and refraction waves by the ionosphere.
( Refer Page no 667 to 681. Electro magnetic waves and
radiating Systems .By. C.JORDAN and G.BALMAIN )
19. Explain
a. Effect of the earth magnetic field.
b. Faraday rotation in Sky wave Propagation.
Effect of the earth magnetic field
Electrons and ions in the ionosphere are influenced not
only by the fields of a passing elecro magnetic wave but
also by the earth magnetic field, which causes the charged
particles to move in circular or spiral paths.
( Refer Page no 687. Electro magnetic waves and radiating
Systems .By. C.JORDAN and G.BALMAIN )
Faraday rotation in Sky wave Propagation
Due to the earth’ s magnetic fields, the
ionosheric medium becomes anisotropic and the incident
plane wave entering the ionosphere will split into ordinary
and extra ordinary waves/modes.
When these modes re-emerge from the
ionosphere they recombine into a single plane wave again.
Finally the plane of polarization will usually
have changed, this phenomenon is known as Faraday’ s
rotation.
( Refer Page no 693. Electro magnetic waves and radiating
Systems .By. C.JORDAN and G.BALMAIN )
20. Derive the expression for Permitivity and conductivity
of ionized gas.?
Plasma: .Assembly of charged particles in which the time
average charge density is
Zero.
Plasma is formed Whenver the atoms ina gas
are ionized to produce equal number of ions and electrons.
Eg earth ionosphere.
r , = 1- Ne2 / ( P v 2 2 )
>1H2 P 2 2 )]
Note: Conductivity is maximum means the wave will pass
through that medium.
Conductivity is small, waves gets reflected.
( Refer Page no 670
fn. Electro magnetic waves and radiating Systems .By.
C.JORDAN and G.BALMAIN )
21.Explain the concept of Reflection and refraction waves
by the ionosphere.
The reflection and refraction of radio waves by
the ionosphere is a function of frequency.
Briefly describe the following.
i. Reflection at low frequency.
ii. Reflection at high frequency.
iii. Maximum usable frequency.
iv. Optimum frequency.
v. Skip distance.
Important formula for problems:
i Critical frequency,
fcr = 9¥1max
ii. Relative Dielectric constant r = 1- Ne2 P 2 + v2 )
iii. Phase constant,
b = (2p/l) ¥ - (fc / f)
iv. Wave impedance. 0 /¥ - (fc / f)
v. Wave velocity.
vp = c / ¥ - (fc / f)2
vi Group velocity,
vp vg = c2
vg = c2 / vp
vii. Incident angle .
sin i = ¥ - (fc / f)
Thursday, September 23, 2010
Quick Revision for Electronic Circuits II
Electronic Circuits II
1. Define positive feedback?
If the feedback signal is in phase with input signal, then the net effect of the
feedback will increase the input signal given to the amplifier. This type of feedback is
said to be positive or regenerative feedback.
2. Define negative feedback?
If the feedback signal is out of phase with the input signal then the input
voltage applied to the basic amplifier is decreased and correspondingly the output is
decreased. This type of feedback is known as negative or degenerative feedback.
3. Define sensitivity?
Sensitivity is defined as the ratio of percentage change in voltage gain with
feedback to the percentage change in voltage gain without feedback.
4. What are the types of feedback?
i. Voltage-series feedback
ii. Voltage-shunt feedback
iii. Current-series feedback
iv. Current-shunt feedback
5. Define feedback?
A portion of the output signal is taken from the output of the amplifier and is
combined with the normal input signal. This is known as feedback.
6. Write the expression for input and output resistance of voltage series feedback
amplifier.
Input resistance with feedback, Rif $ 5i
Output resistance with feedback, Rof = Ro $
7. Give an example for voltage-series feedback.
The Common collector or Emitter follower amplifier is an example for
voltage series feedback.
8. Write the expression for input and output resistance of current shunt feedback
amplifier.
Input resistance with feedback, Rif = Ri $
Electronic Circuits II
Output resistance with feedback, Rof = Ro $
9. Give the properties of negative feedback.
i. Negative feedback reduces the gain
ii. Distortion is very much reduced
10. Give the effect of negative feedback on amplifier characteristics.
Type of feedback
Characteristics
Current-series Voltage-series Voltage-shunt Current-shunt
Voltage gain Decreases Decreases Decreases Decreases
Bandwidth Increases Increases Increases Increases
Input resistance Increases Increases Decreases Decreases
Output resistance Increases Decreases Decreases Increases
11. What is Oscillator circuit?
A circuit with an active device is used to produce an alternating current is called
an oscillator circuit.
12. What are the classifications of Oscillators?
*Based on wave generated:
i. Sinusoidal Oscillator,
ii. Non-sinusoidal Oscillator or Relaxation Oscillator
Ex: Square wave, Triangular wave, Rectangular wave etc.
*According to principle involved:
i. Negative resistance Oscillator,
ii. Feedback Oscillator.
*According to frequency generated:
i. Audio frequency oscillator
20 Hz – 20 kHz
ii. Radio frequency Oscillator
30 kHz – 30 MHz
iii. Ultrahigh frequency Oscillator
30 MHz – 3 GHz
iv. Microwave Oscillator
3 GHz – above.
* Crystal Oscillators.
13. Define Barhausen Criterion.
7KH SURGXFW $v is greater than one this is called Barhausen criterion.
Avf = Av/1- $v
Avf = ’ 1/0
=>1- $v < 0 ! $v > 1 this is the condition for feedback Oscillator.
An Oscillator which follows Barkhausen criterion is called the Feedback
Oscillator.
14. What are the types of feedback oscillators?
* RC-Phase shift Oscillator,
* LC-Oscillators
i. Tuned collector Oscillator
ii. Tuned emitter Oscillator
iii. Tuned collector base Oscillator
iv. Hartley Oscillator
v. Colpits Oscillator
vi. Clap Oscillator
15. What are the conditions for oscillation?
The total phase shift of an oscillator should be 360o. For feedback oscillator it
should satisfies Barhausen criterion.
16. Define Piezoelectric effect.
When applying mechanical energy to some type of crystals called piezoelectric
crystals the mechanical energy is converted into electrical energy is called piezoelectric
effect.
) 1/T
17. Draw the equivalent circuit of crystal oscillator.
18. What is Miller crystal oscillator? Explain its operation.
It is nothing but a Hartley oscillator its feedback Network is replaced by a crystal.
Crystal normally generate higher frequency reactance due to the miller
capacitance are in effect between the transistor terminal.
19. State the frequency for RC phase shift oscillator.
The frequency of oscillation of RC-phase shift oscillator is
F=1/��
Where k=2.639.
20. Define Oscillator
A circuit with an active device is used to produce an alternating current is called
an oscillator circuit.
21. What is a tuned amplifier?
The amplifier with a circuit that is capable of amplifying a signal over a narrow band of
frequencies
Are called tuned amplifiers.
22. What is the expression for resonant frequency?
fr=1/2š¥/&
23. What happens to the circuit above and below resonance?
Above resonance the circuit acts as capacitive and below resonance the circuit acts as
inductive.
24. What are the different coil losses?
Hysteresis loss
Copper loss
Eddy current loss
25. What is Q factor?
It is the ratio of reactance to resistance.
26. What is dissipation factor?
It is referred as the total loss within a component i.e1/Q
27. What is the classification of tuned amplifiers?
Single tuned
Double tuned
Stagger tuned
28. What is a single tuned amplifier?
An n amplifier circuit that uses a single parallel tuned circuit as a load is called single
tuned amplifier.
29. What are the advantages of tuned amplifiers?
They amplify defined frequencies.
Signal to noise ratio at output is good
They are suited for radio transmitters and receivers
30. What are the disadvantages of tuned amplifiers?
The circuit is bulky and costly
The design is complex.
They are not suited to amplify audio frequencies.
31. What is neutralization?
The effect of collector to base capacitance of the transistor is neutralized by
introducing a signal that cancels the signal coupled through collector base capacitance.
This process is called neutralization.
32. What are double tuned amplifiers?
The amplifiers having two parallel resonant circuit in its load are called double tuned
amplifiers.
33. What is a stagger tuned amplifier?
It is a circuit in which two single tuned cascaded amplifiers having certain bandwidth are
taken and their resonant frequencies are adjusted that they are separated by an amount
equal to the bandwidth of each stage. Since resonant frequencies are displaced it is called
stagger tuned amplifier.
34. What are the advantages of stagger tuned amplifier?
The advantage of stagger tuned amplifier is to have better flat, wideband characteristics.
35. What are the advantages of double tuned over single tuned?
1. Possess flatter response having steeper sides
2. Provides larger 3 db bandwidth
3. Provides large gain-bandwidth product.
36. What are the different types of neutralization?
1. Hazeltine neutralization
2. Rice neutralization
3. Neutrodyne neutralization.
37. What is rice neutralization?
It uses center tapped coil in the base circuit. The signal voltages at the end of tuned base
coil are equal and out of phase.
38. What is unloaded Q?
It is the ratio of stored energy to the dissipated energy in a reactor or resonator.
39. What are the applications of mixer circuits?
Used in radio receivers. Used to translate signal frequency to some lower frequency
40. What is up converter?
When the mixer circuit is used to translate signal to high frequency, then it is called up
converter.
41 What is an amplifier?
An amplifier is a device which produces a large electrical output of similar
characteristics to that of the input parameters.
42. How are amplifiers classified according to the input?
1. Small – signal amplifier 2. Large – signal amplifier
43. How are amplifiers classified according to the transistor configuration?
1. Common emitter amplifier 2. Common base amplifier 3. Common collector
amplifier
44. What is the different analysis available to analyze a transistor?
1. AC analysis 2. DC analysis
45. How can a DC equivalent circuit of an amplifier be obtained?
By open circuiting the capacitor.
46. How can a AC equivalent circuit of a amplifier be obtained?
By replacing dc supply by a ground and short- circuiting capacitors.
47. What is feed back?
It is the process of injecting some energy from the output and then returns it back to
the input.
48. What is the disadvantage of negative feed back?
Reduces amplifier gain.
49. Define sensitivity.
It is the ratio of percentage change in voltage gain with feedback to the percentage
change in voltage gain without feed back.
50. Define Desensitivity.
It is the ratio of percentage change in voltage gain without feedback to the percentage
change in voltage gain with feed back. the reciprocal of sensitivity.
51, What is a Multivibrator?
The electronic circuits which are used to generate nonsinusoidal waveforms are
called Multivibrators.
52, Name the types of Multivibrators?
Bistable Multivibrator, Monostable Multivibrator,Astable Multivibrator
53, How many stable states do bistable Multivibrator have?
Two stable states.
54, When will the circuit change from stable state in bistable Multivibrator ?
when an external trigger pulse is applied, the circuit changes from one stable state
to another.
55, What are the different names of bistable Multivibrator?
Eccles Jordan circuit, trigger circuit, scale-of-2 toggle circuit, flip-flop and binary.
56, What are the applications of bistable Multivibrator?
It is used in the performance of many digital operations such as counting and
storing of the
Binary information. It also finds applications in the generation and processing of
pulse – type waveforms.
57, What are the other names of monostable Multivibrator?
One-shot, Single-shot, a single-cycle, a single swing, a single step Multivibrator,
Univibrator.
58, Why is monostable Multivibrator called gatting circuit?
The circuit is used to generate the rectangular waveform and hence can be used to
gate other
Circuits hence called gating circuit.
59, Why is monostable Multivibrator called delay circuit?
The time between the transition from quasi-stable state to stable state can be
predetermined and
hence it can be used to introduce time delays with the help of fast transition. Due
to this application is Called delay circuit.
60, What is the main characteristics of Astable Multivibrator
The Astable Multivibrator automatically makes the successive transitions from
one quasi- stable
State to other without any external triggering pulse.
61, What is the other name of Astable Multivibrator- why is it called so?
As it does not require any external pulse for transition, it is called free running
Multivibrator.
62, What are the two types of transister bistable Multivibrator?
i. Fixed bias transistor circuit
ii. Self bias transistor circuit.
63, Why does one of the transistor start conducting ahead of other?
The characteristic of both the transistors are never identical hence after giving
supply one of the
Transistors start conducting ahead of the other.
64, What are the two stable states of bistable Multivibrator?
i. Q1 OFF (cut off) and Q2 ON (Saturation)
ii. Q2 OFF (Cut off) and Q1 On (Saturation)
65, What finally decides the shape of the waveform for bistable multivibrator?
The spacing of the triggering pulses
66, How are the values R1, R2 and VBB chosen in bistable Multivibrator?
It is chosen in such a way that in one state the base current is large enough to
drive the transistor into saturation while in other state the emitter junctions is well below
off.
67, What is the self biased Multivibrator?
The need for the negative power supply in fixed bias bistable Multivibrator can be
eliminated by rising a common emitter resistance RE. The resistance previous the
necessary bias to keep one transistor or and the other OFF in the stable state such
type of biasing is called self biasing and the circuit is called self biased bistable
Multivibrator.
68, What are the other names of speed up capacitors.
i. Commutating Capacitors
ii. Transpose capacitors
69 Define transition time?
It is defined as the time interval during which conduction transfers from one
transistor to other.
70, What is the value of commutating capacitor.
It lies in the range of tens to some hundreds of Pico farads.
71. Define resolving time.
The smallest allowable interval between triggers is called resolving time.
72, Give the expression of fmax with respect to resolving time
Fmax = 1/resolving time.
73, Define gate width
The pulse width is the time for which the circuit remains in the quasi stable state. It is
also called gate width.
74, What are the advantages of monostable Multivibrator.
- used to introduce time delays as gate width is adjustable
- used to produce rectangular waveform and hence can be used as gating circuit.
75, What are the applications of astable Multivibtrator.
- used as a clock for binary login signals
- used as a square wave generator, voltage to frequency converter.
76, What is a complementary Multivibrator
It is turning half the circuit upside down. So one transistor is n-p-n while the
other is p-n-p.
The circuit is called complementary Multivibrator circuit.
77, What is UTP of the Schmitt trigger
When Vi reaches to VBE1 +VE the Q1 gets driven to active region. This input
voltage level is
called upper threshold point.
78, What is the other name for UTP
It is also called input turn on threshold level.
79, What is LTP Schmitt trigger.
The level of Vi at which Q1 becomes OFF and Q2 on is called lower threshold
point.
80, Define transfer Characteristics
The graph of output voltage against input voltage is called transfer characteristics of
Schmitt trigger.
81, What is the important application of Schmitt trigger?
- It is used as an amplitude comparator
- It is used as a squaring circuit.
82, Define Blocking Oscillator?
A special type of wave generator which is used to produce a single narrow pulse
or train of pulses.
83, What are the two important elements of Blocking Oscillator?
Transistor and pulse transformer
84, What are the applications of blocking Oscillator?
It is used in frequency dividers, counter circuits and for switching the other
circuits.
86, Give the expression for co-efficient of coupling
K=M/ÖLpLs
M-> Mututal Inductance
Lp -> Primary Inductance
Ls -> Secondary Inductance
87, Give the formula for transformation ratio
n= Ns/Np = transformation ratio
Ns= Secondary Turns;
Np= Primary turns
88, Define rise time
It is defined by the time required by the pulse to rise from 10% of its amplitude to
90% of its amplitude.
89, Define overshoot.
It is the amount by which the output exceeds its amplitude during first attempt.
90, Define flat top response.
The position of the response between the trailing edge and the leading edge.
91, Define droop or a tilt
The displacement of the pulse amplitude during its flat response is called droop or
a tilt.
92, What are the applications of pulse transformer.
i. to invert the polarity of the pulse
ii. to differentiate pulse
93, When do the core saturates?
When L->o as B-> Bm, the core saturates
94, What is the other name of astable Blocking Oscillator
Free running blocking Oscillator
95, What are the two types of astable Blocking Oscillator?
1, Diode controlled Astable Blocking Oscillator.
2, Re controlled Astable Blocking Oscillator.
96, Define Sweeptime in sawtooth generator
The period during which voltage increases linearly is called sweep time.
97, What is the other name of sawtooth generator?
Ramp generator
98, Define Displacement error in the sawtooth generator?
It is defined as the maximum differenece between the actual sweep voltage and
linear sweep
which passes through the beginning and end points of the actual sweep.
99, What is constant current charging?
A capacitor is charged with a constant current source.
100, What is the miller circuit
Integrator is used to convert a step waveform into ramp waveform.
PART B
1, Explain bistable Multivibrator and its types?
General form of bistable Multivibrator circuit.
· fixed Bias transistor bistable Multivibrator circuit
· self Bias transistor biastable Multivibrator circuit
· Applications
2, Explain about speedup capacitors or commutating capacitors
· Practical self biased bistable Multivibrator
· Explanation about the circuit
3, Explain about Monostable Multivibrator
· Explanation about the circuit diagram
· Pulse width of collector coupled Monostable Multivibrator
· Wareforms
· Applications
4, Explain about collector coupled astable Multivibrator
· Explanation about the circuit diagram
· Wareforms
· Distration & its eliminator
· Applications
5, Explain emitter coupled astable Multivibrator
· Operation and Mathematical analysis
· Practical circuit
· Advantages and disadvantages of the Multivibrator
6, Write in detail about Schmitt Trigger circuit?
· Circuit diagram
· Operation of the circuit
· Schmitt trigger wareforms.
· Hysterisis
· Applications
7, Explain about pulse transformer?
· Ideal pulse transformer model
· Practical equivalent circuit
· Pulse response characteristics
· Applications of pulse transformer
8, Explain Monostable blocking oscillator using emitter timing?
· Circuit Diagram
· Mathematical analysis
· Expression for pulse width
· Triggering circuit for monostable blocking oscillator
9, Write about the core saturation method
· Circuit diagram
· Waveforms of ic and iB when core Saturates.
10, Write about astable blocking oscillator.
· Diode controlled astable blocking Oscillator
· RC controlled astable blocking Oscillator
11, Write about UJT sawtooth generator
· Operation
· Circuit diagram
12, What will happen when a step input voltage is applied to the high pass RC Circuit?
· Derivation
· The output Waveform
13 .Explain the relevant information ,how the negative feed back improves stability
reduce noise and increase input impedance?
Draw the circuit diagram.
Explain detail the following ¾ transfer gain. ¾ stability of gain.
The transfer of gain of the amplifier is not constant as it is depends upon the factors
such as operating point temperature ,etc. This lack of stability can be reduced by
introducing negative feed back.
The signal feed back reduces the amount of the noise signal and non linear distortion.
The factor (1+bA)reduces both input noise and resulting non linear distortion for
considerable improvement. Thus ,noise and non linear distortion also reduced by
same factor.
14.Explain voltage shunt feed back amplifiers?
¾ Draw the circuit diagram. ¾ Draw the equivalent circuit . ¾ Find the input and output impedance after feed back.
15.Explain current series feed back amplifiers?
¾ Draw the circuit diagram. ¾ Draw the equivalent circuit . ¾ Find the input and output impedance after feed back.
16.Explain the classification of amplifiers?
Explain the following in detail. ¾ Voltage amplifier. ¾ Current amplifier. ¾ Trans conductance amplifier. ¾ Trans resistance amplifier.
17.Explain current shunt and voltage shunt feed back amplifiers?
¾ Draw the circuit diagram.
¾ Draw the equivalent circuit . ¾ Find the input and output impedance after feed back.
18. With simple diagrams explain the operation of negative resistance oscillator using
tunnel diode?.
¾ Draw the circuit diagram and graph. ¾ Draw the characteristics of tunnel diode. ¾ Get the expression for time period ‘t’. ¾ Draw the wave form for negative resistance oscillator.
19. Explain RC phase shift oscillator?.
¾ Draw the circuit diagram ¾ Draw the equivalent circuit. ¾ Derive the minimum value of hfe for oscillation.
20. Explain Clapp’s oscillator and derive the expression for frequency of oscillation .
Also explain how frequency stability can be improved Clapp’s oscillator.?
¾ Draw the circuit diagram ¾ Draw the equivalent circuit. ¾ Derive the frequency of oscillation.
21. Explain Hartly oscillator and derive the equation for oscillation ?
¾ Draw the circuit diagram ¾ Draw the equivalent circuit. ¾ Derive the frequency of oscillation.
22. Explain pierce crystal oscillator and derive the equation for oscillation?
¾ Draw the circuit diagram ¾ Draw the equivalent circuit. ¾ Derive the frequency of oscillation.
23. Explain in detail about single tuned amplifier
¾ Draw the circuit diagram
¾ Draw the equivalent circuit. ¾ Derive the expression for band width
24. Explain in detail about double tuned amplifier
¾ Draw the circuit diagram ¾ Draw the equivalent circuit. ¾ Derive the expression for band width
25. Explain in detail about stagger-tuned amplifier
¾ Draw the circuit diagram ¾ Draw the equivalent circuit. ¾ Derive the expression for band width
26. Compare single tuned and double tuned amplifier
¾ Compare the circuit diagram ¾ Compare the equivalent circuit. ¾ Compare the expression for band width
27. Explain the different types of neutralization?
¾ Explain Hazeltine neutralization ¾ Explain Rice neutralization. ¾ Explain Neutrodyne neutralization
1. Define positive feedback?
If the feedback signal is in phase with input signal, then the net effect of the
feedback will increase the input signal given to the amplifier. This type of feedback is
said to be positive or regenerative feedback.
2. Define negative feedback?
If the feedback signal is out of phase with the input signal then the input
voltage applied to the basic amplifier is decreased and correspondingly the output is
decreased. This type of feedback is known as negative or degenerative feedback.
3. Define sensitivity?
Sensitivity is defined as the ratio of percentage change in voltage gain with
feedback to the percentage change in voltage gain without feedback.
4. What are the types of feedback?
i. Voltage-series feedback
ii. Voltage-shunt feedback
iii. Current-series feedback
iv. Current-shunt feedback
5. Define feedback?
A portion of the output signal is taken from the output of the amplifier and is
combined with the normal input signal. This is known as feedback.
6. Write the expression for input and output resistance of voltage series feedback
amplifier.
Input resistance with feedback, Rif $ 5i
Output resistance with feedback, Rof = Ro $
7. Give an example for voltage-series feedback.
The Common collector or Emitter follower amplifier is an example for
voltage series feedback.
8. Write the expression for input and output resistance of current shunt feedback
amplifier.
Input resistance with feedback, Rif = Ri $
Electronic Circuits II
Output resistance with feedback, Rof = Ro $
9. Give the properties of negative feedback.
i. Negative feedback reduces the gain
ii. Distortion is very much reduced
10. Give the effect of negative feedback on amplifier characteristics.
Type of feedback
Characteristics
Current-series Voltage-series Voltage-shunt Current-shunt
Voltage gain Decreases Decreases Decreases Decreases
Bandwidth Increases Increases Increases Increases
Input resistance Increases Increases Decreases Decreases
Output resistance Increases Decreases Decreases Increases
11. What is Oscillator circuit?
A circuit with an active device is used to produce an alternating current is called
an oscillator circuit.
12. What are the classifications of Oscillators?
*Based on wave generated:
i. Sinusoidal Oscillator,
ii. Non-sinusoidal Oscillator or Relaxation Oscillator
Ex: Square wave, Triangular wave, Rectangular wave etc.
*According to principle involved:
i. Negative resistance Oscillator,
ii. Feedback Oscillator.
*According to frequency generated:
i. Audio frequency oscillator
20 Hz – 20 kHz
ii. Radio frequency Oscillator
30 kHz – 30 MHz
iii. Ultrahigh frequency Oscillator
30 MHz – 3 GHz
iv. Microwave Oscillator
3 GHz – above.
* Crystal Oscillators.
13. Define Barhausen Criterion.
7KH SURGXFW $v is greater than one this is called Barhausen criterion.
Avf = Av/1- $v
Avf = ’ 1/0
=>1- $v < 0 ! $v > 1 this is the condition for feedback Oscillator.
An Oscillator which follows Barkhausen criterion is called the Feedback
Oscillator.
14. What are the types of feedback oscillators?
* RC-Phase shift Oscillator,
* LC-Oscillators
i. Tuned collector Oscillator
ii. Tuned emitter Oscillator
iii. Tuned collector base Oscillator
iv. Hartley Oscillator
v. Colpits Oscillator
vi. Clap Oscillator
15. What are the conditions for oscillation?
The total phase shift of an oscillator should be 360o. For feedback oscillator it
should satisfies Barhausen criterion.
16. Define Piezoelectric effect.
When applying mechanical energy to some type of crystals called piezoelectric
crystals the mechanical energy is converted into electrical energy is called piezoelectric
effect.
) 1/T
17. Draw the equivalent circuit of crystal oscillator.
18. What is Miller crystal oscillator? Explain its operation.
It is nothing but a Hartley oscillator its feedback Network is replaced by a crystal.
Crystal normally generate higher frequency reactance due to the miller
capacitance are in effect between the transistor terminal.
19. State the frequency for RC phase shift oscillator.
The frequency of oscillation of RC-phase shift oscillator is
F=1/��
Where k=2.639.
20. Define Oscillator
A circuit with an active device is used to produce an alternating current is called
an oscillator circuit.
21. What is a tuned amplifier?
The amplifier with a circuit that is capable of amplifying a signal over a narrow band of
frequencies
Are called tuned amplifiers.
22. What is the expression for resonant frequency?
fr=1/2š¥/&
23. What happens to the circuit above and below resonance?
Above resonance the circuit acts as capacitive and below resonance the circuit acts as
inductive.
24. What are the different coil losses?
Hysteresis loss
Copper loss
Eddy current loss
25. What is Q factor?
It is the ratio of reactance to resistance.
26. What is dissipation factor?
It is referred as the total loss within a component i.e1/Q
27. What is the classification of tuned amplifiers?
Single tuned
Double tuned
Stagger tuned
28. What is a single tuned amplifier?
An n amplifier circuit that uses a single parallel tuned circuit as a load is called single
tuned amplifier.
29. What are the advantages of tuned amplifiers?
They amplify defined frequencies.
Signal to noise ratio at output is good
They are suited for radio transmitters and receivers
30. What are the disadvantages of tuned amplifiers?
The circuit is bulky and costly
The design is complex.
They are not suited to amplify audio frequencies.
31. What is neutralization?
The effect of collector to base capacitance of the transistor is neutralized by
introducing a signal that cancels the signal coupled through collector base capacitance.
This process is called neutralization.
32. What are double tuned amplifiers?
The amplifiers having two parallel resonant circuit in its load are called double tuned
amplifiers.
33. What is a stagger tuned amplifier?
It is a circuit in which two single tuned cascaded amplifiers having certain bandwidth are
taken and their resonant frequencies are adjusted that they are separated by an amount
equal to the bandwidth of each stage. Since resonant frequencies are displaced it is called
stagger tuned amplifier.
34. What are the advantages of stagger tuned amplifier?
The advantage of stagger tuned amplifier is to have better flat, wideband characteristics.
35. What are the advantages of double tuned over single tuned?
1. Possess flatter response having steeper sides
2. Provides larger 3 db bandwidth
3. Provides large gain-bandwidth product.
36. What are the different types of neutralization?
1. Hazeltine neutralization
2. Rice neutralization
3. Neutrodyne neutralization.
37. What is rice neutralization?
It uses center tapped coil in the base circuit. The signal voltages at the end of tuned base
coil are equal and out of phase.
38. What is unloaded Q?
It is the ratio of stored energy to the dissipated energy in a reactor or resonator.
39. What are the applications of mixer circuits?
Used in radio receivers. Used to translate signal frequency to some lower frequency
40. What is up converter?
When the mixer circuit is used to translate signal to high frequency, then it is called up
converter.
41 What is an amplifier?
An amplifier is a device which produces a large electrical output of similar
characteristics to that of the input parameters.
42. How are amplifiers classified according to the input?
1. Small – signal amplifier 2. Large – signal amplifier
43. How are amplifiers classified according to the transistor configuration?
1. Common emitter amplifier 2. Common base amplifier 3. Common collector
amplifier
44. What is the different analysis available to analyze a transistor?
1. AC analysis 2. DC analysis
45. How can a DC equivalent circuit of an amplifier be obtained?
By open circuiting the capacitor.
46. How can a AC equivalent circuit of a amplifier be obtained?
By replacing dc supply by a ground and short- circuiting capacitors.
47. What is feed back?
It is the process of injecting some energy from the output and then returns it back to
the input.
48. What is the disadvantage of negative feed back?
Reduces amplifier gain.
49. Define sensitivity.
It is the ratio of percentage change in voltage gain with feedback to the percentage
change in voltage gain without feed back.
50. Define Desensitivity.
It is the ratio of percentage change in voltage gain without feedback to the percentage
change in voltage gain with feed back. the reciprocal of sensitivity.
51, What is a Multivibrator?
The electronic circuits which are used to generate nonsinusoidal waveforms are
called Multivibrators.
52, Name the types of Multivibrators?
Bistable Multivibrator, Monostable Multivibrator,Astable Multivibrator
53, How many stable states do bistable Multivibrator have?
Two stable states.
54, When will the circuit change from stable state in bistable Multivibrator ?
when an external trigger pulse is applied, the circuit changes from one stable state
to another.
55, What are the different names of bistable Multivibrator?
Eccles Jordan circuit, trigger circuit, scale-of-2 toggle circuit, flip-flop and binary.
56, What are the applications of bistable Multivibrator?
It is used in the performance of many digital operations such as counting and
storing of the
Binary information. It also finds applications in the generation and processing of
pulse – type waveforms.
57, What are the other names of monostable Multivibrator?
One-shot, Single-shot, a single-cycle, a single swing, a single step Multivibrator,
Univibrator.
58, Why is monostable Multivibrator called gatting circuit?
The circuit is used to generate the rectangular waveform and hence can be used to
gate other
Circuits hence called gating circuit.
59, Why is monostable Multivibrator called delay circuit?
The time between the transition from quasi-stable state to stable state can be
predetermined and
hence it can be used to introduce time delays with the help of fast transition. Due
to this application is Called delay circuit.
60, What is the main characteristics of Astable Multivibrator
The Astable Multivibrator automatically makes the successive transitions from
one quasi- stable
State to other without any external triggering pulse.
61, What is the other name of Astable Multivibrator- why is it called so?
As it does not require any external pulse for transition, it is called free running
Multivibrator.
62, What are the two types of transister bistable Multivibrator?
i. Fixed bias transistor circuit
ii. Self bias transistor circuit.
63, Why does one of the transistor start conducting ahead of other?
The characteristic of both the transistors are never identical hence after giving
supply one of the
Transistors start conducting ahead of the other.
64, What are the two stable states of bistable Multivibrator?
i. Q1 OFF (cut off) and Q2 ON (Saturation)
ii. Q2 OFF (Cut off) and Q1 On (Saturation)
65, What finally decides the shape of the waveform for bistable multivibrator?
