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CHAPTER-II

LITERATURE REVIEW

The growing complexities of radar and communication systems have created a need

for antennas capable of forming multiple simultaneous beams. The main component

of this antenna is a BFN, capable of generating multiple, independent and highly

directional beam patterns, using a single linear antenna array. Developed in 1963 by

Rotman and Turner, the Rotman lens is a passive structure capable of driving arrays

containing hundreds of broadband elements. Rotman lens was the name given after its

invention by an American scientist Sir Walter Rotman who contributed a lot in the

field of Radar and antenna design. His inventions were Rotman lens, sandwich wire

antenna and trough wave guide.

In this chapter the overall detailed literature survey and review of research and

technical papers regarding the design and development of the Rotman lens antenna

from time to time has been carried out. The observations and the proposals given by

the contributors in the area to improve the performance of the lens along with the

concluding remarks have been summarized.

2.1 INTRODUCTION

Due to the rapid advancement in wireless communication system the need for

efficient antenna design with good radiation capability, multiple simultaneous beams

and small size is required (FCC, 2002). Research work to improve the antenna design

for obtaining desired goals has been carried out by various researchers in the last few

decades. Smart antennas with wide scanning angle capabilities have emerged as a

result of continuous effort in making an efficient antenna design. Modern day cutting

edge applications like Radar and Satellite communication require antennas with wide

scanning angle capabilities and better performance over a broad frequency range

(Archer, 1984). Antennas used in various applications should satisfy some common

criteria, i.e. small size, light weight and good radiation properties.

To appreciate the significance of the most popular of the constrained lens

architectures, the Rotman lens antenna, it is necessary to provide a review of the

constrained lens development. To fully understand the concept of these complicated

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and complex lenses, the basic history behind the development of the microwave must

be dealt with. The constrained lens arrays are special groups of BFN’s. They share

some similarities with the dielectric lenses and reflector antennas on one hand and

with the antenna arrays on the other. Their function is to form beams in multiple

directions which correspond to the location of the feed antennas at the focal surface.

The name constrained comes from the fact that a wave incident on one face of the

array does not necessarily obey Snell’s law when passing through the lens array; it is

instead constrained to follow the transmission line paths (Gagnon, 1989). Unlike

dielectric lenses or reflector antennas, lens arrays do their collimation (transmission)

and focusing (reception) discretely, using antenna arrays.

The design procedure of a microwave lens demonstrates how a lens model can be

simulated. A significant number of studies include the overall development in the

design of the lens. In 1950s, J. Ruze came with the concept of wide angle metal plate.

Eventually, after gradual development the microwave lens emerged as a BFN and was

used in many evolving applications (Smith, 1983; Dong and Zaghloul, 2010). Due to

the advancement in the materials science and several fabrication technologies, new

implementations of the microwave lenses using waveguide, striplines and microstrip

came into subsistence (Tao and Delisle, 1997; Hall et al.2000; Zayed et al.2004).

Multiple beam arrays for mm wave indoor communication also picked up when the

concept was presented by Delisle et al. Many important advancements have been

made to reduce the overall phase error of the lens. New design parameters as well as

the shape of the lens have been analyzed to see the overall performance of the lens

(Sinjjari and Chowdhury, 2008). Due to the overall development in the antenna

pattern; a maximum radiation could be displayed in the direction of the influencing

signal. This was the basis of microwave beamforming.

To understand the significance of the most popular of constrained lens architectures,

the Rotman lens, it is necessary to provide a review of the same. The history and

development of the microwave lens acquaints with various designs that researchers

presented to improvise the working. The review of the past development and

emerging applications of microwave lens forms the basis of newly proposed designs.

The Rotman lens is of the bootlace lens type, a constrained optical scanner as given

by Hansen in 1998. In this chapter, the origins of the bootlace lens along with the

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brief history of its design and development have been dealt. Beam forming was

achieved by designing a lens for equal path-lengths between a point source and the

desired EM wave front. These lens antennas have been the true-time delay devices.

