2012(2) ECE EMTL Kattaswamy

Vignana Bharathi Institute of Technology

1 Academic Plan 2012-13

ELECTROMAGNETIC WAVES AND TRANSMISSION LINES

ACADEMIC PLAN 2012 -2013 ( Sem - I)I FACULTY PROFILE

1 Name : Katta Swamy Mergu

2 Department : Electronics and Communication Engineer

3 Designation : Assistant Professor

4 Email - ID : [email protected]

5 Mobile No. : 9666497849

6 Subject : ELECTROMAGNETIC WAVES and TRANSMISSION LINES

7 : Year Branch Section Classes

a. II ECE B II ECE - B

b. -

c. -

d. -

II COURSE OBJECTIVES

Class(s) Allotment

The applications involving electromagnetism are so pervasive that it is difficult to estimate their contribution to modern life: generation and transmission of electric energy, electric motors and actuators, radio, television, magnetic information storage, and even the mundane little magnet used to hold papers to the refrigerator all use electromagnetic fields. This subject not only provides students with a good theoretical understanding of electromagnetic field equations but it also treats a large number of applications. No topic is presented unless it is directly applicable to engineering design or unless it is needed for the understanding of another topic.



III SYLLABUS as per JNTU

UNIT-I ELECTROSTATICS – I: Coulomb’s Law, Electric Field Intensity – Fields due to Different Charge Distributions, Electric Flux Density, Gauss Law and Applications, Electric Potential, Relations Between E and V, Maxwell’s Two Equations for Electrostatics Fields, Energy Density, Illustrative Problems.UNIT – II ELECTROSTATICS – II: Convection and Conduction Currents, Dielectric Constant, Isotropic and Homogeneous Dielectrics, Continuity Equation, Relaxation Time, Poisson’s and Laplace’s Equations; Capacitance – Parallel Plate, Coaxial, Spherical Capacitors, Illustrative Problems.UNIT –III MAGNETOSTATICS:Biot – Savart’s law, Ampere’s Circuital Law and Applications, Magnetic Flux Density, Maxwell’s Two equations for Magnetic Fields, Magnetic Scalar and Vector Potentials, Forces due to Magnetic Fields, Ampere’s Force Law, Inductance and Magnetic Energy, Illustrative Problems. UNIT – IV MAXWELL’S EQUATIONS (Time Varying Fields): Faraday’s Law and Transformer emf, Inconsistency of Ampere’s Law and Displacement Current Density, Maxwell’s Equations indifferent Final Forms and Word Statements, Conditions at a Boundary Surface: Dielectric – Dielectric and Dielectric – Conductor Interfaces, Illustrative Problems. ). UNIT – V EM WAVE CHARACTERISTICS - I:Wave Equations for Conducting and Perfect Dielectric Media, Uniform Plane Waves, All Relations between E & H, Sinusoidal Variations, Wave Propagation in Lossless and Conducting Media, Conductors & dielectrics – Characterization, Wave Propagation in good Conductors and Good Dielectrics, Polarization, Illustrative ProblemsUNIT – VI EM WAVE CHARACTERISTICS - II:Reflection and Refraction of Plane Waves – Normal and Oblique Incidences, for both Perfect Conductor and Perfect Dielectrics, Brewster Angle, Critical Angle and Total Internal Reflection, Surface Impedance, Poynting Vector and Poynting Theorem – Applications, Power Loss in a Plane Conductor, Illustrative ProblemsUNIT – VII TRANSMISSION LINES - I:Types, Parameters, Transmission Line Equations, Primary & Secondary Constants, Expression for Characteristics Impedance, Propagation Constant, Phase and Group Velocities, Infinite Line Concepts, Lossless ness/Low Loss Characterization, Distortion – Condition for Distortion less ness and minimum Attenuation, Loading – Types of Loading, Illustrative Problems.UNIT – VIII TRANSMISSION LINES - II:Input Impedance Relations, SC and OC Lines, Reflection Coefficient, VSWR, UHF Lines as Circuit Element: λ/4, λ/2, λ/8 Lines – Impedance Transformations, Significance of Zmin and Zmax Smith Chart – Configuration and Applications, Single and Double Stub Matching, Illustrative Problems.