The spacing of the triggering pulses
66, How are the values R1, R2 and VBB chosen in bistable Multivibrator?
It is chosen in such a way that in one state the base current is large enough to
drive the transistor into saturation while in other state the emitter junctions is well below
off.
67, What is the self biased Multivibrator?
The need for the negative power supply in fixed bias bistable Multivibrator can be
eliminated by rising a common emitter resistance RE. The resistance previous the
necessary bias to keep one transistor or and the other OFF in the stable state such
type of biasing is called self biasing and the circuit is called self biased bistable
Multivibrator.
68, What are the other names of speed up capacitors.
i. Commutating Capacitors
ii. Transpose capacitors
69 Define transition time?
It is defined as the time interval during which conduction transfers from one
transistor to other.
70, What is the value of commutating capacitor.
It lies in the range of tens to some hundreds of Pico farads.
71. Define resolving time.
The smallest allowable interval between triggers is called resolving time.
72, Give the expression of fmax with respect to resolving time
Fmax = 1/resolving time.
73, Define gate width
The pulse width is the time for which the circuit remains in the quasi stable state. It is
also called gate width.
74, What are the advantages of monostable Multivibrator.
- used to introduce time delays as gate width is adjustable
- used to produce rectangular waveform and hence can be used as gating circuit.
75, What are the applications of astable Multivibtrator.
- used as a clock for binary login signals
- used as a square wave generator, voltage to frequency converter.
76, What is a complementary Multivibrator
It is turning half the circuit upside down. So one transistor is n-p-n while the
other is p-n-p.
The circuit is called complementary Multivibrator circuit.
77, What is UTP of the Schmitt trigger
When Vi reaches to VBE1 +VE the Q1 gets driven to active region. This input
voltage level is
called upper threshold point.
78, What is the other name for UTP
It is also called input turn on threshold level.
79, What is LTP Schmitt trigger.
The level of Vi at which Q1 becomes OFF and Q2 on is called lower threshold
point.
80, Define transfer Characteristics
The graph of output voltage against input voltage is called transfer characteristics of
Schmitt trigger.
81, What is the important application of Schmitt trigger?
- It is used as an amplitude comparator
- It is used as a squaring circuit.
82, Define Blocking Oscillator?
A special type of wave generator which is used to produce a single narrow pulse
or train of pulses.
83, What are the two important elements of Blocking Oscillator?
Transistor and pulse transformer
84, What are the applications of blocking Oscillator?
It is used in frequency dividers, counter circuits and for switching the other
circuits.
86, Give the expression for co-efficient of coupling
K=M/ÖLpLs
M-> Mututal Inductance
Lp -> Primary Inductance
Ls -> Secondary Inductance
87, Give the formula for transformation ratio
n= Ns/Np = transformation ratio
Ns= Secondary Turns;
Np= Primary turns
88, Define rise time
It is defined by the time required by the pulse to rise from 10% of its amplitude to
90% of its amplitude.
89, Define overshoot.
It is the amount by which the output exceeds its amplitude during first attempt.
90, Define flat top response.
The position of the response between the trailing edge and the leading edge.
91, Define droop or a tilt
The displacement of the pulse amplitude during its flat response is called droop or
a tilt.
92, What are the applications of pulse transformer.
i. to invert the polarity of the pulse
ii. to differentiate pulse
93, When do the core saturates?
When L->o as B-> Bm, the core saturates
94, What is the other name of astable Blocking Oscillator
Free running blocking Oscillator
95, What are the two types of astable Blocking Oscillator?
1, Diode controlled Astable Blocking Oscillator.
2, Re controlled Astable Blocking Oscillator.
96, Define Sweeptime in sawtooth generator
The period during which voltage increases linearly is called sweep time.
97, What is the other name of sawtooth generator?
Ramp generator
98, Define Displacement error in the sawtooth generator?
It is defined as the maximum differenece between the actual sweep voltage and
linear sweep
which passes through the beginning and end points of the actual sweep.
99, What is constant current charging?
A capacitor is charged with a constant current source.
100, What is the miller circuit
Integrator is used to convert a step waveform into ramp waveform.
PART B
1, Explain bistable Multivibrator and its types?
General form of bistable Multivibrator circuit.
· fixed Bias transistor bistable Multivibrator circuit
· self Bias transistor biastable Multivibrator circuit
· Applications
2, Explain about speedup capacitors or commutating capacitors
· Practical self biased bistable Multivibrator
· Explanation about the circuit
3, Explain about Monostable Multivibrator
· Explanation about the circuit diagram
· Pulse width of collector coupled Monostable Multivibrator
· Wareforms
· Applications
4, Explain about collector coupled astable Multivibrator
· Explanation about the circuit diagram
· Wareforms
· Distration & its eliminator
· Applications
5, Explain emitter coupled astable Multivibrator
· Operation and Mathematical analysis
· Practical circuit
· Advantages and disadvantages of the Multivibrator
6, Write in detail about Schmitt Trigger circuit?
· Circuit diagram
· Operation of the circuit
· Schmitt trigger wareforms.
· Hysterisis
· Applications
7, Explain about pulse transformer?
· Ideal pulse transformer model
· Practical equivalent circuit
· Pulse response characteristics
· Applications of pulse transformer
8, Explain Monostable blocking oscillator using emitter timing?
· Circuit Diagram
· Mathematical analysis
· Expression for pulse width
· Triggering circuit for monostable blocking oscillator
9, Write about the core saturation method
· Circuit diagram
· Waveforms of ic and iB when core Saturates.
10, Write about astable blocking oscillator.
· Diode controlled astable blocking Oscillator
· RC controlled astable blocking Oscillator
11, Write about UJT sawtooth generator
· Operation
· Circuit diagram
12, What will happen when a step input voltage is applied to the high pass RC Circuit?
· Derivation
· The output Waveform
13 .Explain the relevant information ,how the negative feed back improves stability
reduce noise and increase input impedance?
Draw the circuit diagram.
Explain detail the following ¾ transfer gain. ¾ stability of gain.
The transfer of gain of the amplifier is not constant as it is depends upon the factors
such as operating point temperature ,etc. This lack of stability can be reduced by
introducing negative feed back.
The signal feed back reduces the amount of the noise signal and non linear distortion.
The factor (1+bA)reduces both input noise and resulting non linear distortion for
considerable improvement. Thus ,noise and non linear distortion also reduced by
same factor.
14.Explain voltage shunt feed back amplifiers?
¾ Draw the circuit diagram. ¾ Draw the equivalent circuit . ¾ Find the input and output impedance after feed back.
15.Explain current series feed back amplifiers?
¾ Draw the circuit diagram. ¾ Draw the equivalent circuit . ¾ Find the input and output impedance after feed back.
16.Explain the classification of amplifiers?
Explain the following in detail. ¾ Voltage amplifier. ¾ Current amplifier. ¾ Trans conductance amplifier. ¾ Trans resistance amplifier.
17.Explain current shunt and voltage shunt feed back amplifiers?
¾ Draw the circuit diagram.
¾ Draw the equivalent circuit . ¾ Find the input and output impedance after feed back.
18. With simple diagrams explain the operation of negative resistance oscillator using
tunnel diode?.
¾ Draw the circuit diagram and graph. ¾ Draw the characteristics of tunnel diode. ¾ Get the expression for time period ‘t’. ¾ Draw the wave form for negative resistance oscillator.
19. Explain RC phase shift oscillator?.
¾ Draw the circuit diagram ¾ Draw the equivalent circuit. ¾ Derive the minimum value of hfe for oscillation.
20. Explain Clapp’s oscillator and derive the expression for frequency of oscillation .
Also explain how frequency stability can be improved Clapp’s oscillator.?
¾ Draw the circuit diagram ¾ Draw the equivalent circuit. ¾ Derive the frequency of oscillation.
21. Explain Hartly oscillator and derive the equation for oscillation ?
¾ Draw the circuit diagram ¾ Draw the equivalent circuit. ¾ Derive the frequency of oscillation.
22. Explain pierce crystal oscillator and derive the equation for oscillation?
¾ Draw the circuit diagram ¾ Draw the equivalent circuit. ¾ Derive the frequency of oscillation.
23. Explain in detail about single tuned amplifier
¾ Draw the circuit diagram
¾ Draw the equivalent circuit. ¾ Derive the expression for band width
24. Explain in detail about double tuned amplifier
¾ Draw the circuit diagram ¾ Draw the equivalent circuit. ¾ Derive the expression for band width
25. Explain in detail about stagger-tuned amplifier
¾ Draw the circuit diagram ¾ Draw the equivalent circuit. ¾ Derive the expression for band width
26. Compare single tuned and double tuned amplifier
¾ Compare the circuit diagram ¾ Compare the equivalent circuit. ¾ Compare the expression for band width
27. Explain the different types of neutralization?
¾ Explain Hazeltine neutralization ¾ Explain Rice neutralization. ¾ Explain Neutrodyne neutralization
Quick Revision for Logic Circuits
Digital Logic Circuits
1) Given the two binary numbers X = 1010100 and Y = 1000011, perform the subtraction (a) X
-Y and (b) Y - X using 2’s complements.
a) X = 1010100
2’s complement of Y = + 0111101
--------------
Sum = 10010001
Discard end carry
Answer: X - Y = 0010001
b) Y = 1000011
2’s complement of X = + 0101100
---------------
Sum = 1101111
There is no end carry,
Therefore the answer is Y-X = -(2’s complement of 1101111) = -0010001
2). Given the two binary numbers X = 1010100 and Y = 1000011, perform the subtraction (a)
X -Y and (b) Y - X using 1’s complements.
a). X - Y = 1010100 - 1000011
X = 1010100
1’s complement of Y = + 0111100
--------------
Sum = 10010000
End -around carry = + 1
--------------
Answer: X - Y = 0010001
b). Y - X = 1000011 - 1010100
Y = 1000011
1’s complement of X = + 0101011
-----------
Sum = + 1101110
There is no end carry.
Therefore the answer is Y - X = -(1’s complement of 1101110) = -0010001
3). What is meant by parity bit?
A parity bit is an extra bit included with a message to make the total number of 1’s either
even or odd. Consider the following two characters and their even and odd parity:
With even parity With odd parity
ASCII A = 1000001 01000001 11000001
ASCII T = 1010100 11010100 01010100
In each case we add an extra bit in the left most position of the code to produce an even number of
1’s in the character for even parity or an odd number of 1’s in the character for odd parity. The
parity bit is helpful in detecting errors during the transmission of information from one location to
another.
4).What are registers?
register is a group of binary cells. A register with n cells can store any discrete quantity of
information that contains n bits. The state of a register is an n-tuple number of 1’s and 0’s, with
each bit designating the state of one cell in the register.
5). What is meant by register transfer?
A register transfer operation is a basic operation in digital systems. It consists of transfer of
binary information from one set of registers into another set of registers. The transfer may be direct
from one register to another, or may pass through data processing circuits to perform an operation.
6). Define binary logic?
Binary logic consists of binary variables and logical operations. The variables are
designated by the alphabets such as A, B, C, x, y, z, etc., with each variable having only two
distinct values: 1 and 0. There are three basic logic operations: AND, OR, and NOT.
7). Define logic gates?
Logic gates are electronic circuits that operate on one or more input signals to produce an
output signal. Electrical signals such as voltages or currents exist throughout a digital system in
either of two recognizable values. Voltage- operated circuits respond to two separate voltage levels
that represent a binary variable equal to logic 1 or logic 0.
8).Define duality property.
Duality property states that every algebraic expression deducible from the postulates of
Boolean algebra remains valid if the operators and identity elements are interchanged. If the dual
of an algebraic expression is desired, we simply interchange OR and AND operators and replace
1’s by 0’s and 0’s by 1’s.
9).Find the complement of the functions F1 = x’yz’ + x’y’z and F2 = x(y’z’ + yz). By applying
De Morgan’s theorem as many times as necessary.
F1’ = (x’yz’ + x’y’z)’ = (x’yz’)’(x’y’z)’ = (x + y’ + z)(x + y +z’)
F2’ = [x(y’z’ + yz)]’ = x’ + (y’z’ + yz)’
= x’ + (y’z’)’(yz)’
= x’ + (y + z)(y’ + z’)
10).Find the complements of the functions F1 = x’yz’ + x’y’z and F2 = x(y’z’ + yz). by taking
their duals and complementing each literal.
F1 = x’yz’ + x’y’z
The dual of F1 is (x’ + y + z’)(x’ + y’ + z)
Complementing each literal: (x + y’ + z)(x + y + z’)
F2 = x(y’z’ + yz).
The dual of F2 is x + (y’ + z’)(y + z).
Complement of each literal: x’ + (y + z)(y’ + z’)
11).State De Morgan’s theorem.
De Morgan suggested two theorems that form important part of Boolean algebra. They are,
1) The complement of a product is equal to the sum of the complements.
(AB)’ = A’ + B’
2) The complement of a sum term is equal to the product of the complements.
(A + B)’ = A’B’
12).Reduce A.A’C
A.A’C = 0.c [A.A’ = 1]
= 0
13). Reduce A(A + B)
A(A + B) = AA + AB
= A(1 + B) [1 + B = 1]
= A.
14. Reduce A’B’C’ + A’BC’ + A’BC
A’B’C’ + A’BC’ + A’BC = A’C’(B’ + B) + A’B’C
= A’C’ + A’BC [A + A’ = 1]
= A’(C’ + BC) = A’(C’ + B) [A + A’B = A + B]
15.) Reduce AB + (AC)’ + AB’C(AB + C)
AB + (AC)’ + AB’C(AB + C) = AB + (AC)’ + AAB’BC + AB’CC
= AB + (AC)’ + AB’CC [A.A’ = 0]
= AB + (AC)’ + AB’C [A.A = 1]
= AB + A’ + C’ =AB’C [(AB)’ = A’ + B’]
= A’ + B + C’ + AB’C [A + AB’ = A + B]
= A’ + B’C + B + C’ [A + A’B = A + B]
= A’ + B + C’ + B’C
=A’ + B + C’ + B’
=A’ + C’ + 1
= 1 [A + 1 =1]
16. Simplify the following expression Y = (A + B)(A + C’ )(B’ + C’ )
Y = (A + B)(A + C’ )(B’ + C’ )
= (AA’ + AC +A’B +BC )(B’ + C’) [A.A’ = 0]
= (AC + A’B + BC)(B’ + C’ )
= AB’C + ACC’ + A’BB’ + A’BC’ + BB’C + BCC’
= AB’C + A’BC’
17).Simplify the following using De Morgan’s theorem [((AB)’C)’’ D]’
[((AB)’C)’’ D]’ = ((AB)’C)’’ + D’ [(AB)’ = A’ + B’]
= (AB)’ C + D’
= (A’ + B’ )C + D’
18.Show that (X + Y’ + XY)( X + Y’)(X’Y) = 0
(X + Y’ + XY)( X + Y’)(X’Y) = (X + Y’ + X)(X + Y’ )(X’ + Y) [A + A’B = A + B]
= (X + Y’ )(X + Y’ )(X’Y) [A + A = 1]
= (X + Y’ )(X’Y) [A.A = 1]
= X.X’ + Y’.X’.Y
= 0 [A.A’ = 0]
19).Prove that ABC + ABC’ + AB’C + A’BC = AB + AC + BC
ABC + ABC’ + AB’C + A’BC =AB(C + C’) + AB’C + A’BC
=AB + AB’C + A’BC
=A(B + B’C) + A’BC
=A(B + C) + A’BC
=AB + AC + A’BC
=B(A + C) + AC
=AB + BC + AC
=AB + AC +BC ...Proved
20).Convert the given expression in canonical SOP form Y = AC + AB + BC
Y = AC + AB + BC
=AC(B + B’ ) + AB(C + C’ ) + (A + A’)BC
=ABC + ABC’ + AB’C + AB’C’ + ABC + ABC’ + ABC
=ABC + ABC’ +AB’C + AB’C’ [A + A =1]
21).Convert the given expression in canonical POS form Y = ( A + B)(B + C)(A + C)
Y = ( A + B)(B + C)(A + C)
= (A + B + C.C’ )(B + C + A.A’ )(A + B.B’ + C)
= (A + B + C)(A + B + C’ )(A + B +C)(A’ + B +C)(A + B + C)(A + B’ + C) [A + BC
= (A + B)(A + C)
Distributive law]
= (A + B + C)(A + B + C’)(A’ + B + C)(A’ + B + C)(A + B’ + C)
22). Find the minterms of the logical expression Y = A’B’C’ + A’B’C + A’BC + ABC’
Y = A’B’C’ + A’B’C + A’BC + ABC’
=m0 + m1 +m3 +m6
=™P
23).Write the maxterms corresponding to the logical expression Y = (A + B + C’ )(A + B’ +
C’)(A’ + B’ + C)
Y = (A + B + C’ )(A + B’ + C’)(A’ + B’ + C)
=M1.M3.M6
=š0
24).Convert (4021.2)5 to its equivalent decimal.