The beam forming operation is entirely mechanical. Because of its features they are

inherently frequency independent. However, a limitation on the achievable frequency

bandwidth depends on the components used to fabricate the lens antenna, such as the

feed port. Contour integral analysis of planar components was given by Mittal et al. in

2003.

Development of the bootlace lens, work done in the improvisation of side lobes

developed in the main beam of the lens, Microwave BFN, reduction of the phase

error, insertion of the dielectric material, mutual coupling between the ports, the shape

of the lens and general trends in the design of the Rotman lens have been surveyed.

The evolution of constrained lenses from dielectric lenses and reflector antennas have

been presented in the following sections.

2.2 THE BOOTLACE LENS

In 1957, H. Gent presented an extra degree of freedom to the constrained lens of Ruze

developed in 1950. The Gent's lens did not require the waveguide plates to meet the

antenna aperture at the same height. For this reason, these parallel conducting plates

were replaced by flexible transmission line, such as coaxial cable. As these flexible

lines of transmission resembled the laces of the boots, Gent’s lens was named as

bootlace lens. This new way of connecting a lens device has many advantages. The

size and space of the array element is no longer confined to the parallel plate

waveguides of the lens. Initially, the lens and the radiating aperture were the part of

the same structure but now they have been split into two different components,

namely the lens and the antenna array. For this reason, the bootlace lens is not

categorized as a metal-lens antenna, although it has been adapted from it. In 1946,

W. E. Kock, introduced the concept of metal-lens antennas. In the 1960's there had

been a large demand for the bootlace lens due to its true-time delay and simultaneous

beam forming capability. It was cheaper and more robust over its counter-part; the

Butler matrix. The concept of multibeam antenna array was given in 1973 by Archer

et al. and was further improvised in 1984. In 1986, J. A. Kong developed the lens

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design by making use of the optical ray theorem which stated that the optical path-

lengths between two constant phase fronts were equal. As the technology progressed,

the main advantage of the bootlace lens remained its simplicity as provided in 2005

by Archer and Maybell. The popular bootlace lenses and its implementation have

been discussed below.

2.2.1 Popular Bootlace Lens Types and Implementations

The earliest constrained lens was the R-2R lens, as given by Brown in 1950 and 1969,

where the inner and outer surface of the lens and the outer radius was twice the inner

radius. The R-2R lens concept originated during wartime. The shape provided perfect

collimation for the feed points on the focal arc. However, due to the amplitude

asymmetry between beams, the side lobe level increased. The problem was overcome

by W. Rotman and R.F. Turner in 1963. They shared design equations for the trifocal

bootlace lens. The lens designed by Rotman and Turner applied refocusing of the

focal arc as derived by Ruze in 1950. Rotman and Turner introduced Rotman lens

phenomena. The Rotman lens is the most popularly implemented bootlace lens

device. This gave a “near optimum" design for a least phase error distribution.

Trifocal lenses are generally called as Rotman lenses, whether they use the concept of

refocusing or no. The path in the metal lens configuration is formed using parallel

metal plates. The formation of the lens contour depends on the thickness of the lens

and the desired refractive index. The focal arc is a circle, centered on the origin that

passes through the two focal points. A correction to wide angle microwave for line

source applications was developed by Leonakis in 1986. The aberrations due to the

path length associated with a metal lens can be large and are dependent on the design

of the lens. To combat aberrations, a refocusing of the lens is carried out. The lenses

take different forms depending on how the equations describing the Ruze lens have

been applied.

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The Figure 2.1 shown below represents four types of Ruze lens designs based on the

lens requirement. The choice of lens configuration has a significant effect on the

refocused focal arc, size of the lens and the weight. The Figure 2.1 (a) represents a

constant thickness but requires significant refocusing to achieve optimal performance.

Figure 2.1(b) shows variable thickness and does not require refocusing, but results in

a very heavy lens. This weight is reduced using zoning as shown in Figure 2.1 (c) by

stepping the lens using multiples of the wavelengths. Figure 2.1 (d) uses a flat front

face and requires limited refocusing.

