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Code No: RT22044

II B. Tech II Semester Regular Examinations, May/June - 2015

EM WAVES AND TRANSMISSION LINES(Com to ECE, EIE)

Time: 3 hours Max. Marks: 70

Note: 1. Question Paper consists of two parts (Part-Aand Part-B)2. Answer ALLthe question in Part-A

3. Answer any THREEQuestions from Part-B

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PART-A

1. a) Find the capacitance of a parallel-plate capacitor containing two dielectrics, 21 =r and

3.32 =r , each comprising one-half of the volume. Here, A=4m2and d=10

-3m.

b) Compare the boundary conditions of magnetic field with those of electric field.

c) Explain about the characteristics of uniform plane waves.

d) Write the difference between Conduction Current density and displacement current density.e) Define characteristic impedance and propagation constants of transmission lines.

f) Explain about single stub matching. (4M+4M+3M+4M+3M+4M)

PART-B

2. a) Derive an expression for the electric field intensity due to a finite length line charge along

the Z- axis at an arbitrary point Q( x,y,z)

b) A line charge L= 200pC/m lies along the X- axis. The surface of zero potential passes

through the point P(0,5,4). Find the potential at point (1,3,-2) (8M+8M)

3. a) State all Maxwells equations in differential and integral form for time varying fields.

b) Define and explain the terms: i) skin depth ii) intrinsic impedance of free spaceiii) phase constant. (8M+8M)

4. a) Derive the expression for attenuation and phase constants of uniform plane wave.

b) If r= 9, =0for the medium in which a wave with frequency f= 0.3GHz is propagating

determine propagation constant and intrinsic impedance of the medium when i) =0 and

ii) = 10 mho/m (8M+8M)

5. a) State and prove Poynting theorem.

b) A plane wave travelling in air is normally incident on a material with r= 1 and r= 4. Find

the reflection and transmission coefficients. (8M+8M)

6.

a) Define and explain both lossless and distortion less transmission lines in terms oftransmission line parameters.

b) State the impedance relations, reflection coefficient and SWR for i) shorted line ii) open

circuited transmission line (8M+8M)

7. a) Define Reflection coefficient and VSWR. Explain the relation between the two quantities in

terms of their definition.

b) Discuss the applications of Smith chart. (8M+8M)

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Code No: RT22044






~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PART-A

1. a) Give the limitations of Gauss Law.

b) Define vector magnetic potential and magnetic scalar potential.

c) Write about the wave propagation in a Lossless Media.

d) What is meant by total internal reflection explain?

e) Write in brief about the different types of transmission lines.

f) Discuss in brief reflection coefficient of a transmission line. (3M+4M+4M+3M+4M+4M)

PART-B

2. a) State the applications of Gauss Law with respect to a) point charge b) infinite line charge

b) Point charges 4 mC and -3 mC are located at (2, 1, -3) and (-1, -2, 4) respectively. Calculate

the electric force on a 12 nC charge located at (0, 3, 1) and the electric field intensity at that

point. (8M+8M)

3. a) Discuss the boundary conditions at the interface separating one dielectric and another.

b) Region y 0 consists of a perfect conductor while region y 0 is a dielectric medium

(1r

= 2). If there is a surface charge of 4 n C/m2on the conductor, determine E and D at

(1, -3, 2) (9M+7M)

4. a) Derive the relation between E and H in uniform plane wave propagation.

b) For a uniform plane wave in space =12cm. In a loss less material of unknown

characteristics, =8cm. In this material E= 50V/m, H =0.1A/M find f, r , r (8M+8M)

5. a) State and prove Poynting theorem.

b) For good dielectrics derive the expression for , , and (8M+8M)

6. a) What are the major losses that occur in transmission lines? How is a lossless line

characterized?

b) What are the types of loading? A lossless transmission line having Z0= 120is operating at500M rad/s. If the velocity on the line is 2.4x10

8m/s, find the distributed parameters L and

C. (8M+8M)

7. a) Discuss the configuration of the Smith chart considering the two families of constant

circles.

b) What are the advantages and disadvantages of stub matching? (9M+7M)

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Code No: RT22044






~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PART-A

1. a) Define the terms electric field, electric displacement and electric flux density

b) Write Maxwells equations for electrostatic fields.

c) Explain briefly about Biot-Savarts Law.

d) What is meant by total internal reflection? Explain.

e) Explain about the primary and secondary constants of transmission lines.f) Discuss in brief about the types of loading of a transmission line.

