ECE_471_-_Final_Exam

ECE_471_-_Final_Exam - . .J . . - 7 2 J -  # - @. $  # ...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . .J . . - 7 2 J -  # - @. $  #   $   D m/s EM Plane-Wave Propagation EM Wave Equations in Lossless Media 0 . H 0H Good Conductor { -{ { -{ H General Relation between E & H in TEM Wave . 0H 0 H {{ {{ Linear Polarization or Circular Polarization IJ # EM Wave Polarization {{ { { { { É{ {É I$ IJJ $ { H 0? { {- H { {- {{ / { {C ? { {. { {C H { {- H { { For a coaxial cable, the surface resistance is as follows: " y H Current Flow in Good Conductor For the conductors to be thick enough to be considered infinitely thick as far as the flow of current is concerned if: is large H{{ " . IJ  $ { - I$ IJJ $ { # I …‘• { . - { I …‘• { . { H . -{ The AC resistance of the cable is as follows: # # $ Instantaneous & Average Power Densities {{ {{  " H{ { {{ { { { $ "  # H {# { H Elliptical Polarization I ,I , I I and /  $ .  $ HH for positive z-direction {{ ÉÉ { 0 H{ 0H $ {{ …‘• { { {  < É "É ÉÉ $ ?…‘• "  .  < . - …‘• { {C Poynting Vector for Lossless Media Poynting Vector for Lossy EM Wave Reflection & Transmission EM Wave Reflection/Transmission at Normal Incidence (Lossless Case) The rotation angle , is the angle between the major axis and reference direction Reflected Wave: & & # #{ # –ƒ{ –ƒ{ 2 R is known as the axial ratio –ƒ{ { –ƒ { {…‘• { { "{ Shape and handedness are characterized by ellipticity angle #   –ƒ { { /  / plus sign for left-handed . 3 3 { •‹{ {•‹ { { .3 $ . 3 3 Incident Wave: {{ Transmitted Wave:  % {{ .3 $   3 ; •‹ { { 2 ;Left-handed rotation ; •‹ { { ;Right-handed rotation 2 if …‘• { { 2 if …‘• { { 1) If given in time domain, must go back to phasor domain to get right phase difference 2) Need to rewrite sin as cosine, and convert to phasor domain.  3  , , {{ " " and H { { " and H { { and H { { . $  $ 3 " 3  $ Reflected/Transmitted Power Flow in Lossless Media #{ # $ $ #{ , for normal incidence { 0 H# { { { { EM Plane-Wave Propagation in Lossy Media If a medium is conducting:  The complex permittivity: . , and –ƒ{ { Low Loss Dielectric  $ @-  $ #   $     ${ ${ ${ { { { " # $ { . ÉÉ$ { | ${ " " | "{ - { 0 H$ { { 0 " {0 " # { . {| Note that É É$ #= D Np/m rad/m Normal Incidence at a Perfect Conducting Plane Boundary:  . , and , and no wave is transmitted across the boundary. Normal Incidence between Lossy Media $ $ $ $ | Incident Wave: H, , ,{ Reflected Wave: H, , System now has finite conductivity. Medium 1(replace with and with { - { #{ {  . { H# { { { H$ { { # ): Medium 2 ${ { # # Boundary Conditions: | •‹ { $ { •‹ { # { # $ Snell’s Law - # and J$ •‹{ { J# Fiber Optics $ # J# J$ # H# { #{   #  { { H$ { ${ { { , ü, Reflection and Transmission Coefficients a = G{b { a = G{b { , { { a = G{b a = G{b $a = G{b { GC GC = G{b { a = G{b { a = G{b { {b { {b { # Transmitted Wave : 7 , , 7 7 7 {. …‘•{ { - •‹ { {{ { …‘•{ { - •‹ { {{ , { { { { , { { { { { , 7 , {{ { { { {{ { { {{ { {{ { {{ { {{ {{ For a nonmagnetic material, = G{b { Parallel (TM) Polarization ü, $ { - , { " = Gb = Gb $ # $ Incident Wave: H { In order to have total internal reflection inside the core/cladding, we have the following: …‘•{ $ { 4 . The value of $ is related to the angle of incidence. •‹{ # { 3 J J .J Wave Reflection/Transmission at Oblique Incidence *Very Important The data rate that can be transmitted and fully distinguished through the fiber is at most: IJ # J. $ J$ Reflected Wave: H . 7 { 7 { •‹{ { . •‹ { {{ { •‹{ { - •‹ { {{ { {{ { # { {{ # , where NA is defined as the numerical aperture 7 { {{ { {{ { {{ { { { { {{ Transmitted Wave : 7 H a = G{b a = G{b $a = G{b { _ 9_ = G{b { $ {{  For a nonmagnetic material, _ 9_ = G{b { GC GC ü Reflection and Transmission Coefficients a = G{b { a = G{b {  { { a = G{b { a = G{b { {b { # Brewster Angle Defined as the incident angle at which the Fresnel reflection coefficient is zero 1. Perpendicular (TE) Polarization: •‹ •‹ –ƒ # , {b { ü $ { -{ " = Gb = Gb E-field parallel to plane incidence: parallel polarization or Transverse Magnetic (TM) E-field perpendicular to plane incidence: perpendicular polarization or (TE) Perpendicular (TE) Polarization . For this type of polarization, the Brewster angle does not exist for nonmagnetic materials 2. Parallel (TM) Polarization: . . $ #9 #9 $ #$ $ . # $9 #9 $ $# $ For nonmagnetic materials: # $ " # # •‹{ # { $ - $ •‹ { $ { $ , { {{ { {{ Waveguides and Cavity Resonators ...
View Full Document

This note was uploaded on 04/10/2010 for the course ECE 471 taught by Professor Majedi during the Winter '10 term at W. Alabama.

Ask a homework question - tutors are online