Universidad Nacional de Chimborazo
NOVASINERGIA, 2018, Vol. 1, No. 1, diciembe-mayo, (59-66)
ISSN: 2631-2654
https://doi.org/10.37135/unach.ns.001.01.07
Research Article
Beamforming Networks for antenna array, useful in WiFi applications
Redes Beamforming para agrupaci
´
on de antenas,
´
utiles en aplicaciones WiFi
Carlos Ramiro Pe
˜
nafiel-Ojeda
12
*, Luis Fernando Carrera-Su
´
arez
3
, Diana Ver
´
onica
Navarro-M
´
endez
3
, Mariano Baquero-Escudero
2
, Miguel Ferrando-Bataller
2
1
Facultad de Ingenier
´
ıa, Universidad Nacional de Chimborazo, Riobamba, Ecuador, 060108
2
Instituto de Telecomunicaciones y Aplicaciones Multimedia, Universitat Polit
`
ecnica de Val
`
encia, Valencia, Spain, 46022
3
Escuela Polit
´
ecnica Nacional, Quito, Ecuador, 170119; fernando.carrera@epn.edu.ec; veronica.navarro@epn.edu.ec;
mbaquero@dcom.upv.es; mferrand@dcom.upv.es
* Correspondence: carlospenafiel@unach.edu.ec
Recibido 6 mayo 2018; Aceptado 21 mayo 2018; Publicado 14 junio 2018
Abstract:
In this paper several types of beamforming networks have been presented, this proposal
can be used for an array antenna, which are used in several types of WiFi applications,
IEEE 802.11b/g/draft-n. The first design corresponds to a 4x4 Butler Matrix for a
resonance frequency at 2.45 GHz, depending on the port through which the signal is
excited, it will be possible to obtain several variations in phase at the output ports
(45
◦
, 135
◦
, -45
◦
and -135
◦
), the proposed Butler matrix has been optimized from a
generalized matrix scheme, reducing the size through a simple overlap of multiple
transmission lines to λ/4 at the central frequency. The second design corresponds to
a Rotman lens with a characteristic resonance frequency of 5.8 GHz, with a maximum
focal angle of 30
◦
, for this design has been used geometric optics concept, and the
last design has been made for a frequency of 5.8 GHz using a slot array designed with
Substrate Integrated Waveguide technology.
Keywords:
Array Antena, Butler Matrix, Rotman Lens, Slots array with SIW guide, WiFi
Resumen:
En este art
´
ıculo se han presentado varios tipos de redes conformadoras de haz, estas
propuestas pueden ser utilizadas para una agrupaci
´
on de antenas
´
utiles en diversos
tipos de aplicaciones. El primer dise
˜
no corresponde a una Matriz de Butler de 4X4 para
una frecuencia de resonancia de 2.45 GHz, dependiendo del puerto por la cual la se
˜
nal
sea excitada, se podr
´
an obtener diversas variaciones en fase en los puertos de salida
(45
◦
, 135
◦
, -45
◦
y -135
◦
), la matriz de Butler propuesta ha sido optimizada a partir
de un esquema de matriz generalizada, reduciendo el tama
˜
no a trav
´
es de una simple
superposici
´
on de m
´
ultiples l
´
ıneas de transmisi
´
on a λ/4. El segundo dise
˜
no corresponde
a una lente de Rotman con una frecuencia de resonancia caracter
´
ıstica de 5.8 GHz, con
un m
´
aximo
´
angulo focal de 30
◦
, para este dise
˜
no se ha utilizado el concepto de la
´
optica
geom
´
etrica, y el
´
ultimo dise
˜
no ha sido realizado para una frecuencia de 5.8 GHz usando
una agrupaci
´
on de ranuras dise
˜
nadas con tecnolog
´
ıa Substrate Integrated Waveguide.
Palabras clave:
Agrupaci
´
on de antenas, Matriz de Butler, Lentes de Rotman, Agrupaci
´
on de ranuras
con gu
´
ıas SIW, WiFi
http://novasinergia.unach.edu.ec
1 Introduction
Multibeam and beam-scanning antennas are
crucial to modern communication systems such as
Direct-Broadcast Satellite (DBS), Multipurpose
Radar, multiple beam antenna for mobile
communications. Talking about these systems
is talking about the smart antennas and indirectly
of multibeam systems the require wide-angle
coverage with very directive beams. Multibeam and
beam-scanning antennas are implemented using
multiple antennas to create several beam patterns
in different directions, either as beam switch or
continuous beam terminated in a sophisticated
signal processor, which can adjust or adapt its
own beam pattern in order to emphasize signals
of interest and to minimize interfering signals
(Abdelghani et al., 2012a,b; Bialkowski et al.,
2008; Moscoso-M
´
artir et al., 2014).
