Electro Magnetic Waves and Transmission Lines

JNTUW

ORLD

Code No: V0424

II B. Tech II Semester, Supplementary Examinations, Nov/ Dec - 2011

ELECTRO MAGNETIC WAVES AND TRANSMISSION LINES (Electronics and Communications Engineering)

Time: 3 hours Max. Marks: 80 Answer any FIVE Questions

All Questions carry equal marks

1. a) State and prove Gausss law. Give three applications of Gausss law with suitable examples.

b)When six equal charges of Q =10 pico coulombs are located at (2,0,0),(3,0,0),(4,0,0), (5,0,0),(6,0,0) and (7,0,0); find the potential at the origin. (8M+8M)

2. a) State Amperes current law. Specify the conditions to be met for determining magnetic field strength H, based on Amperes circuital law.

b) Find the magnetic field strength, H at the centre of square conducting loop of side a in z = 0 plane if the loop is carrying a current I in anti clock wise direction. (6M+10M)

3. a) Derive Maxwells equations from their basics. b) Given E= 25 sin (t-z) ay V/m in free space, Determine D, B and H (8M+8M)

4. a) For good dielectrics derive the expressions for , , and . b) A medium like copper conductor which is characterized by the parameters = 5.8x107

mho/m, r = 1, r = 1 supports a uniform plane wave of frequency 50Hz. Find , , , and . (8M+8M)

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

b) A polarized wave is incident from air to polystyrene with = o, = 2.6o at Brewster angle. Determine the transmission angle. (8M+8M)

1 of 2

SET - 1 R07

www.jntuworld.com

www.jntuworld.com

JNTUW

ORLD

Code No: V0424

6. a) Discuss the presence of TE, TM, TEM waves in parallel plane wave guides and explain their significance.

b) A hallow rectangular waveguide has the dimensions of a =2.286 cm, and b=1.016cm. Find the cutoff frequencies of TM11 and TM20. (8M+8M)

7. a) Using the general line equations obtain an expression for the input impedance of a line. b) A loss less transmission line has a capacitance of 50 pF/m and an inductor of 200nH/m.

Find the characteristic impedance for section of a line 10m long and 500m long. (8M+8M)

8. a) Discuss about single and double stub matching. b) A load of (25 j50) is connected across a 50 line. Design a short circuited stub in

order to provide impedance matching between the two at a signal frequency of 60MHz. (8M+8M)

2 of 2

SET - 1 R07

www.jntuworld.com

www.jntuworld.com

JNTUW

ORLD

Code No: V0424





1. a) Derive Poissons and Laplaces equations starting from Gauss law. b) There exists a potential of V= -2.5V on a conductor at r = 0.02 m and V=15V at r =

0.35m. A dielectric material whose r= 3.0 exists between the conductors. Determine the surface charge densities on the conductors. (8M+8M)

2. a) What do you mean by vector magnetic potential? What are the characteristics of vector magnetic potential, Derive A for surface current?

b) The vector magnetic potential A due to a direct current in a conductor in free space is given by a A= (x2+y2) az Wb/m2. Determine the magnetic field produced by the current element at (1, 2, 3) (8M+8M)

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) In free space the magnetic field of an EM wave is given by H = 0.2 0 cos(t 25x) azA/m. Find the electric field E and displacement current density D (8M+8M)

4. a) Define uniform plane wave. Prove that uniform plane wave does not have field components in the direction of propagation.

b) If r = 9, = 0 for a medium in which a wave with a frequency of f = 0.3GHz is propagating , determine the propagation constant and intrinsic impedance of the medium

when = 0 (8M+8M)

1 of 2

SET - 2 R07

www.jntuworld.com

www.jntuworld.com

JNTUW

ORLD

Code No: V0424

5. a) Show that in a good conductor, the skin depth is always much shorter than the wavelength.

b) Write short notes on i) total internal reflection ii) surface impedance (8M+8M) 6. a) Explain the factors on which cutoff frequency of a parallel plate waveguide depend. b) A hallow rectangular waveguide operates at 10 GHz. If the cutoff frequency of TM21

mode is 6 GHz, find its phase velocity, wavelength and phase constant. (8M+8M)

7. a) Explain about the propagation constant in transmission lines. b) Write short notes on distortion less line. c) A lossy cable which has R =2.25/m, L =1.0 H/m, C = 1pF/m and G = 0 operates at f

= 0.5GHz. Find out the attenuation constant of the line. (4M+4M+8M)

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

b) A transmission line of length 0.40 has a characteristics impedance of 50 and is terminated in a load impedance of (100 + j90). Find the i) voltage reflection coefficient and ii) voltage standing wave ratio. (8M+8M)

