Antennas 116 Antenna Synthesis

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Antenna Synthesis

Given a radiation pattern, find the required currentdistribution to realize it.

Synthesis Principles

For a line source, the normalized pattern is

where is normalized to give the normalized pattern.Let

We have

This is Fourier Transform. The inverse gives

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Usually, the derived from the inverse FourierTransform of a given is infinite in extent. Toapproximate, truncate the current as follows

Example 8-1

Given

The current is

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The generated pattern is

Woodward-Lawson Sampling MethodLet

where .

Then

where

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Note that Provide better match than Fourier transform.

Linear Array Shaped Beam Synthesis Methods

Fourier Series Method

Expand in interval by Fourier series

Then

Compare to a equal space linear array with current

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amplitude and spacing

We can make

to approximate the pattern.

Woodward-Lawson Sampling Method

where , ,

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Comparison

Ripple R: in main beam.

Transition width T:

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Dolph-Chebyshev Linear Array Method

Chebyshev Polynomials

which is a polynomial of with order n.A few examples,

Properties:

1.

2.3. Number of extreme values in : n–1.4. Number of roots: n. Roots are all in .5. All curves pass through (1,1), and (-1, 1) for even

order, (-1,-1) for odd order.

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Suppose a linear array with spacing , total number ofelement . Then, array factor is

where If the current distribution is symmetric, that is,

or rewrite it this way using the mid-point as the phasereference,

for

for Rewrite it again,

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In both cases, is a polynomial of with order

.Let

then

Beam maximum occurs at , or . Then the

maximum .

Visible regions: , or , or

.

Maximum side lode level: To compute

or

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For narrowest mainbeam width for a given side lobelevel,

where

Half-power beamwidth:

where

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or

Directivity: