set no. 1 - pvpsit · code no: r05220404 set no. 1 ii b.tech ii semester supplimentary...

Code No: R05220404 Set No. 1

II B.Tech II Semester Supplimentary Examinations, Aug/Sep 2007ELECTROMAGNETIC WAVES AND TRANSMISSION LINES

( Common to Electronics & Communication Engineering and Electronics &Telematics)

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

All Questions carry equal marks⋆ ⋆ ⋆ ⋆ ⋆

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 dueto another charge 300µ C located at Q (1, 2, 3).

(c) State and express Gauss’s law in both integral and differential forms. [8+4+4]

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

(b) Find the magnetic field strength, H at the centre of a square conducting loopof side ‘2a’ in Z=0 plane if the loop is carrying a current , I, in anti clock wisedirection. [6+10]

3. (a) What is the inconsistency of Amperes law?

(b) A circular loop conductor of radius 0.1m lies in the z=0plane and has a resis-tance of 5Ω given B=0.20 sin 103 t az T. Determine the current [8+8]

4. (a) Explain the propagation of wave in a loss less medium.

(b) A uniform plane wave at a frequency of 1GHz is travelling in a large block ofTeflon (∈ r = 2.1, µr = 1andσ = 0). Determine V, η, β and λ [8+8]

5. (a) What is Total Internal Reflection on the basis of EM theory of light and whatare its applications.

(b) An EM wave traveling in air is incident normally on a boundary between airand a dielectric having permeability same as free space and permittivity as 4.Prove that one-ninth of the incident power is reflected and eight-ninths of itis transmitted into the second medium. [8+8]

6. (a) Explain about attenuation in parallel-plate wave guides. Also draw attenu-ation versus frequency characteristics of waves guided between parallel con-ducting plates.

(b) A parallel plate wave guide made of two perfectly conducting infinite planesspaced 3 cm apart in air operates at a frequency of 10 GHz. Find the maximumtime average power that can be propagated per unit width of the guide forTE1andTM1 modes. [8+8]

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7. (a) Explain the meaning of the terms characteristic impedance and propagationconstant of a uniform transmission line and obtain the expressions for themin terms of Parameters of line?

(b) A telephone wire 20 km long has the following constants per loop km resistance90 Ω, capacitance 0.062 µF , inductance 0.001H and leakage = 1.5 x 10−6

mhos. The line is terminated in its characteristic impedance and a potentialdifference of 2.1 V having a frequency of 1000 Hz is applied at the sendingend. Calculate :

i. The characteristic impedance

ii. Wavelength.

iii. The velocity of propagation [8+8]

8. (a) Describe all the characteristics of UHF Lines?

(b) Explain the significance and design of single stub impedance Matching. Dis-cuss the Factors on which stub length depends. [6+10]

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1. (a) State and prove Gauss’s law. Express Gauss’s law in both integral and differ-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) Obtain an expression for differential magnetic field strength dH due to differ-ential current element I dl at the origin in the positive Z- direction.

(b) Find the magnetic field strength, H at the centre of a square conducting loopof side ‘2a’ in Z=0 plane if the loop is carrying a current , I, in anti clock wisedirection. [6+10]

3. (a) Write down Maxwell?s equations in their general integral form. Derive thecorresponding equations for fields varying harmonically with time

(b) In free space D = Dm sin (ωt + βz) ax use Maxwell?s equations to find B.[8+8]

4. (a) Derive wave equations for sinusoidal time variations

(b) A 100v/m plane wave of frequency 300 MHz travels in an infinite, losslessmedium having µr = 1,∈ r = 9 σ = 0 write the complete time domainexperements for E and H field vectors. [8+8]

5. An EM wave in dielectric medium 1 (ε1, µ0) impinges obliquely on a boundary planewith dielectric medium 2 (ε2, µ0). Let θ1, θt denote the incident and refraction an-gles respectively and show that for perpendicular polarization, reflection coefficientis equal to

sin(θt−θi)sin(θt+θi)

and transmission coefficient is

2 sin θt cos θi

sin(θi+θt)[16]

6. Derive the expressions for the E and H field components for TE waves in a parallelplane wave guide, using Maxwell?s equations approach. [16]

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7. (a) What is meant by the polarization of wave? When is the wave linearly polar-ized and circularly polarized?

(b) A traveling wave has two linearly polarized components Ex = 2 Cos wt andEy =3Cos (wt + π/2)

i. what is the axial ratio.

ii. What is the tilt angle of the major axis of the polarization ellipse?

iii. What is the sense of rotation? [8+8]

8. (a) Derive the expression for the input impedance of a transmission line of lengthL

(b) Explain the application of smith?s chart. [8+8]

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1. (a) Derive an expression for the electric field intensity due to a finite length linecharge along the z-axis at an arbitrary point Q(x, y, z).

(b) Find the force on a 100µC charge at (0, 0, 3)m if four like charges of 20µCare located on x and y axes at ± 4m. [8+8]

2. (a) Find magnetic field strength, H, on the Z- axis at a point P(0,0,h), due to acurrent carrying circular loop, x2 + y2 = A2 in Z=0 plane.

