A Method for Minimising the Phase Errors of Rotman Lenses ELECO2009 BURSA

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A Method for Minimising the Phase Errors of
Rotman Lenses ELECO2009 BURSA

• Rasime Uyguroglu and Abdullah Y. Öztoprak
• Electrical and Electronic Engineering Department
• Eastern Meriterranean University
• North Cyprus

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• In some radar and communication applications, it
  is necessary to have high gain and wide angular
  coverage systems.

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• These systems, need generation of directional and
  multiple beams.

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• Rotman lens fed array antennas are one of the
  microwave lens used to obtain simultaneous
  multiple beams over wide angles.

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• Rotman lens design is based on path length
  equality.
• Rotman lens is a two dimensional constrained lens
  with three focal points.

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Rotman Lens Geometry
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• on axis focal length.
• off axis focal length.
• angle suspended by the off axis focal
  points.
• angle of the beam for the off axis focal
  points.

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• x,y and w are determined by using geometrical
  principles, by considering that for a perfect
  phase front the length from the focal point to
  any point on the corresponding wavefront should
  be constant.

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• The coordinates of the inner lens curve and the
  lengths of the transmission lines are the design
  variables of the lens (x,yw).

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• For each position of the radiating array the
  values of these variables are obtained by
  equating the path lengths from the three focal
  points to the appropriate phase fronts.

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• The phase fronts obtained by placing feed
  antennas at focal points have no phase error, the
  phase fronts for the feed antennas at points
  between focal points (on the feed curve) have
  some phase errors.

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• The phase errors cause deterioration in the gain
  and side lobe level of the beams.

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• Rotman and Turner have a circular arc passing
  through the focal points.
• Hansen and Singhal proposed an elliptical curve
  to be used as a feed curve.

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Equations Obtained From the Rotman Lens Geometry
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• The coordinates of the points on the inner lens
  curve, and the lengths of the transmission lines
  are obtained by solving these three equations
  given above.

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• Path length difference to the phase front
  determines the phase errors.

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• Path length error studies show that the path
  length errors for off focal point feed positions
  are large for the end elements (or for elements
  near the end) of the radiating array when
  circular or elliptical feed curves are used.

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• If the path length errors for these elements are
  reduced, the overall phase performance will be
  improved.

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• Here a simple but very effective method is
  proposed to reduce the phase errors for off focal
  feed points.

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• The method we propose is based on having zero
  phase error at three points on the radiating
  array.

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• First, we obtain the inner lens curve for chosen
  three focal point positions.

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• In this method an optimized feed curve is used.

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• The coordinates of the other points on the feed
  curve can be obtained such that, the path
  lengths from each point F on the feed curve
  through the two end elements of the radiating
  array (A1 and A2) to the corresponding phase
  front are equal to the path length from F through
  the centre element to the same phase front.

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• These equations are solved for
  values on the feed curve.

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• Rather than the end points of the radiating
  array, we can, alternatively, choose two points
  close to the end points for path length equality
  for better results.

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• The distance from the end points of the radiating
  array can be used as a design parameter.
• This small shift in the position of the points
  will reduce the maximum path length error
  further.

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Path Length Errors

• The path length errors determine the phase errors
  of the multiple beams of the Rotman lens fed
  array.

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Rotman lens with a circular feed curve
The parameters of the lens are
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• is normalized to .

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Path length error of the Rotman Lens with
circular feed array
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• We can observe that beam is furthest
  away from the focal beams and it has the largest
  errors.

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The path length errors for the same Rotman lens
with an elliptical feed curve.
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• As there is no unique ellipse passing through
  the three focal points, we chose the ellipse
  which had the smallest maximum path length error,
  which had an eccentricity of 0.4.

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• In the following two figures show the path length
  errors for the same Rotman lens with a feed curve
  obtained by using the optimized method introduced
  here.

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Errors when the two end points ( )
of the radiating array have zero error .
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The errors when the two points at ( )
have zero error.
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Conclusion

• A method is introduced for determining the feed
  curves of Rotman lenses such that the phase
  errors are minimised.
• The results show that the path length errors are
  considerably lower(41) when the new curve is
  used.