(4021.2)5 = 4 x 53 + 0 x 52 + 2 x 51 + 1 x 50 + 2 x 5-1
= (511.4)10
25) Using 10’s complement subtract 72532 - 3250
M = 72532
10’s complement of N = + 96750
-----------
Sum = 169282
Discard end carry
Answer = 69282
26) What are called don’t care conditions?
In some logic circuits certain input conditions never occur, therefore the corresponding output
never appears. In such cases the output level is not defined, it can be either high or low. These
output levels are indicated by ‘X’ or‘d’ in the truth tables and are called don’t care conditions or
incompletely specified functions.
27) Write down the steps in implementing a Boolean function with levels of NAND Gates?
Simplify the function and express it in sum of products.
Draw a NAND gate for each product term of the expression that has at least two literals.
The inputs to each NAND gate are the literals of the term. This constitutes a group of first
level gates. Draw a single gate using the AND-invert or the invert-OR graphic symbol in
the second level, with inputs coming from outputs of first level gates.
A term with a single literal requires an inverter in the first level. How ever if the single literal
is complemented, it can be connected directly to an input of the second level NAND gate.
28) Give the general procedure for converting a Boolean expression in to multilevel NAND
diagram?
Draw the AND-OR diagram of the Boolean expression.
Convert all AND gates to NAND gates with AND-invert graphic symbols.
Convert all OR gates to NAND gates with invert-OR graphic symbols.
Check all the bubbles in the same diagram. For every bubble that is not compensated by
another circle along the same line, insert an inverter or complement the input literal.
29) What are combinational circuits?
A combinational circuit consists of logic gates whose outputs at any time are determined
from the present combination of inputs. A combinational circuit performs an operation that can be
specified logically by a set of Boolean functions. It consists of input variables, logic gates, and
output variables.
30) Give the design procedures for the designing of a combinational circuit.
The procedure involves the following steps,
From the specification of the circuit, determine the required number of inputs and outputs and
assign a symbol to each.
Derive the truth table that defines the required relationships between inputs and outputs.
Obtain the simplified Boolean functions for each output as a function of the input variables.
Draw the logic diagram and verify the correctness of the design.
31) Define half adder.
A combinational circuit that performs the addition of two bits is called a half adder. A half
adder needs two binary inputs and two binary outputs. The input variables designate the augend
and addend bits; the output variables produce the sum and carry
32) Define full adder?
A combinational circuit that performs the adtion of three bits is a full adder.It consists of
three inputs and two outputs.
33) Define binary adder.
A binary adder is a digital circuit that produces the arithmetic sum of two binary numbers. It
can be constructed with full adders constructed in cascade, with the output carry from each full
adder connected to the input carry of the next full adder in the chain.
34) What is overflow?
Over flow is a problem in digital computers because the number of bits that hold the
number is finite and a result that contains n + 1 bits cannot be accommodated. For this reason
many computers detect the occurrence of an overflow, and when it occurs a corresponding flip flop
is set that can be checked by the user. An overflow condition can be detected by observing the
carry into sign bit position and the carry out of the sign bit position. If these two carries are not
equal, an overflow has occurred.
35) Define magnitude comparator?
A magnitude comparator is a combinational circuit that compares two numbers, A and B,
and determines their relative magnitudes. The outcome of the comparison is specified by three
binary variables that indicate whether a>b, A = b, or A < B.
36) What are decoders?
A decoder is a combinational circuit that converts binary information from n input lines to a
maximum of 2n unique output lines. If the n bit coded information has unused combinations, he
decoder may have fewer than 2n outputs.
37) What are encoders?
An encoder is a digital circuit that performs the inverse operation of a decoder. An encoder
has 2n and n output lines. The output lines generate the binary code corresponding to the input
value.
38) Define priority encoder?
A priority encoder is an encoder circuit that includes the priority function. The operation of
priority encoder is such that if two or more inputs are equal to 1 at the same time, the input having
the highest priority will take precedence.
39) Define multiplexer?
A multiplexer is combinational circuit that selects binary information from one of many input
lines and directs it to a single output line. The selection of a particular input line is controlled by a
set of selection lines. Normally there are 2n input lines and n selection lines whose bit combinations
determine which input is selected.
40) Define binary decoder?
A decoder which has an n- bit binary input code and a one activated output out-of -2n
output code is called binary decoder. A binary decoder is used when it is necessary to activate
exactly one of 2n outputs based on an n-bit input value.
41. Represent binary number 1101 - 101 in power of 2 and find its decimal equivalent
N = 1 x 2 3 + 1 x 2 2 + 0 x 2 1 + 1 x 2 0 + 1 x 2 -1 + 0 x 2 -2 + 1 x 2 -3
= 13.625 10
42. Convert (634) 8 to binary
6 3 4
110 011 100
Ans = 110 011 100
43. Convert (9 B 2 - 1A) H to its decimal equivalent.
N = 9 x 16 2 + B x 16 1 + 2 x 16 0 + 1 x 16 -1 + A (10) x 16 -2
= 2304 + 176 + 2 + 0.0625 + 0.039
= 2482.1 10
44. What are the different classification of binary codes?
1. Weighted codes
2. Non - weighted codes
3. Reflective codes
. Sequential codes
5. Alphanumeric codes
6. Error Detecting and correcting codes.
45. Convert 0.640625 decimal number to its octal equivalent.
0.640625 x 8 = 5.125
0.125 x 8 = 1.0
Ans. = 0.640 625 10 = 0.51
46. Convert 0.1289062 decimal number to its hex equivalent
0.1289062 x 16 = 2.0625
0.0625 x 16 = 1.0
Ans. = 0.21 16
47. Convert decimal number 22.64 to hexadecimal number.
16 22 -6
16 1 -1
0
0.64 x 16 = 10.24
0.24 x 16 = 3.84
0.84 x 16 = 13.44
.44 x 16 = 7.04
Ans. = (16 . A 3 D 7) 16.3
48. What are the two steps in Gray to binary conversion?
The MSB of the binary number is the same as the MSB of the gray code number.
So write it down.To obtain the next binary digit, perform an exclusive OR operation
b/n the bit just written down and the next gray code bit. Write down the result.
49. Convert gray code 101011 into its binary equivalent.
Gray Code : 1 0 1 0 1 1
Binary Code 1 1 0 0 1 0
50. Convert 10111011 is binary into its equivalent gray code.
Binary Code: 1 0 1 1 1 0 1 0 1 1
Gray code : 1 1 1 0 0 1 1 0
1 0 1 0
0 0 1 1
1 1 0 1
52. Substract (0 1 0 1) 2 from (1 0 1 1) 2
1 0 1 0
0 1 0 1
0 1 1 0
53. Find 2’S complement of (1 0 1 0 0 0 1 1) 2
0 1 0 1 1 1 0 0 1 1’s Complement
+ 0 0 0 0 0 0 0 1
0 1 0 1 1 1 0 1 0 2’s complement.
54. Substract 1 1 1 0 0 1 2 from 1 0 1 0 1 1 2 using 2’s complement method
1 0 1 0 1 1
+ 0 0 0 1 1 1 2’s comp. of 1 1 1 0 0 1
1 1 0 0 1 0 Ans. in 2’s complement form
- 0 0 1 1 1 0 Answer in true form.
55. What are the advantages of 1’s complement subtraction?
1) The 1’s complement subtraction can be accomplished with an binary adder.
Therefore, this method is useful in arithmetic logic circuits.
2) The is complement of a number is easily obtained by inverting each bit in the
number
56. Find the excess -3 code and 9’s complement of the number 403 10
4 0 3
0 1 0 0 0 0 0 0 0 0 1 1
0 0 1 1 0 0 1 1 0 0 1 1 +
0 1 1 1 0 0 1 1 0 1 1 0 excess 3 code
9’s complement 1 0 0 0 1 1 0 0 1 0 0 1
57. Write the names of basic logical operators.
1. NOT / INVERT
2. AND
3. OR
58. Simplify the following expression
y = (A + B) (A = C) (B + C)
= (A A + A C + A B + B C) (B + C)
= (A C + A B + B C) (B + C)
= A B C + A C C + A B B + A B C + B B C + B C C
= A B C = A B C
59. Show that the NAND connection is not associative
The NAND connection is not associative says that
A . B . C A . B. C
A . B + C A + B C
AB + C A + BC
60. What is a Logic gate?
Logic gates are the basic elements that make up a digital system. The electronic gate is a
circuit that is able to operate on a number of binary inputs in order to perform a particular
logical function.
61. Write the names of Universal gates.
1. NAND gate
2. NOR gate
62. Why are NAND and NOR gates known as universal gates?
The NAND and NOR gates are known as universal gates, since any logic function
can be implemented using NAND or NOR gates.
63. Define combinational logic
When logic gates are connected together to produce a specified output for certain
specified combinations of input variables, with no storage involved, the resulting
circuit is called combinational logic.
64. Explain the design procedure for combinational circuits
¢ The problem definition
¢ The determination of number of available input variables & required O/P
variables.
¢ Assigning letter symbols to I/O variables
¢ Obtain simplified boolean expression for each O/P.
¢ Obtain the logic diagram.
65. Define half adder and full adder
The logic circuit which performs the addition of two bits is a half adder.
The circuit which performs the addition of three bits is a full adder.
66. Define Decoder?
A decoder is a multiple - input multiple output logic circuit which converts coded
inputs into coded outputs where the input and output codes are different.
67. What is binary decoder?
A decoder which has an n-bit binary i/p code and a one activated output out of 2l.
output code is called binary decoder. It is used when it is necessary to activate
exactly one of 2 n out puts based on an n - bit input value.
68. Define Encoder?
An encoder has 2n input lines and n output lines. In encoder the output lines generate
the binary code corresponding to the input value.
69. What is priority Encoder?
A priority encoder is an encoder circuit that includes the priority function. In priority encoder, if 2 or
more inputs are equal to 1 at the same time, the input having the highest priority will take
precedence.
70. Define multiplexer?
Multiplexer is a digital switch. If allows digital information from several sources to
be routed onto a single output line.
71. What do you mean by comparator
A comparator is a special combinational circuit designed primarily to compare the
relative magnitude of two binary numbers.
72. List basic types of programmable logic devices.
1. Read only memory
2. Programmable logic Array
3. Programmable Array Logic
73. Define ROM
A read only memory is a device that includes both the decoder and the OR gates
within a single IC package.
74. Define address and word:
In a ROM, each bit combination of the input variable is called on address. Each bit
combination that comes out of the output lines is called a word.
75. What are the types of ROM
1. Masked ROM.
2. Programmable Read only Memory
3. Erasable Programmable Read only memory.
4. Electrically Erasable Programmable Read only Memory.
76. What is programmable logic array? How it differs from ROM?
In some cases the number of don™t care conditions is excessive, it is more economical to use a
second type of LSI component called a PLA
A PLA is similar to a ROM in concept; however it does not provide full decoding of the variables
and does not generates all the minterms as in the ROM..12
77. What is mask - programmable?
With a mask programmable PLA, the user must submit a PLA PLA program table to the
manufacturer.
78. What is field programmable logic array?
The second type of PLA is called a field programmable logic array. The EPLA can
be programmed by the user by means of certain recommended procedures.
79. Give the comparison between prom and PLA.
PROM PLA
1. And array is fixed and or Both AND and OR arrays are
array is programmable. Programmable.
2. Cheaper and simple to use. Costliest and complex than PROMS.
80. Define even parity
In even parity the added parity bit will make the total number of 1s an even amount.
81. Define sequential circuit?
In sequential circuits the output variables dependent not only on the present input
variables but they also depend up on the past history of these input variables.
82. Give the comparison between combinational circuits and sequential circuits.
Memory unit is not required Memory unity is required
Parallel adder is a combinational circuit Serial adder is a sequential circuit
83. What do you mean by present state?
The information stored in the memory elements at any given time define™s the present state of the
sequential circuit.
84. What do you mean by next state?
The present state and the external inputs determine the outputs and the next state of the
sequential circuit.
85. What are the types of sequential circuits?
1. Synchronous sequential circuits
2. Asynchronous sequential circuits
86. Define synchronous sequential circuit
In synchronous sequential circuits, signals can affect the memory elements only at
discrete instant of time.
87. Define Asynchronous sequential circuit?
In asynchronous sequential circuits change in input signals can affect memory element at any
instant of time
88. Define flip-flop
Flip - flop is a sequential device that normally. samples its inputs and changes its
outputs only at times determined by clocking signal.
89. List various types of flip-flop
1] S.R. latch
2] D latch
3] Clocked J.K. flip-flop
4] T flip-flop
90. What is race around condition?
In the JK latch, the output is feedback to the input, and therefore change in the
output results change in the input. Due to this in the positive half of the clock pulse
if J and K are both high then output toggles continuously. This condition is known
as race around condition.
91. Define rise time and fall time?
The time required to change the voltage level from 10% to 90% is known as rise
time, and the time required to change the voltage level from 90% to 10% is known
as fall time.
92. Define propagation Delay?
A propagation delay is the time required to change the output after application of the input.
93. Define shift Registers
The binary information in a register can be moved from stage to stage within the
register or into or out of the register upon application of clock pulses. This type of
bit movement or shifting is essential for certain arithmetic and logic operations used
in microprocessors.
This gives rise to a group of registers called shift registers.
94. What are the types of shift register?
1. Serial in serial out shift register?
2. Serial in parallel out shift register
3. Parallel in serial out shift register
4. Parallel in parallel out shift register
5. Bidirectional shift register shift register.
95. What are the types of counter?
1. Synchronous counter
2. Asynchronous Counter
96. What are the two models in synchronous sequential circuits.
1. Moore circuit
2. Mealy circuit
97. What is moore circuit?
When the output of the sequential circuit depends only on the present state of the
flip-flop, the sequential circuit is referred to as moore circuit.
98. What is Mealy circuit?
When the output of the sequential circuit depends on both the present state of flipflop
and on the input, the sequential circuit is referred to as mealy circuit.