IV SYLLABUS for GATE

V SYLLABUS for IES

UNIT-I ELECTROSTATICS – I: Coulomb’s Law, Electric Field Intensity – Fields due to Different Charge Distributions, Electric Flux Density, Gauss Law and Applications, Electric Potential, Relations Between E and V, Maxwell’s Two Equations for Electrostatics Fields, Energy Density, Illustrative Problems.UNIT – II ELECTROSTATICS – II: Convection and Conduction Currents, Dielectric Constant, Isotropic and Homogeneous Dielectrics, Continuity Equation, Relaxation Time, Poisson’s and Laplace’s Equations; Capacitance – Parallel Plate, Coaxial, Spherical Capacitors, Illustrative Problems.UNIT –III MAGNETOSTATICS:Biot – Savart’s law, Ampere’s Circuital Law and Applications, Magnetic Flux Density, Maxwell’s Two equations for Magnetic Fields, Magnetic Scalar and Vector Potentials, Forces due to Magnetic Fields, Ampere’s Force Law, Inductance and Magnetic Energy, Illustrative Problems. UNIT – IV MAXWELL’S EQUATIONS (Time Varying Fields): Faraday’s Law and Transformer emf, Inconsistency of Ampere’s Law and Displacement Current Density, Maxwell’s Equations indifferent Final Forms and Word Statements, Conditions at a Boundary Surface: Dielectric – Dielectric and Dielectric – Conductor Interfaces, Illustrative Problems. ). UNIT – V EM WAVE CHARACTERISTICS - I:Wave Equations for Conducting and Perfect Dielectric Media, Uniform Plane Waves, All Relations between E & H, Sinusoidal Variations, Wave Propagation in Lossless and Conducting Media, Conductors & dielectrics – Characterization, Wave Propagation in good Conductors and Good Dielectrics, Polarization, Illustrative ProblemsUNIT – VI EM WAVE CHARACTERISTICS - II:Reflection and Refraction of Plane Waves – Normal and Oblique Incidences, for both Perfect Conductor and Perfect Dielectrics, Brewster Angle, Critical Angle and Total Internal Reflection, Surface Impedance, Poynting Vector and Poynting Theorem – Applications, Power Loss in a Plane Conductor, Illustrative ProblemsUNIT – VII TRANSMISSION LINES - I:Types, Parameters, Transmission Line Equations, Primary & Secondary Constants, Expression for Characteristics Impedance, Propagation Constant, Phase and Group Velocities, Infinite Line Concepts, Lossless ness/Low Loss Characterization, Distortion – Condition for Distortion less ness and minimum Attenuation, Loading – Types of Loading, Illustrative Problems.UNIT – VIII TRANSMISSION LINES - II:Input Impedance Relations, SC and OC Lines, Reflection Coefficient, VSWR, UHF Lines as Circuit Element: λ/4, λ/2, λ/8 Lines – Impedance Transformations, Significance of Zmin and Zmax Smith Chart – Configuration and Applications, Single and Double Stub Matching, Illustrative Problems.

UNIT I Maxwell’s Two Equations for Electrostatics FieldsUNIT II NA UNIT III Maxwell’s two equations for Magnetic FieldsUNIT IV Maxwell’s Equations indifferent Final Forms and Word Statements UNIT V Wave Equations for Conducting and Perfect Dielectric Media UNIT VI Reflection and Refraction of Plane Waves-Poyinting vectorUNIT VII Transmission Line Equations, Primary & Secondary Constants, Expression for Characteristics Impedance, Propagation Constant, Phase and Group Velocities UNIT VIII Smith Chart – Configuration and Applications

UNIT I & UNIT II Analysis of electrostatic and magneto static fields; Laplace's and Poisson's equations. Boundary value problems and their solutions; Maxwell’s Two Equations for Electrostatics Fields and Magneto static fields UNIT III Maxwell’s Two Equations for Magneto static fields UNIT IV Maxwell’s equations for time varying fieldsUNIT V and UNIT VI Application to wave propagation in bounded and unbounded mediaUNIT VII & UNIT VIII Transmission lines: basic theory, standing waves, matching applications



VI PRE - REQUISITES

VII TOPICS BEYOND SYLLABUS

UNIT I & UNIT II Analysis of electrostatic and magneto static fields; Laplace's and Poisson's equations. Boundary value problems and their solutions; Maxwell’s Two Equations for Electrostatics Fields and Magneto static fields UNIT III Maxwell’s Two Equations for Magneto static fields UNIT IV Maxwell’s equations for time varying fieldsUNIT V and UNIT VI Application to wave propagation in bounded and unbounded mediaUNIT VII & UNIT VIII Transmission lines: basic theory, standing waves, matching applications

To understand this subject student should have thorough knowledge about vector calculus, Circuit theory, basic knowledge of engineering physics and strong mathematic analysis.

Introduction to Vectors, Vector Caluclus, coordinating systems, Electricity and magnetism basics, Polarization, Basic concepts of quantum theory.



IX REFERENCES

i. Text books prescribed by JNTU & Faculty

BOOK TITLE with Author & Edition

A1 Elements of Electromagnetics – Mathew N. O. Sadiku, 4th Edn., 2008. Oxford Univ. Press.

A2

A3

A4 Engineering Electromagnetics – Nathan Ida, 2nd ed., 2005, Springer (India) Pvt. Ltd., new Delhi.

A5 Engineering Electromagnetics – William H. hayt Jr. and John A. Buck, 7th ed., 2006, TMH.

A6 Networks Line and Fields – John D. ryder, 2nd ed., 1999, PHI

A7

A8

A9

A10

ii. Websites & e-books

Websites

B1 www.iitk.ac.in

B2 www.iitm.ac.in

B3 www.mit.edu

B4 www.gsas.harward.edu

B5 www.electronics-tutorials

Electromagnetic Waves and Radiating Systems – E.C. Jordan and K.G. Balmain, PHI, 2nd ed., 2000

Transmission Lines and Networks – Umesh Sinha, Satya Prakashan, 2001, (Tech. India Publication), New Delhi

Introduction to Vectors, Vector Caluclus, coordinating systems, Electricity and magnetism basics, Polarization, Basic concepts of quantum theory.



B6

B7

B8

B9

B10

iii. JOURNALS (International , National & Regional)

C1 Journal of the Institution of Electronics and Telecommunication Engineers (IETE)

C2 IEEE transactions on Electromagnetic

C3 IEEE Transactions on Propagation

C4 e-journal of Radio Propagation

C5 Electronics for you

C6

C7

C8

C9

C10

iv. SUBJECT EXPERT DETAILS (International , National & Regional)

D1 Mr.E.C. Jordan and Mr. Balanis

D2 Mr.N.O.Sadiku

D3 Dr.Ratnajith Bhattacharjee,IITG

D4 Prof.R.K.Shevgoankar,IITB

D5 Dr.G.S.N.Raju,AU

D6



D7

D8

D9

D10

XI COURSE OBJECTIVES AND OUTCOME UNIT WISE

UNIT - I

UNIT - II

UNIT - III

COURSE OBJECTIVES:In this chapter we first study two fundamental laws governing the electrostatic fields, viz, Coulomb's Law and Gauss's Law. Based on Coulomb's law, the concept of electricfield intensity will be introduced and applied to cases involving point, line, surface, and volumec harges. Special problems that can be solved with much effortusing Coulomb's law will be solved with ease by applying Gauss'slaw .COURSE OUTCOME:The outcome of this chapter is students will know the concept of finding force existing between two charges. Finally students will know how to find point, line, surface and volume charges and electric field intensity.

COURSE OBJECTIVES: In this we can discuss electric fields in material media. Materials are broadly classified interms of their electrical properties as conductors and noncon-ductors. A brief discussion of the electrical properties of materials ingeneral will be given to provide abasis for understanding the concepts of conduction, electriccurrent, and polarization. Further discussion will be on some properties of dielectricmaterials such as susceptibility, permittivity, linearity, isotropy, homogeneity, dielectricstrength, and relaxationtime. Poisson's or Laplace's equation or the method of images, and they are usually referred to asboundary-value problems. The concepts of resistance and capacitance will be covered. C OURSE OUTCOME: The outcome of this chapter is caluclating convention current, finding dielectric constants and capacitance values.



UNIT - IV

UNIT - V

UNIT - VI

COURSE OBJECTIVES:The two major laws governing magneto staticfields:Biot-Savart'slaw, andAmpere's circuit law are discussed in this chapter. we are prepared to study the force a magnetic field exerts on charged particles,current elements, and loops. Further more,we will consider magnetic fields in material media.OUTCOME: Biot-savart's law and ampere's law and its applications are studied in this chapter.

COURSE OBJECTIVES:Our aim in this chapter is to lay a firm foundation for our subsequent studies.This willinvolve introducing two major concepts:(1)electromotive force based on Faraday's experiments, and (2) displacement current, which resulted from Maxwell's hypothesis. In this chapter, our major goal is to solve Maxwell's equations and derive EM wave motion in the following media: Freespace, Lossless dielectrics, Lossy dielectrics, Good conductors . COURSE OUTCOME: Maxwell's equations are studied and EM wave motion in Freespace, Lossless dielectrics, Lossy dielectrics, Good conductors are derived.

COURSE OBJECTIVES:In this chapter, Wave Equations for Conducting and Perfect Dielectric Media, Uniform Plane Waves, All Relations between E & H, Sinusoidal Variations, Wave Propagation in Lossless and Conducting Media, Conductors & dielectrics – Characterization, Wave Propagation in good Conductors and Good Dielectrics, Polarization, Illustrative ProblemsCOURSE OUTCOME: Relation between E and V is derived. Wave Propagation in good Conductors and Good Dielectrics, Polarization concepts are studied.



UNIT - VII

UNIT - VIII

COURSE OBJECTIVES:In this we consider wave motion in different media, we can study the characteristics of waves in general. Power considerations, reflection, and transmission between two different media will be discussed.COURSE OUTCOME: Reflection and Refraction of Plane Waves are studied. Poynting vector and poynting theorem and its applications are studied.

COURSE OBJECTIVES:In this we discuss the analysis of transmission lines will include the derivation of the transmission-line equations and characteristic quantities, Lossless ness/Low Loss Characterization, Distortion – Condition for Distortion less ness and minimum Attenuation, Loading – Types of Loading. COURSE OUTCOME: The concept of transmission lines are studied. Line equations and characteristics equations are also studied. Concept of loading and types of loading is studied.

