# Active Reflectors: Possible Solutions Based on Reflectarrays and Fresnel Reflectors

Authors: Lorena Cabria; José Ángel García; Julio Gutiérrez-Ríos; Antonio Tazón; Juan Vassal'lo
Journal: International Journal of Antennas and Propagation
 (2009)

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## Abstract

An overview about some of the recent Spanish developments on active reflectors is presented. In the first part, a novel beamsteering active reflectarray is deeply studied. It is based on implementing in each elementary radiator an IQ modulator structure, in which amplitude and phase control of the scattered field is achieved. Finally, a special effort is made in offering solutions to overcome the active antenna integration problems. In the second part, the active concept is firstly extended to Fresnel reflectors. Thanks to the development of a proper simulator, this special structure can be easily analysed. This simulator allows the study of performance of this kind of reflectors and, applying evolutionary algorithms, to find optimal configurations of reflector in accordance with the given specifications for the conformal radiation pattern.


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## Body

## 1. Introduction

Nowadays, the development of antennas with
reconfigurable beam pattern capabilities represents one of the keys issues for
the future of the telecommunications and remote sensing applications.
Considering this aspect, this paper proposes two different reconfigurable
reflectors: an active reflectarray and a Fresnel reflector. The reflectarray is
formed by resonant microstrip patches coupled to an active circuit which
provides the amplitude and phase control of the reflected signal. The Fresnel
reflector is based on the use of small reflecting cells, integrating each of
them a mechanical control to regulate its position with respect to a reference
one.A reflectarray is a type of antenna that
combines the best features of conventional reflector with those of the phased
printed arrays. In this structure a horn or small antenna array illuminates a
planar array of microstrip radiators, which, by using suitable phasing
circuits, converts an incident spherical wave into a plane wave, collimating
the reflected field in a desired direction [1]. Their low cost, flatness, and
easiness to install and manufacture convert these structures into ideal
solutions to modern communication systems [2]. Moreover, spatial signal
distribution avoids the complexity and losses associated to the microstrip
feeding distribution network.The possibility of employing active
antennas as reflectarray cells offers additional advantages derived from their
power combining features. In this sense, amplifying functions have been already
added in individually phased active antenna elements [3]. Nevertheless, only a
few works have considered the possibility of varying the scattered field phase
from each element, achieving beam steering capabilities [4].The control over the capacitance, obtained
in [4] through the use of a varactor diode, has been also proposed for the
design of reconfigurable reflectarrays with scanning capability, either
serially connecting two halves of a microstrip patch [5] or phase tuning a high-impedance surface [6].  MEMS are also
standing as a promising solution for the design of tuneable reflectarrays,
mainly in terms of linearity, power consumption, losses, and size, as suggested
from recent results [7].Despite all their advantages, some problems
have to be faced when designing or implementing active reflectarrays. As a way
of illustration, if high gain amplifying stages were employed between the
orthogonal feeds of a patch, a poor out of band isolation between feeds might
lead to amplifier oscillations. In this type of solutions, attention should be
put to the radiator isolation characteristic versus frequency as well as to
the detection of instabilities through the use of linear [8] but also nonlinear
analysis techniques. In transmitting reflectarrays, especially when power
amplifiers are integrated, especial attention should be put to thermal aspects.
The available heat sink capability for power dissipation would impose a limit
to the device output power level. The introduction of novel highly efficient
technologies, as the case of GaN HEMTs, or the application of emerging
transmitting concepts, could help overcoming this power handling limit.With respect to Fresnel reflectors, as it
is well-known, their surface efficiency cannot be greater than the provided by
a parabolic reflector [9–11]. Nevertheless, they can offer advantages
that a parabola cannot provide, as for example, the feeder of a Fresnel
reflector can a change of position, out the focal point, without any important
variation on performance.This property is used to develop an active
Fresnel reflector, placing a distribution of reflecting cells over a flat
surface. Each one of these cells is coupled to an active mechanism which allows
a change of position with respect to the feeder. So, any distribution of
Fresnel zones can be configured over the whole reflecting surface.The inclusion of active elements on these
kinds of antennas (reflectarrays and Fresnel reflectors) provides a control over
the antenna radiation pattern in the reflecting surface. So, the designer can
work with a new freedom degree if this possibility is added to the classical
control on the feeder.


## 2. Active
Reflectarray Development

In this paper,
an active reflectarray with attractive capability of varying the pencil-beam or
shaped beam radiation pattern is presented. Based on the vector sum method, the
amplitude and phase of the reradiated field from each elementary radiator is
controlled by means of applying a DC voltage through the IF port of two double
balanced diode mixers in an IQ configuration. This kind of structure can
provide a new freedom degree, because the steering can be found from a control
of active circuits in the feeder (as in a not very old manner) and also be
included in the reflector surface.By means of an
accurate adjustment of each element phase shift, it is possible not only to
convert the spherical wave into plane one but also to steer the main beam. In
this sense, in order to demonstrate the proposed radiating architecture
potentialities, different radiation patterns have been measured.As the idea is
to put in evidence advantages and drawbacks of this kind of antenna, a
laboratory demonstrator was designed, manufactured, and measured. To optimize
time and efforts, the selected reflectarray was designed to have a planar
configuration of4×2 radiating elements.


### 2.1. Radiating Element

An aperture coupled microstrip patch [12]
with two orthogonal feeds has been selected as a reflectarray elementary radiator.
One of its ports is employed to receive the signal from the feeder while the
other is used to retransmit it with the amplitude and phase selected in the
vector summing unit. Therefore,
the square patch has two microstrip feeding inputs placed at perpendicular
sides, exciting the TM01 and TM10 orthogonal modes for the same resonating
frequency, aimed to the simultaneous reception and retransmission of the microwave
signals using orthogonal polarizations. The dual feeding provides a reasonable
isolation between its two ports, which is an important characteristic to be
achieved when active elements are incorporated. The gain of the active path,
from reception to retransmission, is limited by the isolation between both
input ports, achieving an unstable state when such condition is not fulfillled.Figure1 illustrates the designed square
microstrip patch. The active circuit and the feed microstrip lines have been
printed in substrate ARLON 25N with εr =  3.38 and thickness of 30 miles
(0.762 mm).
In order to improve the gain and the bandwidth, the air is employed as radiator
substrate. Consequently, an auxiliary layer is needed to print the patch on it.
The working frequency band, around 5.8 GHz in our particular application,
determines the dimensions.Figure 1
Top and side view of the designed square microstrip patch.A commercial electromagnetic simulator (Ansoft
Ensemble) has been employed to design and analyze the structure. In Figure2,
the simulated and measured input matching and isolation between both ports are
shown.Figure 2
Measured and simulated input matching and isolation.


### 2.2. Amplitude and Phase Control Unit

Figure3
shows a scheme of the amplitude/phase control unit implemented in each elementary
radiator. The received signal is equally divided through a 90° hybrid coupler
exciting the LO ports of a pair of double balanced diode mixers. By proper
adjustment of the DC voltage, applied in the IF port, it is possible to vary
the amplitude and to switch the phase, between two values with a 180° shift
(depending on the DC sign) of the RF signals. Finally, these output signals
are combined employing a Wilkinson circuit achieving a complete (360°) phase
control range.Figure 3
Amplitude/phase control unit used in each reflectarray
elementary radiator.In order to
clarify this behavior, a summing scheme can be used. The output signal is the
resultant vector obtained through a sum of two perpendicular variable vectors.
Consequently, using a pair of conveniently selected voltage values, the
magnitude and phase of the resultant vector may be controlled in a complete
phase range.


### 2.3. Integration of the Active Circuits on the Radiating Element

The radiating element and the
amplitude/phase control circuitry were integrated in the same PCB employing the (Active Integrated Antenna (AIA)) concept to minimize the cable and feeding line
losses in a similar way to [13].In order to compensate the associated
attenuation of the IQ control circuit two commercial amplifiers were added in
each unit. In Figure4, a clarifying schematic as well as a detailed photograph of the active elementary
radiating unit can be seen.(a) Schematic  and (b) photograph of the reflectarray unit.
(a)(b)In the photograph some, parts of the
reflectarray unit have been highlighted. The MBA-671 mixers from Minicircuits,
and the NBB 400 amplifiers from RF Microdevices constitute the active parts
with a power consumption of 665 mW. In the IQ structure, the input 90° hybrid
coupler is a high-quality and small size commercial circuit from Anaren, while
the combination of the output signals of each mixer was done through a
microstrip Wilkinson circuit specifically designed for it. To accurately adjust
the phase/gain of each circuit, different SMA connectors were added to take
samples of the signal in different parts.The active
control circuit was measured independently of the patch obtaining a maximum
gain of 12 dB. Complete phase range was also measured for different gains.Once the structure was measured with the SMA
connectors and its correct performance verified, the complete radiating
structure was probed appearing undesired oscillating frequencies around 5 GHz.
The problem came associated to the poor isolation between the antenna ports at
this band of frequencies, comparable to the gain of the active path, as it  has
been highlighted in Figure2. Consequently, it was necessary to eliminate this
unpleasant effect. Taking into account the limited space available in the
reflectarray unit, a stub was added to reduce the coupling in the previously
mentioned band, as it can be observed in Figure 4.


