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EC6602 - AWP UNIT-2
- 1. EC6602 ANTENNA AND WAVE PROPAGATION M.KRISHNAMOORTHY Asst.Professor/ECE GOJAN SCHOOL OF BUSINESS AND TECHNOLOGY
- 2. UNIT-II WIRE ANTENNAS AND ANTENNA ARRAYS
- 3. Categories Radiation Pattern a) Engineering point of view Wire Antennas b) Analytical point of view Aperture Antennas Equivalence Theorem Basic Antennas c) Technical point of view Composite Antennas - Dipole, Loop, Helix - Slot, Horn, Frequ. Indep. - Arrays (linear, planar, Yagi) - Reflectors (corner, parab.)
- 4. Basic Structures a) Dipole - Coordinate system Blackboard! x y z Load Tr. Line r r … (radial) distance θ θ … Elevation φ φ … Azimuth - Electric and Magnetic Field Vector H Er The “longer” the vectors E & H at point r, the more energy is available at that point. BUT! We are also interested in the changes from location to location.
- 5. Basic Structures a) Dipole - Radiation Pattern Blackboard! Radiation Pattern is defined as … “… the variation of the magnitude of the electric or magnetic field as a function of direction (at a distance far from the antenna).” half wave one wave length 1.5 wave lengthvery short dipole
- 7. Current Sheet x y z P(r, , ) J ( ) = − zyxzyxJ r e A z jkr z ddd,, '4 '
- 9. Nyquist Criterion x y z P(r, , ) J Aperture Array > 2d
- 10. Linear Antenna Array Assumption: equal antenna elements Current variation along z ( ) ( ) ( ) − = −= 1 0 , N n nnz xxzIzxK ( ) ( )zgIzI nn = Complex nth terminal current ( ) ( ) = + zx ezxKP zx j z dd,, 212 21 ( )21,sin 2 Array jkr P r e jH = −
- 11. Principle of Pattern Multiplication Individual Pattern ( ) ( )120sin 2 1 fP r e jH jkr = − HE = Principle of Pattern Multiplication ARRAY FACTOR ( ) ( ) = z ezgP jkz d2 20 ( ) 1 1 0 1 − = = njkx N n n eIf ( ) ( ) ( ) 1 221, f PP =
- 12. Collinear Antenna Array ( ) ( ) ( ) − = −= 1 0 , N n nnz zzgIxzxK ( ) ( ) = z ezgP jkz d2 20 ( ) 2 1 0 2 − = = njkz N n n eIf ( ) ( ) ( ) 2 221, f PP = Principle of Pattern Multiplication AF just on elevation dependent!
- 13. M N Planar Antenna Array ( ) ( ) ( ) − = − = −−= 1 0 1 0 , M m N n nnnmz xxzzgIzxK ( ) ( ) = z ezgP jkz d2 20 ( ) − = − = = 1 0 1 0 21 21 , M m jkzjkx N n nm nm eeIf ( ) ( ) ( ) 21 221 , , f PP = Principle of Pattern Multiplication
- 15. Progressive Phaseshift Array nj nn eII = max, An array for which the following phase relationship holds is called progressive phaseshift array: nn = ( ) +− = = 121 0 max,1 d njN n n eIf Progressive Phaseshift Array Factor: Main Beam: d 2 1 −=
- 16. Broadside Array 0= 1 2 3 4 5 30 210 60 240 90 270 120 300 150 330 180 0 x Main Beam orthogonal to the Array
- 17. Endfire Array d 2−= Main Beam along the Array 1 2 3 4 5 30 210 60 240 90 270 120 300 150 330 180 0 x
- 18. Uniform Array
- 19. Uniform Array An array with equispaced elements which are fed with current of equal magnitude and having a progressive phase-shift along the array is called … UNIFORM ARRAY ( ) − = = 1 0 N n unj euf with cos2 1 kd d u +=+= ( ) ( ) ( )u Nu uf 2 1sin 2 1sin = Principle Maximum: Zeros: Secondary Maxima: 0=u N n u 2= N m u 12 + =
- 20. Uniform Array 1. Sidelobe level = 13.5dB → independent of N! N 2 N u N 22 +− -8 -6 -4 -2 0 2 4 6 8 0 1 2 3 4 5 6 7 13.5dB 2. Beamwidth → dependent of N!
- 21. Broadside Array Main beam is for u=0. → N kd 2 2 cos = + Broadside Array cos2 1 kd d u +=+= kd −=cos 2/90 == → 0= Main Beamwidth (MBW)BS ( ) == Nd arcsin22MBW BS →
- 22. Ordinary Endfire Array Main beam is for u=0. → ( ) N kd 2 1cos =− Ordinary Endfire Array cos2 1 kd d u +=+= kd −=cos 00 == → kd−= Main Beamwidth (MBW)OE ( ) = Nd2 arcsin4MBW OE →
- 23. Endfire Array with increased Directivity (71% of OE) ( ) Nn kd 2 1cos =−− Endfire Array with increased Directivity cos2 1 kd d u +=+= kd −=cos 00 == → +−= N kd Main Beamwidth (MBW)EID ( ) = Nd4 arcsin4MBW EID →
- 24. Pattern Analysis
- 25. Array Polynomial cos1 = ( ) 1 1 0 1 − = = dnkj N n n eIf nj nn eII = max, ' nn n += Progressive Phase Shift Deviation from progressive PS ( )nuj N n n n eIf + − = = ' 1 0 max, )(1 1 0 zPzAf N n N n n − − = = ;ju ez = ' max, nj nn eIA = coskdu +=
- 26. Array Polynomial Nulls on unity circle indicate no- radiation in that particular direction! )(1 1 110 zPzAzAAf N N N − − − +++= ( ) ( ) ( )1211 )( −− −−−= NN zzzzzzzP i N i zzf −= − = 1 1 u=0 u=/2 1 Visible Region
- 27. N=4 Broadside Array Nulls on unity circle indicate no- radiation in that particular direction! 123 +++= zzzf u=0 u=/2 1 z1 z2 z3 2 1 1 j ez = j ez =2 2 1 3 j ez − = Broader Mainlobe? Narrower Mainlobe?
- 28. Binomial Array for d=/2 ( ) 1331 233 +++=+= zzzzf u=0 u=/2 1z1 z2 z3 1−=nz Broadest Mainlobe Always just one lobe! ( ) 1 1 − += N zf
- 29. Filled Disk
- 30. Westerbork
- 31. VLA