# module 3b - 2/23/2009 Module 3 Lecture 2 Uniform plane...

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2/23/2009 1 Page 1 Material from “Applied Electromagnetics: Early Transmission Lines Approach” By Wentworth (Wiley) Module 3 Lecture 2 Uniform plane waves in various media Page 2 On the program today… • Review the general equations for electromagnetic wave propagation • Provide expressions for the propagation constant, the phase constant, the attenuation constant in terms of material parameters and frequency • Study electromagnetic wave propagation in dielectrics and define loss tangent • Study electromagnetic wave propagation in conductors and define skin depth • Define the polarization of an electromagnetic wave •Introduce linear, elliptical and circular polarizations

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2/23/2009 2 Page 3 We will deal only with uniform plane waves Page 4 Review of the general wave equation Maxwell’s Equations for simple, charge-free media : 0 , , 0 tt     EH H E E              H   2 2 t t t t       E E E EE   2 2 (since       E 0 E E = ) 2 2 2 = Helmholtz wave equation for E E
2/23/2009 3 General solutions for harmonic waves   2 22 2 time-harmonic ss jj tt       EE E E E   or 0 where j j j Consider 2 2 2 E ( ) ( ) E 0 then xs s xs xs d z E z dz x Ea A solution to this differential equation: z xs E Ae So 0 zz Ae Ae    or 0 or    0 First solution is  , or z xs E Ae or   cos z x E Ae t z  More descriptive:   ( , ) cos z o z t E e t z x From the second solution: , z xs o E E e or   ( , ) cos . z o z t E e t z  x the general instantaneous solution is     ( , ) cos cos o o z t E e t z E e t z   xx E a a For the special case of a wave with only one E field component, along y, propagating towards positive z. Page 6 What is the corresponding magnetic field? The magnetic field can be found by j     EH   s o o E e E e    y so oo s ee     y Ha Starting with ( ) ( ) s ys z H z y in our wave derivation would lead to   s o o H e H e y Definition: intrinsic impedance o o E j H  j H H j   H 0 + = E 0 + /(j ) H 0 - = - E 0 - /(j ) The intrinsic impedance is used to calculate E from H (or the opposite) in a plane wave that propagates in one direction. Same as the characteristic impedance of a T-line

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2/23/2009 4 Page 7 Some parameters from life Material (S/m) r r Copper 5.8 X 10 7 1 0 Seawater 5 72 12 Glass 10 -12 10 0.010 Page 8 1-Magnitude of the E field in V/m is equal to the magnitude of the H field in A/m multiplied by 124.
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## This note was uploaded on 09/27/2011 for the course ENGINEERIN 3600 taught by Professor Victor during the Spring '11 term at Carleton CA.

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module 3b - 2/23/2009 Module 3 Lecture 2 Uniform plane...

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