11903 Electromagnetic Waves And Transmission Lines

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Code No: R05411903
Set No. 1
IV B.Tech I Semester Regular Examinations, November 2008
ELECTROMAGNETIC WAVES AND TRANSMISSION LINES
(Electronics & Computer Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks

1. (a) Obtain an expression for electric eld intensity at a point, P(x, y, z) due to a
point charge located at ( )
(b) Derive an expression for the electric eld intensity due to an in nite length
line charge along the z-axis at an arbitrary point Q (x, y, z).
(c) A charge of -0 3 is located at A (25, -30, 15) Cm and a second charge of
0.5 C is located at B (-10, 8, 12) Cm. Find the electric eld strength, ?E?
at
i. The origin
ii. Point P (15, 20, 50) Cm [4+6+6]

2. (a) Obtain an expression for di erential magnetic eld strength dH due to di er-
ential current element I dl at the origin in the positive Z- direction.
(b) Find the magnetic eld strength, H at the centre of a square conducting loop
of side ‘2a’ in Z=0 plane if the loop is carrying a current , I, in anti clock wise
direction. [6+10]

3. (a) Write down Maxwell?s equations in their general integral form. Derive the
corresponding equations for elds varying harmonically with time
(b) In free space D = Dm sin ( t + z) ax use Maxwell?s equations to nd B.
[8+8]

4. (a) Derive wave Equations for source free regions.
(b) The electric eld in free space is given by E=50 cos (108 + )ay V/m
i. Find the direction of propagation
ii. Calculate b and the time it takes to travel a distance of 2
iii. Sketch the wave at t=0, T/4 and T/2 [8+8]

5. (a) State and explain Poynting theorem.
(b) A plane wave traveling in free space has an average poynting vector of 5
2. Find the average energy density. [8+8]

6. (a) Explain the signi cance of TEM wave in a parallel plane guide, and derive an
expression for the attenuation factor for TEM waves.
(b) Explain and sketch the nature of variations of attenuation with frequency in
a parallel plate wave guide for TE, TM and TEM waves. [8+8]

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Code No: R05411903
Set No. 1
7. (a) De ne characteristic impedance and propagation constants of transmission
lines and obtain lossless conditions.
(b) A lossless transmission line of length 100m has an inductance of 28 H and
capacitance of 20 nF. Find out.
i. propagation velocity
ii. phase constant at an operating frequency of 100 KHz [8+8]
iii. characteristic impedance of the line.

8. (a) De ne the i/p impedance of a transmission line and derive the expression for
it.
(b) The characteristic impedance of a certain lines is 810 ?140 = 0.009+
j0.028 per km. The line is terminated in a 200 resistor. Calculate the i/p
impedance of the line if its length is 100 km. [8+8]

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Code No: R05411903
Set No. 2

1. (a) Obtain an expression for electric eld intensity at a point, P(x, y, z) due to a
point charge located at ( )
(b) Derive an expression for the electric eld intensity due to an in nite length
line charge along the z-axis at an arbitrary point Q (x, y, z).
(c) A charge of -0 3 is located at A (25, -30, 15) Cm and a second charge of
0.5 C is located at B (-10, 8, 12) Cm. Find the electric eld strength, ?E?
at
i. The origin
ii. Point P (15, 20, 50) Cm [4+6+6]

2. (a) Obtain an expression for di erential magnetic eld strength dH due to di er-
ential current element I dl at the origin in the positive Z- direction.
(b) Find the magnetic eld strength, H at the centre of a square conducting loop
of side ‘2a’ in Z=0 plane if the loop is carrying a current , I, in anti clock wise
direction. [6+10]

3. (a) Give the word statement for di erent boundary conditions

(b) The magnetic circuit shown in gure 3b has a uniform cross section of10 3 2.
If the circuit is energized by a current I(t)=3 sin 100 t A in the coil of 1
= 200 turns nd the emf induced in the coil of 2=100 turns. Assume that
= 500 0 [8+8]

Figure 3b
4. (a) Explain about uniform plane waves.
(b) In a loss less medium for which = 60 = 1 and H=-0.1 cos (wt-z)ax+0.5
sin (wt-z)ay A/m. calculate r and w. [8+8]

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Code No: R05411903
Set No. 2
5. (a) Explain the di erence between the Intrinsic Impedance and the Surface Im-
pedance of a conductor. Show that for a goo d conductor , the surface im-
pedance is equal to the intrinsic impedance.
(b) De ne and distinguish between the terms perpendicular polarization, parallel
polarization, for the case of re ection by a perfect conductor under oblique
incident. [8+8]

6. (a) For a parallel plane wave guide having z-propagation, explain the nature of
variation and sketch the variation of E and H for 10waves.
(b) Explain the impossibility of TEM wave propagation in wave guides. [10+6]

7. (a) Derive an expression for the attenuation factor for the 10 wave between
parallel Conduction planes.
(b) For a wave guide derive the relation between , free space wave length, g
guide wave Length and c cut o wave length. [8+8]

8. (a) Explain clearly why the short circuited stubs are preferred over to a open
circuited stubs?
(b) Derive the expression for the input impedance of a loss-less line. Hence eval-
uate SC and OC and sketch their variation with line length [6+10]

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Code No: R05411903
Set No. 3