Beamforming networks are a great solution to
generate several beams with great directivity and
good bandwidth, they have been classified into
several ways, it was reported in the applications
cited previously, so to facilitate our learning it
has been divided into 3 groups according to
their applications: based on transmission lines
(Network BFNS), based on quasi-optical lenses
(Quasioptical BFNS) and based on digital data
processing networks (digital BFN), (Lo and Lee,
1988; Hansen, 2009; Hall and Vetterlein, 1990;
Josefsson and Persson, 2015).
All these solutions offer multiple-beam or
beam-scanning capabilities by selecting one or
several input ports, or mechanically displacing a
moving feed, but the Butler matrix and Rotman
lens are widely used since they can achieve a
large number of switched beams using well-known
design algorithms.
In the present research, three microwave circuits
to generate multiple beams are proposed, each
proposed beamforming network have been designed
for a different resonance frequency. This paper is
described in 3 sections, in the first section a 4X4
Butler Matrix design at 2.45 GHz is described in
detail, in the next section a Rotman lens at 5.8
GHz is developed, and it is compared with a slots
array designed with Substrate Integrated Waveguide
(SIW) technology, which is described in section
3, finally the conclusions are presented in the last
section.
Figure 1: Scheme Butler Matrix 4X4.
2 Butler Matrix
A 4 x 4 Butler Matrix is designed using four -3
dB Quadrature (90 degree) Hybrid Coupler, two 0
dB Crossovers Coupler and two 45
◦
phased shifter
(Nachouane et al., 2014), it is shown in figure 1.
The prototype has been optimized at the center
frequency of f = 2.45 GHz in WiFi applications
(IEEE 802.11b/g/draft-n), with a characteristic
impedance of Z
0
= 50Ω. The material considered
for the design has the following characteristics:
Roger 4003C with ε
r
= 3.38, height h = 0.813mm,
Tan (δ) = 0.0027.
2.1 -3 dB Quadrature (90
◦
) Hybrid
Coupler
Quadrature hybrids are 3 dB directional couplers
with a 90
◦
phased difference in the outputs of the
through and coupled arms. In the design of -3 dB
Quadrature (90 degree) for Hybrid Coupler. The
dimensions of the transmission lines are shown in
table 1, these values have been obtained from the
equations provided in (Pozar, 2011; Balanis, 2005).
A generic hybrid coupler was designed based
on the values specified in table 1, however the
technological advancements require miniaturization
of the systems to optimize space and compact
http://novasinergia.unach.edu.ec 60
Table 1: Hybrid coupler dimensions.
Impedance Lenght Width
50 Ω 18.7438 mm 1.84139 mm
35.35 Ω 18.3137 mm 3.1044 mm
Figure 2: -3 dB quadrature (90 degree) hybrid coupler
optimized.
structure, therefore each of the elements of the
hybrid coupler have been divided into five equal
segments, as a overlapping transmission lines
resulting in a size reduction 30%, it is shown in
figure 2.
2.2 Butler Matrix proposal
To build a Butler Matrix we have relied on the
criterion of figure 1, where it requires hybrid
couplers, crossover couplers, and phased shifters.
Crossover couplers are known as couplers to 0
dB, these are an efficient way for crossing two
transmission lines with minimal coupling between
them, the simplest form of designing such devices
is by means of a connection of two hybrid couplers
90
◦
. Additionally, it is important to considerate
the symmetry properties (Kholodniak et al., 2000).
In figure 3 is depicted the proposal Butler Matrix;
to design the phased shifter we have decided to
change the length value, this because a length at 45
degrees is too short to use, therefore, the new phased
shifter length was calculated with an angle at 405
degrees. The resulting size was 7.8cm x 7cm, which
corresponds to the proposal Butler Matrix.