Figure 2.1 Ruze lens configuration (Ruze J., 1950)

Until the bootlace lens was reported by Gent in 1957, constrained lenses were treated

merely as a convenient refractive medium. The bootlace lens changed this perception

by considering constrained lenses as arrays of antennas connected by lengths of

transmission line. The first antenna array forms the input contour and the second is

referred to as the lens contour. The lens is then driven by individual antennas placed

along the focal arc.

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The bootlace aerial demonstrated that constrained lenses could be implemented using

a wide variety of transmission line types connecting several types of radiators. The

use of non-dispersive transmission lines, coaxial or parallel wire cable, for example,

makes very broadband lens systems practical. Microstrip or Stripline

implementations, combined with a high dielectric substrate, allow very compact

constrained lens designs as given by Maybell et al. in 2005. An LTCC based folded

Rotman lens antenna for phased array applications was designed by Tudosie and

Vahldieck in 2006.

The bootlace lens is similar to the Ruze lens. The three degrees of freedom available

in the metal lens was supplemented by a fourth in the bootlace lens given by Gent.

The four degrees of freedoms were:

1. The shape of the input contour or antenna array.

2. The shape of the output contour or lens contour.

3. The length of the transmission line connecting corresponding antenna elements and

the ports.

4. The relative positions of the antenna elements and ports on the antenna array and

the lens contour respectively.

In contrast to the lens topologies described so far, the R-2R and R-KR lens makes use

of a uniformly spaced circular antenna array instead of a linear antenna array. The R-

2R geometry is unique because it is perfectly focused for all beam angles; however, it

is limited by a maximum field-of-view of 180 degrees. The R-KR lens is able to scan

through 360 degrees, but has no perfect focal points (Clapp, 1984).

2.3 THE SIDE LOBES OF ANTENNA ARRAYS FED BY MULTIPLE BEAM

FORMERS

For the reception of the signal, the role of the beam former is to combine the received

signals of the antenna elements and deliver it to the single output port. These signals

are added with phase shifts that increases from one element to the next and results in

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an antenna radiation pattern with single beam pointing in a certain direction in the

space. In 1997 Rausch and Peterson designed a millimeter wave Rotman lens. This

was based on the contour integral. A mm wave Rotman lens that operated between the

frequencies of 33-37 GHz was designed. Various parameters were analyzed.

Maximum side lobe levels ≤ - 30 dB was obtained. In 1998, Rausch designed a

conventional antenna array using Rotman lens similar to a linear array which

consisted of a large number of array ports. The frequency of operation was 30-40

GHz and lower side lobes were achieved. To achieve lower side lobes, attenuator was

used between the array ports and antenna elements to produce a Taylor amplitude

taper across the array. But the use of an attenuator reduced the gain of the whole

antenna system. Tekkouk et al., in 2012 gave the concept of folded Rotman lens

antenna which had multibeam capability in SIW technology at 24 GHz to improve the

side lobes. Broadband beam forming was given by Jafari et al. 2013, which intended

to reduce side lobes.

2.4 SIDE WALL ABSORPTION ON THE PRINTED ROTMAN LENS

Microstrip Rotman lens is the multiple beam forming device for antenna arrays. The

research investigated factors limiting the performance of microstrip lens compared to

parallel plate lenses. New techniques for sidewall absorption and lens port pointing

were identified and demonstrated. In 1983, Smith presented a new design approach

for reduction of side wall absorption, which was one of the performances limiting

parameter. Smith emphasized the flexibility of designing large scan angle Rotman

lens by applying small subtended beam regions. The proposal of the effect of side

wall absorption was given by Musa and Smith in 1989. They proposed the design of

microstrip Rotman lens port design, which had a parallel plate region of height <λ/2

filled with dielectric material, r =10.5. Large numbers of array ports were connected

to the array elements via micro-strip and coaxial lines. They proposed that if the lens

line lengths were equal, as that of the Ruze Lens then only two foci were available

and if the line lengths varied as that of the Rotman design, then three foci would be

available, which considerably reduced the side wall absorption. Numerical techniques

were provided in 1999 by Peterson and Rausch for the analysis of various lenses.