(3M+4M+4M+4M+4M+3M)

PART-B

2. a) Derive expression for electric field due to an infinitesimal electric dipole.

b) On a flat conducting surface, if a surface charge density s= 1 coulomb per square meter is

placed on it, what would be the value of the electric field strength E at its surface?

(8M+8M)

3.

a) State Amperes circuit law. What are its applications?

b) What is displacement current? A parallel plate capacitor with plate area of 6 cm2and plate

separation of 4 mm has a voltage 50sin103t V applied to its plates. Calculate the

displacement current assuming = 20 (8M+8M)

4. a) Derive the relation between E and H in uniform plane wave propagation.

b) A uniform plane wave in air with H=4 sin(t-5x) ayA/m is normally incident on a plastic

region with parameters = 40, =0,=0. Obtain the total electric field in air, and calculate

the average power density in the plastic region. (8M+8M)

5. Prove that under the condition of no reflection at an interface, the sum of the Brewster angle

and the angle of refraction is 90 degrees for parallel polarization for the case of reflection by a

perfect conductor under oblique incidence, with neat sketches. (16M)

6. a) Show that a transmission line will be distortion free if CR= LG

b) A high frequency line has the following primary constants L=1.2 mH/Km, C=0.05F/Km.R = G = negligible. Determine the characteristics impedance and propagation constant of the

line. (8M+8M)

7. a) Define the reflection coefficient and derive the expression for the input impedance in terms

of reflection coefficient.

b) Explain with sketches how the input impedance varies with the frequency (8M+8M)

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Code No: RT22044






~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PART-A

1. a) Derive the expression for capacitance of the spherical conductors.

b) Write short notes on Lorentz force equation

c) Explain briefly about Faradays law for time varying fields.

d) What is meant by depth of penetration?

e) Describe the characteristics of UHF lines.

f) Draw the directions of electric and magnetic fields in parallel plate and coaxial lines(4M+4M+4M+3M+4M+3M)

PART-B

2. a) Derive expression for magnetic field at any point on the axis at a distance h from the centre

of a circular loop of radius a and carrying current I.

b) Find the magnetic field strength, H on the Z- axis at a point P(0,0,4) due to a current

carrying conductor loop, x2+y

2=a

2in Z =0 plane (8M+8M)

3. a) State and explain Biot Savarts law. Give expressions of Biot Savarts law for line, surface

and volume currents.b) Find an expression for the magnetic field produced by a straight current carrying conductor

at a distance x from it. (8M+8M)

4. A plane wave with E=2.0 V/m and has a frequency of 300MHz is moving in free space

impinging on thick copper sheet located perpendicular to the direction of the propagation . Find

i) E and H at the plane surface, ii) Depth of penetration and iii) The surface impedance. (16M)

5. a) State and prove the critical angle theorem.

b) Derive an expression for reflection when a wave is incident on a dielectric obliquely with

parallel polarization. (8M+8M)

6. a) Derive the relationship between secondary constant and primary constants of a transmission

line.

b) What is meant by inductive loading? What are its advantages and disadvantages? (8M+8M)

7. a) Explain the significance and utility of /8,/4 and /2 lines

b) A low transmission line of 100characteristics impedance is connected to a load of 400.