2 of 2

SET - 2 R07

www.jntuworld.com

www.jntuworld.com

JNTUW

ORLD

Code No: V0424





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

b) An infinite length of uniform line charge has L= 10 PC/m and it lies along the Z axis. Determine electric field E at (4,3,3) (8M+8M)

2. a) Explain the following terms: i) Magnetic flux density ii) Vector Magnetic potential iii) Magnetic scalar potential

b) If the magnetic field is H = (0.01/0) ax A/m, What is the force on a charge of 1.0 pico coulomb moving with a velocity of 106 ax m/s (8M+8M)

3. a) Obtain the integral form of Maxwells equations from Amperes circuital law. b) An electric filed 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. (8M+8M)

4. a) Discuss about uniform plane waves in lossless dielectrics and establish the relationship between electric and magnetic fields in the medium.

b) The wavelength of an x-directed plane wave in a loss less medium is 0.25m and the velocity of propagation is 2.51010 cm/s. The wave has z- directed electric filed with an amplitude equal to 10 v/m. Find the frequency and permittivity of the medium. Assume = 0 (8M+8M)

1 of 2

SET - 3 R07

www.jntuworld.com

www.jntuworld.com

JNTUW

ORLD

Code No: V0424

5. a) Derive an expression for reflection when a wave is incident on a dielectric obliquely with parallel polarization.

b) Define surface impedance and explain its significance. (8M+8M)

6. a) Obtain the frequency in terms of cut off frequency fc at which the attenuation constant due to conductor losses for TMn mode is minimum for parallel plate waveguide.

b) A rectangular waveguide with dimensions 3x2 cm operates at 10 GHz. Find fc, c, , g, g, Vp of TE10 mode. (8M+8M)

7. a) What are different types of losses in transmission lines explain? b) A transmission line in which no distortion is present has the following parameters, z0 = 50, = 0.020m-1 , = 0.6v0 .Determine R, L, G, C and wave length at 0.1GHz (8M+8M)

8. a) Explain how the input impedance of transmission lines varies with the frequency with sketches

b) Describe the characteristics of UHF lines. c) Find the input impedance of 75 loss less transmission lines of length (0.1) if it is

terminated in open circuit. (4M+6M+6M)

2 of 2

SET - 3 R07

www.jntuworld.com

www.jntuworld.com

JNTUW

ORLD

Code No: V0424





1. a) Define and distinguish between the terms electric filed, electric displacement and electric flux density.

b) An infinite line charge L = 10nc/m parallel to z axis is at x=2, y= 3 in free space find E at (0,1,2) (8M+8M)

2. a) Obtain an expression for differential magnetic field strength dH due to differential current element Idl at the origin in the positive Z-direction.

b) If the separation between two infinitely long current elements is 5m and the elements carry 2 Amperes in opposite direction, find the magnetic field at 1m from one current

element. (8M+8M)

3. a) State the boundary conditions satisfied by electromagnetic fields E and H at any surface of discontinuity. (8M+8M)

b) If two regions are defined by X1< 0, X2 > 0 and characterized by r1=3.0 and r2= 5.0 If the magnetic filed in region 1 is given by H1 = 4.0 ax + 1.5ay 3.0 az,a/m find H2

4. a) Discuss about the propagation characteristics of EM waves in conducting medium. b) An elliptically polarized wave has an electric field of E = sin (t z) ax + 2sin

(t-z+750) ay v/m. Find the power per unit area conveyed by the wave in free space. (8M+8M)

5. a) State and prove pointing theorem. b) An EM wave in free space is incident normally on a dielectric whose r =5.0 Find the

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

1 of 2

SET - 4 R07

www.jntuworld.com

www.jntuworld.com

JNTUW

ORLD

Code No: V0424

6. a) What are the field components for TM waves? Derive them and draw the sketches for TM10 mode.

b) Find the broad wall dimension of a rectangular waveguide when the cutoff frequency for TE10 mode is 6 GHz. (8M+8M)

7. a) Explain how the input impedance varies with frequency with sketches. b) What is loading? Explain different types of loading in transmission lines. (8M+8M)

8. a) Explain the principle of impedance matching with quarter wave transformer. b) A 75 line is terminated by a load of (60+j80). Find the maximum and minimum

impedances on the line. c) Mention the application of Schmitt chart. (8M+6M+2M)

2 of 2

SET - 4 R07

www.jntuworld.com

www.jntuworld.com

Documents

Electro Magnetic Waves and Transmission Lines