99. Define successor
In a state diagram, if an input sequence, x takes a machine from state si to state sj,
then sj is said to be the x - successor of si.
100. Define strongly connected machine?
In a sequential machine many times certain subsets of states may not be reachable
from other subsets of states, even if the machine does not contain any terminal state.
However, if for every pair of states si, sj of a sequential machine, there eights an
input sequence which takes M from Si to Sj then sequential machine M is said to be
strongly connected.
1) Given the two binary numbers X = 1010100 and Y = 1000011, perform the subtraction (a) X
-Y and (b) Y - X using 2’s complements.
a) X = 1010100
2’s complement of Y = + 0111101
--------------
Sum = 10010001
Discard end carry
Answer: X - Y = 0010001
b) Y = 1000011
2’s complement of X = + 0101100
---------------
Sum = 1101111
There is no end carry,
Therefore the answer is Y-X = -(2’s complement of 1101111) = -0010001
2). Given the two binary numbers X = 1010100 and Y = 1000011, perform the subtraction (a)
X -Y and (b) Y - X using 1’s complements.
a). X - Y = 1010100 - 1000011
X = 1010100
1’s complement of Y = + 0111100
--------------
Sum = 10010000
End -around carry = + 1
--------------
Answer: X - Y = 0010001
b). Y - X = 1000011 - 1010100
Y = 1000011
1’s complement of X = + 0101011
-----------
Sum = + 1101110
There is no end carry.
Therefore the answer is Y - X = -(1’s complement of 1101110) = -0010001
3). What is meant by parity bit?
A parity bit is an extra bit included with a message to make the total number of 1’s either
even or odd. Consider the following two characters and their even and odd parity:
With even parity With odd parity
ASCII A = 1000001 01000001 11000001
ASCII T = 1010100 11010100 01010100
In each case we add an extra bit in the left most position of the code to produce an even number of
1’s in the character for even parity or an odd number of 1’s in the character for odd parity. The
parity bit is helpful in detecting errors during the transmission of information from one location to
another.
4).What are registers?
register is a group of binary cells. A register with n cells can store any discrete quantity of
information that contains n bits. The state of a register is an n-tuple number of 1’s and 0’s, with
each bit designating the state of one cell in the register.
5). What is meant by register transfer?
A register transfer operation is a basic operation in digital systems. It consists of transfer of
binary information from one set of registers into another set of registers. The transfer may be direct
from one register to another, or may pass through data processing circuits to perform an operation.
6). Define binary logic?
Binary logic consists of binary variables and logical operations. The variables are
designated by the alphabets such as A, B, C, x, y, z, etc., with each variable having only two
distinct values: 1 and 0. There are three basic logic operations: AND, OR, and NOT.
7). Define logic gates?
Logic gates are electronic circuits that operate on one or more input signals to produce an
output signal. Electrical signals such as voltages or currents exist throughout a digital system in
either of two recognizable values. Voltage- operated circuits respond to two separate voltage levels
that represent a binary variable equal to logic 1 or logic 0.
8).Define duality property.
Duality property states that every algebraic expression deducible from the postulates of
Boolean algebra remains valid if the operators and identity elements are interchanged. If the dual
of an algebraic expression is desired, we simply interchange OR and AND operators and replace
1’s by 0’s and 0’s by 1’s.
9).Find the complement of the functions F1 = x’yz’ + x’y’z and F2 = x(y’z’ + yz). By applying
De Morgan’s theorem as many times as necessary.
F1’ = (x’yz’ + x’y’z)’ = (x’yz’)’(x’y’z)’ = (x + y’ + z)(x + y +z’)
F2’ = [x(y’z’ + yz)]’ = x’ + (y’z’ + yz)’
= x’ + (y’z’)’(yz)’
= x’ + (y + z)(y’ + z’)
10).Find the complements of the functions F1 = x’yz’ + x’y’z and F2 = x(y’z’ + yz). by taking
their duals and complementing each literal.
F1 = x’yz’ + x’y’z
The dual of F1 is (x’ + y + z’)(x’ + y’ + z)
Complementing each literal: (x + y’ + z)(x + y + z’)
F2 = x(y’z’ + yz).
The dual of F2 is x + (y’ + z’)(y + z).
Complement of each literal: x’ + (y + z)(y’ + z’)
11).State De Morgan’s theorem.
De Morgan suggested two theorems that form important part of Boolean algebra. They are,
1) The complement of a product is equal to the sum of the complements.
(AB)’ = A’ + B’
2) The complement of a sum term is equal to the product of the complements.
(A + B)’ = A’B’
12).Reduce A.A’C
A.A’C = 0.c [A.A’ = 1]
= 0
13). Reduce A(A + B)
A(A + B) = AA + AB
= A(1 + B) [1 + B = 1]
= A.
14. Reduce A’B’C’ + A’BC’ + A’BC
A’B’C’ + A’BC’ + A’BC = A’C’(B’ + B) + A’B’C
= A’C’ + A’BC [A + A’ = 1]
= A’(C’ + BC) = A’(C’ + B) [A + A’B = A + B]
15.) Reduce AB + (AC)’ + AB’C(AB + C)
AB + (AC)’ + AB’C(AB + C) = AB + (AC)’ + AAB’BC + AB’CC
= AB + (AC)’ + AB’CC [A.A’ = 0]
= AB + (AC)’ + AB’C [A.A = 1]
= AB + A’ + C’ =AB’C [(AB)’ = A’ + B’]
= A’ + B + C’ + AB’C [A + AB’ = A + B]
= A’ + B’C + B + C’ [A + A’B = A + B]
= A’ + B + C’ + B’C
=A’ + B + C’ + B’
=A’ + C’ + 1
= 1 [A + 1 =1]
16. Simplify the following expression Y = (A + B)(A + C’ )(B’ + C’ )
Y = (A + B)(A + C’ )(B’ + C’ )
= (AA’ + AC +A’B +BC )(B’ + C’) [A.A’ = 0]
= (AC + A’B + BC)(B’ + C’ )
= AB’C + ACC’ + A’BB’ + A’BC’ + BB’C + BCC’
= AB’C + A’BC’
17).Simplify the following using De Morgan’s theorem [((AB)’C)’’ D]’
[((AB)’C)’’ D]’ = ((AB)’C)’’ + D’ [(AB)’ = A’ + B’]
= (AB)’ C + D’
= (A’ + B’ )C + D’
18.Show that (X + Y’ + XY)( X + Y’)(X’Y) = 0
(X + Y’ + XY)( X + Y’)(X’Y) = (X + Y’ + X)(X + Y’ )(X’ + Y) [A + A’B = A + B]
= (X + Y’ )(X + Y’ )(X’Y) [A + A = 1]
= (X + Y’ )(X’Y) [A.A = 1]
= X.X’ + Y’.X’.Y
= 0 [A.A’ = 0]
19).Prove that ABC + ABC’ + AB’C + A’BC = AB + AC + BC
ABC + ABC’ + AB’C + A’BC =AB(C + C’) + AB’C + A’BC
=AB + AB’C + A’BC
=A(B + B’C) + A’BC
=A(B + C) + A’BC
=AB + AC + A’BC
=B(A + C) + AC
=AB + BC + AC
=AB + AC +BC ...Proved
20).Convert the given expression in canonical SOP form Y = AC + AB + BC
Y = AC + AB + BC
=AC(B + B’ ) + AB(C + C’ ) + (A + A’)BC
=ABC + ABC’ + AB’C + AB’C’ + ABC + ABC’ + ABC
=ABC + ABC’ +AB’C + AB’C’ [A + A =1]
21).Convert the given expression in canonical POS form Y = ( A + B)(B + C)(A + C)
Y = ( A + B)(B + C)(A + C)
= (A + B + C.C’ )(B + C + A.A’ )(A + B.B’ + C)
= (A + B + C)(A + B + C’ )(A + B +C)(A’ + B +C)(A + B + C)(A + B’ + C) [A + BC
= (A + B)(A + C)
Distributive law]
= (A + B + C)(A + B + C’)(A’ + B + C)(A’ + B + C)(A + B’ + C)
22). Find the minterms of the logical expression Y = A’B’C’ + A’B’C + A’BC + ABC’
Y = A’B’C’ + A’B’C + A’BC + ABC’
=m0 + m1 +m3 +m6
=™P
23).Write the maxterms corresponding to the logical expression Y = (A + B + C’ )(A + B’ +
C’)(A’ + B’ + C)
Y = (A + B + C’ )(A + B’ + C’)(A’ + B’ + C)
=M1.M3.M6
=š0
24).Convert (4021.2)5 to its equivalent decimal.
(4021.2)5 = 4 x 53 + 0 x 52 + 2 x 51 + 1 x 50 + 2 x 5-1
= (511.4)10
25) Using 10’s complement subtract 72532 - 3250
M = 72532
10’s complement of N = + 96750
-----------
Sum = 169282
Discard end carry
Answer = 69282
26) What are called don’t care conditions?
In some logic circuits certain input conditions never occur, therefore the corresponding output
never appears. In such cases the output level is not defined, it can be either high or low. These
output levels are indicated by ‘X’ or‘d’ in the truth tables and are called don’t care conditions or
incompletely specified functions.
27) Write down the steps in implementing a Boolean function with levels of NAND Gates?
Simplify the function and express it in sum of products.
Draw a NAND gate for each product term of the expression that has at least two literals.
The inputs to each NAND gate are the literals of the term. This constitutes a group of first
level gates. Draw a single gate using the AND-invert or the invert-OR graphic symbol in
the second level, with inputs coming from outputs of first level gates.
A term with a single literal requires an inverter in the first level. How ever if the single literal
is complemented, it can be connected directly to an input of the second level NAND gate.
28) Give the general procedure for converting a Boolean expression in to multilevel NAND
diagram?
Draw the AND-OR diagram of the Boolean expression.
Convert all AND gates to NAND gates with AND-invert graphic symbols.
Convert all OR gates to NAND gates with invert-OR graphic symbols.
Check all the bubbles in the same diagram. For every bubble that is not compensated by
another circle along the same line, insert an inverter or complement the input literal.
29) What are combinational circuits?
A combinational circuit consists of logic gates whose outputs at any time are determined
from the present combination of inputs. A combinational circuit performs an operation that can be
specified logically by a set of Boolean functions. It consists of input variables, logic gates, and
output variables.
30) Give the design procedures for the designing of a combinational circuit.
The procedure involves the following steps,
From the specification of the circuit, determine the required number of inputs and outputs and
assign a symbol to each.
Derive the truth table that defines the required relationships between inputs and outputs.
Obtain the simplified Boolean functions for each output as a function of the input variables.
Draw the logic diagram and verify the correctness of the design.
31) Define half adder.
A combinational circuit that performs the addition of two bits is called a half adder. A half
adder needs two binary inputs and two binary outputs. The input variables designate the augend
and addend bits; the output variables produce the sum and carry
32) Define full adder?
A combinational circuit that performs the adtion of three bits is a full adder.It consists of
three inputs and two outputs.
33) Define binary adder.
A binary adder is a digital circuit that produces the arithmetic sum of two binary numbers. It
can be constructed with full adders constructed in cascade, with the output carry from each full
adder connected to the input carry of the next full adder in the chain.
34) What is overflow?
Over flow is a problem in digital computers because the number of bits that hold the
number is finite and a result that contains n + 1 bits cannot be accommodated. For this reason
many computers detect the occurrence of an overflow, and when it occurs a corresponding flip flop
is set that can be checked by the user. An overflow condition can be detected by observing the
carry into sign bit position and the carry out of the sign bit position. If these two carries are not
equal, an overflow has occurred.
35) Define magnitude comparator?
A magnitude comparator is a combinational circuit that compares two numbers, A and B,
and determines their relative magnitudes. The outcome of the comparison is specified by three
binary variables that indicate whether a>b, A = b, or A < B.
36) What are decoders?
A decoder is a combinational circuit that converts binary information from n input lines to a
maximum of 2n unique output lines. If the n bit coded information has unused combinations, he
decoder may have fewer than 2n outputs.
37) What are encoders?
An encoder is a digital circuit that performs the inverse operation of a decoder. An encoder
has 2n and n output lines. The output lines generate the binary code corresponding to the input
value.
38) Define priority encoder?
A priority encoder is an encoder circuit that includes the priority function. The operation of
priority encoder is such that if two or more inputs are equal to 1 at the same time, the input having
the highest priority will take precedence.
39) Define multiplexer?
A multiplexer is combinational circuit that selects binary information from one of many input
lines and directs it to a single output line. The selection of a particular input line is controlled by a
set of selection lines. Normally there are 2n input lines and n selection lines whose bit combinations
determine which input is selected.
40) Define binary decoder?
A decoder which has an n- bit binary input code and a one activated output out-of -2n
output code is called binary decoder. A binary decoder is used when it is necessary to activate
exactly one of 2n outputs based on an n-bit input value.
41. Represent binary number 1101 - 101 in power of 2 and find its decimal equivalent
N = 1 x 2 3 + 1 x 2 2 + 0 x 2 1 + 1 x 2 0 + 1 x 2 -1 + 0 x 2 -2 + 1 x 2 -3
= 13.625 10
42. Convert (634) 8 to binary
6 3 4
110 011 100
Ans = 110 011 100
43. Convert (9 B 2 - 1A) H to its decimal equivalent.
N = 9 x 16 2 + B x 16 1 + 2 x 16 0 + 1 x 16 -1 + A (10) x 16 -2
= 2304 + 176 + 2 + 0.0625 + 0.039
= 2482.1 10
44. What are the different classification of binary codes?
1. Weighted codes
2. Non - weighted codes
3. Reflective codes
. Sequential codes
5. Alphanumeric codes
6. Error Detecting and correcting codes.
45. Convert 0.640625 decimal number to its octal equivalent.
0.640625 x 8 = 5.125
0.125 x 8 = 1.0
Ans. = 0.640 625 10 = 0.51
46. Convert 0.1289062 decimal number to its hex equivalent
0.1289062 x 16 = 2.0625
0.0625 x 16 = 1.0
Ans. = 0.21 16
47. Convert decimal number 22.64 to hexadecimal number.
16 22 -6
16 1 -1
0
0.64 x 16 = 10.24
0.24 x 16 = 3.84
0.84 x 16 = 13.44
.44 x 16 = 7.04
Ans. = (16 . A 3 D 7) 16.3
48. What are the two steps in Gray to binary conversion?
The MSB of the binary number is the same as the MSB of the gray code number.
So write it down.To obtain the next binary digit, perform an exclusive OR operation
b/n the bit just written down and the next gray code bit. Write down the result.
49. Convert gray code 101011 into its binary equivalent.
Gray Code : 1 0 1 0 1 1
Binary Code 1 1 0 0 1 0
50. Convert 10111011 is binary into its equivalent gray code.
Binary Code: 1 0 1 1 1 0 1 0 1 1
Gray code : 1 1 1 0 0 1 1 0
1 0 1 0
0 0 1 1
1 1 0 1
52. Substract (0 1 0 1) 2 from (1 0 1 1) 2
1 0 1 0
0 1 0 1
0 1 1 0
53. Find 2’S complement of (1 0 1 0 0 0 1 1) 2
0 1 0 1 1 1 0 0 1 1’s Complement
+ 0 0 0 0 0 0 0 1
0 1 0 1 1 1 0 1 0 2’s complement.
