Antenna Engineering Lecture 8: Antenna Arrays

Transcription

1 Atea Egieerig Lecture 8: Atea Arrays ELCN45 Sprig 211 Commuicatios ad Computer Egieerig Program Faculty of Egieerig Cairo Uiversity

2 2 Outlie 1 Array of Isotropic Radiators Array Cofiguratios The Space Factor 2 The Patter Multiplicatio Priciple 3 Beam Steerig Beam Steerig (Scaig) Techiques Electroic Scaig Frequecy Scaig 4 Array Feedig Networks

3 3 Outlie 1 Array of Isotropic Radiators Array Cofiguratios The Space Factor 2 The Patter Multiplicatio Priciple 3 Beam Steerig Beam Steerig (Scaig) Techiques Electroic Scaig Frequecy Scaig 4 Array Feedig Networks

4 Array Cofiguratios Some Array Cofiguratios 4 Plaar Array Liear Array Circular Array Atea arrays are arragemets of idetical ateas i arbitrary cofiguratios. What is the motivatio of usig atea arrays?

5 Space Factor Space Factor for Cotiuous ad Discrete Source Distributios 5 jkrcos ψ Erad J r e dv V Space Factor (Cotiuous Distributio) E rad Space Factor (Discrete Distributio) N Ie 1 jkr cosψ N r r r r J dv ψ r r ψ r r O 1 O

6 Space Factor Space Factor for Liear Arrays z Array o Z-Axis 6 I N N N N jφ jkr cosψ jφ jkz cosθ 1 1 SF I e e I e e N 1 Progressive Phase Shift j 1 β jk 1 d cosθ I e e Equidistat Elemets φ 1 β 1 z d I 1 1 SF N 1 e 1 cos j kd θ β 1 e 1 e jn kd cos θβ j kd cos θβ

7 Space Factor Space Factor for Uiform Liear Array 7 z SF θ kd sin cos θ cos θ 2 kd si cos θ cos θ 2 β kd cos θ I N N SF ψ kd sin cosψ cosψ 2 kd si cosψ cosψ 2 β kd cos ψ I 1 1 The cosie ca be replaced by sie i the space factor expressio if the agle is measured from the ormal to the array axis.

8 Space Factor Example Mai Beam Measured from the ormal Normalized θ SF θ kd sin siθ siθ 2 kd N si siθ siθ 2 β kd siθ 8 Side Lobes Array Axis β Broadside Radiatio β π π kd si β kd si 6 4 kd π N 6

9 Space Factor Mai Parameters 9 SF θ kd sin siθ siθ 2 kd N si siθ siθ 2 Mai beam: at the directio determied by the progressive phase shift. Special cases: Broad-side ad ed-fire. Nulls: whe the umerator goes to zero, but the deomiator is ot zero. Side lobes: Occur half-way betwee two ulls (excludig the mai beam). Side lobe level (SLL): Prove that the first side-lobe level for a sufficietly large array is approximately 13 db (below the mai beam level).

10 1 Outlie 1 Array of Isotropic Radiators Array Cofiguratios The Space Factor 2 The Patter Multiplicatio Priciple 3 Beam Steerig Beam Steerig (Scaig) Techiques Electroic Scaig Frequecy Scaig 4 Array Feedig Networks

11 Patter Multiplicatio Total Radiatio Patter of Array of Kow Atea Elemet 11 Radiatio Patter = Elemet Patter x Array Factor x = The patter multiplicatio priciple eglects the effect of mutual couplig (mutual impedace) betwee elemets, i.e., it assumes that the elemets are isolated. Discuss these assumptios.

12 12 Outlie 1 Array of Isotropic Radiators Array Cofiguratios The Space Factor 2 The Patter Multiplicatio Priciple 3 Beam Steerig Beam Steerig (Scaig) Techiques Electroic Scaig Frequecy Scaig 4 Array Feedig Networks

13 Beam Steerig Methods Mechaical, Electroic ad Frequecy Scaig Mechaical Scaig: The beam is steered by physically rotatig the whole atea/atea array. 2. Electroic Scaig: The beam is steered by electroically chagig the relative phases of the feedig currets of the array elemets. 3. Frequecy Scaig: The beam is steered by chagig the operatig frequecy of the source, which i tur results i chagig the relative phases of the elemet feedig curret. What are the advatages ad disadvatages of each?

14 Electroic Scaig Visible Rage ad Maximum Sca Agle SF kd sin u u 2 kd N si u u 2 SF λd Gratig Lobe 14 u Visible Rage u u λ λ 1 siθ max 1 d d max

15 Electroic Scaig Visible Rage ad Iter-Elemet Spacig SF kd sin u u 2 kd N si u u 2 SF λd Gratig Lobe 15 u Visible Rage u u max λ 1 d d u λ max 1

16 Electroic Scaig Example 16 Example 1. Determie the iter-elemet spacig for a liear array that will allow steerig the beam arbitrarily without the appearace of gratig lobes. 2. Determie the iter-elemet spacig for broadside radiatio of a liear array to have oly oe mai beam (o gratig lobes). Solutio:

17 Electroic Scaig Example 17 Example Fid the space factor i the followig cases (use covetioal coordiate system): Two equal i-phase sources at (,, ) ad (d,, ). Two equal i-phase sources at (,, ) ad (d, d, ). Four equal i-phase sources at (,, ), (d,, ), (, d, ) ad (d, d, ). Three i-phase sources at (,, ), (,, d) ad (,, 2d) with ratio of magitudes 1:2:1. Solutio:

18 Frequecy Scaig Slotted Waveguide Atea Arrays 18 Trasverse Broad-Wall Slots Logitudial Broad-Wall Slots Tilted Narrow- Wall Slots Waveguide slots are excited if they itercept surface curret (tagetial to the magetic field). Explai how frequecy scaig works i slotted waveguide arrays?

19 Frequecy Scaig Example 19 Example Desig a slotted X-bad waveguide atea array at 9 GHz usig: a. Trasverse slots for ed-fire radiatio. b. Logitudial slots for broad-side radiatio. Neglect the couplig betwee elemets ad assume the power reachig all elemets is uchaged. Discuss the previous assumptios. The desig should be doe uder the followig coditios: a. The waveguide is termiated i matched load. b. The waveguide is termiated i short-circuit termiatio. Solutio:

20 2 Outlie 1 Array of Isotropic Radiators Array Cofiguratios The Space Factor 2 The Patter Multiplicatio Priciple 3 Beam Steerig Beam Steerig (Scaig) Techiques Electroic Scaig Frequecy Scaig 4 Array Feedig Networks

21 21 Coclusio Atea arrays may be used to boost the gai of the radiatig system ad provide cotrol o the beam directio. Atea arrays play a importat role i radar systems (electroic scaig) ad may commuicatio systems. A compact ad low-loss feedig etwork is oe of the desig challeges i array desig. The feedig etwork may limit the system badwidth (how?) I some arrays, ot all the elemets are drive; some elemets are excited parasitically (e.g. Yagi-Uda array).