### 2.4. Active Reflectarray Implementation

Figure5 shows the layout of the reflectarray.
In such antenna, the selected feeder is an aperture-coupled microstrip patch
equal to the reflectarray radiating elements, which transmits a signal in the
working band with vertical polarization. The reflectarray active circuits, not
included in this illustration in order to clarify the whole radiating
structure, were inserted in the feeding layer.Figure 5
Layout of reflectarray, feeder included.In order to avoid feed blockage-an offset
feeding configuration was used, placing the feeder at 200 mm down from the
center and 55 mm out from the array.A photograph of the reflectarray feed layer
is shown in Figure6.  As it has been
previously commented, each unit has two varying bias voltages to control the
mixers and one fixed voltage to supply the amplifiers.Figure 6
Reflectarray feeding layer.Each element demands a phase shift value as
a function of its position with respect to the feeder to convert the spherical
incident wave to a planar one. There are different ways to achieve the required
phase shift per cell: in [14] equal size microstrip patches are employed with
passive coupled delay lines of different lengths, while in [15] the phase of
the scattered field is controlled by means of the patch size. Although these
methods permit to assure the correct antenna performance in a higher bandwidth,
the proposed system takes advantage of the total phase control in each element
provided by the active circuit. Additionally, the possibility of controlling the
phase shift between microstrip patches allows the change of the main beam
direction.In such case, the field phase in each unit
is calibrated independently to fulfill, (1) [15, 16]:(1)ϕi=k0⋅(Ri−r˜i⋅r˜0), where: Ri  is the distance from the feeder
phase center to the element, r˜i is the vector from the array center to the element, and r˜0  is the unit vector in the main beam
direction.In order to
vary the reflectarray beam pointing, the required phase shift values per
radiating unit have to be recalculated following (1).


### 2.5. Measurement Results

A specific test setup was implemented in
an anechoic chamber to measure the described antenna. In such scenario, a
perfect calibrated horn antenna was employed in reception to measure the
reflectarray response, assuring a far field distance between them. As it has
been commented before, the radiation pattern phase evolution for each unit was
calibrated in the main direction for different gains.  In this way, it was possible to select those
biasing points per unit to fulfill (1) for different pointing directions.Due to the
huge number of different controlling bias voltages and in order to generate a
portable and compactness radiating structure, a special bias control circuitry
was also implemented. The required voltages per unit, obtained in a previous
step, were then introduced in a hexadecimal table in the PC as a function of
the required gain and phase values. By means of an RS232 interface, the PC and
the control board are connected, being able to provide the required bias to
each mixer and amplifier. A rear view of the manufactured prototype can be seen
in Figure7.Figure 7
Rear view of the final manufactured prototype.Finally,
the far field radiation pattern of the reflectarray was measured for three main
pointing directions (0°, 10°, −10°). The individual amplitude control would
also permit to conform different amplitude distributions if desired. In Figures
8, 9, and 10, measurements of normalized radiation patterns for a uniform
amplitude distribution have been represented. A comparative study between the
resultant measurements and the calculated array factor of the retransmitted
patterns has been done and illustrated in these figures.Figure 8
Measured and calculated reflectarray radiation pattern, pointing to
0°.Figure 9
Measured and calculated reflectarray radiation pattern, pointing to −10°.Figure 10
Measured and calculated reflectarray radiation pattern, pointing
to 10°.As it can be seen, the similarity among the
obtained results and the calculated ones demonstrates the potentiality of the
proposed architecture.


### 2.6. Some Consequences of the Developed Prototype

As it can be seen in the photograph of the
demonstrator, one of the drawbacks of the implementation of the active elements
on the reflecting surface is the positioning of the control and feeding DC
circuitry.In a reflectarray of small number of
elements (only eight radiators), the drawback can be easily solved as it can be
seen in the photograph of the developed demonstrator. But in the case of
reflectarrays with high number of elements, it is necessary to achieve other
kinds of solutions.There are several possibilities now under
development, for example, by means of a laser link between each module with a
central unit or by using the DC circuitry as link of the control signal at low
RF. Obviously, this solution has a better implementation by using a modular
design.Nevertheless, this restriction can be
avoided if radiating elements are feeding from its radiating face. In this
configuration, active circuits can be placed over the radiating face, and the
control and DC circuitry can cross the microstrip patch through a metallic post
placed on its center, because this central part of the radiator has a cero per
impedance.Then, the distribution circuitry of control
and DC can be easily manufactured on a multilayer substrate and placed behind
of the radiator microstrip ground plane. Figure11 shows this solution.Figure 11
Structural concept to integrate DC and control circuit on active
reflectarrays.


## 2.1. Radiating Element

An aperture coupled microstrip patch [12]
with two orthogonal feeds has been selected as a reflectarray elementary radiator.
One of its ports is employed to receive the signal from the feeder while the
other is used to retransmit it with the amplitude and phase selected in the
vector summing unit. Therefore,
the square patch has two microstrip feeding inputs placed at perpendicular
sides, exciting the TM01 and TM10 orthogonal modes for the same resonating
frequency, aimed to the simultaneous reception and retransmission of the microwave
signals using orthogonal polarizations. The dual feeding provides a reasonable
isolation between its two ports, which is an important characteristic to be
achieved when active elements are incorporated. The gain of the active path,
from reception to retransmission, is limited by the isolation between both
input ports, achieving an unstable state when such condition is not fulfillled.Figure1 illustrates the designed square
microstrip patch. The active circuit and the feed microstrip lines have been
printed in substrate ARLON 25N with εr =  3.38 and thickness of 30 miles
(0.762 mm).
In order to improve the gain and the bandwidth, the air is employed as radiator
substrate. Consequently, an auxiliary layer is needed to print the patch on it.
The working frequency band, around 5.8 GHz in our particular application,
determines the dimensions.Figure 1
Top and side view of the designed square microstrip patch.A commercial electromagnetic simulator (Ansoft
Ensemble) has been employed to design and analyze the structure. In Figure2,
the simulated and measured input matching and isolation between both ports are
shown.Figure 2
Measured and simulated input matching and isolation.


## 2.2. Amplitude and Phase Control Unit

Figure3
shows a scheme of the amplitude/phase control unit implemented in each elementary
radiator. The received signal is equally divided through a 90° hybrid coupler
exciting the LO ports of a pair of double balanced diode mixers. By proper
adjustment of the DC voltage, applied in the IF port, it is possible to vary
the amplitude and to switch the phase, between two values with a 180° shift
(depending on the DC sign) of the RF signals. Finally, these output signals
are combined employing a Wilkinson circuit achieving a complete (360°) phase
control range.Figure 3
Amplitude/phase control unit used in each reflectarray
elementary radiator.In order to
clarify this behavior, a summing scheme can be used. The output signal is the
resultant vector obtained through a sum of two perpendicular variable vectors.
Consequently, using a pair of conveniently selected voltage values, the
magnitude and phase of the resultant vector may be controlled in a complete
phase range.


## 2.3. Integration of the Active Circuits on the Radiating Element

The radiating element and the
amplitude/phase control circuitry were integrated in the same PCB employing the (Active Integrated Antenna (AIA)) concept to minimize the cable and feeding line
losses in a similar way to [13].In order to compensate the associated
attenuation of the IQ control circuit two commercial amplifiers were added in
each unit. In Figure4, a clarifying schematic as well as a detailed photograph of the active elementary
radiating unit can be seen.(a) Schematic  and (b) photograph of the reflectarray unit.
(a)(b)In the photograph some, parts of the
reflectarray unit have been highlighted. The MBA-671 mixers from Minicircuits,
and the NBB 400 amplifiers from RF Microdevices constitute the active parts
with a power consumption of 665 mW. In the IQ structure, the input 90° hybrid
coupler is a high-quality and small size commercial circuit from Anaren, while
the combination of the output signals of each mixer was done through a
microstrip Wilkinson circuit specifically designed for it. To accurately adjust
the phase/gain of each circuit, different SMA connectors were added to take
samples of the signal in different parts.The active
control circuit was measured independently of the patch obtaining a maximum
gain of 12 dB. Complete phase range was also measured for different gains.Once the structure was measured with the SMA
connectors and its correct performance verified, the complete radiating
structure was probed appearing undesired oscillating frequencies around 5 GHz.
The problem came associated to the poor isolation between the antenna ports at
this band of frequencies, comparable to the gain of the active path, as it  has
been highlighted in Figure2. Consequently, it was necessary to eliminate this
unpleasant effect. Taking into account the limited space available in the
reflectarray unit, a stub was added to reduce the coupling in the previously
mentioned band, as it can be observed in Figure 4.


## 2.4. Active Reflectarray Implementation

Figure5 shows the layout of the reflectarray.
In such antenna, the selected feeder is an aperture-coupled microstrip patch
equal to the reflectarray radiating elements, which transmits a signal in the
working band with vertical polarization. The reflectarray active circuits, not
included in this illustration in order to clarify the whole radiating
structure, were inserted in the feeding layer.Figure 5
Layout of reflectarray, feeder included.In order to avoid feed blockage-an offset
feeding configuration was used, placing the feeder at 200 mm down from the
center and 55 mm out from the array.A photograph of the reflectarray feed layer
is shown in Figure6.  As it has been
previously commented, each unit has two varying bias voltages to control the
mixers and one fixed voltage to supply the amplifiers.Figure 6
Reflectarray feeding layer.Each element demands a phase shift value as
a function of its position with respect to the feeder to convert the spherical
incident wave to a planar one. There are different ways to achieve the required
phase shift per cell: in [14] equal size microstrip patches are employed with
passive coupled delay lines of different lengths, while in [15] the phase of
the scattered field is controlled by means of the patch size. Although these
methods permit to assure the correct antenna performance in a higher bandwidth,
the proposed system takes advantage of the total phase control in each element
provided by the active circuit. Additionally, the possibility of controlling the
phase shift between microstrip patches allows the change of the main beam
direction.In such case, the field phase in each unit
is calibrated independently to fulfill, (1) [15, 16]:(1)ϕi=k0⋅(Ri−r˜i⋅r˜0), where: Ri  is the distance from the feeder
phase center to the element, r˜i is the vector from the array center to the element, and r˜0  is the unit vector in the main beam
direction.In order to
vary the reflectarray beam pointing, the required phase shift values per
radiating unit have to be recalculated following (1).


## 2.5. Measurement Results

A specific test setup was implemented in
an anechoic chamber to measure the described antenna. In such scenario, a
perfect calibrated horn antenna was employed in reception to measure the
reflectarray response, assuring a far field distance between them. As it has
been commented before, the radiation pattern phase evolution for each unit was
calibrated in the main direction for different gains.  In this way, it was possible to select those
biasing points per unit to fulfill (1) for different pointing directions.Due to the
huge number of different controlling bias voltages and in order to generate a
portable and compactness radiating structure, a special bias control circuitry
was also implemented. The required voltages per unit, obtained in a previous
step, were then introduced in a hexadecimal table in the PC as a function of
the required gain and phase values. By means of an RS232 interface, the PC and
the control board are connected, being able to provide the required bias to
each mixer and amplifier. A rear view of the manufactured prototype can be seen
in Figure7.Figure 7
Rear view of the final manufactured prototype.Finally,
the far field radiation pattern of the reflectarray was measured for three main
pointing directions (0°, 10°, −10°). The individual amplitude control would
also permit to conform different amplitude distributions if desired. In Figures
8, 9, and 10, measurements of normalized radiation patterns for a uniform
amplitude distribution have been represented. A comparative study between the
resultant measurements and the calculated array factor of the retransmitted
patterns has been done and illustrated in these figures.Figure 8
Measured and calculated reflectarray radiation pattern, pointing to
0°.Figure 9
Measured and calculated reflectarray radiation pattern, pointing to −10°.Figure 10
Measured and calculated reflectarray radiation pattern, pointing
to 10°.As it can be seen, the similarity among the
obtained results and the calculated ones demonstrates the potentiality of the
proposed architecture.


## 2.6. Some Consequences of the Developed Prototype

As it can be seen in the photograph of the
demonstrator, one of the drawbacks of the implementation of the active elements
on the reflecting surface is the positioning of the control and feeding DC
circuitry.In a reflectarray of small number of
elements (only eight radiators), the drawback can be easily solved as it can be
seen in the photograph of the developed demonstrator. But in the case of
reflectarrays with high number of elements, it is necessary to achieve other
kinds of solutions.There are several possibilities now under
development, for example, by means of a laser link between each module with a
central unit or by using the DC circuitry as link of the control signal at low
RF. Obviously, this solution has a better implementation by using a modular
design.Nevertheless, this restriction can be
avoided if radiating elements are feeding from its radiating face. In this
configuration, active circuits can be placed over the radiating face, and the
control and DC circuitry can cross the microstrip patch through a metallic post
placed on its center, because this central part of the radiator has a cero per
impedance.Then, the distribution circuitry of control
and DC can be easily manufactured on a multilayer substrate and placed behind
of the radiator microstrip ground plane. Figure11 shows this solution.Figure 11
Structural concept to integrate DC and control circuit on active
reflectarrays.


## 3. Active Fresnel Reflector Development

Fresnel reflectors having arbitrary main
beam transversal section, by means of conformed Fresnel zones, were presented in
[17]. This possibility allows the design of a new concept on active reflectors,
based on squared reflecting cells, each one coupled to a mechanical actuator.
This configuration provides a degree of freedom about the position of each cell
in the z-axis to be able to conform a
good approximation to any desired Fresnel reflector geometry.The idea that is explained in this
paragraph is based on a flat structure formed by small reflectors, whose
position is electronically controlled by means of mechanical actuators. So, a
flat reflector with this configuration can work with any Fresnel distribution.
The lattice of small reflecting cells is electronically controlled to provide
any Fresnel distribution over the reflector surface and then to have a real control
of the radiation pattern.The number of
mechanical actuators can be a problem of manufacturing, weight, and cost of the
final prototype, and consequently it can constitute a limit for the approach of
different radiation patterns to be generated. Nevertheless, in applications
where the number of desired beams is small and previously known, the cell size
can be optimized in order to reduce the number of actuators. The consequence is
a final prototype of more easy manufacturing process and lower weight and cost.Reflectors
having Fresnel zones with axial symmetry have been analyzed in [18]. Results
show that the behavior can be optimized  depending of special parameter of
this kind of reflectors, as for example, the number of levels of reflecting Fresnel
zones. So, a specific simulator for Fresnel reflectors of squared cells has
been developed, and its results are to be commented below.


### 3.1. Active Fresnel Reflector

#### 3.1.1. Electrical Concept

The radiation pattern
of a reflected signal can be modified by changes in the geometrical
characteristics of the reflecting surface. As it is known, perturbations on
parabolic surfaces allow any desired 3 dB transversal section in the main beam,
being actually the best solution applied in geosatellite antennas for communication
links.This concept was
translated in [17] to the Fresnel reflector technology, and a general behavior
of Fresnel reflectors can be seen in [18], being the case of reflectors with 2
or 3 levels as the more interesting ones from performance and manufacturing
point of view.A Fresnel reflector design with 144
actuators of two positions, controlling an array of12×12 reflecting cells, is
to be described in this paper. The antenna has been designed to provide a beam
scanning in the principal plane direction, having the main beam at the symmetric
direction to the focal position of the feeder from the central point of
reflecting surface (see Figure 12).Figure 12
Geometry of the synthesized Fresnel reflector configuration.The selected working frequency was 18.75 GHz, which must be in accordance with the distance separation among levels, which
is provided by the selected actuator. The cell size was selected taking into
account the supposed application of the example, in order to avoid grating
lobes and the area to be covered by the scanning. The desired beam scanning
zone is between 0° and −20°, in the
principal plane, which includes the focal point.Once the geometry of the reference Fresnel
configuration is determined, the movement of the synthesized geometry over the
reflector surface will provide the beam scanning. So, the Fresnel configuration
of reference must be synthesized over a surface bigger than that of the
reflector. This allows the changes as it is shown in Figure13, where there are
three reflector configurations for different appointments.Reflector configuration for different positions of the Fresnel
configuration.
(a)(b)(c)It is obvious
that in this structural concept, the feeder is always in the same position. The
unique change on the antenna, which provides the desired scanning, is the
change of the position of the Fresnel configuration on the reflector surface,
as it can be seen in Figure13. Figure 14 shows the superposition of simulated
array factors of the Fresnel configurations to cover the selected scanning
area. The evolution of the radiation pattern is shown in Figure 14, and
consequently it can be understood that any reflected direction can be obtained
by placing the Fresnel configuration at the adequate place over the reflector
surface.Figure 14
Superposition of simulated array factors, which are obtained by
movement of the synthesized Fresnel distribution.


#### 3.1.2. Mechanical Concept

To allow the change of Fresnel level of any reflecting cell, each
Fresnel level is associated to a different position of the reflecting surface
of the cell, thinking that this different position is referred to the
perpendicular direction to the reflector surface.To provide this position change, a
commercial actuator (solenoids, series 45B) was selected from the web page of
RS AMIDATA. Figure15 shows the geometry data sheet.Figure 15
Actuator data sheet.As it can be seen in
Figure16, the actuator is placed under each reflecting cell, and it allows a
displacement of the reflecting cell of 4.5 mm, which is electronically controlled.
This figure shows two complete active reflecting cells, at both states: 0 and 1,  which corresponds to both
Fresnel levels. The actuator is placed at the position 1 when there is a voltage of 6 V at the inputs of actuator terminal, and it is placed at the position 0 when the voltage is 0 V. The
actuator works over the reflecting cell as it can be seen in Figure 16.Figure 16
Views of two mechanical actuators, working over its respective
reflecting cell, at both Fresnel levels: 0 and 1.When the aim is to
implement reconfigurable Fresnel reflectors with more than two levels, the
actuator should be different form that commercially available. However there is
not a great technological problem, including a continuous shift solution. We
can think about a little screw pin moved by a small electrical motor, step-by-step or continuous type.Figures17 and 18 show,
a view of the whole Active Fresnel Reflector, respectively with the Fresnel
configuration of Figures 13(b) and 12. The case that is shown in Figure 17
corresponds to the synthesized Fresnel configuration which is centered on the
surface of the reflector.Figure 17
View of the active Fresnel reflector with the configuration of
Figure13(b).Figure 18
View of the active Fresnel reflector with the configuration of
Figure12.


### 3.2. Simulator of Fresnel Reflectors

Performance of Fresnel reflectors depends
on the number of levels implemented but the result obtained with a three
levels implementation is very reasonable. As a matter of fact, gain of a three
levels reflector is usually about 1.5 dB under a same aperture and same focus
paraboloid. However Fresnel reflectors have several important advantages: first,
the fact being smaller in terms of occupied room. Second, the deployment system
is easier for them. Third, the possibility of combining several Fresnel
distributions in a same reflector surface to get multibeam radiation patterns.
Finally, the manufacturing process is very easy and very cheap by means of
photoetched procedures.Fresnel reflectors performance has been
widely studied by means of a computer simulator developed by ourselves which is
specially adequate and flexible for reflectors with circular symmetry [19–21]. We also have developed a methodology to optimize shaping of Fresnel
reflectors [22, 23].Now, a new simulator has been specifically developed for reconfigurable
reflectors composed by squared elements, with any number of levels or
continuous shifting. In order to get a good efficiency,  we have extracted the
response of a squared element with uniform illumination. In this way, the response
of the reflector is the superposition of the responses of all elements,
once situated each one in its location and level. The assumption that resonance
effects and boundary conditions in edges of squared elements are small enough
to be neglected is very reasonable because they affect mainly to radiation far
from the main lobes. Besides, there are structural media to minimize those
effects, as we will try to prove in the future when physical experimentation
becomes possible.On the other hand, the assumption of
uniform illumination in the whole area of each conformable element could  not be too much closed to the real case; we use a grid to decompose the surface of the
reflecting elements in smaller squares (rectangles in general terms) to the end
of getting simulation elements small enough to be considered, each one as
uniformly illuminated.Although the
normal case is to have squared elements, we are going to consider rectangular
ones for giving more generality and flexibility to the simulator.


#### 3.2.1. Rectangular Reflecting Cell

A rectangular surface is used as a reference. The center of this
element will be located at(xo,yo,zo)=(0,0,0) as shown in Figure 19.
In this case, the function of luminance of a rectangle
with dimensions a×h can be represented by the following expression (2) [24, 25]:(2)U(x,y)=f(x,y)⋅Π(xa)⋅Π(yh), being f(x,y)
the function of luminance inside the rectangle, and Π(u/b) a pulse in axis u of
amplitude 1 between −b/2 and b/2. But,
if luminance is uniform of amplitude A,
function (2) is reduced to(3)U(xo,yo)=A⋅Π(xoa)⋅Π(yoh). In order to get
the far field radiation pattern of the rectangular element, we will use the
Fresnel-Kirchhoff diffraction formula [24] as follows:(4)U(xi,yi)=1jλ∬exp(jkr)r⋅U(xo,yo)⋅dxodyo. According to
Figure 19,  the distance r of an
elementary emitter in xo,yo to an arbitrary far field
point in a plane xi,yi,
parallel to the plane of the radiating element will be calculated as follows:(5)r2=zi2+(xi−xo)2+(yi−yo)2,zi2≫(xi−xo)2+(yi−yo)2,r=zi⋅1+(xi−xo)2+(yi−yo)2zi2≅zi(1+(xi−xo)2+(yi−yo)22⋅zi2),r≅zixi2+yi22⋅zi2−xi⋅xo+yi⋅yozi. Then, introducing this expression of r and the luminance in (4) in the
Fresnel-Kirchhoff diffraction formula in (5), we get
the far field (Fraunhofer space) due to a rectangular element as follows:(6)U(xi,yi)=a⋅hjλ⋅ziexp[jk(zi+(xi2+yi2)2⋅zi)]⋅sinc(axiλ⋅zi)⋅sinc(hyiλ⋅zi).Figure 19
Geometry and notation of the radiating cell.


#### 3.2.2. Fresnel Reflector Conformed by Squared Reflecting Cells

Once developed a method to get the optimal
shape for a flat Fresnel reflector [22], the approaching procedure to obtain a
reflector conformed by squared reflecting cells will consist of setting every
squared cell at the same level that had its central point in the ideal Fresnel
reflector.As an example, Figure20 shows the layout
of a reflector configured by means of a reconfigurable reflector of 480×480 mm
and 36×36 elements. The shape of the original reflector has been indicated by circles
in the same figure. The reflector has been designed at three levels (each level
a different color); the focal distance is 500 mm and has been tuned
to 18.75 GHz.Figure 20
Fresnel reflector of square cells and 3 levels.It is easy to
see in Figure20 that there is a misalignment between the optimal shape of the
Fresnel reflector and that conformed by squares. Of course, increasing the density
of elements, they become smaller, and the approximation to the ideal Fresnel
reflector, as well as the efficiency of the reflector, is better. However, the
reconfigurable system would be more complex and expensive. We will describe
below the procedure to get the fair dimensions.


#### 3.2.3. Grid and Feeding Distribution for Simulation

Simulation process has nothing to do with
the configuration of the reflector. Any configuration will be simulated by
iteratively applying formula (6) for each one of the squared (or rectangular if
it were the case) elements once moved to the position x,y,z relative to each point of the de radiation pattern one want to find.This fact implies that we must know the
location, the level (z), and the
luminance A of every element, and also
that we can suppose that squares are uniformly illuminated. The location and
shifting of the elements are well-known parameters. However, the fact of being
correct or not to, consider uniform illumination on the surface of the elements,
depends on the size of the facets and of the feeding conditions as, for
example, radiation pattern of the feeder (or feeders), focal distance, or
location and orientation of the feeder.In order to avoid erroneous considerations
about this aspect, the simulator has been designed in such a way that the
elements for making simulation can be smaller than the real elements. That is,
the real elements can be decomposed into any number of squared or rectangular
cells, small enough to be able to consider uniform illumination in each cell.In other words, the grid used to decompose
the surface of the reflector will be smaller than the one defined by the moving
facets or squared elements of the reflector. Of course, the simulation cells
will be an entire fraction of the moving facets. Figure21 shows a grid for
simulation of the Fresnel reflector whose layout is in Figure 20. As it can be
seen, the grid has been made dividing each element into 2×2 cells.Figure 21
Grid for simulation proposal.Once determined the grid for simulation,
the next step consists in calculating the intensity of illumination received by
all its cells. Knowing the radiation pattern of the feeding system, this
calculus is immediate.As what we
want in principle is to know the behavior of a reconfigurable reflector based
on squared elements, we are going to consider an ideal feeder which radiates
uniformly in any direction but only in the coverage of the aperture of the
reflector (squared in this case of study). In Figure22, it can be seen a color
map of the luminance on the grid from the feeder in that conditions.Figure 22
Luminance on the grid under ideal feeding conditions.


#### 3.2.4. Response Analysis

As mentioned above, the analysis of the
response consists in the superposition of the response of all the cells
according to (6). As, in general, the aperture of a reconfigurable reflector
can have an arbitrary shape, the radiation pattern will not be symmetrical but
will have a different pattern depending on the considered cut. For example, in
a squared aperture, as our case of study, the cut of the radiation pattern in a
direction parallel to a reflector side will be different from the cut in the
direction of a diagonal, or something else. Consequently, it is necessary to
specify the angle of the cut to be considered with respect to one of the axis
transversal to propagation direction. Another variant we have implemented is the
simulator 3D which is able to represent the full diagram, all around the propagation
axis (see Figure 23).Figure 23
Radiation pattern from the 3D simulator.Also, to have an idea about performance of
the configuration designed and implemented in the reconfigurable reflector, we
will represent the radiation pattern of an absolutely ideal parabolic reflector
of the same aperture. The radiation pattern of our case of study as well as of
the absolutely ideal paraboloid of the same aperture, in parallel and diagonal
directions  can be seen in Figure24.Figure 24
Radiation pattern at 0° and 45° obtained from developed
simulator.What we have adopted asabsolutely ideal paraboloid is the
radiation of its aperture under condition of uniform field in amplitude and
phase, that is, the result of applying (6) to the whole aperture. Due to the
fact that in our case of study we have not uniform illumination (Figure 22) but
uniform radiation of the feeder, a difference of 4.48 dB from ideal paraboloid
(Figure 24) is quite acceptable.However, if we would conform a paraboloid
by means of the reconfigurable reflector (supposed that it was permitted by its
structure) in the same conditions of feeding as in the case of the squared
Fresnel reflector, the difference only is 1.66 dB as can be seen in Figure25.
The results of simulation for the conformed Fresnel reflector used as a case of
study in 3D can be seen in Figure 23.Figure 25
Comparison between parabolic shape and Fresnel reflector of
squared cells.As mentioned above, the
selection of the size of the grid  is very important for simulation. In fact, if the simulation grid
is of the same size as the division in facets of the reconfigurable reflector,
simulation can be poor, but if the grid is too much dense, simulation process
proves to be very heavy and results can be indistinguishable from  those
obtained with a less compact grid.In order to illustrate this simulation
effect, we have made simulation of our case of study using grid cells of the
same size of the facets (1×1) in comparison with simulation with grid dividing
facets in2×2 and also with a grid 3×3.
As it can be seen in Figure 26, there is a sensible difference between results
from 1×1 and 2×2. However, between 2×2 and 3×3, difference is negligible.Figure 26
Comparison of simulations1×1, 2×2, and 3×3.It is also interesting to evaluate the
efficiency of the reconfigurable reflector when conforming Fresnel reflectors,
depending on the implemented number of levels, that is, the number of steps
that can establish the shifting actuator like that shown in Figure26 whose
number of levels is two. However, it is important to take into account that the
efficiency versus number of levels is not independent of the size of the facets
of the reconfigurable reflector. As a matter of fact, the greater the number of
levels is, the narrower the size of the Fresnel zones will be. On the contrary,
the size of the facets can become wider than many Fresnel zones, which means
that the approach to the Fresnel reflector of reference could be very poor. Then,
it is necessary to use a size of facets according to the wavelength and to the
number of levels to be implemented.For example, in the initial case of having a
reflector of480×480 mm with 36×36 facets, gain varies with the number of
implemented levels as follows: 40.3 dB for two levels (N  =  2), 42.43 dB for
three levels (N = 3), and 43.29 dB for four levels (N = 4). In Figure 27, it can
be seen the radiation patterns for these three configurations.Figure 27
Radiation pattern of Fresnel reflectors of squared cells of 2, 3, and
4 levels.However, if we
would use a reconfigurable reflector of the same dimensions but with72×72
elements instead of 36×36, performance gets much better since it also betters
the approach to the Fresnel reflector of reference. As it can be seen in Figure 28, gain is better with three levels (N = 3) in the case of 72×72 than with higher number of levels (N  =  4) in the case
of36×36. Concretely, in the first case
gain is 43.55 dB, while in the second it is 43.29 dB. In both cases, the grid
of simulation is really of 72×72 cells, because in the first case each element
of simulation is equal to one facet, while in the second one, each facet is
divided in 2×2 simulation cells.Figure 28
Comparison of Fresnel reflectors of72×72 and 36×36 reflecting
squared cells, having the same radiating aperture.


## 3.1. Active Fresnel Reflector

### 3.1.1. Electrical Concept

The radiation pattern
of a reflected signal can be modified by changes in the geometrical
characteristics of the reflecting surface. As it is known, perturbations on
parabolic surfaces allow any desired 3 dB transversal section in the main beam,
being actually the best solution applied in geosatellite antennas for communication
links.This concept was
translated in [17] to the Fresnel reflector technology, and a general behavior
of Fresnel reflectors can be seen in [18], being the case of reflectors with 2
or 3 levels as the more interesting ones from performance and manufacturing
point of view.A Fresnel reflector design with 144
actuators of two positions, controlling an array of12×12 reflecting cells, is
to be described in this paper. The antenna has been designed to provide a beam
scanning in the principal plane direction, having the main beam at the symmetric
direction to the focal position of the feeder from the central point of
reflecting surface (see Figure 12).Figure 12
Geometry of the synthesized Fresnel reflector configuration.The selected working frequency was 18.75 GHz, which must be in accordance with the distance separation among levels, which
is provided by the selected actuator. The cell size was selected taking into
account the supposed application of the example, in order to avoid grating
lobes and the area to be covered by the scanning. The desired beam scanning
zone is between 0° and −20°, in the
principal plane, which includes the focal point.Once the geometry of the reference Fresnel
configuration is determined, the movement of the synthesized geometry over the
reflector surface will provide the beam scanning. So, the Fresnel configuration
of reference must be synthesized over a surface bigger than that of the
reflector. This allows the changes as it is shown in Figure13, where there are
three reflector configurations for different appointments.Reflector configuration for different positions of the Fresnel
configuration.
(a)(b)(c)It is obvious
that in this structural concept, the feeder is always in the same position. The
unique change on the antenna, which provides the desired scanning, is the
change of the position of the Fresnel configuration on the reflector surface,
as it can be seen in Figure13. Figure 14 shows the superposition of simulated
array factors of the Fresnel configurations to cover the selected scanning
area. The evolution of the radiation pattern is shown in Figure 14, and
consequently it can be understood that any reflected direction can be obtained
by placing the Fresnel configuration at the adequate place over the reflector
surface.Figure 14
Superposition of simulated array factors, which are obtained by
movement of the synthesized Fresnel distribution.


### 3.1.2. Mechanical Concept

To allow the change of Fresnel level of any reflecting cell, each
Fresnel level is associated to a different position of the reflecting surface
of the cell, thinking that this different position is referred to the
perpendicular direction to the reflector surface.To provide this position change, a
commercial actuator (solenoids, series 45B) was selected from the web page of
RS AMIDATA. Figure15 shows the geometry data sheet.Figure 15
Actuator data sheet.As it can be seen in
Figure16, the actuator is placed under each reflecting cell, and it allows a
displacement of the reflecting cell of 4.5 mm, which is electronically controlled.
This figure shows two complete active reflecting cells, at both states: 0 and 1,  which corresponds to both
Fresnel levels. The actuator is placed at the position 1 when there is a voltage of 6 V at the inputs of actuator terminal, and it is placed at the position 0 when the voltage is 0 V. The
actuator works over the reflecting cell as it can be seen in Figure 16.Figure 16
Views of two mechanical actuators, working over its respective
reflecting cell, at both Fresnel levels: 0 and 1.When the aim is to
implement reconfigurable Fresnel reflectors with more than two levels, the
actuator should be different form that commercially available. However there is
not a great technological problem, including a continuous shift solution. We
can think about a little screw pin moved by a small electrical motor, step-by-step or continuous type.Figures17 and 18 show,
a view of the whole Active Fresnel Reflector, respectively with the Fresnel
configuration of Figures 13(b) and 12. The case that is shown in Figure 17
corresponds to the synthesized Fresnel configuration which is centered on the
surface of the reflector.Figure 17
View of the active Fresnel reflector with the configuration of
Figure13(b).Figure 18
View of the active Fresnel reflector with the configuration of
Figure12.