54. Substract 1 1 1 0 0 1 2 from 1 0 1 0 1 1 2 using 2’s complement method
1 0 1 0 1 1
+ 0 0 0 1 1 1 2’s comp. of 1 1 1 0 0 1
1 1 0 0 1 0 Ans. in 2’s complement form
- 0 0 1 1 1 0 Answer in true form.
55. What are the advantages of 1’s complement subtraction?
1) The 1’s complement subtraction can be accomplished with an binary adder.
Therefore, this method is useful in arithmetic logic circuits.
2) The is complement of a number is easily obtained by inverting each bit in the
number
56. Find the excess -3 code and 9’s complement of the number 403 10
4 0 3
0 1 0 0 0 0 0 0 0 0 1 1
0 0 1 1 0 0 1 1 0 0 1 1 +
0 1 1 1 0 0 1 1 0 1 1 0 excess 3 code
9’s complement 1 0 0 0 1 1 0 0 1 0 0 1
57. Write the names of basic logical operators.
1. NOT / INVERT
2. AND
3. OR
58. Simplify the following expression
y = (A + B) (A = C) (B + C)
= (A A + A C + A B + B C) (B + C)
= (A C + A B + B C) (B + C)
= A B C + A C C + A B B + A B C + B B C + B C C
= A B C = A B C
59. Show that the NAND connection is not associative
The NAND connection is not associative says that
A . B . C A . B. C
A . B + C A + B C
AB + C A + BC
60. What is a Logic gate?
Logic gates are the basic elements that make up a digital system. The electronic gate is a
circuit that is able to operate on a number of binary inputs in order to perform a particular
logical function.
61. Write the names of Universal gates.
1. NAND gate
2. NOR gate
62. Why are NAND and NOR gates known as universal gates?
The NAND and NOR gates are known as universal gates, since any logic function
can be implemented using NAND or NOR gates.
63. Define combinational logic
When logic gates are connected together to produce a specified output for certain
specified combinations of input variables, with no storage involved, the resulting
circuit is called combinational logic.
64. Explain the design procedure for combinational circuits
¢ The problem definition
¢ The determination of number of available input variables & required O/P
variables.
¢ Assigning letter symbols to I/O variables
¢ Obtain simplified boolean expression for each O/P.
¢ Obtain the logic diagram.
65. Define half adder and full adder
The logic circuit which performs the addition of two bits is a half adder.
The circuit which performs the addition of three bits is a full adder.
66. Define Decoder?
A decoder is a multiple - input multiple output logic circuit which converts coded
inputs into coded outputs where the input and output codes are different.
67. What is binary decoder?
A decoder which has an n-bit binary i/p code and a one activated output out of 2l.
output code is called binary decoder. It is used when it is necessary to activate
exactly one of 2 n out puts based on an n - bit input value.
68. Define Encoder?
An encoder has 2n input lines and n output lines. In encoder the output lines generate
the binary code corresponding to the input value.
69. What is priority Encoder?
A priority encoder is an encoder circuit that includes the priority function. In priority encoder, if 2 or
more inputs are equal to 1 at the same time, the input having the highest priority will take
precedence.
70. Define multiplexer?
Multiplexer is a digital switch. If allows digital information from several sources to
be routed onto a single output line.
71. What do you mean by comparator
A comparator is a special combinational circuit designed primarily to compare the
relative magnitude of two binary numbers.
72. List basic types of programmable logic devices.
1. Read only memory
2. Programmable logic Array
3. Programmable Array Logic
73. Define ROM
A read only memory is a device that includes both the decoder and the OR gates
within a single IC package.
74. Define address and word:
In a ROM, each bit combination of the input variable is called on address. Each bit
combination that comes out of the output lines is called a word.
75. What are the types of ROM
1. Masked ROM.
2. Programmable Read only Memory
3. Erasable Programmable Read only memory.
4. Electrically Erasable Programmable Read only Memory.
76. What is programmable logic array? How it differs from ROM?
In some cases the number of don™t care conditions is excessive, it is more economical to use a
second type of LSI component called a PLA
A PLA is similar to a ROM in concept; however it does not provide full decoding of the variables
and does not generates all the minterms as in the ROM..12
77. What is mask - programmable?
With a mask programmable PLA, the user must submit a PLA PLA program table to the
manufacturer.
78. What is field programmable logic array?
The second type of PLA is called a field programmable logic array. The EPLA can
be programmed by the user by means of certain recommended procedures.
79. Give the comparison between prom and PLA.
PROM PLA
1. And array is fixed and or Both AND and OR arrays are
array is programmable. Programmable.
2. Cheaper and simple to use. Costliest and complex than PROMS.
80. Define even parity
In even parity the added parity bit will make the total number of 1s an even amount.
81. Define sequential circuit?
In sequential circuits the output variables dependent not only on the present input
variables but they also depend up on the past history of these input variables.
82. Give the comparison between combinational circuits and sequential circuits.
Memory unit is not required Memory unity is required
Parallel adder is a combinational circuit Serial adder is a sequential circuit
83. What do you mean by present state?
The information stored in the memory elements at any given time define™s the present state of the
sequential circuit.
84. What do you mean by next state?
The present state and the external inputs determine the outputs and the next state of the
sequential circuit.
85. What are the types of sequential circuits?
1. Synchronous sequential circuits
2. Asynchronous sequential circuits
86. Define synchronous sequential circuit
In synchronous sequential circuits, signals can affect the memory elements only at
discrete instant of time.
87. Define Asynchronous sequential circuit?
In asynchronous sequential circuits change in input signals can affect memory element at any
instant of time
88. Define flip-flop
Flip - flop is a sequential device that normally. samples its inputs and changes its
outputs only at times determined by clocking signal.
89. List various types of flip-flop
1] S.R. latch
2] D latch
3] Clocked J.K. flip-flop
4] T flip-flop
90. What is race around condition?
In the JK latch, the output is feedback to the input, and therefore change in the
output results change in the input. Due to this in the positive half of the clock pulse
if J and K are both high then output toggles continuously. This condition is known
as race around condition.
91. Define rise time and fall time?
The time required to change the voltage level from 10% to 90% is known as rise
time, and the time required to change the voltage level from 90% to 10% is known
as fall time.
92. Define propagation Delay?
A propagation delay is the time required to change the output after application of the input.
93. Define shift Registers
The binary information in a register can be moved from stage to stage within the
register or into or out of the register upon application of clock pulses. This type of
bit movement or shifting is essential for certain arithmetic and logic operations used
in microprocessors.
This gives rise to a group of registers called shift registers.
94. What are the types of shift register?
1. Serial in serial out shift register?
2. Serial in parallel out shift register
3. Parallel in serial out shift register
4. Parallel in parallel out shift register
5. Bidirectional shift register shift register.
95. What are the types of counter?
1. Synchronous counter
2. Asynchronous Counter
96. What are the two models in synchronous sequential circuits.
1. Moore circuit
2. Mealy circuit
97. What is moore circuit?
When the output of the sequential circuit depends only on the present state of the
flip-flop, the sequential circuit is referred to as moore circuit.
98. What is Mealy circuit?
When the output of the sequential circuit depends on both the present state of flipflop
and on the input, the sequential circuit is referred to as mealy circuit.
99. Define successor
In a state diagram, if an input sequence, x takes a machine from state si to state sj,
then sj is said to be the x - successor of si.
100. Define strongly connected machine?
In a sequential machine many times certain subsets of states may not be reachable
from other subsets of states, even if the machine does not contain any terminal state.
However, if for every pair of states si, sj of a sequential machine, there eights an
input sequence which takes M from Si to Sj then sequential machine M is said to be
strongly connected.
Quick revision for Electromagnetism
1.State stokes theorem.
The line integral of a vector around a closed path is equal to the surface integral of the normal component of its curl over any surface bounded by the path
H.dl = (ÑxH)ds
2.State coulombs law.
Coulombs law states that the force between any two point charges is directly
proportional to the product of their magnitudes and inversely proportional to the square
of the distance between them. It is directed along the line joining the two charges.
F=Q1Q2 / 4ðår2 ar
3.State Gauss law for electric fields
The total electric flux passing through any closed surface is equal to the total charge enclosed by that surface.
4.Define electric flux.
The lines of electric force is electric flux.
5.Define electric flux density.
Electric flux density is defined as electric flux per unit area.
6.Define electric field intensity.
Electric field intensity is defined as the electric force per unit positive charge.
E =F/ Q =Q/4ðår2 V/m
Electro Magnetic Theory
7.Name few applications of Gauss law in electrostatics.
Gauss law is applied to find the electric field intensity from a closed surface.e.g)Electric field can be determined for shell, two concentric shell or cylinders etc.
8.What is a point charge?
Point charge is one whose maximum dimension is very small in comparison with any
other length.
9.Define linear charge density.
It is the charge per unit length.
10.Write poisson’s and laplace ’s equations.
Poisson ‘s eqn:
Ñ2V= - ñv / å
Laplace’ s eqn:
Ñ2V= 0
11.State the condition for the vector F to be solenoidal.
Ñ·F =0
12. .State the condition for the vector F to be irrotational.
ÑxF =0
13.Define potential difference.
Potential difference is defined as the work done in moving a unit positive charge
from one point to another point in an electric field.
14.Define potential.
Potential at any point is defined as the work done in moving a unit positive charge
from infinity to that point in an electric field.
V=Q / 4ðår
15.Give the relation between electric field intensity and electric flux density.
D=åE C/m2
16.Give the relationship between potential gradiant and electric field.
E= - ÑV
17.What is the physical significance of div D ?
Ñ·D=-ñv
The divergence of a vector flux density is electric flux per unit volume leaving a small volume. This is equal to the volume charge density.
18. Define current density.
Current density is defined as the current per unit area.
J= I/A Amp/m2
19.Write the point form of continuity equation and explain its significance.
Ñ·J= - ñv / t
20.Write the expression for energy density in electrostatic field.
W=1 / 2 åE2
21.Write the boundary conditions at the interface between two perfect dielectrics.
i)The tangential component of electric field is continuous i.e)Et1=Et2
ii)The normal component of electric flux density is continuous I.e)Dn1=Dn2
22.Write down the expression for capacitance between two parallel plates.
C=åA / d
23.What is meant by displacement current?
Displacement current is nothing but the current flowing through capacitor.
J= D / t
24.State point form of ohms law.
Point form of ohms law states that the field strength within a conductor is
proportional to the current density.J=óE
25 Define surface charge density.
It is the charge per surface area.
26.State amperes circuital law.
Magnetic field intensity around a closed path is equal to the current enclosed by the
path. H·dl=I
27.State Biot –Savarts law.
It states that the magnetic flux density at any point due to current element is
proportional to the current element and sine of the angle between the elemental length
and inversely proportional to the square of the distance between them
dB=μ 0Idl sinè / 4ðr2
28.Define magnetic vector potential.
It is defined as that quantity whose curl gives the magnetic flux density.
B=Ñ x A =μ / 4ð J/r dv web/m2
29.Write down the expression for magnetic field at the centre of the circular coil.
H = I/2a.
30.Give the relation between magnetic flux density and magnetic field intensity.
B =μ H
31.Write down the magnetic boundary conditions.
i) The normal components of flux density B is continuous across the boundary.
ii) The tangential component of field intensity is continuous across the boundary.
32.Give the force on a current element.
dF = BIdlsinè
33..Define magnetic moment.
Magnetic moment is defined as the maximum torque per magnetic induction of
flux density. m=IA
34.State Gauss law for magnetic field.
The total magnetic flux passing through any closed surface is equal to zero.
B.ds =0
35.Define a wave.
If a physical phenomenon that occurs at one place at a given time is reproduced at
other places at later times , the time delay being proportional to the space separation
from the first location then the group of phenomena constitutes a wave.
36. Mention the properties of uniform plane wave.
i) At every point in space ,the electric field E and magnetic field H are perpendicular to each other.
ii)The fields vary harmonically with time and at the same frequency everywhere in
space.
37.Write down the wave equation for E and H in free space.
Ñ2H– μ 0å0
2H / t 2 =0.
38.Define intrinsic impedance or characteristic impedance.
It is the ratio of electric field to magnetic field.or It is the ratio of square root of permeability to permittivity of medium.
39.Give the characteristic impedance of free space.
377ohms
40.Define propagation constant.
Propagation constant is a complex number
ã =á +jâ
where á is attenuation constant
â is phase constant
ã = jùμ (ó +jùå)
41.Define skin depth
It is defined as that depth in which the wave has been attenuated to 1/e or
approximately 37% of its original value.
Ä = 1/á = 2 / jùó
42.Define Poynting vector.
The poynting vector is defined as rate of flow of energy of a wave as it propagates.
P =E X H
43. State Poyntings Theorem.
The net power flowing out of a given volume is equal to the time rate of decrease
of the the energy stored within the volume- conduction losses.
44.Give significant physical difference between poisons and laplaces equations.
When the region contains charges poisons equation is used and when
there is no charges laplaces equation is applied.
45.Give the difficulties in FDM.
FDM is difficult to apply for problems involving irregular boundaries and non
homogenious material properties.
46.Explain the steps in finite element method.
i) Discretisation of the solution region into elements.
ii) Generation of equations for fields at each element
iii) Assembly of all elements
iv) Solution of the resulting system
47.State Maxwells fourth equation.
The net magnetic flux emerging through any closed surface is zero.
48. State Maxwells Third equation
The total electric displacement through the surface enclosing a volume is equal to the total charge within the volume.
49.State the principle of superposition of fields.
The total electric field at a point is the algebraic sum of the individual electric field at that point.
50.Define ohms law at a point
Ohms law at appoint states that the field strength within a conductor is proportional
to current density.
51.Define self inductance.
Self inductance is defined as the rate of total magnetic flux linkage to the current
through the coil.
52.Define pointing vector.
The vector product of electric field intensity and magnetic field intensity at a point is a measure of the rate of energy flow per unit area at that point.
53.Give the formula to find potential at a point which is surrounded by four
orthogonal points in FDM.
V0= ¼(V1+V2+V3+V4)
54.Give the formula to find potential at a point which is surrounded by six
orthogonal points in FDM.
V0= ¼(V1+V2+V3+V4 +V5+V6)
55.State Lenz law.
Lenz’s law states that the induced emf in a circuit produces a current which opposes the change in magnetic flux producing it.
56.What is the effect of permittivity on the force between two charges?
Increase in permittivity of the medium tends to decrease the force between two
charges and decrease in permittivity of the medium tends to increase the force between
two charges.
57.State electric displacement.
The electric flux or electric displacement through a closed surface is equal to the charge enclosed by the surface.
58.What is displacement flux density?
The electric displacement per unit area is known as electric displacement density or
electric flux density.
59.What is the significance of displacement current?
The concept of displacement current was introduced to justify the production of
magnetic field in empty space. It signifies that a changing electric field induces a
magnetic field .In empty space the conduction current is zero and the magnetic fields are entirely due to displacement current.
60.Distinguish between conduction and displacement currents.
The current through a resistive element is termed as conduction current whereas the
current through a capacitive element is termed as displacement current.
61.Define magnetic field strength.
The magnetic field strength (H) is a vector having the same direction as magnetic flux
density.
H=B/μ
62.Give the formula to find the force between two parallel current carrying
conductors.
F=μI I1 / 2ðR
63.Give the expression for torque experienced by a current carrying loop situated in
a magnetic field.
T = IABsinè
64 What is torque on a solenoid?
T = NIABsinè
65.Explain the conservative property of electric field.
The work done in moving a point charge around a closed path in a electric field is zero. Such a field is said to be conservative.