Investigations and measurements of termination of sidewalls of microstrip lens

antenna was given by Dong and Zaghloul in 2009. The traditional design equations do

35

not enumerate the purview of the sidewall that connects the lens focal port to array

port. They specify the port location but do not specify port width. The parameters,

especially side lobe level, side wall absorption, phase error and insertion loss affects

the overall performance of the lens.

2.5 PHASE ERROR IMPROVEMENT

In 1984 an upgraded design method for Rotman lens antenna was proposed by

Takashi Katagi et al. They used a new design parameter to design the Rotman lens.

The use of this variable reduced the phase error for large array length. This method

made it possible to design small and low loss Rotman lens antenna. Katagi also

suggested that the shape of the beam contour is not necessarily a circular arc. By

varying the original design equations, the shape of the lens and the radiation angle

resulted in the low phase error. In 2005, Rappaport and Zaghloul carried out a review

of the concept of design of multifocal bootlace lens. It was observed that the Rotman

or bootlace offers more degree of freedom that helped in realizing multiple focal

points. The lens has three radiating structures which are the feed array on one side of

the lens and radiating array on the other side of the lens. The degree of freedom can

be achieved with the location of the feed element and the lengths of the transmission

lines between the receiving and the radiating ports. A modified approach to design

Rotman (1963) type multiple beam forming lens was proposed by Singhal et al., in

2003. The path length error at the wavefront was calculated. The error obtained was

compared to the conventional approach. 2D EM field analysis of the lens obtained by

the modified approach and by the conventional approach lens was carried out using

the contour integral method. The results obtained for both the lenses were

comparable. In 2009 Uyguroglu et al. introduced a new concept of feed curves such

that the phase error reduced. The method was based on having almost zero error

positions on the radiating array for each feed curve point and eventually he made use

of the PSO optimization technique to reduce the phase error.

2.6 DEVELOPMENT OF BEAM FORMING TECHNIQUES

Multiple beam antennas allow a number of beams to be simultaneously transmitted

and received from a single array aperture. The multiple-beam systems are used in

many applications such as in electronic counter measures, satellite communications,

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multiple-target radars, and in adaptive nulling (Skolnik and Meads, 2001). Lens beam

formers have fixed beam angles, while beam-widths change with frequency. The

simplest BFN is simply N fixed phase or time delay feeds connected to each element

by an N-way power divider. The power divider causes a 1/N signal reduction making

preamplifiers necessary to maintain the signal to noise ratio. This type of network is

practical, only for small numbers of beams and elements. A Butler network is a

simple network using components which can be easily implemented in strip-line or

microstrip; however the layout is difficult due to conductor crossovers. The ideal

Butler matrix is the analogue circuit equivalent of the Fast Fourier transforms

(Uyguroglu et al., 2014). The Rotman lens (Rotman and Turner 1963) is one of the

most functional linear array feed networks because of its excellent aberration

characteristics and frequency-invariant beam pointing. The Rotman lens achieves path

length errors in an order of magnitude smaller than that of dual focal point lens

(Smith, 1982). The excellent aberration characteristics is a product of an additional

focal point made possible by the extra degree of freedom offered by the bootlace lens.

This improvement in performance satisfies the low phase error requirements of wide

apertures forming narrow beams. For this reason the Rotman lens has become the

accepted standard when driving linear antenna arrays. In 1995, Peik and Heinstadt

designed the multiple beam microstrip array fed by Rotman Lens. In 1996 Lee and

Valentine applied the heterodyne technique to the Rotman lens to reduce the size of

the BFN for airborne antenna operating at L- band (1.4 GHz). An alternative to the

above is the use of the RF heterodyne method. This was accomplished by mixing two

higher frequencies in Rotman without dielectric loading. Tao and Delisle, in 1997

designed the lens for indoor communications. They suggested that multi beam

antenna has the potential to produce numerous beams in distinctive directions from

the same aperture, which is different from electronically scanned array which has one

port for each beam. The capability of the system can be increased by reducing

interference.