Calculate the reflection coefficient and standing wave ratio. (8M+8M)

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Code No: R22042

II B. Tech II Semester Supplementary Examinations Jan/Feb - 2015

ELECTRO MAGNETIC WAVES AND TRANSMISSION LINES(Com. to ECE, EIE)


Answer any FIVEQuestionsAll Questions carry EqualMarks

~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Let V = xy2z, calculate the energy expended in transferring a 2C point charge from

(1, - 1, 2) to (2, 1,-3).

b) State Gauss Law for electrostatic fields and obtain it in point form. (8M+7M)

2. a) For a current distribution in free space, A= (2x2y + yz)ax+ (xy

2- xz

3)ay- (6xyz 2x

2y

2)az

Wb/m. Calculate Band also show thatdivergence of A = 0 and divergence of B = 0.

b) State Biot-Savarts law.

c) Applying Amperes law to obtain the expression for Hdue to a infinite line current assuming

symmetrical current distribution. (7M+2M+6M)

3. a) Check whether the following field is genuine EM field i.e whether it satisfies Maxwell's

equations. Assume that the fields exist in charge-free regions.

E= (32cota+1/ (cos)a)sint

b) Write the Maxwells equations in point and integral forms.

c) Derive the expression for displacement current density. (7M+4M+4M)

4. a) Discuss about wave propagation in free space.

b) A plane wave propagating through a medium with r=8 r = 2 has E= 0.5e-z/3

sin(108t - z)

axV/m. Determine , loss tangent, wave impedance, wave velocity. (8M+7M)

5. Explain the reflection by a perfect conductor at oblique incidence and obtain the expressions

for fields for both horizontal and vertical polarizations. (15M)

6.

a) For parallel plane waveguide explain and analyze the concept of TE modes and obtain the

expressions for fields.

b) Define attenuation factor and obtain the attenuation factor for the TEM wave between

perfectly conducting parallel planes. (8M+7M)

7. a) A distortion less line operating at 120 MHz hasR = 20 /m,L = 0.2 H/m, and C=63 pF/m.

i) Determine and Zo. ii) How far will a voltage wave travel before it is reduced to 20%

of its initial magnitude?

b) Derive the transmission line equations. (8M+7M)

8.

a) Explain the steps involved in double stub matching.

b) A 75 transmission line is terminated by a load impedance ZL. If the line is 5/8 long,

calculate Zinwhen: (a)ZL=j45 , (b)ZL= 25 - j65 (8M+7M)

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~~~~~~~~~~~~~~~~~~~~~~~~

1. a) In free space, V = x2y(z + 3) V. Find E at (3, 4, -6) and the charge within the cube

0


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~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Three point charges Q1= 1 mC, Q2= -2mC, and Q3= 3 mC are respectively located at

(0, 0, 4), (-2, 5, 1) and (3, - 4, 6). Find the potential VPat P (-1, 1, 2) and also calculate the

potential difference VPQif Q is (1, 2, 3).

b) Derive the expressions for conduction current and convection current. Also obtain point

form of Ohms law. (8M+7M)

2.

a) If H=yax- xayA/m on planez = 0, determine the current density and also verify Ampere's

law by taking the circulation of Haround the edge of the rectangle,

Z = 0, 0


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Code No: R22042

5. a) Explain the reflection by a perfect dielectric at normal incidence and obtain the expressions

for fields, reflection and transmission coefficients.

b) Explain the reflection by a perfect dielectric at oblique incidence for perpendicular

polarization and obtain the expressions for fields, reflection and transmission coefficient

(15M)

6. a) Explain the propagation of TEM wave in a parallel plane wave guide and draw the sketch of

a TEM wave between parallel planes.

b) Define attenuation factor and obtain the attenuation factor for the TE wave between

perfectly conducting parallel planes. (8M+7M)

7. a) What is a loss less transmission line. For a loss less line obtain the expressions for , , , Zo.

b) A telephone line hasR = 30 /km,L = 100 mH/km, G = 0, and C = 20 F/km. At f = 2 kHz,

obtain: the characteristic impedance of the line, the propagation constant and the phase

velocity. (8M+7M)

8. a) Explain the application of a /4 line as a quarter wave transformer.

b) A certain transmission line operating at = 106rad/s has = 6 dB/m, = 1 rad/m, and

Zo= 60 +j40 , and is 2 m long. If the line is connected to a source of 10 V, Zg= 40 and

terminated by a load of 20 + j50 , determine the input impedance and the sending-end

current. (8M+7M)

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Code No: R22042


ELECTRO MAGNETIC WAVES AND TRANSMISSION LINES

(Com. to ECE, EIE)

Time: 3 hours Max. Marks: 75Answer any FIVEQuestions

All Questions carry EqualMarks

~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Define electric potential. Derive the relationship between electric potential and electric field

b) Derive continuity equation and explain the significance of relaxation using relevant

expressions. (8M+7M)

2. a) Planes z = 0 andz = 4 carry current K= -10axA/m and K= 10axA/m, respectively.

