Lecture 30. An Array of Two Hertzian Dipole Antennas

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1 Lctu 30 An A f Tw tin Di Antnns n tis ctu u wi n: tin di ntnn s ntfnc nd f-fid ditin ttns C 303 F 005 Fn Rn Cn Univsit Cctistics f Sing tin Di Antnn Antnn in: F tin di t gin is: S(, t ) 3 (, ) Pd ( ) (, 0) (, 0) Antnn Rditin Pttn: (dgs) F tin di t ditin ttn is: ( ) (, ), m ( ) C 303 F 005 Fn Rn Cn Univsit

2 C 303 F 005 Fn Rn Cn Univsit A Sing tin Di Antnn Nt t Oigin - d 3 δ Wt if n s tin di sitting t sm bit int? f n is intstd in ditin f-fids n, tn ssum: d << << λ, d µ [ ] d [ ] d S w gt: Additin s fct d A dv A µ µ ' ' ' ' d A µ C 303 F 005 Fn Rn Cn Univsit A Sing tin Di Antnn Nt t Oigin - d 3 δ m: [ ] d cs cs Sus: Nt tt: [ ] cs d Tf: [ ] cs d [ ] d

3 3 d δ ( ) 3 d δ ( ) Tw tin Dis n Cs Cn wit t -fid nd t -fid in t f-fid dict: d ( ) ( d ) d d Rmmb tt: ( ) cs( ) ( ) ( ) cs( ) C 303 F 005 Fn Rn Cn Univsit 3 d δ ( ) 3 d δ ( ) Tw tin Dis n Cs Cn wit t -fid in t f-fid s: d Dnds n n t diting tis f t individu ntnns (LMNT FACTOR) Dnds n t tiv sitins s w s t tiv cunt mituds f t tw ntnns (ARRAY FACTOR) C 303 F 005 Fn Rn Cn Univsit Dscibs NTRFRNC in t f-fid btwn t ditin mittd b t tw dis 3

4 Tw tin Dis n X-Ais in nd Rditin Pttn - T mituds nd ss f t cunts in t tw dis nt t sm: (, ) α A Qustin: Wt is t ditin ttn in t - n? cs( ) cs( ) α d A cs( ) cs( ) d α A d cs cs α S A C 303 F 005 Fn Rn Cn Univsit Tw tin Dis n X-Ais in nd Rditin Pttn - α A Tt Pw Rditd: P d d ( A ) sum f t w ditd b individu dis Pnting vct: S ( ) d cs cs α A in: Pttn: (, ) (, ) S P d (, t ) 3 A Acs[ cs( ) α ] A, [ ] A Acs cs α m A C 303 F 005 Fn Rn Cn Univsit

5 Cs : A λ / α - / Cs : Tw tin Dis n X-Ais α A (, ) Pttn: (, ) cs cs( ) λ C 303 F 005 Fn Rn Cn Univsit Cs : A λ / α - / Cs : Tw tin Dis n X-Ais α A (, ) (, ) n t - n n 3D C 303 F 005 Fn Rn Cn Univsit 5

6 Tw tin Dis n X-Ais Sm Psic Rsning Wn tving in t dictin : cs( ) α A T wvs fm di v s d f α cmd t ts fm di But t wvs fm di tv distnc cs() m tn fm di Tis mns t wud g b s f cs() Cnsqunt: T nt s dinc btwn wvs fm di nd di in t dictin is: α cs On cud tf ct mimum in t ditin ttn in t dictin if t nt s dinc is intg muti f : ( ) ± n { n KK α cs,,3, C 303 F 005 Fn Rn Cn Univsit Cs : A λ / α 0 Cs : Tw tin Dis n X-Ais α A (, ) Pttn: (, ) ( cs[ cs( )]) λ C 303 F 005 Fn Rn Cn Univsit 6

7 Cs : A λ / α - / Cs : Tw tin Dis n X-Ais α A (, ) Pttn: (, ) cs cs( ) λ C 303 F 005 Fn Rn Cn Univsit Tw tin Dis n Z-Ais in nd Rditin Pttn - T mituds nd ss f t cunts in t tw dis nt t sm: α A Qustin: Wt is t ditin ttn (, )? d ( ) cs( ) cs( ) α A d ( ) ( ) cs( ) cs( ) α A S d ( ) ( ) cs cs α A C 303 F 005 Fn Rn Cn Univsit 7

8 Tw tin Dis n Z-Ais in nd Rditin Pttn - Tt Pw Rditd: P d d ( A ) sum f t w ditd b individu dis Pnting vct: S d ( ) ( ) cs cs α A in: (, ) S(, t ) 3 P ( ) A Acs A [ cs( ) α ] Pttn: (, ) (, ) (, ) A A m cs[ cs( ) α ] A C 303 F 005 Fn Rn Cn Univsit Cs: A λ / α - Cs: Tw tin Dis n Z-Ais d d d α A (, 0) Pttn: ( ) (, ) ( cs[ cs( ) ]) 90 Ntic t ctins f t nus? Cn u figu ut t ngu ctin f t nus b sic sning? C 303 F 005 Fn Rn Cn Univsit 8

Cs: A λ / α - Cs: Tw tin Dis n Z-Ais α A (, ) (, 0) 0 30 60 90 0 80 50 C 303 F 005 Fn Rn Cn Univsit tin Di Ov Pfct Mt Pn: mg Di Cnsid tin di

9 Cs: A λ / α - Cs: Tw tin Dis n Z-Ais α A (, ) (, 0) C 303 F 005 Fn Rn Cn Univsit tin Di Ov Pfct Mt Pn: mg Di Cnsid tin di v mt gund n t 5-dgs b 3 ( ) d δ ( b ) T bm cn svd b imgining n img di b 3 ( ) d δ ( b ) mg Di 3 ( ) d δ ( b ) C 303 F 005 Fn Rn Cn Univsit 9

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