1. (a) State and explain Coulomb’s law using vector form of Coulomb?s force ex-
pression.
(b) Find the force on a charge of -100mC located at P (2, 0, 5) in free space due
to another charge 300 C located at Q (1, 2, 3).
(c) State and express Gauss’s law in both integral and di erential forms. [8+4+4]

2. (a) State Biot- Savart law
(b) Derive an expression for magnetic eld strength, H, due to a nite lamentary
conductor carrying a curent I and placed along Z- axis at a point ’P’ on y-
axis. Hence deduce the magnetic eld strength for the length of the conductor
extending from - 8 to + 8. [4+12]

3. In a source less medium the which J=0 and v = 0, assume the rectangular coor-
dinates system in which E and H are functions only of z and t. The medium has
permittivity and permeability

(a) If E=Ex ax and H=Hy ay. begin with max wells equations and determine the
second order partial di erential equation that Ex must satisfy
(b) Show that Ey=5 (300 + )2 is a solution of that equation for a particular
value of b. [8+8]

4. (a) Explain skin depth and derive expression for depth of penetration for good
conductor.
(b) Find for a material in which at 100MHz, uniform plane wave has
= 2 = 1 | | = 200 . [8+8]

5. (a) A uniform plane wave is normally incident from air on a perfect conductor.
Determine the resulting E and H elds. Sketch their variations.
(b) An plane EM wave is normally incident on the boundary between two di-
electrics. What must be the ratio of the refractive indices of the two media in
order that the re ected and transmitted waves may have equal magnitudes of
average power. [8+8]

6. For a parallel plane wave guide of 3 cm separation, determine all the propagation
characteristics, for a signal at 10 GHz, for

(a) 10 waves
(b) TEM waves [16]

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Code No: R05411903
Set No. 3
Explain the terms used.

7. (a) De ne characteristic impedance and propagation constants of transmission
lines and obtain lossless conditions.
(b) A lossless transmission line of length 100m has an inductance of 28 H and
capacitance of 20 nF. Find out.
i. propagation velocity
ii. phase constant at an operating frequency of 100 KHz [8+8]
iii. characteristic impedance of the line.

8. (a) What is the signi cance of standing wave ratio in a transmission line? Calcu-
late the Re ection coe cient and VSWR for a 50 lines, terminated with
i. matched Load
ii. Short circuit
iii. +j50 loads
iv. -j50 load
(b) A 50 transmission line is terminated by an unknown impedance. The VSWR
is 4 and the rst minimum is formed at 2 cm from the load end. The frequency
of operation is 1 GHz. Design a single stub line matching for the Above
conditions. [8+8]

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Code No: R05411903
Set No. 4

1. (a) State and prove Gauss’s law. Express Gauss’s law in both integral and di er-
ential forms.
(b) Discuss the salient features and limitations of Gauss’s law .
(c) Derive Poisson’s and Laplace’s equations starting from Gauss’s law. [6+4+6]

2. (a) State Biot- Savart law
(b) Derive an expression for magnetic eld strength, H, due to a nite lamentary
conductor carrying a curent I and placed along Z- axis at a point ’P’ on y-
axis. Hence deduce the magnetic eld strength for the length of the conductor
extending from - 8 to + 8. [4+12]

3. In gure 3 let B=0-2cos 120 t T, and assume that the conductor joining the two
ends of the resistor is perfect. It may be assumed that the magnetic eld produced
by I(t) is negligible nd

(a) ab (t)
(b) I(t) [8+8]

Figure 3
4. (a) For a conducting medium derive expressions for .
(b) Determine the phase velouty of propagation, attenuation constant, phase con-
stant and intrinsic impedance for a forward travelling wave in a large block
of copper at 1 MHz ( = 5 8 × 107 = = 1) determine the distance that
the wave must travel to be attenuated by a factor of 100 (40 dB) [8+8]

5. (a) What is Total Internal Re ection on the basis of EM theory of light and what
are its applications.

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Code No: R05411903
Set No. 4
(b) An EM wave traveling in air is incident normally on a boundary between air
and a dielectric having permeability same as free space and permittivity as 4.
Prove that one-ninth of the incident power is re ected and eight-ninths of it
is transmitted into the second medium. [8+8]
v where is free space wave length, g is
6. (a) Derive the relation = c g
2
the wave length measured in the guide, and c is the cut o wave length.
g+ 2 c

(b) For a parallel plane wave guide having z-propagation, explain the nature of
variation and sketch the variation of E and H for 10 waves. [8+8]

7. (a) Explain the di erent types of transmission lines. What are limitations to the
maximum power that they can handle.
(b) A coaxial limes with an outer diameter of 8 mm has 50 ohm characteristic
impedance. If the dielectric constant of the insulation is 1.60, calculate the
inner diameter.
(c) Describe the losses in transmission lines [8+4+4]

8. (a) Explain the metho d of determining the input impedance of line using Smith
chart, for a loss less Line of length L , at any frequency f, for a complex load
of R.

(b) A loss less Line of 300 is terminated by a load of R. If the VSWR at
200MHz is 4.48, and the rst min is lo cated at 6 cm from the load. Calculate
the re ection coe cient and R. [8+8]

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11903 Electromagnetic Waves And Transmission Lines

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