Determine H at (1,1,1) and H at (0, - 3,10).

b) Explain the terms magnetic scalar and vector potentials using relevant expressions.c) State Amperes force law. (7M+4M+4M)

3. a) Check whether the following field is genuine EM field i.e whether it satisfies Maxwell's

equations. Assume that the fields exist in charge-free regions. E= 40 sin(t + 10x)az

b) Derive the electrostatic boundary conditions at the dielectric- dielectric interface. (8M+7M)

4. a) Define polarization of a uniform plane wave. Discuss different types of polarizations using

relevant expressions and diagrams.

b) What is skin effect? Define skin depth.

c) A uniform plane wave propagating in a medium has E= 2e-z

sin (108t - 3z) ayV/m.

If the medium is characterized by r= 1, r= 20, and = 3 mhos/m, find , , and H.(4M+4M+7M)

5. a) Explain the reflection by a perfect dielectric at oblique incidence for parallel polarization and

obtain the expressions for fields, reflection and transmission coefficients.

b) State and prove Poynting theorem. (8M+7M)

6. a) Explain the characteristics of TE and TM waves.

b) Derive the relationship between phase velocity, the velocity with which the wave propagates

and free space velocities. (8M+7M)

7. a) A transmission line operating at 400 MHz has Zo= 80 , = 0.04 Np/m, =1.5 rad/m. Find

the line parametersR, L, G, and C.

b) What is a distortion less transmission line? For a distortion less line obtain the expressionsfor , , , Zo. (8M+7M)

8.

a) Derive the relationship between input impedance of a shorted line, input impedance of a

open circuited line and characteristic impedance of the line. Obtain the input impedance of a

line terminated in characteristic impedance of the line.

b) Mention the salient features of a smith chart and discuss its use in transmission line theory

(8M+7M)

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Code No: R22042

II B. Tech II Semester Regular Examinations, August 2014




~~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Derive an expression for electric field intensity due to a finite length line charge along the z-

axis at an arbitrary point P(x, y, z).

b) An infinite line charge L =10 nC/m parallel to z-axis is at x=2 m, y=3m in free space. Find

E at (0, 1, 2) m (8M+7M)

2. a) Obtain an expression for differential magnetic field strength dHdue to differential current

elementIdlat the origin in the positive Z-direction.b) Find the magnetic field strength, H at the centre of a square conducting loop of side 2a in

Z=0 plane, if the loop is carrying a currentIin anti clock wise direction. (6M+9M)

3. a) Explain how the concept of displacement current was introduced by Maxwell to account for

the production of magnetic fields in the empty space.

b) An electric field in a medium which is source free is given by E=2.5 cos(108t-z) ax V/m.

Obtain B, H and D. Assume r=1, r=1 and =0. (7M+8M)

4. a) Derive the expression for attenuation constant and phase constant of uniform plane wave

b) The electric field intensity associated with a plane wave travelling in a perfect dielectric

medium is given by Ex(z, t) = 10 cos(2x107t - 0.1z) V/m

i) What is the velocity of propagation? ii) Write down an expression for the magnetic fieldintensity associated with the wave if = 0. (7M+8M)

5. a) Obtain the expression for reflection coefficient when a wave is incident on a dielectric with

oblique incident perpendicular polarization

b) A plane wave of frequency 2 MHz and E=2 mV/m is incident normally on a copper

conductor. Find the average power density absorbed by the copper. Take r=1, r = 1 and

=5.8x107S/m for copper. (8M+7M)

6. Starting from Maxwells equations, derive the expressions for the E and H field components

for TE waves in parallel plane waveguide. (15M)

7.

a) A coaxial lines with an outer diameter of 8 mm has 50 ohm characteristic impedance. If thedielectric constant of the insulation is 1.6, calculate the inner diameter and derive the

formula can be used.

b) Derive the characteristic impedance of a transmission line in terms of its line constants.

