ANTENG-CH4sal - 1 Chapter 4 Chapter 4 Linear Wire Antennas...

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Unformatted text preview: 1 Chapter 4 Chapter 4 Linear Wire Antennas Linear Wire Antennas ECE 5318/6352 ECE 5318/6352 Antenna Engineering Antenna Engineering 2 INFINITESIMAL DIPOLE INFINITESIMAL DIPOLE ( only electrical current present ) ( constant current ) l / 50 I l / 2 l / 2 I o Impinging Wave z o I z z a I ) ( ' = ; thin wire ; << l = = F I G m [4-1] 3 INFINITESIMAL DIPOLE INFINITESIMAL DIPOLE (CONT) (CONT) 2 2 2 z y x r + + = Fig. 4.1(a) Geometrical arrangement of an infinitesimal dipole l / 50 4 mixed coordinates in mixed coordinates in expression expression - change to change to spherical spherical 2 2 2 z y x R + + ' ' ' ' ) , , ( 4 A G G d R e z y x (x,y,z) jkR c e o I A << A for ( x,y,z ) ( x,y,z) source points l [4-2] INFINITESIMAL DIPOLE INFINITESIMAL DIPOLE (CONT) (CONT) l / 50 ( ) ( ) ( ) 2 2 2 ' ' ' R x x y y z z = + + 5 mixed coordinates in expression mixed coordinates in expression change to spherical change to spherical [4-4] 2 / 2 / ' 4 A A G G z d r e (x,y,z) jkr o o I a A z jkr o o e r (x,y,z) 4 A G G I a A z ( x,y,z ) ( x,y,z) source points l INFINITESIMAL DIPOLE INFINITESIMAL DIPOLE (CONT) (CONT) l / 50 6 ( ) ( ) ( ) 2 ' 2 ' 2 ' z z y y x x R + + sin 4 sin jkr o o z e r I A A = = A cos 4 cos jkr o o z r e r I A A = = A c d ' A along source = A ( x,y,z ) ( x,y,z) source points l [4-6] INFINITESIMAL DIPOLE INFINITESIMAL DIPOLE (CONT) (CONT) mixed coordinates in expression mixed coordinates in expression need to change to spherical need to change to spherical l / 50 7 Using Vector Potential Using Vector Potential A A , , calculate calculate H & & E fields fields [ ] = r A A r r r ) ( 1 A G [ ] A a A H G G G = = 1 1 [4-7] INFINITESIMAL DIPOLE INFINITESIMAL DIPOLE (CONT) (CONT) l / 50 8 Using Vector Potential Using Vector Potential A A , , calculate calculate H fields fields [4-8] A H G G = 1 jkr o e jkr r I k j H + = 1 1 sin 4 A = r H = H INFINITESIMAL DIPOLE INFINITESIMAL DIPOLE (CONT) (CONT) l / 50 9 Using Maxwell Using Maxwell s s Eqns Eqns to to calculate calculate E fields fields [4-10] H E G G = j 1 jkr o r e jkr r I E + = 1 1 cos 2 2 A = E jkr o e r k jkr r I k j E + = 2 2 1 1 1 sin 4 A Fig. 4.1(b) Geometrical arrangement of an infinitesimal dipole and its associated electric-field components on a spherical surface INFINITESIMAL DIPOLE INFINITESIMAL DIPOLE (CONT) (CONT) l / 50 10 Using Using H , , E r , , E , calculate the complex Poynting vector calculate the complex Poynting vector ( ) = =...
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ANTENG-CH4sal - 1 Chapter 4 Chapter 4 Linear Wire Antennas...

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