E.dl = 0
66.Write he expression for field intensity due to a toroid carrying a filamentary
current ?
I H=NI / 2ïR
67.What are equipotential surfaces?
An equipotential surface is a surface in which the potential energy at every point is of the same vale.
68.Define loss tangent.
Loss tangent is the ratio of the magnitude of conduction current density to displacement current density of the medium.
Tan ä = ó / ùå
69.Defie reflection and transmission coefficients.
Reflection coefficient is defined as the ratio of the magnitude of the reflected field to that of the incident field.
70. Define transmission coefficients.
Transmission coefficient is defined as the ratio of the magnitude of the
transmitted field to that of incident field.
71.What will happen when the wave is incident obliquely over dielectric –dielectric
boundary?
When a plane wave is incident obliquely on the surface of a perfect dielectric part of the energy is transmitted and part of it is reflected .But in this case the transmitted wave will be refracted, that is the direction of propagation is altered.
72.What is the expression for energy stored in a magnetic field?
W = ½ LI2
73.What is energy density in magnetic field?
W = ½ μH2
74.Distinguish between solenoid and toroid.
Solenoid is a cylindrically shaped coil consisting of a large number of closely spaced turns of insulated wire wound usually on a non magnetic frame.
If a long slender solenoid is bent into the form of a ring and there by closed on itself it becomes a toroid.
75.Describe what are the sources of electric field and magnetic field?
Stationary charges produce electric field that are constant in time, hence the term
electrostatics. Moving charges produce magnetic fields hence the term magnetostatics.
76.What are the significant physical differences between Poisson ‘s and laplace ‘s
equations.
Poisson ‘s and laplace ‘s equations are useful for determining the electrostatic potential V in regions whose boundaries are known. When the region of interest contains charges poissons equation can be used to find the
potential.
When the region is free from charge laplace equation is used to find the potential.
77.State Divergence Theorem.
The integral of the divergence of a vector over a volume v is equal to the surface integral of the normal component of the vector over the surface bounded by the volume.
78.Give the expression for electric field intensity due to a single shell of charge
E = Q / 4ðår2
79.Give the expression for potential between two spherical shells
V= 1/ 4ð (Q1/a – Q2/b)
80.Define electric dipole.
Electric dipole is nothing but two equal and opposite point charges separated by a finite distance.
81.What is electrostatic force?
The force between any two particles due to existing charges is known as electrostatic
force, repulsive for like and attractive for unlike.
82.Define divergence.
The divergence of a vector F at any point is defined as the limit of its surface integral per unit volume as the volume enclosed by the surface around the point shrinks to zero.
83.How is electric energy stored in a capacitor?
In a capacitor, the work done in charging a capacitor is stored in the form of electric
energy.
84.What are dielectrics?
Dielectrics are materials that may not conduct electricity through it but on applying electric field induced charges are produced on its faces .The valence electron in atoms of a dielectric are tightly bound to their nucleus.
85.What is a capacitor?
A capacitor is an electrical device composed of two conductors which are separated
through a dielectric medium and which can store equal and opposite charges ,independent
of whether other conductors in the system are charged or not.
86.Define dielectric strength.
The dielectric strength of a dielectric is defined as the maximum value of electric field that can b applied to the dielectric without its electric breakdown.
87.What meaning would you give to the capacitance of a single conductor?
A single conductor also possess capacitance. It is a capacitor whose one plate is at
infinity.
88.Why water has much greater dielectric constant than mica.?
Water has a much greater dielectric constant than mica .because water ha a permanent
dipole moment, while mica does not have.
89.What is lorentz force?
Lorentz force is the force experienced by the test charge .It is maximum if the direction of movement of charge is perpendicular to the orientation of field lines.
90.Define magnetic moment.
Magnetic moment is defined as the maximum torque on the loop per unit magnetic
induction.
91.Define inductance.
The inductance of a conductor is defined as the ratio of the linking magnetic flux to the current producing the flux. L = NÔ / I
92.What is main cause of eddy current?
The main cause of eddy current is that it produces ohmic power loss and causes local
heating.
93.How can the eddy current losses be eliminated?
The eddy current losses can be eliminated by providing laminations. It can be proved
that the total eddy current power loss decreases as the number of laminations increases.
94.What is the fundamental difference between static electric and magnetic field
lines?
There is a fundamental difference between static electric and magnetic field lines .The tubes of electric flux originate and terminates on charges, whereas magnetic flux tubes are continuous.
95.What are uniform plane waves?
Electromagnetic waves which consist of electric and magnetic fields that are
perpendicular to each other and to the direction of propagation and are uniform in plane
perpendicular to the direction of propagation are known as uniform plane waves.
96.Write short notes on imperfect dielectrics.
A material is classified as an imperfect dielectrics for ó <<ùå, that is conduction current
density is small in magnitude compared to the displacement current density.
97.What is the significant feature of wave propagation in an imperfect dielectric ?
The only significant feature of wave propagation in an imperfect dielectric compared to
that in a perfect dielectric is the attenuation undergone by the wave.
98.What is the major drawback of finite difference method?
The major drawback of finite difference method is its inability to handle curved
boundaries accurately.
99.What is method of images?
The replacement of the actual problem with boundaries by an enlarged region or with
image charges but no boundaries is called the method of images.
100.When is method of images used?
Method of images is used in solving problems of one or more point charges in the
presence of boundary surfaces.
Part-B
1.Find the electric field intensity of a straight uniformly charged wire of length ‘L’m
and having a linear charge density of +ë C/m at any point at a distance of ‘h’ m.
Hence deduce the expression for infinitely long conductor.
Hints: Field due to charge element is given by:
dE = ëdi/ 4ðîr2
Ex=ë [cos á1+cosá2] /4ðåh
Ey=ë [sin á1-siná2] /4ðåh
For infinitely long conductor
E = ël / 4ðåh
2.Derive the boundary relations for electric fields.
Hints:
i)The tangential component of the electric field is continuous at the surface
.Et1 = Et2
ii)The normal component of the electric flux density is continuous if there is no surface
charge density.
Dn1 = Dn2
3.Find the electric field intensity produced by a point charge distribution at
P(1,1,1)caused by four identical 3nC point charges located at P1(1,1,0)
P2(-1,1,0) P3(-1,-1,0) and P4(1,-1,0).
Hints:
Find the field intensity at P by using the formula
Ep = 1/4åð[( Q1/r1p
2 u1p ) +(q2/r2p
2 u2p) +(q3/r3p
2 u3p)+(q4/r4p
2)u4p)]
4.A circular disc of radius ‘a’ m is charged with a charge density of óC/m2 .Find the
electric field intensity at a point ‘h’m from the disc along its axis.
Hints:
Find the field due to the tangential and normal components
Total field is given by
E =ñs /2å [1-cos á]
5. Four positive charges of 10–9 C each are situated in the XY plane at points
(0,0) (0,1) (1,0) and (1,1).Find the electric field intensity and potential at
(1/2 ,1/2).
Hints:
Find the field intensity at point using the formula
E = Q / 4ðår2 ur
Find the potential at point using the formula
V = Q / 4ðår
Find the field intensity at the point due to all four charges by using the superposition
principle.
6. Given a electric field E = (-6y/x2) x + 6/x y + 5 z .Find the potential difference VAB
given A(-7,2,1) and B( 4,1,2)
Hint:
Find the potential using the formula v=-/E.dl and substitute the points
7.Derive an expression for potential difference between two points in an electric
field.
Hint:
The potential difference between two points r1 and r2 is
V = V1 –V2
V = Q / 4ðår1 _ Q / 4ðår 2
8.Find the magnetic flux density at a point Z on the axis of a circular loop of radius ‘a’ that carries a direct current I.
Hints:
The magnetic flux density at a point due to the current element is given by
dB = μIdl / 4ð r2
B = μIa2 / 2(a2 + z2)3/2
9.Determine the force per meter length between two long parallel wires A and B
separated by 5cm in air and carrying currents of 40A in the same direction.
Hints:
Calculate the force per metre length using the formula
F/L = μI1I2 / 2ðd
In the same direction force is attractive.
10.Derive an expression for magnetic vector potential.
Hint:
magnetic vector potential is
A = μ / 4ð ///J / r dv
11.Derive the magnetic boundary relations.
i)The tangential component of the magnetic field is continuous across the boundary
.Ht1 = Ht2
ii)The normal component of the magnetic flux density is continuous across the boundary
Dn1 = Dn2
12.Find the magnetic field intensity at a distance ‘h’m above an infinite straight wire
carrying a steady current I.
Hints:
The magnetic flux density is calculated starting from Biot savarts law.
The magnetic flux density at any point due to an infinite long conductor is given by
B = μI / 2ðd
13.Two conducting concentric spherical shells with radii a and b are at potentials V0
and 0 respectively. Determine the capacitance of the capacitor.
Hint:
Derive the capacitance between concentric spheres using the formula
C = Q /V
= 4ðå [ ab /(b-a) ]
14State and derive an expression for Poyntings theorem.
Hints:
The net power flowing out of a given volume v is equal to the time rate of decrease of the energy stored within the volume minus the conduction losses.
15.Find the forces /length between two long straight parallel conductors carrying a
current of 10A in the same direction. A distance of 0.2m separates the conductors.
Also find the force/length when the conductors carry currents in opposite directions.
Hints:
Calculate the force per metre length using the formula
F/L = μI1I2 / 2ðd
In opposite direction force is repulsive
16 Derive an expression for torque acting on a loop.
Hints
When a current loop is placed parallel to a magnetic field forces act on the loop that
tends to rotate the tangential force times the radial distance at which it acts is
called torque or mechanicl moment of the loop.
T = m X B
17.Derive an expression for energy and energy density in a electric field.
Energy =CV2/2
Energy density = åE2/2
18. .Derive an expression for energy and energy density in a magnetic field.
Energy =LI2/2
Energy density = μH2/2
19.Derive all the maxwells equations.
Hints:
i)Maxwells equation from electric Gauss law.
ii) Maxwells equation from magnetic Gauss law.
iii)Maxwells equation from Amperes law.
iv) Maxwells equation from Faradays law.
20.Derive an expression for displacement, conduction current densities. Also obtain an
expression for continuity current relations
Hints:
Displacement current density Jd = åäE/ät
Conduction current density Jcond = óE
21.Derive the general Electromagnetic wave equation.
Hint:
Starting from the maxwells equation from Faradays law and Amperes law derive the
Equation
˘ 2 E - μ ó(ä E/ ät )-μå (ä2 E/ät2 )
22.Briefly explain reflection by a perfect dielectric when a wave is incident normally on a perfect dielectric and derive expression for reflection coefficient.
Hints:
When a plane electromagnetic wave is incident on the surface of a perfect dielectric part of the energy is transmitted and part of it is reflected.
Er / Ei = ( 2 – 1) /( 2 + 1)
23. Briefly explain reflection by a perfect dielectric when a wave is incident normally on a perfect conductor.
Hints
When the plane wave is incident normally upon the surface of a perfect conductor the
wave is entirely reflected. Since there can be no loss within a perfect conductor none of the energy is absorbed.
E (x,t) = 2Ei sinâx sinù t
24. Derive the relation between field theory and circuit theory for an RLC series circuit.
Hints :
Starting from field theory erquation for a series RLC circuit derive the circuit equation
V= IR + L dI/dt +(1 /C) / Idt
25.State and explain Faradays and Lenzs law of induction and derive maxwells equation.
Hints:
The total emf induced in a circuit is equal to the time rate of decrease of the total
magnetic flux linking the circuit.
˘ X E = -äB/ ät
The line integral of a vector around a closed path is equal to the surface integral of the normal component of its curl over any surface bounded by the path
H.dl = (ÑxH)ds
2.State coulombs law.
Coulombs law states that the force between any two point charges is directly
proportional to the product of their magnitudes and inversely proportional to the square
of the distance between them. It is directed along the line joining the two charges.
F=Q1Q2 / 4ðår2 ar
3.State Gauss law for electric fields
The total electric flux passing through any closed surface is equal to the total charge enclosed by that surface.
4.Define electric flux.
The lines of electric force is electric flux.
5.Define electric flux density.
Electric flux density is defined as electric flux per unit area.
6.Define electric field intensity.
Electric field intensity is defined as the electric force per unit positive charge.
E =F/ Q =Q/4ðår2 V/m
Electro Magnetic Theory
7.Name few applications of Gauss law in electrostatics.
Gauss law is applied to find the electric field intensity from a closed surface.e.g)Electric field can be determined for shell, two concentric shell or cylinders etc.
8.What is a point charge?
Point charge is one whose maximum dimension is very small in comparison with any
other length.
9.Define linear charge density.
It is the charge per unit length.
10.Write poisson’s and laplace ’s equations.
Poisson ‘s eqn:
Ñ2V= - ñv / å
Laplace’ s eqn:
Ñ2V= 0
11.State the condition for the vector F to be solenoidal.
Ñ·F =0
12. .State the condition for the vector F to be irrotational.
ÑxF =0
13.Define potential difference.
Potential difference is defined as the work done in moving a unit positive charge
from one point to another point in an electric field.
14.Define potential.
Potential at any point is defined as the work done in moving a unit positive charge
from infinity to that point in an electric field.
V=Q / 4ðår
15.Give the relation between electric field intensity and electric flux density.
D=åE C/m2
16.Give the relationship between potential gradiant and electric field.
E= - ÑV
17.What is the physical significance of div D ?
Ñ·D=-ñv
The divergence of a vector flux density is electric flux per unit volume leaving a small volume. This is equal to the volume charge density.
18. Define current density.
Current density is defined as the current per unit area.
J= I/A Amp/m2
19.Write the point form of continuity equation and explain its significance.
Ñ·J= - ñv / t
20.Write the expression for energy density in electrostatic field.
W=1 / 2 åE2
21.Write the boundary conditions at the interface between two perfect dielectrics.
i)The tangential component of electric field is continuous i.e)Et1=Et2
ii)The normal component of electric flux density is continuous I.e)Dn1=Dn2
22.Write down the expression for capacitance between two parallel plates.
C=åA / d
23.What is meant by displacement current?
Displacement current is nothing but the current flowing through capacitor.
J= D / t
24.State point form of ohms law.
Point form of ohms law states that the field strength within a conductor is
proportional to the current density.J=óE
25 Define surface charge density.
It is the charge per surface area.
26.State amperes circuital law.
Magnetic field intensity around a closed path is equal to the current enclosed by the
path. H·dl=I
27.State Biot –Savarts law.
It states that the magnetic flux density at any point due to current element is
proportional to the current element and sine of the angle between the elemental length
and inversely proportional to the square of the distance between them
dB=μ 0Idl sinè / 4ðr2
28.Define magnetic vector potential.
It is defined as that quantity whose curl gives the magnetic flux density.
B=Ñ x A =μ / 4ð J/r dv web/m2
29.Write down the expression for magnetic field at the centre of the circular coil.
H = I/2a.
30.Give the relation between magnetic flux density and magnetic field intensity.
B =μ H
31.Write down the magnetic boundary conditions.
i) The normal components of flux density B is continuous across the boundary.
ii) The tangential component of field intensity is continuous across the boundary.
32.Give the force on a current element.
dF = BIdlsinè
33..Define magnetic moment.
Magnetic moment is defined as the maximum torque per magnetic induction of
flux density. m=IA
34.State Gauss law for magnetic field.
The total magnetic flux passing through any closed surface is equal to zero.
B.ds =0
35.Define a wave.