(9M+6M)

8. a) Explain the principal of Impedance matching with quarter wave Transformer?

b) Define VSWR. Give the relationship between VSWR and Reflection coefficient.

c) Write the application of smith chart (6M+4M+5M)

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Code No: R22042





~~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) State and prove the Gauss law.

b) A line charge L =400 pc/m lies along the x-axis the surface of zero potential passes through

the point P(0, 5, 12)m. Find the potential at (2, 3, -4) m. (8M+7M)

2. a) Define Magnetic flux density, scalar and vector magnetic potential.

b) Find the total magnetic flux crossing a surface, = /2, 12 and 0 z 5 m due to a

vector magnetic potential A = (2/4) azWebers/m

c) Derive Lorentz force equation and explain its significance. (4M+5M+6M)

3. a) State Maxwells equations in differential form and write down their word statements.

b) In a three dimensional space, divided into region 1 (X0), 1=2=0,

E1=1ax+2ay+3azV/m. Find E2and D2, r1=1, r2=2. (7M+8M)

4. a) Define uniform plane wave. Prove that uniform plane wave does not have field components

in the direction of propagation.

b) The electric field in free space is given by E = 50 cos (108

t+ x) ayV/m

i) Find the direction of wave propagation.

ii) Calculate and the time it takes to travel a distance of /2

iii) Sketch the wave at t = 0, T/4, and T/2. (5M+10M)

5. a) State and prove the Poynting theorem.

b) A plane wave travelling wave in free space has an average Poynting vector of 1 W/ m2

.

Find the average energy density. (12M+3M)

6. a) What are the field components for TM wave? Derive them, draw sketches for TM10Mode.

b) Derive the relation2 2

c g

g c

=

+

, where is free space wavelength, g is

wavelength measured in the guide and c is the cutoff wavelength. (9M+6M)

7.

a) Starting from the equivalent circuit, derive the transmission line equations for V and I, in

terms of the source parameters.

b) Give T and equivalent network representation for a transmission line. (11M+4M)

8. a) Define the reflection coefficient and derive the expression for input impedance in terms of

reflection coefficient.

b) Explain the construction of smith chart. (7M+8M)

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Code No: R22042





~~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) State the Coulombs law of force between any two point charges and indicate the units of the

quantities in the force equation.

b) Derive Poissons and Laplaces equations starting from Gauss law.

c) Define capacitance. Find the capacitance of a parallel plate capacitor with dielectric mica

filled between the plates rof the mica is 6 .The plates of capacitor are in shape with 0.254

cm side, separation between the two plates is 0.254 cm. (5M+5M+5M)

2.

a) State Maxwells equations for magnetostatic fields.

b) Derive an expression for magnetic field strength, H, due to a current carrying conductor of

finite length placed along the y- axis, at a point P in x-z plane and r distant from the origin.

Hence deduce expressions for H due to semi-infinite length of the conductor. (5M+10M)

3. a) Explain the equation of continuity in time varying fields.

b) A certain material has = 0, r=1, if H=4 sin(106t - 0.01z) ayA/m. Find r using Maxwells

equations. (7M+8M)

4.

a) Discuss about propagation characteristics of EM waves in a conducting medium.

b) In a nonmagnetic medium E=50 cos(109t-8x) ay+ 40 sin(10

9t-8x) azV/m. Find the

dielectric constant r and the corresponding H . (6M+9M)

5.

a) Obtain the expression for reflection coefficient when a wave is incident on a dielectric with

Oblique incident parallel polarization

b) Derive the expression for surface impedance of conductor in terms of skin depth. (10M+5M)

6.

a) Discuss about the existence of TEM wave in parallel plane guide.

b) Define attenuation factor. Explain how the attenuation vary with frequency in parallel plate

wave guide. (8M+7M)

7.

a) A telephone wire 20 km long has the following constants per loop km: resistance 90,

capacitance 0.062 F, inductance 0.001H and leakage = 1.5x106

mhos. The line is

terminated in its characteristic impedance and a potential difference of 2.1 V having afrequency of 1000 Hz is applied at the sending end. Calculate: i) The characteristic

impedance ii) Wavelength iii) The velocity of propagation

b) What is meant by distortion? Derive the conditions for distortion less transmission line.

