Antennas 116 Antenna Synthesis
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Antennas 116 116 Antenna Synthesis Given a radiation pattern, find the required current distribution 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
Transcript of 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:
