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ECE_471_-_Final_Exam

# ECE_471_-_Final_Exam - .J 7 2 J  \$    \$   D m/s EM...

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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: & & # #{ # { { 2 R is known as the axial ratio { {  { { { { "{ Shape and handedness are characterized by ellipticity angle #    { { /  / 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 { { Low Loss Dielectric  \$ @-  \$ #   \$     \${ \${ \${ { { { " # \$ { . ÉÉ\$ { | \${ " " | "{ - { 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:    # , {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 ...
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