(9M+6M)

8. a) Derive the expression for the input impedance of a loss-less line. Hence evaluate ZSCand

ZOCand sketch their variation with line length.

b) Explain why short circuited stubs are preferred over open circuited stubs. (10M+5M)

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~~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Find the force on a 100C charge at (0, 0, 3) m, if four like charges of 20 C are located on

x, y axis at 4m.

b) Define capacitance? Derive the expression for capacitance of a spherical type capacitor.

(8M+7M)

2. a) Define and explain the Biot- Savarts law.

b) Find magnetic field strength, H, on the z- axis at a point P(0,0,h), due to a current carrying

Circular loop, x2+ y

2= A

2in z=0 plane. (7M+8M)

3. a) Verify that the displacement current in the parallel plate capacitor is the same as the

conduction current in the connecting wires.

b) Derive the boundary conditions for dielectric to conductor interface. (7M+8M)

4. a) Find , , and , for Ferrite at 10 GHz , r= 9, r= 4, = 10 mhos/m.

b) What is meant by polarization? Explain in detail about circular polarization. (7M+8M)

5. a) Define Brewster angle and derive an expression for Brewster angle when a wave is parallelly

polarized.

b) Derive the expression for surface impedance of a conductor. (8M+7M)

6. Starting from Maxwells equations, derive the expressions for the E and H field components

for TM waves in parallel plane waveguide. (15M)

7. a) List out types of transmission lines and draw their schematic diagrams.

b) Describe the losses in transmission lines

c) A transmission line in which no distortion is present has the following parameters: Zo= 60,

= 20 mNP/m, V = 0.7V0. Determine R, L, G, C and wavelength at 0.1GHz.

(4M+4M+7M)

8. a) Explain how Quarter wave transformer acts as impedance inverter.

b) What is meant by stub? Explain single stub matching concept. (6M+9M)

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Code No: R22042

II B. Tech II Semester Supplementary Examinations January 2014


(Com. to ECE, EIE)