The return loss and phase difference between the
output ports of the Butler matrix (see figure 4), give
us to identify that the proposed design is resonating
at 2.45 GHz of frequency with a bandwidth about
28%; i.e. it has a working window of approximately
500 MHz.
In table 2 is shown the variation of the phase angle
between the ports of entry (P
in1
, P
in2
, P
in3
, P
in4
) with
respect to the output ports (P
out
5
, P
out
6
, P
out7
, P
out8
)
of the designed Butler matrix. In figure 5(a), the
phase diagram is obtained; for entering input port
Figure 3: Optimized Butler Matrix.
Figure 4: S parameters of the optimized Butler Matrix
(1-4 are input ports and 5-8 are output ports).
1 is shown, which presents an angular variation of
-45 degrees. On the other hand, figure 5(b) depicted
the second case, input port 2, describes the angular
variation of 135 degrees. Based on both results,
we could build a four elements array antenna to
increase directivity.
Table 2: Variation of the phase angle between the ports of
entry.
Ports P
out
5
P
out
6
P
out
7
P
out
8
β
P
in
1
-41.36
◦
-86.96
◦
-131.8
◦
-176.7
◦
-45
◦
P
in
2
-131.6
◦
2.85
◦
138.6
◦
-86.69
◦
135
◦
P
in
3
-86.69
◦
138.6
◦
2.85
◦
-131.6
◦
-135
◦
P
in
4
-176.7
◦
-131.8
◦
-86.69
◦
-41.36
◦
45
◦
http://novasinergia.unach.edu.ec 61
(a)
(b)
Figure 5: Phased output ports of the Butler matrix
optimized. (a) Output ports with respect to the input port
1. (b) Output ports with respect to input port 2.
3 Rotman Lens
A Rotman lens is a device that uses the spread of
an injected signal into the gap between two parallel
metal plates to achieve the condition of a linear
phase distribution in the output ports of the lens.
The geometry of the metal plates and the length of
the output cables are obtained using the geometrical
optics model.
In practice, this condition is only true for the
ports on the perfect focal points, whereas for the
other ports located along focal arc, the phase
variation will be approximately linear, resulting in
phase errors (optical aberrations) that affect the
performance of the lens.
The outputs of the lens will be used to feed a linear
antenna array in order to change passively the phase
distribution at the input ports of the array. By
controlling the phase shift in the array ports, it is
possible to direct the radiation pattern of the antenna
toward a predefined direction (see figure 6 ).
A prototype of a Rotman lens using a NELTEC
Figure 6: Rotman lens scheme used in the geometrical
optics model.
NY9220 substrate was designed and simulated. The
dielectric substrate has a permittivity of 2.2 and
thickness of 0.127mm. The parameters used in the
design of the lens are described in table 3.
Table 3: Rotman lens parameters.
Parameter Value
Central frequency f
0
5.8 GHz
Bandwidth (BW) 4 MHz
Maximum scan angle (Ψ) 30
0
Maximum focal angle (α) 30
0
Output ports (antennas) 11
Distance between output ports 1.955cm
Input ports (beams) 7
3.1 Rotman Lens design using the
geometrical optics model
In general, the design of a Rotman lens should
follow a systematic procedure to obtain the expected
results. A standard design procedure consists of
definition of the lens specifications, this is proposed
in two stages.
In the first stage are defined: maximum scan angle,
maximum focal angle, number of beams, return
losses, phase errors, amplitude errors, bandwidth,
efficiency, among others. In order to determine the
length of the normalized aperture of the lens (η
max
),
the path length errors for different pointing angles
were evaluated (Rotman and Turner, 1963). Trough
figure 7 it is possible to verify that, to get an error
less than 5x10-4, η
max
should be less than 0.5. That
value will be taken as the maximum value for the
normalized aperture.
In the second stage, the data contained in table 3 and
the geometrical optics model were used to calculate
the coordinates of the output ports of the cavity, and
http://novasinergia.unach.edu.ec 62
Figure 7: Path length errors for some pointing angles.
the length of the lines between these ports and the
lens output ports (see figure 6).
The length of the central focal point (the width
of the lens), can be calculated using the equation
(1), where N
e
= number of antenna elements, d =
distance between elements, η
max
= 0.5and ε
r
= 2.2
is the permittivity of the substrate.
F
min
=
(N
e
−1)d
2
1
√
ε
r
η
max
(1)
The positions of the lens elements are depicted in
figure 8(a): the red dots correspond to the beam
ports (input ports), the blue dots are the array ports
(inner ports), orange squares are the dummy ports
and the green squares are the output ports (linear
array). The lengths of the lines connecting the array
ports with antenna ports is plotted in figure 8(b).