If a physical phenomenon that occurs at one place at a given time is reproduced at
other places at later times , the time delay being proportional to the space separation
from the first location then the group of phenomena constitutes a wave.
36. Mention the properties of uniform plane wave.
i) At every point in space ,the electric field E and magnetic field H are perpendicular to each other.
ii)The fields vary harmonically with time and at the same frequency everywhere in
space.
37.Write down the wave equation for E and H in free space.
Ñ2H– μ 0å0
2H / t 2 =0.
38.Define intrinsic impedance or characteristic impedance.
It is the ratio of electric field to magnetic field.or It is the ratio of square root of permeability to permittivity of medium.
39.Give the characteristic impedance of free space.
377ohms
40.Define propagation constant.
Propagation constant is a complex number
ã =á +jâ
where á is attenuation constant
â is phase constant
ã = jùμ (ó +jùå)
41.Define skin depth
It is defined as that depth in which the wave has been attenuated to 1/e or
approximately 37% of its original value.
Ä = 1/á = 2 / jùó
42.Define Poynting vector.
The poynting vector is defined as rate of flow of energy of a wave as it propagates.
P =E X H
43. State Poyntings Theorem.
The net power flowing out of a given volume is equal to the time rate of decrease
of the the energy stored within the volume- conduction losses.
44.Give significant physical difference between poisons and laplaces equations.
When the region contains charges poisons equation is used and when
there is no charges laplaces equation is applied.
45.Give the difficulties in FDM.
FDM is difficult to apply for problems involving irregular boundaries and non
homogenious material properties.
46.Explain the steps in finite element method.
i) Discretisation of the solution region into elements.
ii) Generation of equations for fields at each element
iii) Assembly of all elements
iv) Solution of the resulting system
47.State Maxwells fourth equation.
The net magnetic flux emerging through any closed surface is zero.
48. State Maxwells Third equation
The total electric displacement through the surface enclosing a volume is equal to the total charge within the volume.
49.State the principle of superposition of fields.
The total electric field at a point is the algebraic sum of the individual electric field at that point.
50.Define ohms law at a point
Ohms law at appoint states that the field strength within a conductor is proportional
to current density.
51.Define self inductance.
Self inductance is defined as the rate of total magnetic flux linkage to the current
through the coil.
52.Define pointing vector.
The vector product of electric field intensity and magnetic field intensity at a point is a measure of the rate of energy flow per unit area at that point.
53.Give the formula to find potential at a point which is surrounded by four
orthogonal points in FDM.
V0= ¼(V1+V2+V3+V4)
54.Give the formula to find potential at a point which is surrounded by six
orthogonal points in FDM.
V0= ¼(V1+V2+V3+V4 +V5+V6)
55.State Lenz law.
Lenz’s law states that the induced emf in a circuit produces a current which opposes the change in magnetic flux producing it.
56.What is the effect of permittivity on the force between two charges?
Increase in permittivity of the medium tends to decrease the force between two
charges and decrease in permittivity of the medium tends to increase the force between
two charges.
57.State electric displacement.
The electric flux or electric displacement through a closed surface is equal to the charge enclosed by the surface.
58.What is displacement flux density?
The electric displacement per unit area is known as electric displacement density or
electric flux density.
59.What is the significance of displacement current?
The concept of displacement current was introduced to justify the production of
magnetic field in empty space. It signifies that a changing electric field induces a
magnetic field .In empty space the conduction current is zero and the magnetic fields are entirely due to displacement current.
60.Distinguish between conduction and displacement currents.
The current through a resistive element is termed as conduction current whereas the
current through a capacitive element is termed as displacement current.
61.Define magnetic field strength.
The magnetic field strength (H) is a vector having the same direction as magnetic flux
density.
H=B/μ
62.Give the formula to find the force between two parallel current carrying
conductors.
F=μI I1 / 2ðR
63.Give the expression for torque experienced by a current carrying loop situated in
a magnetic field.
T = IABsinè
64 What is torque on a solenoid?
T = NIABsinè
65.Explain the conservative property of electric field.
The work done in moving a point charge around a closed path in a electric field is zero. Such a field is said to be conservative.
E.dl = 0
66.Write he expression for field intensity due to a toroid carrying a filamentary
current ?
I H=NI / 2ïR
67.What are equipotential surfaces?
An equipotential surface is a surface in which the potential energy at every point is of the same vale.
68.Define loss tangent.
Loss tangent is the ratio of the magnitude of conduction current density to displacement current density of the medium.
Tan ä = ó / ùå
69.Defie reflection and transmission coefficients.
Reflection coefficient is defined as the ratio of the magnitude of the reflected field to that of the incident field.
70. Define transmission coefficients.
Transmission coefficient is defined as the ratio of the magnitude of the
transmitted field to that of incident field.
71.What will happen when the wave is incident obliquely over dielectric –dielectric
boundary?
When a plane wave is incident obliquely on the surface of a perfect dielectric part of the energy is transmitted and part of it is reflected .But in this case the transmitted wave will be refracted, that is the direction of propagation is altered.
72.What is the expression for energy stored in a magnetic field?
W = ½ LI2
73.What is energy density in magnetic field?
W = ½ μH2
74.Distinguish between solenoid and toroid.
Solenoid is a cylindrically shaped coil consisting of a large number of closely spaced turns of insulated wire wound usually on a non magnetic frame.
If a long slender solenoid is bent into the form of a ring and there by closed on itself it becomes a toroid.
75.Describe what are the sources of electric field and magnetic field?
Stationary charges produce electric field that are constant in time, hence the term
electrostatics. Moving charges produce magnetic fields hence the term magnetostatics.
76.What are the significant physical differences between Poisson ‘s and laplace ‘s
equations.
Poisson ‘s and laplace ‘s equations are useful for determining the electrostatic potential V in regions whose boundaries are known. When the region of interest contains charges poissons equation can be used to find the
potential.
When the region is free from charge laplace equation is used to find the potential.
77.State Divergence Theorem.
The integral of the divergence of a vector over a volume v is equal to the surface integral of the normal component of the vector over the surface bounded by the volume.
78.Give the expression for electric field intensity due to a single shell of charge
E = Q / 4ðår2
79.Give the expression for potential between two spherical shells
V= 1/ 4ð (Q1/a – Q2/b)
80.Define electric dipole.
Electric dipole is nothing but two equal and opposite point charges separated by a finite distance.
81.What is electrostatic force?
The force between any two particles due to existing charges is known as electrostatic
force, repulsive for like and attractive for unlike.
82.Define divergence.
The divergence of a vector F at any point is defined as the limit of its surface integral per unit volume as the volume enclosed by the surface around the point shrinks to zero.
83.How is electric energy stored in a capacitor?
In a capacitor, the work done in charging a capacitor is stored in the form of electric
energy.
84.What are dielectrics?
Dielectrics are materials that may not conduct electricity through it but on applying electric field induced charges are produced on its faces .The valence electron in atoms of a dielectric are tightly bound to their nucleus.
85.What is a capacitor?
A capacitor is an electrical device composed of two conductors which are separated
through a dielectric medium and which can store equal and opposite charges ,independent
of whether other conductors in the system are charged or not.
86.Define dielectric strength.
The dielectric strength of a dielectric is defined as the maximum value of electric field that can b applied to the dielectric without its electric breakdown.
87.What meaning would you give to the capacitance of a single conductor?
A single conductor also possess capacitance. It is a capacitor whose one plate is at
infinity.
88.Why water has much greater dielectric constant than mica.?
Water has a much greater dielectric constant than mica .because water ha a permanent
dipole moment, while mica does not have.
89.What is lorentz force?
Lorentz force is the force experienced by the test charge .It is maximum if the direction of movement of charge is perpendicular to the orientation of field lines.
90.Define magnetic moment.
Magnetic moment is defined as the maximum torque on the loop per unit magnetic
induction.
91.Define inductance.
The inductance of a conductor is defined as the ratio of the linking magnetic flux to the current producing the flux. L = NÔ / I
92.What is main cause of eddy current?
The main cause of eddy current is that it produces ohmic power loss and causes local
heating.
93.How can the eddy current losses be eliminated?
The eddy current losses can be eliminated by providing laminations. It can be proved
that the total eddy current power loss decreases as the number of laminations increases.
94.What is the fundamental difference between static electric and magnetic field
lines?
There is a fundamental difference between static electric and magnetic field lines .The tubes of electric flux originate and terminates on charges, whereas magnetic flux tubes are continuous.
95.What are uniform plane waves?
Electromagnetic waves which consist of electric and magnetic fields that are
perpendicular to each other and to the direction of propagation and are uniform in plane
perpendicular to the direction of propagation are known as uniform plane waves.
96.Write short notes on imperfect dielectrics.
A material is classified as an imperfect dielectrics for ó <<ùå, that is conduction current
density is small in magnitude compared to the displacement current density.
97.What is the significant feature of wave propagation in an imperfect dielectric ?
The only significant feature of wave propagation in an imperfect dielectric compared to
that in a perfect dielectric is the attenuation undergone by the wave.
98.What is the major drawback of finite difference method?
The major drawback of finite difference method is its inability to handle curved
boundaries accurately.
99.What is method of images?
The replacement of the actual problem with boundaries by an enlarged region or with
image charges but no boundaries is called the method of images.
100.When is method of images used?
Method of images is used in solving problems of one or more point charges in the
presence of boundary surfaces.
Part-B
1.Find the electric field intensity of a straight uniformly charged wire of length ‘L’m
and having a linear charge density of +ë C/m at any point at a distance of ‘h’ m.
Hence deduce the expression for infinitely long conductor.
Hints: Field due to charge element is given by:
dE = ëdi/ 4ðîr2
Ex=ë [cos á1+cosá2] /4ðåh
Ey=ë [sin á1-siná2] /4ðåh
For infinitely long conductor
E = ël / 4ðåh
2.Derive the boundary relations for electric fields.
Hints:
i)The tangential component of the electric field is continuous at the surface
.Et1 = Et2
ii)The normal component of the electric flux density is continuous if there is no surface
charge density.
Dn1 = Dn2
3.Find the electric field intensity produced by a point charge distribution at
P(1,1,1)caused by four identical 3nC point charges located at P1(1,1,0)
P2(-1,1,0) P3(-1,-1,0) and P4(1,-1,0).
Hints:
Find the field intensity at P by using the formula
Ep = 1/4åð[( Q1/r1p
2 u1p ) +(q2/r2p
2 u2p) +(q3/r3p
2 u3p)+(q4/r4p
2)u4p)]
4.A circular disc of radius ‘a’ m is charged with a charge density of óC/m2 .Find the
electric field intensity at a point ‘h’m from the disc along its axis.
Hints:
Find the field due to the tangential and normal components
Total field is given by
E =ñs /2å [1-cos á]
5. Four positive charges of 10–9 C each are situated in the XY plane at points
(0,0) (0,1) (1,0) and (1,1).Find the electric field intensity and potential at
(1/2 ,1/2).
Hints:
Find the field intensity at point using the formula
E = Q / 4ðår2 ur
Find the potential at point using the formula
V = Q / 4ðår
Find the field intensity at the point due to all four charges by using the superposition
principle.
6. Given a electric field E = (-6y/x2) x + 6/x y + 5 z .Find the potential difference VAB
given A(-7,2,1) and B( 4,1,2)
Hint:
Find the potential using the formula v=-/E.dl and substitute the points
7.Derive an expression for potential difference between two points in an electric
field.
Hint:
The potential difference between two points r1 and r2 is
V = V1 –V2
V = Q / 4ðår1 _ Q / 4ðår 2
8.Find the magnetic flux density at a point Z on the axis of a circular loop of radius ‘a’ that carries a direct current I.
Hints:
The magnetic flux density at a point due to the current element is given by
dB = μIdl / 4ð r2
B = μIa2 / 2(a2 + z2)3/2
9.Determine the force per meter length between two long parallel wires A and B
separated by 5cm in air and carrying currents of 40A in the same direction.
Hints:
Calculate the force per metre length using the formula
F/L = μI1I2 / 2ðd
In the same direction force is attractive.
10.Derive an expression for magnetic vector potential.
Hint:
magnetic vector potential is
A = μ / 4ð ///J / r dv
11.Derive the magnetic boundary relations.
i)The tangential component of the magnetic field is continuous across the boundary
.Ht1 = Ht2
ii)The normal component of the magnetic flux density is continuous across the boundary
Dn1 = Dn2
12.Find the magnetic field intensity at a distance ‘h’m above an infinite straight wire
carrying a steady current I.
Hints:
The magnetic flux density is calculated starting from Biot savarts law.
The magnetic flux density at any point due to an infinite long conductor is given by
B = μI / 2ðd
13.Two conducting concentric spherical shells with radii a and b are at potentials V0
and 0 respectively. Determine the capacitance of the capacitor.
Hint:
Derive the capacitance between concentric spheres using the formula
C = Q /V
= 4ðå [ ab /(b-a) ]
14State and derive an expression for Poyntings theorem.
Hints:
The net power flowing out of a given volume v is equal to the time rate of decrease of the energy stored within the volume minus the conduction losses.
15.Find the forces /length between two long straight parallel conductors carrying a
current of 10A in the same direction. A distance of 0.2m separates the conductors.
Also find the force/length when the conductors carry currents in opposite directions.
Hints:
Calculate the force per metre length using the formula
F/L = μI1I2 / 2ðd
In opposite direction force is repulsive
16 Derive an expression for torque acting on a loop.
Hints
When a current loop is placed parallel to a magnetic field forces act on the loop that
tends to rotate the tangential force times the radial distance at which it acts is
called torque or mechanicl moment of the loop.
T = m X B
17.Derive an expression for energy and energy density in a electric field.
Energy =CV2/2
Energy density = åE2/2
18. .Derive an expression for energy and energy density in a magnetic field.
Energy =LI2/2
Energy density = μH2/2
19.Derive all the maxwells equations.
Hints:
i)Maxwells equation from electric Gauss law.
ii) Maxwells equation from magnetic Gauss law.
iii)Maxwells equation from Amperes law.
iv) Maxwells equation from Faradays law.
20.Derive an expression for displacement, conduction current densities. Also obtain an
expression for continuity current relations
Hints:
Displacement current density Jd = åäE/ät
Conduction current density Jcond = óE
21.Derive the general Electromagnetic wave equation.
Hint:
Starting from the maxwells equation from Faradays law and Amperes law derive the
Equation
˘ 2 E - μ ó(ä E/ ät )-μå (ä2 E/ät2 )
22.Briefly explain reflection by a perfect dielectric when a wave is incident normally on a perfect dielectric and derive expression for reflection coefficient.
Hints:
When a plane electromagnetic wave is incident on the surface of a perfect dielectric part of the energy is transmitted and part of it is reflected.
Er / Ei = ( 2 – 1) /( 2 + 1)
23. Briefly explain reflection by a perfect dielectric when a wave is incident normally on a perfect conductor.
Hints
When the plane wave is incident normally upon the surface of a perfect conductor the
wave is entirely reflected. Since there can be no loss within a perfect conductor none of the energy is absorbed.
E (x,t) = 2Ei sinâx sinù t
24. Derive the relation between field theory and circuit theory for an RLC series circuit.
Hints :
Starting from field theory erquation for a series RLC circuit derive the circuit equation
V= IR + L dI/dt +(1 /C) / Idt
25.State and explain Faradays and Lenzs law of induction and derive maxwells equation.
Hints:
The total emf induced in a circuit is equal to the time rate of decrease of the total
magnetic flux linking the circuit.
˘ X E = -äB/ ät
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