Design of 2 D-Bootlace Lens with Five Focal Feed for Multiple Beam Forming

Utility of microwave bootlace lens is well established. For broadband and wide scanning network, it is required to optimize and use features of this lens for better communication and scanning device. This report presents the design of a compact 2D bootlace lens with five focal feed for multiple beam forming. This design will help in reducing phase error and will provide power efficiency and better resolution during target tracking. This design will provide better aperture efficiency and scanning angle.


Introduction
In many radar and communication applications, it is often required to scan a wide area using an antenna array.A multiple beam-forming network is required to control the amplitude and phase at each element of the antenna array.Microwave bootlace lens forms an important class of multiple beam forming networks.Ruze [1] suggested a lens for wide-angle scanning.Rotman and Turner [2,3] suggested modification in Ruze's lens to improve the scanning capabilities.Wide-angle scanning capabilities of these lenses are well established [4][5][6].P. K. Singhal et al. [7] suggested modified design equations to improve the performance of the bootlace lens.
Bootlace lenses have traditionally offered great design flexibility without the excessive cost and reliability difficulties of phased array.This present report proposes to improve the current lens technology by developing a five focal point lens with scanning capability in a plane.As with previously developed multifocal bootlace lenses, specifying several adjacent perfectly focused scanned beam gives a well-focused field of view across the region bounded by the focal points.The entire aperture is used for all beams, providing optimum efficiency for this antenna.

Lens Design
Figure 1 shows the geometry of five focal point bootlace lenses.For a lens with five perfect focal points, the focal points are positioned as two pairs in different scan planes and one central point.Un-scanned focus to accommodate a wide, two-dimensional field of view [8].
Using the design approach suggested in [9] and modified for this design following equations are written: where The five path length equation (counting each choice of '±' as a single equation) are now simplified and solved numerically to give the surface and transmissions line length N = Indicate the position of the radiating elements, called the lens aperture.
 r = Substrate dielectric constant. re = Effective dielectric constant of the transmission lines.
Design parameters are normalized relative to the maximum lens aperture N max and defined as follows: Algebraic manipulation of the equations above gives Now by the Equations (1-5) Squaring ( 21) to (25) sin ψ 2 sinψ 2 sin ψ+2 Equating both  2 0 m a x F P N  by Equation ( 25), (30) Add ( 32) & ( 34), ( 33) & ( 35) By ( 38) & (39) sin ψ sin ; sin sin Value of x & y put into Equation (31) and solve then we get the equation where sin cos sin sin sin cos Again Value of x & y put into Equation ( 40) and solve then we get the equation

Simulated Result
Based on design equations the proposed design has been simulated for the following parametric values:

Conclusion
Design equation of 2D-Bootlace lens with five focal feed for multiple beam forming has been computed and pro-posed geometry has been simulated using MATLAB, which gives result as per prediction of this design and will yield wave-front as per specification.
f3 and f4 are opposite to the f1 and f2.The results shown below in Figure2it is clearly shown that the beam width has been reduced drastically and will provide further power spectral efficiency and better scanning area with less amount of power, thus reducing the effective cost of the equipment used for interfacing antenna array.