Further, in 2002, Chan suggested a Rotman lens feed network to generate a hexagonal

lattice of multiple beams. A rectangular lattice with identical row of column boards of

Rotman lenses to feed a hexagonal array of radiating elements was developed. Very

little work has been done on 2D stack of Rotman lens to produce multiple overlapping

beams that are scanned in both Azimuthal and elevation directions (Dong et al.,

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2009). In 2002, Hall et al. developed a Rotman lens for mm wavelength using 77 GHz

band. Many narrow beams were achieved which could be adjusted and combined to

produce broader beam with high gain. Wider scanning angles and high gains could

also be achieved by careful design. The antenna array was designed using a series of

MPA arrays arranged in column in turn connected to the Rotman lens. A desirable

steerable antenna could be achieved. In 2005, Rotman et al. in their paper provided a

method to analyze the performance of the TID beamformers and compared the results

of photonic beam formers to Rotman lens. It was possible to combine and synthesize

lenses and photonics, as photons gave long delays and lens gave short delays. As the

problem of linearity was not solved for optical link, photonics could not be used

completely in the receiver and hence the lens continued to be superior. In 2007,

Nussler et al. presented a design of Rotman lens for mm wave frequency range. This

frequency range was very useful as multiple BFN for the linear antennas and provided

broadband performance. The construction was also demonstrated for the first time.

Attempt to design a Rotman lens at 35 GHz for wideband was done. Parameters

analyzed were focal angle, focal ratio, beam angle to ray angle ratio, maximum beam

angle, no. of beams, and no. of the array, no of array elements, array element spacing

and design frequency. The major drawback of the analysis was that the parameters did

not have degree of freedom.

2.7 INSERTION OF THE DIELECTRICS AND MUTUAL COUPLING

BETWEEN THE PORTS

In 2001, Jaeheung and Barnes gave the concept of scaling and focusing of the Rotman

lens. The concept of high dielectric constant r was suggested due to which the size of

the Rotman lens could be scaled down by a factor ofr . It was suggested that the

design equations and scaling factor could be amended and interpreted according to the

dimensions and materials. If the lens is combined with the phase shifters, it can

generate multiple focused beams with a relatively small spot size. Kilic and

Dahlstrom, in 2004 designed a dielectric Rotman lens as an alternative for broadband,

multiple beam antennas in multifunctioning RF application. This paper presented new

developments in printed Rotman lens design which could be used in low cost

communication and Radar systems. The design used was the replacement of cavity

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Rotman lens with a dielectric Rotman lens to minimize the overall size of the lens. By

miniaturization of Rotman lens, stacking them at the output port made elevation

scanning possible. In this paper use of surface wave Rotman lens design was used

instead of Microstrip design, which eliminated the need of ground plane at back of the

lens and reduced the use of copper for parallel plate region. Ultimately the copper

losses were reduced. Gagnon introduced refocusing procedure for dielectric-filled

Rotman lens according to Snell’s law. Therefore, applying Snell’s law yields a ratio

of r between the sine’s of the scan angle and the subtended angle of the beam

contour. This approach provided beam and array port positions which gave improved

coupling to the outermost beam ports, especially for printed lenses used with small

arrays.

In 1981, Maybell introduced a structured method for coupling co-efficient analysis of

the 2D Rotman lens. The design view of low side lobe Rotman lens requires

consideration of mutual coupling between feed port and array port. The coupling and

internal reflection affect the amplitude and the phase distribution of the radiating array

element. The model was the basis for improved accuracy of array port coupling

coefficient calculations. In 1991, Hansen developed the design trades for Rotman

lens. The design of Lens involved both geometric trades and mutual coupling effects

between the lens ports. This paper described the geometric design trades. Calculation

of lens gain was presented with lens connected to an array of isotropic elements. In

1999, Peterson and Rausch developed and designed a scattering matrix integral

equation for the design of waveguide Rotman lens. The design equations don’t

specify the shape of a sidewall that joins the lens focal port to lens ray port, which

affect side lobe level and insertion loss.