COURSE OBJECTIVES:In this chapter we can discuss the Input Impedance Relations, SC and OC Lines, Reflection Coefficient, VSWR, UHF Lines, use of the Smithchart, various practical applications of transmissionlines,and transients on transmissionlines.COURSE OUTCOME: Input impedance, SC and OC lines, VSWR and smith chart and configuration is studied.



XII QUESTION BANK

i. Unit wise questions based on previous papers

UNIT - I

UNIT - II

1. a) State the Coulomb’s law in SI units and indicate the parameters used in theequations with the aid of a diagram. (b) Point charges Q1and Q2 are respectively located at (4, 0, -3) and (2, 0, 1). If Q2= 4 nC, find Q1 such that. i. The E at (5, 0, 6) has no Z-component. ii. The force on a test charge at (5, 0, 6) has no X-component. 2. (a) State Gauss’s law. Using divergence theorem and Gauss’s law, relate thedisplacement density D to the volume charge density ρv. [8](b) A sphere of radius “a” is filled with a uniform charge density of ρv c/m3. Determine the electric field inside and outside the sphere. 3. (a) Derive the boundary conditions for the tangential and normal components ofElectrostatic fields at the boundary between two perfect dielectrics. 4. (a) Explain the following terms: [8]i. Homogeneous and isotropic medium and ii. Line, surface and volume charge distributions.(b) A circular ring of radius ‘a’ carries uniform charge ρLC/m and is in xy-plane.Find the Electric Field at Point (0, 0, 2) along its axis. 5. a) Derive Poisson’s and Laplace equations. b) A point charge of 3nc is on the z-axis 2m away from the orgin.Find the result V and E

1. (a) Find the field at the centre of a circular loop of radius ‘a’ , carrying a currentI along φ in z = 0 plane. [5](b) Determine the magnetic flux , for the surface described by [6]i. ρ = 1m., 0 ≤ φ ≤ π/2, 0 ≤ z ≤ 2m.,ii. a sphere of radius 2 m., if the magenic field is of the form H =h1ρCosφ ρ A/m.(c) A conducting plane at y = 1 carries a surface current of 10 Z mA/m. Find Hand B at (0, 0, 0) and at (2, 2, 2). 2. (a) Define Ampere’s Force Law and establish the associated relations. [6](b) A long coaxial cable has an inner conductor carrying a current of 1 mA. along+Z direction , its axis coinciding with Z-axis. Its inner conductor diameter is 6 mm. If its outer conductor has an inside diameter of 12 mm. and a thicknessof 2 mm., determine H at (0, 0, 0), (0, 1.5 mm, 0), (0, 4.5 mm, 0) and (0, 1cm, 0). 3. An infinitely long straight conducting rod of radius ‘a’ carries a current of I in +Z direction. Using Ampere’s Circuital Law, find H in all regions and sketch thevariation of H as a function of radial distance. If I = 3 mA. and a = 2 cm., find H and β at ( 0, 1cm., 0) and (0, 4cm., 0).



UNIT - III

UNIT - IV

1. (a) Find the field at the centre of a circular loop of radius ‘a’ , carrying a currentI along φ in z = 0 plane. [5](b) Determine the magnetic flux , for the surface described by [6]i. ρ = 1m., 0 ≤ φ ≤ π/2, 0 ≤ z ≤ 2m.,ii. a sphere of radius 2 m., if the magenic field is of the form H =h1ρCosφ ρ A/m.(c) A conducting plane at y = 1 carries a surface current of 10 Z mA/m. Find Hand B at (0, 0, 0) and at (2, 2, 2). 2. (a) Define Ampere’s Force Law and establish the associated relations. [6](b) A long coaxial cable has an inner conductor carrying a current of 1 mA. along+Z direction , its axis coinciding with Z-axis. Its inner conductor diameter is 6 mm. If its outer conductor has an inside diameter of 12 mm. and a thicknessof 2 mm., determine H at (0, 0, 0), (0, 1.5 mm, 0), (0, 4.5 mm, 0) and (0, 1cm, 0). 3. An infinitely long straight conducting rod of radius ‘a’ carries a current of I in +Z direction. Using Ampere’s Circuital Law, find H in all regions and sketch thevariation of H as a function of radial distance. If I = 3 mA. and a = 2 cm., find H and β at ( 0, 1cm., 0) and (0, 4cm., 0).

1. (a) Derive Maxwell’s equations in integral form and differential form for timevarying fields. (b) Explain how the concept of Displacement current was introduced by Maxwellto account for the production of Magnetic fields in the empty space. 2. (a) In a perfect dielectric medium, the EM wave has maximum value for E of 10V/m with µr= 1 and εr= 4. Find the velocity of the wave, peak poynting vector, average poynting vector, impedance of the medium and peak value ofthe magnetic field. (b) What is the inconsistency in Ampere’s Law? How it is rectified by Maxwell?(c) Show that the total displacement current between the condenser plates con-nected to an alternating voltage sources is exactly the same as the value ofcharging current (conduction current). 3. (a) In free space D = Dm Sin (wt +β z)ax. Determine B and displacement currentdensity. (b) Region 1, for which µr1= 3 is defined by X < 0 and region 2, X < 0 has µr2= 5 given H1= 4 ax+ 3ay6 az(A/m). Determine H2for X > 0 and theangles that H1and H2 make with the interface.