## 3.1.1. Electrical Concept

The radiation pattern
of a reflected signal can be modified by changes in the geometrical
characteristics of the reflecting surface. As it is known, perturbations on
parabolic surfaces allow any desired 3 dB transversal section in the main beam,
being actually the best solution applied in geosatellite antennas for communication
links.This concept was
translated in [17] to the Fresnel reflector technology, and a general behavior
of Fresnel reflectors can be seen in [18], being the case of reflectors with 2
or 3 levels as the more interesting ones from performance and manufacturing
point of view.A Fresnel reflector design with 144
actuators of two positions, controlling an array of12×12 reflecting cells, is
to be described in this paper. The antenna has been designed to provide a beam
scanning in the principal plane direction, having the main beam at the symmetric
direction to the focal position of the feeder from the central point of
reflecting surface (see Figure 12).Figure 12
Geometry of the synthesized Fresnel reflector configuration.The selected working frequency was 18.75 GHz, which must be in accordance with the distance separation among levels, which
is provided by the selected actuator. The cell size was selected taking into
account the supposed application of the example, in order to avoid grating
lobes and the area to be covered by the scanning. The desired beam scanning
zone is between 0° and −20°, in the
principal plane, which includes the focal point.Once the geometry of the reference Fresnel
configuration is determined, the movement of the synthesized geometry over the
reflector surface will provide the beam scanning. So, the Fresnel configuration
of reference must be synthesized over a surface bigger than that of the
reflector. This allows the changes as it is shown in Figure13, where there are
three reflector configurations for different appointments.Reflector configuration for different positions of the Fresnel
configuration.
(a)(b)(c)It is obvious
that in this structural concept, the feeder is always in the same position. The
unique change on the antenna, which provides the desired scanning, is the
change of the position of the Fresnel configuration on the reflector surface,
as it can be seen in Figure13. Figure 14 shows the superposition of simulated
array factors of the Fresnel configurations to cover the selected scanning
area. The evolution of the radiation pattern is shown in Figure 14, and
consequently it can be understood that any reflected direction can be obtained
by placing the Fresnel configuration at the adequate place over the reflector
surface.Figure 14
Superposition of simulated array factors, which are obtained by
movement of the synthesized Fresnel distribution.


## 3.1.2. Mechanical Concept

To allow the change of Fresnel level of any reflecting cell, each
Fresnel level is associated to a different position of the reflecting surface
of the cell, thinking that this different position is referred to the
perpendicular direction to the reflector surface.To provide this position change, a
commercial actuator (solenoids, series 45B) was selected from the web page of
RS AMIDATA. Figure15 shows the geometry data sheet.Figure 15
Actuator data sheet.As it can be seen in
Figure16, the actuator is placed under each reflecting cell, and it allows a
displacement of the reflecting cell of 4.5 mm, which is electronically controlled.
This figure shows two complete active reflecting cells, at both states: 0 and 1,  which corresponds to both
Fresnel levels. The actuator is placed at the position 1 when there is a voltage of 6 V at the inputs of actuator terminal, and it is placed at the position 0 when the voltage is 0 V. The
actuator works over the reflecting cell as it can be seen in Figure 16.Figure 16
Views of two mechanical actuators, working over its respective
reflecting cell, at both Fresnel levels: 0 and 1.When the aim is to
implement reconfigurable Fresnel reflectors with more than two levels, the
actuator should be different form that commercially available. However there is
not a great technological problem, including a continuous shift solution. We
can think about a little screw pin moved by a small electrical motor, step-by-step or continuous type.Figures17 and 18 show,
a view of the whole Active Fresnel Reflector, respectively with the Fresnel
configuration of Figures 13(b) and 12. The case that is shown in Figure 17
corresponds to the synthesized Fresnel configuration which is centered on the
surface of the reflector.Figure 17
View of the active Fresnel reflector with the configuration of
Figure13(b).Figure 18
View of the active Fresnel reflector with the configuration of
Figure12.


## 3.2. Simulator of Fresnel Reflectors

Performance of Fresnel reflectors depends
on the number of levels implemented but the result obtained with a three
levels implementation is very reasonable. As a matter of fact, gain of a three
levels reflector is usually about 1.5 dB under a same aperture and same focus
paraboloid. However Fresnel reflectors have several important advantages: first,
the fact being smaller in terms of occupied room. Second, the deployment system
is easier for them. Third, the possibility of combining several Fresnel
distributions in a same reflector surface to get multibeam radiation patterns.
Finally, the manufacturing process is very easy and very cheap by means of
photoetched procedures.Fresnel reflectors performance has been
widely studied by means of a computer simulator developed by ourselves which is
specially adequate and flexible for reflectors with circular symmetry [19–21]. We also have developed a methodology to optimize shaping of Fresnel
reflectors [22, 23].Now, a new simulator has been specifically developed for reconfigurable
reflectors composed by squared elements, with any number of levels or
continuous shifting. In order to get a good efficiency,  we have extracted the
response of a squared element with uniform illumination. In this way, the response
of the reflector is the superposition of the responses of all elements,
once situated each one in its location and level. The assumption that resonance
effects and boundary conditions in edges of squared elements are small enough
to be neglected is very reasonable because they affect mainly to radiation far
from the main lobes. Besides, there are structural media to minimize those
effects, as we will try to prove in the future when physical experimentation
becomes possible.On the other hand, the assumption of
uniform illumination in the whole area of each conformable element could  not be too much closed to the real case; we use a grid to decompose the surface of the
reflecting elements in smaller squares (rectangles in general terms) to the end
of getting simulation elements small enough to be considered, each one as
uniformly illuminated.Although the
normal case is to have squared elements, we are going to consider rectangular
ones for giving more generality and flexibility to the simulator.


### 3.2.1. Rectangular Reflecting Cell

A rectangular surface is used as a reference. The center of this
element will be located at(xo,yo,zo)=(0,0,0) as shown in Figure 19.
In this case, the function of luminance of a rectangle
with dimensions a×h can be represented by the following expression (2) [24, 25]:(2)U(x,y)=f(x,y)⋅Π(xa)⋅Π(yh), being f(x,y)
the function of luminance inside the rectangle, and Π(u/b) a pulse in axis u of
amplitude 1 between −b/2 and b/2. But,
if luminance is uniform of amplitude A,
function (2) is reduced to(3)U(xo,yo)=A⋅Π(xoa)⋅Π(yoh). In order to get
the far field radiation pattern of the rectangular element, we will use the
Fresnel-Kirchhoff diffraction formula [24] as follows:(4)U(xi,yi)=1jλ∬exp(jkr)r⋅U(xo,yo)⋅dxodyo. According to
Figure 19,  the distance r of an
elementary emitter in xo,yo to an arbitrary far field
point in a plane xi,yi,
parallel to the plane of the radiating element will be calculated as follows:(5)r2=zi2+(xi−xo)2+(yi−yo)2,zi2≫(xi−xo)2+(yi−yo)2,r=zi⋅1+(xi−xo)2+(yi−yo)2zi2≅zi(1+(xi−xo)2+(yi−yo)22⋅zi2),r≅zixi2+yi22⋅zi2−xi⋅xo+yi⋅yozi. Then, introducing this expression of r and the luminance in (4) in the
Fresnel-Kirchhoff diffraction formula in (5), we get
the far field (Fraunhofer space) due to a rectangular element as follows:(6)U(xi,yi)=a⋅hjλ⋅ziexp[jk(zi+(xi2+yi2)2⋅zi)]⋅sinc(axiλ⋅zi)⋅sinc(hyiλ⋅zi).Figure 19
Geometry and notation of the radiating cell.


### 3.2.2. Fresnel Reflector Conformed by Squared Reflecting Cells

Once developed a method to get the optimal
shape for a flat Fresnel reflector [22], the approaching procedure to obtain a
reflector conformed by squared reflecting cells will consist of setting every
squared cell at the same level that had its central point in the ideal Fresnel
reflector.As an example, Figure20 shows the layout
of a reflector configured by means of a reconfigurable reflector of 480×480 mm
and 36×36 elements. The shape of the original reflector has been indicated by circles
in the same figure. The reflector has been designed at three levels (each level
a different color); the focal distance is 500 mm and has been tuned
to 18.75 GHz.Figure 20
Fresnel reflector of square cells and 3 levels.It is easy to
see in Figure20 that there is a misalignment between the optimal shape of the
Fresnel reflector and that conformed by squares. Of course, increasing the density
of elements, they become smaller, and the approximation to the ideal Fresnel
reflector, as well as the efficiency of the reflector, is better. However, the
reconfigurable system would be more complex and expensive. We will describe
below the procedure to get the fair dimensions.


