Phased (Scanning) Arrays

They direct the main beam of an array by controlling the phase excitation between elements:

oo kdkd

kdo

cos0cos

0cos

==+

=+= = (16)

[Array factor pattern of a 10-element uniform amplitude scanning array. = -kd cos 0, 0 = 600, d = /4]

2 - dimensional pattern

Hansen- Woodyard End fire Array

Hansen and Woodyard found that a larger directivity can be achieved for if the phase :oo or 1800 ==

oforkd

Nkd

Nkd

0

94.2

==

+

+

is used instead of:

(17)

and

oforkd

Nkd

Nkd

180ofinstead

94.2

==

++

++

(18)

These conditions yield larger directivity than in the ordinary end fire antennas, but not the maximumpossible.

For Maximum Radiation along =0

=+

=+

=

=

o

o

kd

andN

kd

180

0

cos

cos

(20) Must be satisfied

(19)

For Maximum Radiation along =180

=+

=+

=

=

o

o

kd

andN

kd

0

180

cos

cos

(22) Must be satisfied

(21)

Directivity of Hanson Woodyard in Figure is 19

Directivity of ordinary end Fire is 11

3-dB Beamwidth of Hanson Woodyard is 37o

3-dB Beamwidth of ordinary End Fire is 74o

What happens if we do not satisfy both conditions?

If both conditions are not satisfied you may end up with some side lobes that are larger than the main beam.

[See Derivation in the Book]

N-element Linear Array Directivity

Broadside arrayCan one calculate the directivity of a uniform array as a function of N & d ?

How do we calculate Do in this case?

For the Broadside array ( ) and for small spacing we have:0=

2

2)(

cos2

cos2

sin)(

cos2

cos2

sin)(

==

=

kdN

kdN

AFU

kdN

kdN

AF(23)

(24)

ddkdN

kdN

U

PU

o

rado

sincos

2

cos2

sin

41

41&

2

2

0 0

=

=

(25)

Since the integration w.r.t. will yield 2

dkdN

kdN

Uo sincos

2

cos2

sin

21

2

0

= (26)

dkdNdzkdNz sin2

cos2

==Let

Eqn (26) becomes:

zdzz

NkdU

Nkd

Nkdo

2

2

2

sin1

= (27)

zdzz

NkdUor

Nkd

Nkdo

2

2

2

sin1

= (28)

For very large arrays

Eqn (28) becomes:

Hence:

NkdUor

zdzz

NkdU

o

o

=

2sin1

(29)

Nkd

NddND

Nkd

NkdUUD

o

oo

22

1max

==

===

(30)

arraysbroadsidefordNDo

= 2Endfire array

Similarly, for ordinary end fire arrays the directivity is:

dNDo 4 (31)

For the Hansen Woodyard end fire:

dNDo 4805.1 (32)

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