1. Prove that under the condition of no reflection at an interface, the sum of theBrewster angle and the angle of refraction is π/2 for parallel polarization for thecas e of reflection by a perfect conductor under oblique incident, with neat sketches. 2. (a) Define uniform plane wave. (b) Prove that uniform plane wave does not have field components in the directionof the propagation. (c) Determine the intrinsic impedance of free space. 3.(a) What is polarization of an EM wave? Distinguish between different types ofpolarizations? Prove that the polarization is circular when the two componentsof electric field are equal and are 90o apart. [8](b) A plane EM wave is normally incident on the boundary between two di-electrics. What must be the ratio of refractive indices of the two media inorder that the reflected and transmitted waves may have average Power ofequal magnitude? [8] 4. (a) Derive the expression for attenuation and phase constants of uniform planewave. [8](b) If εr= 9, µ = µ0 for the medium in which a wave with frequency f = 0.3GHz is propagating, determine propagation constant and intrinsic impedanceof the medium when [8]i. σ = 0 andii. σ = 10 mho/m.



UNIT - V

UNIT - VI

1. Prove that under the condition of no reflection at an interface, the sum of theBrewster angle and the angle of refraction is π/2 for parallel polarization for thecas e of reflection by a perfect conductor under oblique incident, with neat sketches. 2. (a) Define uniform plane wave. (b) Prove that uniform plane wave does not have field components in the directionof the propagation. (c) Determine the intrinsic impedance of free space. 3.(a) What is polarization of an EM wave? Distinguish between different types ofpolarizations? Prove that the polarization is circular when the two componentsof electric field are equal and are 90o apart. [8](b) A plane EM wave is normally incident on the boundary between two di-electrics. What must be the ratio of refractive indices of the two media inorder that the reflected and transmitted waves may have average Power ofequal magnitude? [8] 4. (a) Derive the expression for attenuation and phase constants of uniform planewave. [8](b) If εr= 9, µ = µ0 for the medium in which a wave with frequency f = 0.3GHz is propagating, determine propagation constant and intrinsic impedanceof the medium when [8]i. σ = 0 andii. σ = 10 mho/m.

1. (a) State and Prove Poynting Theorem. [10](b) A Plane wave traveling in a free space has an average poynting vector of 5watts/m2. Find the average energy density. 2. (a) Define and differentiate between the terms: Instantaneous average and com-plex poynting vectors, giving their mathematical expressions. [8](b) An EM wave of 3 W/m2 Power density is incident normally from air on aperfect dielectric boundary. If the resulting VSWR is 2.2, find the reflectedand transmitted powers. 3. a) Derive an expression for reflection when a wave is incident on a dielectric obliquely with parallel polarization. b) State and prove pointing theorem. 4. a) Define reflection and transmission coefficient ofplane wave. b) a plane wave travelling in free space has an average poynting vector of 5 watts/mhe average energy density. 5. a) Define the significance and applications of poynting theorem. b) Explain the utility of pointing vector. If the peak pointing vector in free space is 10N/m2, find the amplitudes of electric and magnetic fields.

1. (a) Explain the factors on which cut off frequency of a parallel plate wave guidedepend. [8](b) Obtain the frequency in terms of cut off frequency fc at which the attenuationconstant due to conductor losses for the T Mn mode is minimum for a parallelplate wave-guide. [8] 2. Starting from Maxwell’s equations, derive the expressions for the E and H fieldcomponents for TE waves in a parallel plane wave guide. 3. For a Parallel plane wave guide of 3 cm seperation, determine all the propogationcharacteristics, for a signal at 10 GHz, for [8+8](a) T E10waves(b) TEM waves Explain the terms used 4. (a) Explain attenuation in parallel-plate wave guides. Also draw attenuationversus frequency characteristics of waves guided between parallel conductingplates. [8](b) A parallel-plate wave guide made of two perfectly conducting infinite planesspaced 3cm apart in air operates at a frequency of 10GHz. Find the maximumtime average power that can be propagated per unit width of the guide forT E1 and T M1 modes.



UNIT - VII

UNIT - VIII

1. (a) Explain the factors on which cut off frequency of a parallel plate wave guidedepend. [8](b) Obtain the frequency in terms of cut off frequency fc at which the attenuationconstant due to conductor losses for the T Mn mode is minimum for a parallelplate wave-guide. [8] 2. Starting from Maxwell’s equations, derive the expressions for the E and H fieldcomponents for TE waves in a parallel plane wave guide. 3. For a Parallel plane wave guide of 3 cm seperation, determine all the propogationcharacteristics, for a signal at 10 GHz, for [8+8](a) T E10waves(b) TEM waves Explain the terms used 4. (a) Explain attenuation in parallel-plate wave guides. Also draw attenuationversus frequency characteristics of waves guided between parallel conductingplates. [8](b) A parallel-plate wave guide made of two perfectly conducting infinite planesspaced 3cm apart in air operates at a frequency of 10GHz. Find the maximumtime average power that can be propagated per unit width of the guide forT E1 and T M1 modes.

