lecture29

lecture29 - Lecture 29 The Hertzian Dipole Antenna In this...

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1 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Lecture 29 The Hertzian Dipole Antenna In this lecture you will learn: • Hertzian dipole antenna • Gain and radiation pattern of an antenna ECE 303 – Fall 2005 – Farhan Rana – Cornell University Hertzian Dipole Antenna - Review • A Hertzian dipole is represented by an arrow whose direction indicates the positive direction of the current and also the orientation of the dipole in space • By assumption, the size of the dipole is much smaller than the wavelength of the emitted radiation, i.e. d << λ x z d q ( t ) -q ( t ) x z I ( t ) In phasor notation • Because d << , the current density associated with the dipole is represented mathematically as a delta function with an appropriate weight () ( ) α ω + = t I t I o cos ( ) ( ) r e d I z r J j o r r r 3 ˆ δ =
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2 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Radiation Emitted by a Hertzian Dipole - Review Need to solve for the radiated fields: () () ( ) r J r A k r A o r r r r r r µ = + 2 2 Use the superposition integral form of the solution: () r k j o r k j o r r k j o e r Id z e r Id z r A dv e r r r J r A = = ∫∫∫ = π 4 ˆ 4 ˆ ' ' 4 ' ' r r r r r r r r r r r r Find the H-field: () () () [] r k j o e r Id r r A = θ 4 sin ˆ cos ˆ r r () () φ sin 1 1 4 ˆ o + = × = r k j e r Id k j r H r A r H r k j r r r r r r x z ( )( ) r d I z r J r r r 3 ˆ δ = Working in spherical coordinates y ECE 303 – Fall 2005 – Farhan Rana – Cornell University Radiation Emitted by a Hertzian Dipole - Review H-field was: sin 1 1 4 ˆ + = r k j e r Id k j r H r k j r r Find the E-field: Use Ampere’s Law: ( ) ( ) ( ) r E j r J r H o r r r r r r ε ω + = × Away from the dipole the current density is zero, therefore: r H j r E o r r r r × = 1 + + + + = η sin 1 1 1 ˆ cos 2 1 1 ˆ 4 2 2 r k j r k j r k j r k j r e r Id k j r E r k j o r r x z ( ) r d I z r J r r r 3 ˆ = Working in spherical coordinates y
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3 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Radiation Emitted by a Hertzian Dipole - Review () + + +
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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.

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lecture29 - Lecture 29 The Hertzian Dipole Antenna In this...

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