### 3.2.3. Grid and Feeding Distribution for Simulation

Simulation process has nothing to do with
the configuration of the reflector. Any configuration will be simulated by
iteratively applying formula (6) for each one of the squared (or rectangular if
it were the case) elements once moved to the position x,y,z relative to each point of the de radiation pattern one want to find.This fact implies that we must know the
location, the level (z), and the
luminance A of every element, and also
that we can suppose that squares are uniformly illuminated. The location and
shifting of the elements are well-known parameters. However, the fact of being
correct or not to, consider uniform illumination on the surface of the elements,
depends on the size of the facets and of the feeding conditions as, for
example, radiation pattern of the feeder (or feeders), focal distance, or
location and orientation of the feeder.In order to avoid erroneous considerations
about this aspect, the simulator has been designed in such a way that the
elements for making simulation can be smaller than the real elements. That is,
the real elements can be decomposed into any number of squared or rectangular
cells, small enough to be able to consider uniform illumination in each cell.In other words, the grid used to decompose
the surface of the reflector will be smaller than the one defined by the moving
facets or squared elements of the reflector. Of course, the simulation cells
will be an entire fraction of the moving facets. Figure21 shows a grid for
simulation of the Fresnel reflector whose layout is in Figure 20. As it can be
seen, the grid has been made dividing each element into 2×2 cells.Figure 21
Grid for simulation proposal.Once determined the grid for simulation,
the next step consists in calculating the intensity of illumination received by
all its cells. Knowing the radiation pattern of the feeding system, this
calculus is immediate.As what we
want in principle is to know the behavior of a reconfigurable reflector based
on squared elements, we are going to consider an ideal feeder which radiates
uniformly in any direction but only in the coverage of the aperture of the
reflector (squared in this case of study). In Figure22, it can be seen a color
map of the luminance on the grid from the feeder in that conditions.Figure 22
Luminance on the grid under ideal feeding conditions.


### 3.2.4. Response Analysis

As mentioned above, the analysis of the
response consists in the superposition of the response of all the cells
according to (6). As, in general, the aperture of a reconfigurable reflector
can have an arbitrary shape, the radiation pattern will not be symmetrical but
will have a different pattern depending on the considered cut. For example, in
a squared aperture, as our case of study, the cut of the radiation pattern in a
direction parallel to a reflector side will be different from the cut in the
direction of a diagonal, or something else. Consequently, it is necessary to
specify the angle of the cut to be considered with respect to one of the axis
transversal to propagation direction. Another variant we have implemented is the
simulator 3D which is able to represent the full diagram, all around the propagation
axis (see Figure 23).Figure 23
Radiation pattern from the 3D simulator.Also, to have an idea about performance of
the configuration designed and implemented in the reconfigurable reflector, we
will represent the radiation pattern of an absolutely ideal parabolic reflector
of the same aperture. The radiation pattern of our case of study as well as of
the absolutely ideal paraboloid of the same aperture, in parallel and diagonal
directions  can be seen in Figure24.Figure 24
Radiation pattern at 0° and 45° obtained from developed
simulator.What we have adopted asabsolutely ideal paraboloid is the
radiation of its aperture under condition of uniform field in amplitude and
phase, that is, the result of applying (6) to the whole aperture. Due to the
fact that in our case of study we have not uniform illumination (Figure 22) but
uniform radiation of the feeder, a difference of 4.48 dB from ideal paraboloid
(Figure 24) is quite acceptable.However, if we would conform a paraboloid
by means of the reconfigurable reflector (supposed that it was permitted by its
structure) in the same conditions of feeding as in the case of the squared
Fresnel reflector, the difference only is 1.66 dB as can be seen in Figure25.
The results of simulation for the conformed Fresnel reflector used as a case of
study in 3D can be seen in Figure 23.Figure 25
Comparison between parabolic shape and Fresnel reflector of
squared cells.As mentioned above, the
selection of the size of the grid  is very important for simulation. In fact, if the simulation grid
is of the same size as the division in facets of the reconfigurable reflector,
simulation can be poor, but if the grid is too much dense, simulation process
proves to be very heavy and results can be indistinguishable from  those
obtained with a less compact grid.In order to illustrate this simulation
effect, we have made simulation of our case of study using grid cells of the
same size of the facets (1×1) in comparison with simulation with grid dividing
facets in2×2 and also with a grid 3×3.
As it can be seen in Figure 26, there is a sensible difference between results
from 1×1 and 2×2. However, between 2×2 and 3×3, difference is negligible.Figure 26
Comparison of simulations1×1, 2×2, and 3×3.It is also interesting to evaluate the
efficiency of the reconfigurable reflector when conforming Fresnel reflectors,
depending on the implemented number of levels, that is, the number of steps
that can establish the shifting actuator like that shown in Figure26 whose
number of levels is two. However, it is important to take into account that the
efficiency versus number of levels is not independent of the size of the facets
of the reconfigurable reflector. As a matter of fact, the greater the number of
levels is, the narrower the size of the Fresnel zones will be. On the contrary,
the size of the facets can become wider than many Fresnel zones, which means
that the approach to the Fresnel reflector of reference could be very poor. Then,
it is necessary to use a size of facets according to the wavelength and to the
number of levels to be implemented.For example, in the initial case of having a
reflector of480×480 mm with 36×36 facets, gain varies with the number of
implemented levels as follows: 40.3 dB for two levels (N  =  2), 42.43 dB for
three levels (N = 3), and 43.29 dB for four levels (N = 4). In Figure 27, it can
be seen the radiation patterns for these three configurations.Figure 27
Radiation pattern of Fresnel reflectors of squared cells of 2, 3, and
4 levels.However, if we
would use a reconfigurable reflector of the same dimensions but with72×72
elements instead of 36×36, performance gets much better since it also betters
the approach to the Fresnel reflector of reference. As it can be seen in Figure 28, gain is better with three levels (N = 3) in the case of 72×72 than with higher number of levels (N  =  4) in the case
of36×36. Concretely, in the first case
gain is 43.55 dB, while in the second it is 43.29 dB. In both cases, the grid
of simulation is really of 72×72 cells, because in the first case each element
of simulation is equal to one facet, while in the second one, each facet is
divided in 2×2 simulation cells.Figure 28
Comparison of Fresnel reflectors of72×72 and 36×36 reflecting
squared cells, having the same radiating aperture.


## 3.2.1. Rectangular Reflecting Cell

A rectangular surface is used as a reference. The center of this
element will be located at(xo,yo,zo)=(0,0,0) as shown in Figure 19.
In this case, the function of luminance of a rectangle
with dimensions a×h can be represented by the following expression (2) [24, 25]:(2)U(x,y)=f(x,y)⋅Π(xa)⋅Π(yh), being f(x,y)
the function of luminance inside the rectangle, and Π(u/b) a pulse in axis u of
amplitude 1 between −b/2 and b/2. But,
if luminance is uniform of amplitude A,
function (2) is reduced to(3)U(xo,yo)=A⋅Π(xoa)⋅Π(yoh). In order to get
the far field radiation pattern of the rectangular element, we will use the
Fresnel-Kirchhoff diffraction formula [24] as follows:(4)U(xi,yi)=1jλ∬exp(jkr)r⋅U(xo,yo)⋅dxodyo. According to
Figure 19,  the distance r of an
elementary emitter in xo,yo to an arbitrary far field
point in a plane xi,yi,
parallel to the plane of the radiating element will be calculated as follows:(5)r2=zi2+(xi−xo)2+(yi−yo)2,zi2≫(xi−xo)2+(yi−yo)2,r=zi⋅1+(xi−xo)2+(yi−yo)2zi2≅zi(1+(xi−xo)2+(yi−yo)22⋅zi2),r≅zixi2+yi22⋅zi2−xi⋅xo+yi⋅yozi. Then, introducing this expression of r and the luminance in (4) in the
Fresnel-Kirchhoff diffraction formula in (5), we get
the far field (Fraunhofer space) due to a rectangular element as follows:(6)U(xi,yi)=a⋅hjλ⋅ziexp[jk(zi+(xi2+yi2)2⋅zi)]⋅sinc(axiλ⋅zi)⋅sinc(hyiλ⋅zi).Figure 19
Geometry and notation of the radiating cell.