1. (a) What are the salient aspects of primary constants of a two wire transmissionline. [8](b) A lossless transmission line used in a TV receiver has a capacitance of 50 PF/m and an inductance of 200 nH/m. Find out the characteristic impedance for10 meter long section of the line and 500 meter section. 2. (a) List out types of transmission lines and draw their schematic diagrams. [5](b) Draw the directions of electric and magnetic fields in parallel plate and coaxiallines. [5](c) A transmission line in which no distortion is present has the following parame-ters Z0 = 50Ω, α= 20mNP/m, υ = 0.6υ0. Determine R, L, G, C and wavelength at 0.1 GHz. 3.(a) Derive a relation between reflection coefficient and characteristic impedance. (b) (b) Determine the reflection coefficients when [8]i. ZL = Z0ii. ZL= short circuitiii. ZL= open circuit.iv. Also find out the magnitude of reflection coefficient when ZL is purely reactive.

1. (a) Explain how UHF lines can be treated as circuit elements, giving the necessaryequivalent circuits. [8](b) A loss less line of 100 Ω is terminated by a load which produces SWR = 3. Thefirst Maxima is found to be occurring at 320 cm. If f = 300 MHz, determine load impedance. 2. (a) Draw the equivalent circuits of a transmission lines when [8]i. length of the transmission line, 1 <λ/4, with shorted loadii. when 1 <λ/4, with open endiii. 1 =λ/4.(b) Find out VSWR if i. Z0= 100 Ω, RL = 80 Ω ii. when Z0= 80 Ω, RL = 100Ω 3. (a) Explain the principle of Impedance matching with Quarter wave Transformer?(b) A 100 Ω loss less line connects a signal of 100 KHz to a load of 140 Ω. Theload power is 100mW . Calculate [8]i. Voltage Reflection coefficient,ii. VSWR,iii. Position of VMax, IMax Vmin and Imin



ii. Assignment questions

Assignment - 1 (Unit I - IV ) / (Unit I & II)*

Assignment - 2 (Unit V - VIII ) / (Unit III - V)*

1. (a) Explain how UHF lines can be treated as circuit elements, giving the necessaryequivalent circuits. [8](b) A loss less line of 100 Ω is terminated by a load which produces SWR = 3. Thefirst Maxima is found to be occurring at 320 cm. If f = 300 MHz, determine load impedance. 2. (a) Draw the equivalent circuits of a transmission lines when [8]i. length of the transmission line, 1 <λ/4, with shorted loadii. when 1 <λ/4, with open endiii. 1 =λ/4.(b) Find out VSWR if i. Z0= 100 Ω, RL = 80 Ω ii. when Z0= 80 Ω, RL = 100Ω 3. (a) Explain the principle of Impedance matching with Quarter wave Transformer?(b) A 100 Ω loss less line connects a signal of 100 KHz to a load of 140 Ω. Theload power is 100mW . Calculate [8]i. Voltage Reflection coefficient,ii. VSWR,iii. Position of VMax, IMax Vmin and Imin

1. a) Derive Poisson’s and Laplace equations. b) Define and distinguish between the terms electric field, electric displacement and electric flux density with necessary mathematical relations. 2. a) Define and explain the Biot- Savarts law. b) State Ampere’s circuital law.Specify the conditions to be met for determining magnetic field strength H, based on Ampere’s circuital law. 3.a) Derive the boundary conditions for the tangential and normal components of Electrostatic fields at the boundary between two perfect dielectrics. b) Derive Maxwell’s equations in integral form and differential form for time varying fields. 4. a) Find all the relations between E and H in a uniform plane wave. Find the value ofintrinsic impedence of free space. b) Explain the terms linear polarization, circular polarization and elliptical polarization. c) For the wave propagation in good dielectrics, derive the expression for intrinsic impedence of a good dielectric d) Derive the expression for skin depth of a good conductor

1. a) Derive an expression for reflection when a wave is incident on a dielectric obliquely with parallel polarization. b) State and prove pointing theorem. (8+8) 2. For a parallel plane wave guide of 3cm separation, determine all the propagation characteristics for a signal at 10 GHz for i)TE 10 waves ii) TEM waves (8+8) 3. a) Derive the expression for the input impedance ofa loss-less line. Hence evaluate Zsc and Zoc and sketch their variation with line length. (b ) What is meant by inductive loading? What are itsadvantages and disadvantages. 4. Write a detailed note on double stub matching on a line using smith chart 5. a) Starting from Maxwell’s equations, derive the expressions for the E and H field components for TE waves in a parallel plane wave guide. b)Define and explain the significance of following terms i) wave impedence ii) Phase and group velocities. 6. a) Explain the significance of TEM waves in parallel plane guide. Derive an expression for the attenuation factor for TEM waves b)Explain the factors on which cut off frequency ofa parallel plate wave guide depend