2.8 OTHER DESIGN TRADES USED FOR THE DEVELOPMENT OF THE

ROTMAN LENS ANTENNA

Besides the extensive survey related to the work done in improvisation of side lobes,

reduction of the phase error, effect of insertion of the dielectric material and mutual

coupling between the ports, few other design trades in the development of the

Rotman lens antenna have been surveyed. In 1989, Chan worked on the concept of

phased array antennas fed by Rotman lens to improve the radar system performance

in a number of areas. In this paper the analysis of stripline and microstrip lens was

39

done. In 1992, Hansen designed the pattern control synthesis in which the antenna

array distribution and its associated patterns were designed for physical principals

based on the placement of zeros of the array polynomial. The control of side lobe

topology in pencil beam patterns, and the synthesis of various shapes of beamed

patterns were discussed. The main emphasis of linear and planar broadside apertures

and arrays using Dolph, Chebyshev and Tailor distributions. The design allowed

adjustable side lobes. In 2005, Weiss and Dahlstrom did the analysis of Rotman lens

at the Army Research Lab. They discussed the development of Rotman lens beam

formers over last 10 years. One successful version was cavity Rotman lens that served

as Azimuthal beam former for ESA, which supported multiple operations in Ka band.

Many patents related to Electronic warfare were developed at Raytheon.

At Raytheon, work was done on reducing the size of the lens by loading the parallel

plate region by dielectric material and the result can be seen in Figure 2.2. In 1970,

Two-dimensional Rotman lens stack was demonstrated. In 1973, Archer et al.,

proposed the idea of implementing Rotman lens using printed technologies to have a

low profile lens. The studies on microstrip/stripline Rotman lens increased.

Figure 2.2 The Gent Bootlace Configuration (Gent, 1957)

a. Lens deign by Rotman and Turner

The Rotman lens design approach by Rotman and Turner started way back in 1963.

This work starts with the review of the conventional Rotman lens antenna design. The

conventional design consisted of a parallel conducting plate, beam port, array port and

array of radiating elements. The transmission lines connect the inner lens contour and

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the radiating array elements as shown in the Figure 2.3. The lens feeds the linear

arrays. The original design had three focal points located on the beam contour which

tried to achieve zero phase errors. It was assumed that the parallel plate was filled

with the air. The shape of the beam contour was restrained to be circular. The values

of the scan angle produced by linear array were assumed to be similar to the

subtended beam port angle.

Figure 2.3 The Conventional Rotman Lens Configuration (Rotman and

Turner, 1963)

In this work, basic design equations of Rotman lens were determined for improving

scanning capability of the lens along with the reduction in beam to array port phase

error. This work still remains the benchmark for researchers in this area. The lens

parameters were defined as shown in Figure 2.4 .The focal arc locates the feeding

elements which are termed as the beam port or the beam contour. The inner lens

contour locates the receiving elements and the outer lens contour or the array port

locates the radiating array elements. For the beam contour design, three focal points

were used: two off-axis focal points (F1 & F2) which were symmetrical and one on-

axis focal point (G).

41

Figure 2.4 Rotman lens geometry (Rotman and Turner, 1963)

The shape of the focal arc was chosen as a circle. In order to derive design equations

for the lens contour, optical path-length equality and the lens geometry was used.

Still, there is scope to further reduce the path length error.

b. Symmetrical Lens approach by Shelton

Figure 2.5 Symmetrical Lens by Shelton (Shelton, 1978)

Shelton, in 1978 developed a symmetrical lens configuration as a modification to the

Rotman lens. The beam and the inner lens contours are identical and symmetrical with

respect to a symmetry plane as shown in Figure 2.5. The design equations of this type

of lens were more complicated than that of Rotman’s.

