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A Simulator for the LWA. Masaya Kuniyoshi (UNM). Outline. 1.Station Beam Model 2.Asymmetry Station Beam 3.Station Beam Error 4.Summary. (Aaron Cohen LWA Memo Series [55]). 256 dipoles. (Leonid Kogan LWA Memo Series [21]). 2π. ( D ・ u ). Ψ =. j. j. λ. 2π. ( D ・ S ). Φ =. j.

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A Simulator for the LWA

Masaya Kuniyoshi (UNM)


Outline

1.Station Beam Model

2.Asymmetry Station Beam

3.Station Beam Error

4.Summary



256 dipoles

(Leonid Kogan LWA Memo Series [21])


( D・ u )

Ψ =

j

j

λ

( D・ S )

Φ =

j

j

λ

= Zenith

S (0,0 )

S (10,0 )

Simulation model for a station beam

255

E(θ,φ)=ΣGaussian(θ,φ)exp(iP )exp(Ψ-Φ)+Noise

j

j

j

j=0

Gaussian(θ,φ) = individual primary beam

Station beam

Station beam

φ[degree]

φ[degree]

θ[degree]

θ[degree]


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

θ[°] (angle form zenith)


Symmetry

Normalized Power Pattern

θ[°] (angle form zenith)


Asymmetry

Normalized Power Pattern

θ[°] (angle form zenith)


Asymmetry

Normalized Power Pattern

θ[°] (angle form zenith)


Normalized Power Pattern

8°

9°

13°

28°

θ[°] (angle form zenith)


80MHz

20MHz

50MHz

Asymmetry rate

HPBW left side/ HPBW right side

θ[°] angle from zenith


θ

Dsinθ

D

As the angle θgoes from 0 to π/2,

the value of cosθ(differentiation of sinθ) gets smaller.

As a result, the beam becomes asymmetric.

This effect increases as the frequency decreases.


θ =-70°

Zenith = 0 °

Beam pattern

peak

θ

(degree)


θ =-60 °

Zenith = 0 °

Beam pattern

peak

θ

(degree)


θ =-50 °

Zenith = 0 °

Beam pattern

θ

(degree)


θ =-40 °

Zenith = 0 °

Beam pattern

θ

(degree)


θ =-30 °

Zenith = 0 °

Beam pattern

θ

(degree)


θ =-20 °

Zenith = 0 °

Beam pattern

θ

θ

(degree)


θ =-10 °

Zenith = 0 °

Beam pattern

θ

θ

(degree)


θ =0 °

Zenith = 0 °

Beam pattern

θ

θ

(degree)


θ =10 °

Zenith = 0 °

Beam pattern

θ

θ

(degree)


θ =20 °

Zenith = 0 °

Beam pattern

θ

θ

(degree)


θ =30 °

Zenith = 0 °

Beam pattern

θ

θ

(degree)


θ =40 °

Zenith = 0 °

θ


θ =50 °

Zenith = 0 °

Beam pattern

θ

θ

(degree)


θ =60 °

Zenith = 0 °

Beam pattern

peak

θ

θ

(degree)


θ =70 °

Zenith = 0 °

Beam pattern

peak

θ

θ

(degree)


θ =-70 °

Grating lobe

Zenith = 0 °

λ

・57.3≒43°

d

Beam pattern

Grating lobe

θ

(degree)


θ =-60 °

Grating lobe

Zenith = 0 °

Beam pattern

Grating lobe

θ

(degree)


θ =-50 °

Grating lobe

Zenith = 0 °

Beam pattern

Grating lobe

θ

(degree)


θ =-40 °

Grating lobe

Zenith = 0 °

Beam pattern

Grating lobe

θ

(degree)


θ =-30 °

Zenith = 0 °

Grating lobe

Beam pattern

θ

(degree)


θ =-20 °

Zenith = 0 °

Grating lobe

Beam pattern

θ

(degree)


θ =-10 °

Zenith = 0 °

Beam pattern

Grating lobe

Grating lobe

θ

(degree)


θ =0 °

Zenith = 0 °

Beam pattern

Grating lobe

Grating lobe

θ

(degree)


θ =10 °

Zenith = 0 °

Beam pattern

Grating lobe

Grating lobe

θ

(degree)


θ =20 °

Zenith = 0 °

Grating lobe

Beam pattern

θ

(degree)


θ =30 °

Zenith = 0 °

Grating lobe

Beam pattern

θ

(degree)


Grating lobe

θ =40 °

Zenith = 0 °

Beam pattern

Grating lobe

θ

(degree)


Grating lobe

θ =50 °

Zenith = 0 °

Beam pattern

Grating lobe

θ

(degree)


θ =60 °

Grating lobe

Zenith = 0 °

Grating lobe


θ =70 °

Grating lobe

Zenith = 0 °

Beam pattern

Grating lobe

θ

(degree)


Station beam at 20MHz

Station Beam

(-60,0)

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 20MHz

Station Beam

(-50,0)

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 20MHz

Station Beam

(-40,0)

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 20MHz

Station Beam

(-30,0)

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 20MHz

Station Beam

(-20,0)

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 20MHz

(-10,0)

Station Beam

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 20MHz

(0,0)

Station Beam

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 20MHz

Station Beam

(10,0)

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 20MHz

Station Beam

(20,0)

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 20MHz

Station Beam

(30,0)

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 20MHz

Station Beam

(40,0)

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 20MHz

Station Beam

(50,0)

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 20MHz

Station Beam

(60,0)

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 60MHz

Station Beam

Grating lobe

(-60,0)

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 60MHz

Station Beam

(-40,0)

Grating lobe

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 60MHz

Station Beam

(-20,0)

Grating lobe

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 60MHz

Station Beam

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 60MHz

Station Beam

(20,0)

Grating lobe

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 60MHz

Station Beam

Grating lobe

(40,0)

Φ[°]

0

20

40

-60

θ[°]

60


Station beam at 60MHz

Grating lobe

Station Beam

(60,0)

Φ[°]

0

20

40

-60

θ[°]

60


Summary

1. Asymmetry rate of a station beam → beam elevation & observing frequency

2.The direction error of a station beam → beam elevation & primary beam

Future Plan

@ Addition of a real dipole beam pattern to the simulator

@ Addition of band widths to the simulator

@ Dipole configuration to remove the grating lobes

@

@

★Completion of the simulator for the LWA


同じ方向を見た場合

20~80MHz


The gap between beams.

29MHz ->172 degrees

30MHz -> 115 degrees

40MHz -> 86 degrees

50MHz -> 69 degrees

60MHz -> 57 degrees

70MHz -> 49 degrees

80MHz -> 43 degrees



3D one station beam figure

20MHz 0deg 20deg 40deg 60deg


HPBW

∝ P

θ


規格化バージョン

0、30、60°


zenith

なぜ小さいか理由も入れる

軸を消してもいいかも!

-40 degrees


We need a simulator because there is no LWA station.

If you get the simulator, you could find some problems in LWA before the construction.


ここにkumarからもらったシミュレーションソフトを

改造してLWA100mバージョンにした

最終的な(クリーン後)を入れる

最終的にこのようなソフトを作りたい

しかし、これは1ステーションを100mと

考えた時の、実際のステーションの位置

を入れたデータである。

実際に256ダイポールからなるステーションビーム

でシミュレーションソフトを作成することが目的。


θ

Dsinθ

D


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