Assignment - 3 (Unit VI - VIII ) *

* Applicable only for I - Year Subjects

iii. Tutorial questions

Tutorial - 1

Tutorial - 2

Tutorial - 3

1. a) Derive an expression for reflection when a wave is incident on a dielectric obliquely with parallel polarization. b) State and prove pointing theorem. (8+8) 2. For a parallel plane wave guide of 3cm separation, determine all the propagation characteristics for a signal at 10 GHz for i)TE 10 waves ii) TEM waves (8+8) 3. a) Derive the expression for the input impedance ofa loss-less line. Hence evaluate Zsc and Zoc and sketch their variation with line length. (b ) What is meant by inductive loading? What are itsadvantages and disadvantages. 4. Write a detailed note on double stub matching on a line using smith chart 5. a) Starting from Maxwell’s equations, derive the expressions for the E and H field components for TE waves in a parallel plane wave guide. b)Define and explain the significance of following terms i) wave impedence ii) Phase and group velocities. 6. a) Explain the significance of TEM waves in parallel plane guide. Derive an expression for the attenuation factor for TEM waves b)Explain the factors on which cut off frequency ofa parallel plate wave guide depend

1. (a) State and Prove Gauss’s law. List the limitations of Gauss’s law.(b) Derive an expression for the electric field strength due to a circular ring of radius ‘a’ and uniform charge density, ρL C/m, using Gauss’s law. Obtain the value of height ‘h’ along z-axis at which the net electric field becomes zero. Assume the ring to be placed in x-y plane. 2. A line charge L= 400 pC /m lies along the X-axis. The surface of zero potential passesthrough the point P(0,5,12)m. Find the potential at point (2,3,-4)m

1. Calculate the capacitance of a parallel-plate capacitor with a dielectric, mica filled between plates. er of mica is 6. The plates of the capacitor are square in shape with 0.254cm side. Separation between the two plates is, 0.254cm.

1. Planes z=0 and z=4 carry current K=-lOa x A/m and K=lOa x A/m,respectively.D etermineHat (a)(1,1,1 ) (b)(0,-3 ,10) 2.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 103t az T. Determine the current



Tutorial - 4

Tutorial - 5

Tutorial - 6

Tutorial - 7

Tutorial - 8

Tutorial - 9

1. A large copper conductor (σ= 5.8×107s/m, εr=µr= 1)support a unifomplane wave at 60 Hz. Determine the ratio of conduction current to displace-ment current compute the attenuation constant. Propagation constant, intrinsic impedance, wave length and phase velocity of propagation.2. In free space D = Dm sin(wωt + βz) ax use Maxwell's equations to find B.

1. The reflected magnetic field Hr =- (2)½ mA/m. and the incident electric field in medium1(free space) is 1 mV/m. The medium 2 has εr2= 18 and σ2= 0. Determine the permeability of medium2. Assume normal incidence of EM wave from medium1 to medium2. 2.What is the inductance of a pair of transmission lines separated by 1.868 m,if the diameter of the each wire is 0.01m and the medium between the lineshas µ= 2 µ0 . The length of line is 10 m.

1. A parallel plate wave guide made of two perfectly conducting infinite planes spaced 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 for TE1andTM1 modes. 2. For a parallel plane wave guide of 3 cm separation, determine all the propagationcharacteristics, for a signal at 10 GHz, for (a)TE 10waves (b) TEM waves . Explain the terms used.

1. At 8 MHz the characteristic impedance of transmission line is (40-j2) Ω and the propagation constant is (0.01+j0.18 ) per meter. Find the primary constants. 2.A transmission line in which no distortion is present has the following parameters Zo = 60ohm, a = 20mNP/m, V = 0.7V0. Determine R, L, G, C and wavelength at 0.1GHz.

1. An aerial of (200-j300) Ω is to be matched with 500 Ω lines. The matching isto be done by means of low loss 600Ω stub line. Find the position and lengthof the stub line used if the operating wave length is 20 meters. 2. A low transmission line of 100 Ω characteristic impedance is connected to aload of 400 Ω. Calculate the reflection coefficient and standing wave ratio.Derive the Relationships use



Tutorial - 10

iv. Seminar Topics

1 Introduction to vectors, Vector caluclas

2 Electricity and magnetism

3 Gauss's law and its applications

4 Dielectric amterial and types of dielectrics, different types of capacitors

5 Maxwell's equations

6 Introduction to EM Waves

7 Polarization, Reflection and Refraction

8 Poynting Theorem – Applications

9

10 Smith Chart – Configuration and Applications

XIII REMARKS / SUGGESTIONS

Introduction to transmission line: Types, Parameters, Transmission Line Equations