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c. Lens design approach by Katagi

In 1984, Katagi improvised the design equations given by Rotman and Turner by

adding a new variable which reduced the phase error on the aperture of the linear

array antenna as shown in Figure 2.6 below. This design parameter helped in reducing

the size of the lens. Katagi defined a subtended angle (α) corresponding to one of the

off-axis focal points as defined in Rotman’s model. However, the scan angle (β)

corresponding to the excitation from F1 is assumed to be different from the subtended

angle (α) though scan angles were assumed to be equal to the corresponding

Figure 2.6 Katagi’s design of the lens (Katagi et al., 1984)

subtended angles in Rotman’s design model. The new design variable provided a new

degree of freedom compared to the conventional design. Katagi also suggested that it

was not necessary to keep the shape of the beam contour as circular.

d. Design trades by Hansen

In 1991, Hansen used few basic design parameters like, focal angle, focal ratio, beam

angle to ray angle ratio, maximum beam angle, focal length and array element

spacing. One more parameter of ellipticity was introduced which assumed the beam

43

contour to be elliptical instead of circular. The parameter beam angle (subtended

angle) to ray angle (scan angle) ratio and ellipticity were additions to the parameters

of the conventional design. Hansen explained the effects of these design parameters

on the shape, phase and amplitude errors of a Rotman lens.

e. Other design approaches

The quadrufocal bootlace lens was first proposed to design three dimensional lens

BFN’s by Rao in 1982 and modification in the design was presented in 1983. In 2009,

non-focal lens design for reduction of phase error and improvement of scanning lens

was presented by Zaghloul and Dong. It evolved that the phase error in case of a

conventional Rotman lens could be reduced by adopting a non- focal design strategy

as proposed by Dong, Zaghloul and Rotman. In 2009, Uyguroglu et al. introduced a

new concept of feed curves such that the phase error was reduced. The method was

based on having three zero error positions on the radiating array for each feed curve

point. In the same year, Zalevsky et al., proposed improved design of photonic

Rotman lens which was capable of realizing a linear phase profile with a variable

slope, which could be obtained at the output of the lens for any possible position at

the input to the lens.

After 2009 various researchers are still trying to improve the design of the lens so as

to achieve a wide angle scanning with low loss and minimum phase error. Use of

various existing optimization techniques, namely GA, PSO, simulated annealing, etc.

can come handy in improving the performance of the lens (Weile and Michielssen,

1997; Goldberg, 1989; Liang et. al., 2005; Venkatraman and Yen, 2005).

In 2012, Christie et al. proposed a new type of broadband retro directive array, which

had been constructed using a microstrip Rotman lens. Automatic tracking of targets

was obtained by exploiting the conjugate phase response of the BFN, which was

exhibited when the input ports were terminated with either open or short circuits.

Singhal et al. designed Rotman lens for wide area scanning and compared the lens

with the various other existing designs. He also proposed the fact that the height of the

array and feed contours must be same for maximum power transfer and better lens

44

performance. Effect on shape of beam and array contour by variation in scanning

angle, focal ratio and element spacing were prime issues of his work.

In 2012, Rajabalian and Zakeri presented the concept of non-focal microwave lens

design with optimization of phase errors and amplitude performance. In the same year

Hung-I Lin and Wen proposed the array antenna which consisted of a Rotman lens

and four element antennas. In 2013, Zongxin et al. developed a compact printable

multibeam antenna array. The antenna system was composed of a printed Rotman

lens and an antipodal dual elliptically tapered slot antenna array; both the components

were studied, respectively, at first, and then integrated on a single printed circuit

board to make up the integrated unit of the multibeam antenna array. In the same year

Yunhua Zhang et al. came up with the concept of side lobe modulation scrambling

transmitter using Fourier Rotman lens, wherein they developed a means for

scrambling the digital modulation content in the side lobes of a radio transmission

from a steerable antenna array. In 2013; Fonseca developed an improved design

method for two-dimensional Rotman lens with reduced phase-aberrations. This paper

introduced an improved design method supported by analytical formulas defining the

focal curve of a Rotman lens with reduced worst-case phase-aberrations. In the same

year, Joo-Rae Park and Dong Chung Park proposed a refocusing method for

minimizing the phase errors of Rotman lenses. The method was based on finding the

optimal α, F, and γ minimizing the phase errors by moving off-axis focal points along

a beam curve. It ensured the additional phase error reduction without significant

