lecture28 - 1 ECE 303 Fall 2005 Farhan Rana Cornell...

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Unformatted text preview: 1 ECE 303 Fall 2005 Farhan Rana Cornell University Lecture 28 Antennas and Radiation and the Hertzian Dipole In this lecture you will learn: Generation of radiation by oscillating charges and currents Hertzian dipole antenna ECE 303 Fall 2005 Farhan Rana Cornell University Maxwells Equations and Radiation Maxwells equation predict outgoing radiation from sinusoidally time-varying currents (and charges - recall that current and charge densities are related through the continuity equation: ( ) , . = t r H o r r ( ) ( ) t t r H t r E o = , , r r r r ( ) ( ) t r t r E o , , . r r r = ( ) ( ) ( ) t t r E t r J t r H o + = , , , r r r r r r Time-varying currents as the source or the driving term for the wave equation: ( ) ( ) ( ) ( ) ( ) ( ) ( ) t t r J t t r E c t r E t t r E c t t r J t t r H t r E o o o = + = = , , 1 , , 1 , , , 2 2 2 2 2 2 r r r r r r r r r r r r r r ( ) ( ) , , . = + t t r t r J r r r 911 2 ECE 303 Fall 2005 Farhan Rana Cornell University Electro- and Magneto-quasistatics and Potentials ( ) ( ) t r t r E o , , . r r r = ( ) ( ) t r J t r H , , r r r r = ( ) , . = t r H o r r ( ) , = t r E r r Electroquasistatics Magnetoquasistatics ( ) , = t r E r r Since: One could write: ( ) ( ) t r t r E , , r r r = Since: One could write: ( ) ( ) t r A t r H , , o r r r r = ( ) , . = t r H o r r Scalar potential Vector potential ECE 303 Fall 2005 Farhan Rana Cornell University Electrodynamics and Potentials - I ( ) , . = t r H o r r ( ) ( ) t t r H t r E o = , , r r r r ( ) ( ) t r t r E o , , . r r r = ( ) ( ) ( ) t t r E t r J t r H o + = , , , r r r r r r One still has: ( ) , . = t r H o r r Therefore, one can still introduce a vector potential: ( ) ( ) t r A t r H , , o r r r r = Faradays law then becomes: ( ) ( ) ( ) ( ) ( ) ( ) , , , , , , = + = = t t r A t r E t t r A t r E t t r H t r E o r r r r r r r r r r r r Vector Potential 3 ECE 303 Fall 2005 Farhan Rana Cornell University Electrodynamics and Potentials - II Using the vector and scalar potentials, the expressions for E-field and H-field become: ( ) ( ) t r A t r H , , o r r r r = ( ) ( ) ( ) t r t t r A t r E , , , r r r r r = Scalar Potential Since: ( ) ( ) , , = + t t r A t r E r r r r One may introduce a scalar potential as follows: ( ) ( ) ( ) ( ) ( ) ( ) t r t t r A t r E t r t t r A t r E , , , , , , r r r r r r r r r r = = + ECE 303 Fall 2005 Farhan Rana Cornell University...
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This note was uploaded on 02/02/2008 for the course ECE 3030 taught by Professor Rana during the Fall '06 term at Cornell University (Engineering School).

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lecture28 - 1 ECE 303 Fall 2005 Farhan Rana Cornell...

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