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Problem 9.34: Solution

The document considers a two-element dipole array with identical feeding coefficients of 1 and phase of 0 degrees. It is asked to choose the spacing d/λ to have a maximum in the array factor at 45 degrees. The solution shows that for a maximum at 45 degrees, d/λ must equal 1.414 to satisfy the condition that the argument of the cosine function is an integer multiple of pi.

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92 views1 page

Problem 9.34: Solution

The document considers a two-element dipole array with identical feeding coefficients of 1 and phase of 0 degrees. It is asked to choose the spacing d/λ to have a maximum in the array factor at 45 degrees. The solution shows that for a maximum at 45 degrees, d/λ must equal 1.414 to satisfy the condition that the argument of the cosine function is an integer multiple of pi.

Uploaded by

omairakhtar12345
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Problem 9.34 Consider the two-element dipole array of Fig. 9-29(a).

If the two
dipoles are excited with identical feeding coefficients (a0 = a1 = 1 and 0 = 1 = 0),
choose (d/ ) such that the array factor has a maximum at = 45 .
Solution: With a0 = a1 = 1 and 0 = 1 = 0,

j(2 d/ ) cos 2 d
Fa ( ) = |1 + e | = 4 cos 2
cos .

Fa ( ) is a maximum when the argument of the cosine function is zero or a multiple


of . Hence, for a maximum at = 45 ,
d
cos 45 = n , n = 0, 1, 2, . . . .

The first value of n, namely n = 0, does not provide a useful solution because it
requires d to be zero, which means that the two elements are at the same location.
While this gives a maximum at = 45 , it also gives the same maximum at all
angles in the y-z plane because the two-element array will have become a single
element with an azimuthally symmetric pattern. The value n = 1 leads to

d 1
= = 1.414.
cos 45

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