Answer anyFIVE

QuestionsAll Questions carry EqualMarks

~~~~~~~~~~~~~~~~~~~~~~~~~~

1.

a) What is a point charge? Derive the expression for electric field intensity using coulombs law

from fundamentals.

b) Two point charges 5nC and -2nC are located at (2,0,4) and (-3,0,5) respectively.

i) Determine the force on a point charge located at (1,-3,7)

ii) Find the electric field E at (1,-3,7).

2.

a) State Biot-Savarts law and find field at arbitrary point p due to a straight filamentary

conductor.

b) A circular loop located on x2

+y2

= 9, z=0 carries a direct current of 10 A along a.Determine Hat (0,0,4) and (0,0,-4).

3. a) Differentiate conduction and displacement current densities.

b) In a medium, conduction current density given byJ= 10 z sin2aA/m

2, find the current

through the cylindrical surface = 2, 1 z 5 m.

4.

a) Derive the wave equation for conducting medium.

b) A plane wave is propagating in a medium having the properties r= 4, r= 36, = 1 S/mand the E= 100e

-azcos(10

9t-z)axV/m, determine the associated magnetic field.

5.

a) Explain the factors on which cut off frequency of a parallel plane wave guide depend.

b) Obtain the frequency in terms of cut off frequencyfcat which the attenuation constant due toconductor losses for the TMnmode is minimum for a parallel plane wave-guide.

6.

a) Explain the principal of impedance matching with quarter-wave transformer.

b) A 50 loss less line connects a signal of 50 kHz to a load of 140. The load power is75mW. Calculate

i) Voltage Reflection coefficient ii) VSWR, iii) Position of VMax, Imax ,Vmin and Imin

7. a) A transmission line of length 70 meters is terminated in an impedance of ZR= 125 + j48. If

the frequency is 3 MHz and the characteristic impedance is 230 , find the sending endimpedance using Smith chart, explaining the procedure.

b) What is meant by inductive loading? With the help of suitable expressions explain the

advantages of loading and also discuss the disadvantages.

8. a) Define the Brewster angle and derive an expression for Brewster angle when a wave is

parallely polarized.

b) A plane wave traveling in a medium of r= 1; r= 1 has an electric field intensity of 200 x V/m. Determine the energy density in the magnetic field and also the total energydensity.

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Code No: R22042



(Com. to ECE, EIE)


Answer anyFIVE

QuestionsAll Questions carry EqualMarks

~~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Derive the expression for electric field intensity Econsidering the surface charge

distribution.

b) The finite sheet 0 x 1, 0 y 1 on the z = 0 plane has a charge densitys= xy(x

2+y

2+ 25)

3/2nC/m

2. Find: i) Total charge on sheet ii) The electric field at (0,0,5)

iii) The force experienced by a -1mC charge located at (0,0,5)

2. a) Prove that the energy stored in an inductor is given by WL= 1/2 L I2.

b) If the magnetic field is H = (0.01/o ) ax A/m, what is the force on a charge of 1.0 pC movingwith a velocity of 106axm/s.

3. a) Derive the equation of continuity for time varying fields.

b) A Parallel plate capacitor with a plate area of 5cm2 and plate separation of 3mm has a

voltage 50 sin 103t V applied to its plates. Calculate the displacement current assuming

= 2 o.

4. a) Derive the Helmholtz wave equation from the fundamentals and determine the Loss tangent.

What is the significance of the loss tangent?

b) A lossy dielectric has an intrinsic impedance of 030200 at a particular radian frequency. If, at that frequency, the plane wave propagating through the dielectric has the magnitude

field component H= 10 e-xcos(t-0.5x)ayA/m Find E and . Determine the skin depth.

5. a) Discuss the nature of variation of wave impedances for TE, TM and TEM waves with

frequency in a parallel plane wave guide.

b) Define and derive the equations for phase and group velocities in a parallel plane guide.

Explain on which factors these will depend.

6. a) Explain the significance of pointing vector and the pointing theorem.

b) A plane wave traveling in a medium of r= 1; r= 1 has an electric field intensity of100 x V/m. Determine the energy density in the magnetic field and also the total energydensity.

7.

a) Draw the equivalent circuits of the transmission lines wheni) length of the transmission line, L < /4, with shorted loadii) when L < /4, with open endiii) L = /4

b) Find out VSWR if i) Z0= 200; RL= 80 ii) when Z0= 80; RL= 200

8. a) What is single stub matching? How is it used in impedance matching? Find the location of

the stub with respect to the load under matched conditions.

b) A certain low loss line has a characteristic impedance of 400. Determine the standing waveratio with the following receiving end impedance.

i) ZR= 70 + j0.0 ii) ZR= 800 + j0.0 iii) ZR = 650 j4751 of 1

SET - 2R10


16/17 |''|'||'|''|'''|||'|

Code No: R22042