Prepared By :

Katta Swamy Mergu

Assistant Professor

Electronics And Communication Engineering

Date :

Approved By :

H.O.D

Date :


Academic Plan 2012-13

VIII LESSON PLAN

S.no Topic Week Remarks

1 1 1 BB A1,A5

Vector Additions and subtractions 1 1 BB A1,A5

1 1 BB A1,A5

Conversion of different types of coordinate s 1 1 BB A1,A5

Introduction, Coulomb’s law 1 1 BB A1,A5

Electric field intensity 2 1 BB A1,A5

Fields due to different charge distribution 2 2 BB A1,A5

2 1 BB A1,A5

Gauss law and applications 2 2 BB A1,A5

Electric potential 3 1 BB A1,A5

Relation between E and V 3 1 BB A1,A5

Maxwell’s Two equations for Electrostatic fie 3 1 BB A1,A5

Energy density 3 1 BB A1,A5

Problems 3 1 BB A1,A5

2 4 1 BB A1,A5

4 1 BB A1,A5

Continuity equation and Relaxation time 4 1 BB A1,A5

Poisson’s equation, Laplace ‘s equation 4 1 BB A1,A5

4 1 BB A1,A5

* Text Books A1 - A10

Websites or e-books B1 - B10Journals C1 - C10

BB Black BoardPPT Power Point PresentationOHP Over Head ProjectorMM Multimedia (Audio - Vedio )

Unit no

No of sessions planned

Mode of teaching BB/PPT/

OHP/MMReference *

Introduction to Vectors, Vector Caluclus

Introduction to coordiante system

Electric flux density

Convection and conduction currents

Dielectric constant ,isotropic and homogeneous dielectrics Parallel plate capacitor

Problems

AssignmentFor the respective topics please choose the proper reference from the list of references (IX) in Academic Plan with appropriate page no. or chapter no.



S.no Topic Week Reference * Remarks

5 2 BB A1,A5


3 Biot-Savart’s law 5 1 BB A1,A5

Ampere’s circuit law and applications 5 2 BB A1,A5

Magnetic flux density 6 1 BB A1,A5

Maxwell’s two equations for magneto static f 6 1 BB A1,A5

Magnetic scalar and vector potentials 6 1 BB A1,A5

Forces due to magnetic fields 6 1 BB A1,A5

7 1 BB A1,A5

Inductance and magnetic energy 7 2 BB A1,A5


4 7 1 BB A1,A5

Inconsistency of Ampere’s law 7 1 BB A1,A5

Displacement current density 8 1 BB A1,A5

Maxwell’s equation in different final forms 8 2 BB A1,A5

Conditions at a boundary surface-Dielectric-di 8 1 BB A1,A5

Dielectric-conductor interfaces 8 1 BB A1,A5

problems 8 1 BB A1,A5

5 Wave equations for conducting and perfect di 9 1 BB A1,A5

Uniform plane waves-definition 9 1 BB A1,A2,A3

All relations between E &H 9 1 BB A1,A2,A3

Sinusoidal variations 9 1 BB A1,A2,A3

Wave propagation in lossless media 9 1 BB A1,A2,A3

Unit no



OHP/MM

Coaxial capacitor and Spherical capacitor

Ampere’s force law

Faraday’s law and transformer emf




Wave propagation in conducting media 10 1 BB A1,A2,A3

Conductors &dielectrics-characterization 10 1 BB A1,A2,A3

Wave propagation in good conductors and goo 10 1 BB A1,A2,A3

Polarization 10 1 BB A1,A2,A3

Problems 10 2 BB A1,A2,A3

6 Reflection and refraction of plane waves-nor 11 1 BB A1,A2,A3

Brewster angle and critical angle 11 1 BB A1,A2,A3

11 1 BB A1,A2,A3

Pointing vector and pointing theorem-applica 11 2 BB A1,A2,A3

Power loss in a plane conductor 12 1 BB A1,A2,A3

Problems 12 2 BB A1,A2,A3

7 12 1 BB A2,A3

Primary and secondary constants 12 1 BB A2,A3

Expression for characteristic impedance 13 1 BB A2,A3

Propagation constant 13 1 BB A2,A3

Phase and group velocities and Infinite line 13 1 BB A2,A3

Losslessness/Low Loss Characterization 13 1 BB A2,A3

Distortion-condition for distortionlessness a 13 1 BB A2,A3

Types of loading 14 1 BB A2,A3


8 Input impedance relations 14 1 BB A2,A3

SC and OC lines 14 1 BB A2,A3

Reflection coefficient &VSWR 15 1 BB A2,A3

Unit no



OHP/MM

Total Internal Reflection, surface impedance

Types, parameters Tr. Line equations




UHF lines as circuit elements 15 1 BB A2,A3

Smith chart-configuration and applications 15 1 BB A2,A3

Single and Double stub matching 15 1 BB A2,A3


Unit no



OHP/MM



2012(2) ECE EMTL Kattaswamy

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