(b) Find the total magnetic flux crossing a surface, φ = π

2, 1 ≤ ρ ≤ 2 and 0 ≤

Z ≤ 5 due to a vector magnetic potential A = (−ρ2/4).z webers/m [8+8]

3. (a) Obtain the integral form of Maxwell?s equation from amperes circuital law inthe generalized form

(b) Determine the total magnetic flux through the rectangular loop shown inthe figure 3. The source of the magnetic field is the long straight conductorcarrying a current I [8+8]

Figure 3

4. A 3 GHz uniform plane wave propagates through rexolite in the positive Z-directionthe E-field at Z = 0 is 100 6 00v/m

(a) Calculate the RMS value and phase of E at Z=4 cm

(b) Calculate the total attenuation in dB over a distance of 6 wave langths.For rexolite ∈r=2.54 and tan δ=0.0005 [8+8]

5. Write short notes on the following

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(a) Surface Impedance

(b) Brewster angle

(c) Total Internal Reflection [5+5+6]

6. (a) Define and explain the significance of the following terms as applicable toparallel plane guides:

i. Wave impedance

ii. Phase and group velocities

iii. Principal wave and its characteristics [10+6]

(b) Explain the factors on which cut off frequency of a parallel plate wave guidedepend.

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

(b) Draw the directions of electric and magnetic fields in parallel plate and coaxiallines

(c) A transmission line in which no distortion is present has the following pa-rameters Zo = 60Ω, α = 20mNP/m, V = 0.7V0. Determine R, L, G, C andwavelength at 0.1GHz. [5+5+6]

8. (a) A dipole antenna is fed by a transmission line having Zo = 60Ω. The sourceimpedance is 600Ω. If the length of the line is 10λ, determine antenna im-pedance.

(b) Describe how matching is achieved using single stub matching. What are theadvantages and disadvantages compared to double-stub matching. [8+8]

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1. (a) What is capacitance? Differentiate between isotropic and anisotropic materi-als.

(b) Calculate the capacitance of a parallel-plate capacitor with a dielectric, micafilled between plates. εr of mica is 6. The plates of the capacitor are squarein shape with 0.254cm side. Separation between the two plates is, 0.254cm.

(c) As an example of the solution of Laplace’s equation, derive an expressionfor capacitance of a parallel plate capacitors. Make necessary assumptions.[4+6+6]

2. (a) Derive equation of continuity for static magnetic fields.

(b) Derive an expression for magnetic field strength, H, due to a current carryingconductor of finite length placed along the y- axis, at a point P in x-z planeand ‘r’ distant from the origin. Hence deduce expressions for H due to semi-infinite length of the conductor. [6+10]

3. (a) Explain faraday?s law for time varying fields.

(b) Verify that the displacement current in the parallel plate capacitor is the sameas the conduction current in the connecting wires. [8+8]

4. (a) Explain skin depth and derive expression for depth of penetration for goodconductor

(b) Find µr,∈ r and σ for a material in which at 100MHz, uniform plane wave hasα = 2Nρ/m λ = 1m and |η| = 200ohm. [8+8]

5. An EM wave in dielectric medium 1 (ε1, µ0) impinges obliquely on a boundary planewith dielectric medium 2 (ε2, µ0). Let θ1, θt denote the incident and refraction an-gles respectively and show that for perpendicular polarization, reflection coefficientis equal to

sin(θt−θi)sin(θt+θi)

and transmission coefficient is

2 sin θt cos θi

sin(θi+θt)[16]

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6. (a) Define and explain the significance of the following terms as applicable toparallel plane guides:

i. Wave impedance

ii. Phase and group velocities

iii. Principal wave and its characteristics

(b) Explain the impossibility of TEM wave propagation in wave guides. [8+8]

7. (a) Explain the meaning of the terms characteristic impedance and propagationconstant of a uniform transmission line and obtain the expressions for themin terms of Parameters of line?

(b) A telephone wire 20 km long has the following constants per loop km resistance90 Ω, capacitance 0.062 µF , inductance 0.001H and leakage = 1.5 x 10−6

mhos. The line is terminated in its characteristic impedance and a potentialdifference of 2.1 V having a frequency of 1000 Hz is applied at the sendingend. Calculate :

i. The characteristic impedance

ii. Wavelength.

iii. The velocity of propagation [8+8]

8. (a) What is the significance of standing wave ratio in a transmission line? Calcu-late the Reflection coefficient and VSWR for a 50 Ω lines, terminated with

i. matched Load

ii. Short circuit

iii. +j50 Ω loads

iv. -j50 Ω load

(b) A 50 Omega transmission line is terminated by an unknown impedance. TheVSWR is 4 and the first minimum is formed at 2 cm from the load end. Thefrequency of operation is 1 GHz. Design a single stub line matching for theAbove conditions. [8+8]

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set no. 1 - pvpsit · code no: r05220404 set no. 1 ii b.tech ii semester supplimentary...

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