(Com. to ECE, EIE)



~~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Prove J = vV from fundamentals.

b) Find out electric flux density in free space if the electric field, E = 6ax- 2ay+ 3az, V/m also

find v.

2. a) Mention some applications of magneto static fields.

b) A toroid of circular cross section whose center is at origin and the axis the same as the z-axis

has 1000 turns with o(mean radius) = 10 cm, a(radius of the cross circular section) = 1cm.

If the toroid carries a 100mA current, find |H| ati) (3 cm, -4 cm, 0) ii) ( 6cm, 9cm, 0)

3. a) Derive and explain the Maxwell's equations in point form and integral form.

b) Given the conduction current density in a lossy dielectric as Jc = 0.02sin109t (A/m

2). Find

the displacement current density if = 103 S/m and r= 6.5?

4. a) State and prove the Poynting theorem from the fundamentals.

b) A uniform plane wave propagating in a medium has E = 2e-z

sin (108t-z)ayV/m

If the medium is characterized by r= 1, r= 20 and = 3 S/m, find , and H.

5.

a) Explain the significance of TEM wave in a parallel plane guide and derive the expression for

the attenuation factor for TEM waves.b) Explain and sketch the nature of variations of attenuation with frequency in a parallel plane

wave guide for TE, TM and TEM waves.

6. a) Define the following:

i) loss tangent ii) Distinguish between conductors and Dielectrics

b) A good conductor is planar in form and it carries a uniform plane wave that has a wave

length of 0.3 mm and a velocity of 3 x 105m/s assuming the conductor is non-magnetic

determine the frequency and the conductivity.

7. a) What is distortion less line? Determine the condition for distortionlessness and minimum

attenuation.

b) A certain transmission line 2 m long operating at =106rad/s has = 8 dB/m. = 1 rad/mand Z0= 60 + j40. If the line is connected to a source of 0010 V, Zg= 40(Zg sourceimpedance) and terminated by a load of 20 + j50, determinei) The input impedance ii) The sending-end current

8. a) Explain the working principle of quarter-wave transformer.

b) A loss less transmission line with Z0= 50is 30 m long and operates at 2MHz. The line isterminated with a load ZL= 60 + j40. If velocity u= 0.6c (where c is the free spacevelocity) on the line, find the following using smith chart

i) The reflection coefficient ii) The standing wave ratio iii) input impedance

1 of 1

SET - 3R10


17/17

Code No: R22042



(Com. to ECE, EIE)


Answer any FIVEQuestions

All Questions carry EqualMarks

~~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) State Guass law. Explain any two applications of Guass law in detail.

b) The point charges -1nC,4nC, and 3nC are located at (0,0,0), (0,0,1) and (1,0,0) respectively.

Find the energy in the system.

2. a) State Maxwells equations for magneto static fields.

b) Show that the magnetic field due to a finite current element along Z axis at a point P, r

distance away along y- axis is given by H = (I/4r)(sin 1sin 2).a, where I is the currentthrough the conductor , 1, and 2are the angles made by the tips of the conductor elementat P?

3. a) Explain Faradays laws for time-varying fields.

b) Verify the displacement current in the parallel plate capacitor is the same as the conduction

current in the connecting wires.

4. Prove that under the condition of no reflection at an interface, the sum of the Brewster angle

and the angle of refraction is /2 for parallel polarization for the case of reflection by a perfectconductor under oblique incidence, with neat sketches.

5. a) Derive the relation = (c

g)/( (

c

2+

g

2) where is the free space wavelength,

gis the

wave length measured in guide and c is the cut-off wave length.b) Explain the impossibility of TEM mode propagation in the wave guides.

6. a) Explain the principal of impedance matching with quarter-wave transformer.

b) A 50 loss less line connects a signal of 50 kHz to a load of 140. The load power is75mW. Calculate

i) Voltage Reflection coefficient ii) VSWR, iii) Position of VMax, Imax ,Vmin and Imin

7.

a) What is distortion less line? Determine the condition for distortionlessness and minimum

attenuation.

b) A certain transmission line 2 m long operating at =106rad/s has = 8 dB/m. = 1 rad/m

and Z0= 60 + j40. If the line is connected to a source of0

010 V, Zg= 40(Zg sourceimpedance) and terminated by a load of 20 + j50, determinei) The input impedance ii) The sending-end current

8. a) What is single stub matching? How is it used in impedance matching? Find the location of

the stub with respect to the load under matched conditions.

b) A certain low loss line has a characteristic impedance of 400. Determine the standing waveratio with the following receiving end impedance.

i) ZR= 70 + j0.0 ii) ZR= 800 + j0.0 iii) ZR = 650 j475

1 of 1

SET - 4R10

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