## 3.2.2. Fresnel Reflector Conformed by Squared Reflecting Cells

Once developed a method to get the optimal
shape for a flat Fresnel reflector [22], the approaching procedure to obtain a
reflector conformed by squared reflecting cells will consist of setting every
squared cell at the same level that had its central point in the ideal Fresnel
reflector.As an example, Figure20 shows the layout
of a reflector configured by means of a reconfigurable reflector of 480×480 mm
and 36×36 elements. The shape of the original reflector has been indicated by circles
in the same figure. The reflector has been designed at three levels (each level
a different color); the focal distance is 500 mm and has been tuned
to 18.75 GHz.Figure 20
Fresnel reflector of square cells and 3 levels.It is easy to
see in Figure20 that there is a misalignment between the optimal shape of the
Fresnel reflector and that conformed by squares. Of course, increasing the density
of elements, they become smaller, and the approximation to the ideal Fresnel
reflector, as well as the efficiency of the reflector, is better. However, the
reconfigurable system would be more complex and expensive. We will describe
below the procedure to get the fair dimensions.


## 3.2.3. Grid and Feeding Distribution for Simulation

Simulation process has nothing to do with
the configuration of the reflector. Any configuration will be simulated by
iteratively applying formula (6) for each one of the squared (or rectangular if
it were the case) elements once moved to the position x,y,z relative to each point of the de radiation pattern one want to find.This fact implies that we must know the
location, the level (z), and the
luminance A of every element, and also
that we can suppose that squares are uniformly illuminated. The location and
shifting of the elements are well-known parameters. However, the fact of being
correct or not to, consider uniform illumination on the surface of the elements,
depends on the size of the facets and of the feeding conditions as, for
example, radiation pattern of the feeder (or feeders), focal distance, or
location and orientation of the feeder.In order to avoid erroneous considerations
about this aspect, the simulator has been designed in such a way that the
elements for making simulation can be smaller than the real elements. That is,
the real elements can be decomposed into any number of squared or rectangular
cells, small enough to be able to consider uniform illumination in each cell.In other words, the grid used to decompose
the surface of the reflector will be smaller than the one defined by the moving
facets or squared elements of the reflector. Of course, the simulation cells
will be an entire fraction of the moving facets. Figure21 shows a grid for
simulation of the Fresnel reflector whose layout is in Figure 20. As it can be
seen, the grid has been made dividing each element into 2×2 cells.Figure 21
Grid for simulation proposal.Once determined the grid for simulation,
the next step consists in calculating the intensity of illumination received by
all its cells. Knowing the radiation pattern of the feeding system, this
calculus is immediate.As what we
want in principle is to know the behavior of a reconfigurable reflector based
on squared elements, we are going to consider an ideal feeder which radiates
uniformly in any direction but only in the coverage of the aperture of the
reflector (squared in this case of study). In Figure22, it can be seen a color
map of the luminance on the grid from the feeder in that conditions.Figure 22
Luminance on the grid under ideal feeding conditions.


## 3.2.4. Response Analysis

As mentioned above, the analysis of the
response consists in the superposition of the response of all the cells
according to (6). As, in general, the aperture of a reconfigurable reflector
can have an arbitrary shape, the radiation pattern will not be symmetrical but
will have a different pattern depending on the considered cut. For example, in
a squared aperture, as our case of study, the cut of the radiation pattern in a
direction parallel to a reflector side will be different from the cut in the
direction of a diagonal, or something else. Consequently, it is necessary to
specify the angle of the cut to be considered with respect to one of the axis
transversal to propagation direction. Another variant we have implemented is the
simulator 3D which is able to represent the full diagram, all around the propagation
axis (see Figure 23).Figure 23
Radiation pattern from the 3D simulator.Also, to have an idea about performance of
the configuration designed and implemented in the reconfigurable reflector, we
will represent the radiation pattern of an absolutely ideal parabolic reflector
of the same aperture. The radiation pattern of our case of study as well as of
the absolutely ideal paraboloid of the same aperture, in parallel and diagonal
directions  can be seen in Figure24.Figure 24
Radiation pattern at 0° and 45° obtained from developed
simulator.What we have adopted asabsolutely ideal paraboloid is the
radiation of its aperture under condition of uniform field in amplitude and
phase, that is, the result of applying (6) to the whole aperture. Due to the
fact that in our case of study we have not uniform illumination (Figure 22) but
uniform radiation of the feeder, a difference of 4.48 dB from ideal paraboloid
(Figure 24) is quite acceptable.However, if we would conform a paraboloid
by means of the reconfigurable reflector (supposed that it was permitted by its
structure) in the same conditions of feeding as in the case of the squared
Fresnel reflector, the difference only is 1.66 dB as can be seen in Figure25.
The results of simulation for the conformed Fresnel reflector used as a case of
study in 3D can be seen in Figure 23.Figure 25
Comparison between parabolic shape and Fresnel reflector of
squared cells.As mentioned above, the
selection of the size of the grid  is very important for simulation. In fact, if the simulation grid
is of the same size as the division in facets of the reconfigurable reflector,
simulation can be poor, but if the grid is too much dense, simulation process
proves to be very heavy and results can be indistinguishable from  those
obtained with a less compact grid.In order to illustrate this simulation
effect, we have made simulation of our case of study using grid cells of the
same size of the facets (1×1) in comparison with simulation with grid dividing
facets in2×2 and also with a grid 3×3.
As it can be seen in Figure 26, there is a sensible difference between results
from 1×1 and 2×2. However, between 2×2 and 3×3, difference is negligible.Figure 26
Comparison of simulations1×1, 2×2, and 3×3.It is also interesting to evaluate the
efficiency of the reconfigurable reflector when conforming Fresnel reflectors,
depending on the implemented number of levels, that is, the number of steps
that can establish the shifting actuator like that shown in Figure26 whose
number of levels is two. However, it is important to take into account that the
efficiency versus number of levels is not independent of the size of the facets
of the reconfigurable reflector. As a matter of fact, the greater the number of
levels is, the narrower the size of the Fresnel zones will be. On the contrary,
the size of the facets can become wider than many Fresnel zones, which means
that the approach to the Fresnel reflector of reference could be very poor. Then,
it is necessary to use a size of facets according to the wavelength and to the
number of levels to be implemented.For example, in the initial case of having a
reflector of480×480 mm with 36×36 facets, gain varies with the number of
implemented levels as follows: 40.3 dB for two levels (N  =  2), 42.43 dB for
three levels (N = 3), and 43.29 dB for four levels (N = 4). In Figure 27, it can
be seen the radiation patterns for these three configurations.Figure 27
Radiation pattern of Fresnel reflectors of squared cells of 2, 3, and
4 levels.However, if we
would use a reconfigurable reflector of the same dimensions but with72×72
elements instead of 36×36, performance gets much better since it also betters
the approach to the Fresnel reflector of reference. As it can be seen in Figure 28, gain is better with three levels (N = 3) in the case of 72×72 than with higher number of levels (N  =  4) in the case
of36×36. Concretely, in the first case
gain is 43.55 dB, while in the second it is 43.29 dB. In both cases, the grid
of simulation is really of 72×72 cells, because in the first case each element
of simulation is equal to one facet, while in the second one, each facet is
divided in 2×2 simulation cells.Figure 28
Comparison of Fresnel reflectors of72×72 and 36×36 reflecting
squared cells, having the same radiating aperture.


## 4. Conclusions

An active reflectarray with beam steering
capabilities has been designed, manufactured, and measured. Based on an IQ configuration,
the amplitude and phase of the scattered field for each of its radiating units
have been varied.  The obtained phase
control permits to achieve the required phase shift, not only to convert the
spherical incident wave into a plane one but also to steer the main beam. Furthermore,
different amplitude distributions with different gains can be easily
implemented by using these elements. The measurements of the radiation pattern
pointing to different elevation angles have demonstrated the potentiality of
the proposed architecture.On the other hand, a Fresnel reflector
configuration can be electronically modified to provide any desired radiation
pattern. Beam steering or radiation pattern reconfigurability is some of the
possible applications of this new structural concept on active antennas. The design
of a square flat reflector with 144 actuators, working at 18.75 GHz, shows
antenna performance.Simulation of this kind of reconfigurable
reflectors having squared (or rectangular) reflecting cells has also been
proved to be reliable and efficient. The procedure has been made by means of
the superposition of the radiation of all the elements on a simulation grid.
The simulation grid consists in a decomposition of the reflector in a grid of
cells sub-multiple of the elements or facets of the reflector.Reconfigurable reflectors are very adequate
to conform Fresnel plate zones since they are efficient and require only small
shifts of the facets. The efficiency of Fresnel reflectors depends on the number
of levels implemented and on the size and number of available facets. A reasonable
option is to implement three levels with a size of facets adequate for a good sampling
of the corresponding reflector profile.



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*Source: 653952-2009-04-12.xml*