changes of beam and array curve shapes. In 2014; Jaeheung Kim et al. presented their

work on asymmetric ground Rotman lens. A new design of a Rotman lens was

proposed to accommodate a whole beamforming system by providing separate ground

layers for antennas and circuits. The lens had three dielectric layers and four metallic

layers. In the same year he presented a new approach to analyze a Rotman lens for

imaging applications. The Optical Transfer Function (OTF) was used to analyze the

imaging capability of a Rotman lens. As a result, it was found that the cutoff

frequency corresponds to the array size in λ. In 2014; Rusch Christian et al. designed

the 2D-beam-forming device consisting of a Rotman-lens and a holographic antenna.

A lot of design performances get affected by varying different lens parameters. In

view of all the above mentioned facts by various researchers it is quite clear that still

45

there was a scope of improvement in the performance of the lens by applying

optimization techniques in electromagnetics.

2.9 GAP IN THE STUDY

The growing complexity of the overall communication system has motivated the

need for the antenna which is capable of forming multiple simultaneous beams with

reduced path length error. The performance of the system could be limited due to

inefficient lens design. It is based on true time delay (TTD) which means that it is

not dependent on the frequency. This ultimately removes the need of phase shifters,

which are used to steer the beam over wide range angles. After thorough literature

survey it emerged that still lot of work can be done to improve the design of the lens

so as to achieve a wide angle scanning and minimum phase error. The determination

of the main optical parameters of the lens geometry i.e. the positions of the beam

port, the receiving ports and the length of the transmission line has been very

complex. These parameters are the results of many other interdependent design

parameters that affect the phase error performance. These are some of the issues

which can be investigated and simplified further. It has been perceived that still

there is a lot of scope to analyze the effects of various design parameters i.e. the

focal ratio and the element spacing on the performance parameters of the lens like

path length error, array factor, return loss, and insertion loss. To further ameliorate

the scanning angle and the path length error or the phase error of the lens antenna,

few new design parameters such as beam to array phase error and beam to array

coupling amplitude may be introduced and investigated along with the existing

parameters such as return loss, insertion loss and array factor to enhance the overall

performance of the lens. The effect of these new design variables have been rarely

reported in the literature earlier.

From the literature survey, it transpired that, by introducing a new design variable

and by using PSO technique, maximum scanning of 450

could be achieved with

reduced phase error. It appeared that by applying GA and PSO techniques, the

scanning angle can be further improved by reducing phase error and without

distorting the shape of the lens. It emerged from the study that the change of shape

46

and substrate of the lens could also affect various performance parameters of the lens

like array factor, beam to array port phase error, beam to array coupling amplitude

and insertion loss. The work related to the same has been rarely reported in the

survey.

2.10 CONCLUSIONS

Rotman lens has proved to be a popular multiple beam-forming technologies, due to

its simplicity and good performance. The above chapter gives the details of the

various developmental stages in the microwave lens and various BFN. From the

literature survey, it has been concluded that a lot of work has been done in the

designing of the lens and enhancing its performance by working on various

parameters. Different design techniques have been used to attain the desired

performance of the lens.

It has been perceived that the individual contribution of main design parameters of the

lens like path length error or the phase error, return loss, insertion loss, side lobes

levels and focal length on the performance of the lens has been reported earlier, but

the combined effect of all the parameters taken together on the performance of the

lens is rarely available in the literature. Moreover, it has also been observed that the

effect of many important lens parameters like beam to array coupling amplitude and

beam to array phase error have been hardly considered for the design of the Rotman

lens. The effect of design parameters such as element spacing and focal ratio on the

performance of the lens has been rarely considered. Earlier, PSO technique had been

used as the optimization tool for achieving maximum scanning angle and reducing

phase error. There are other optimization mechanisms available such as GA which

can be utilized to further improve the parameters of the lens for better performance.

The effect of change of shape of the lens and the substrate in the cavity may also

affect the performance of the lens. This needs to be further investigated.

The next chapter describes the conventional Rotman lens. It covers the development

and investigation of the basic design equations of the lens and determination of phase

error.