Once the geometrical parameters have been
calculated, the two-dimensional model (Lo and Lee,
1988) was used to evaluate the performance of
the lens. Radiation patterns for different pointing
angles are presented in figure 9. The beams are
pointing in the desired directions and the Side
Lobe Level is better than 16 dB for all beams;
furthermore, the nonexistence of grating lobes can
be verified.
3.2 Ports and connection lines
An important aspect to consider is the proper design
of the transitions between input/output ports and
cavity. For the design of ports, it is necessary to
calculate the value of the microstrip line considering
that the characteristic impedance 50 Ω, the next
step is increase gradually the width (taper) for
the purpose of to vary gently the impedance
characteristics until are similar which presents the
interface between line and parallel plate cavity
(Musa and Smith, 1986, 1989). Another aspect
(a)
(b)
Figure 8: Rotman lens prototype in microstrip
technology. (a) Coordinates ports input and output. (b)
Length of the connecting lines.
Figure 9: Length errors paths for some pointing angles.
to consider is the phase center of a microstrip
port, ports of the lens should be located so that its
phase center coincide with the points calculated in
figure 8(a) and figure 8(b), otherwise, errors will
occur in the phase of the output signals that can
cause unfocused lens. On the other hand, Rotman
equations do not define the geometry of the side
walls, which connects the focal arc with the array
http://novasinergia.unach.edu.ec 63
Figure 10: Rotman lens with microstrip technology.
(a)
(b)
Figure 11: S parameters Rotman lens. (a) S
ii
parameters
of the input ports. (b) S
ii
parameters of the output ports.
lens arc. The side walls can be designed according
to any geometrical shape. In this type of designs,
the energy reflected on the walls, returns to the
lens body, causing additional side lobes, and it can
cause coupling between ports (Rausch and Peterson,
2005). In that reason, in implementations with
microstrip or stripline technology, the absorption
conditions usually are achieved by placing dummy
lenses ports terminated in matched loads along the
side walls (see figure 10).
To avoid direct connections between the loads
matched resistances and the mass plane, a λ/4
stub length terminated in an open circuit is used.
In figure 11(a) and figure 11(a), the reflection
coefficients of the input ports and output ports of
the lens are plotted. The coefficients are calculated
at the center frequency of 5.8 GHz. It shows that for
all ports the parameter is less than -20 dB.
4 Slot Arrays Antenna with
Substrate Integrated Waveguides
A Slot Arrays Antenna with Substrate Integrated
Waveguides (SIW), is designed by placing two
rows of metalized holes in a dielectric substrate,
where, d = holes diameters, b = space between
them and the w = spacing between the rows are
the physical parameters required for the design
of the guide. A SIW guide can be modeled
using a classic rectangular waveguide, so all design
procedures and developed the theoretical basis for
rectangular guides are directly applicable to SIW
guides (Deslandes and Wu, 2006). The parameters
are shown in table 4.
Table 4: SIW parameters used to slot antennas.
f
0
p d w h
GHz mm mm mm mm
5.8 1.55 0.6 19.55 1.143
4.1 Slot antennas design
Given the geometry of SIW guides, the slots are
placed in the wide face of the guide and parallel to
the axis of symmetry. The slots have been shifted an
u distance from the axis so that cut the current lines
of the fundamental mode and to radiate too; this
distance allows to control the power level radiated
by the slot.
For the design, 5 resonant array with axial feed
are used, so the end of the guide is shorted and
the last slot will be at a λ/4 short distance. The
other slots are separated λ/2 distance between them,
and they are located alternately with respect to the
longitudinal axis to compensate for the 180
◦
phase
produced by the standing wave generated inside the
guide.
In table 5 are shown the initial values of the
group of slots obtained through (Johnson and Jasik,
1984; Farrall and Young, 2004), in figure 12(a) the
linear array are represented of slot with SIW guide
used for simulations, in figure 12(b) are describe a
comparison of S parameter of rectangular guide and
SIW guide array.
http://novasinergia.unach.edu.ec 64
Table 5: Slot with rectangular guide and SIW guide
geometric parameters.
λ
g
u c r
mm mm mm mm
Equivalent guide 81.34 1.28 2.96 21.47
SIW guide 81.34 1.38 3.1 22.9
(a)
(b)
Figure 12: Slot Lineal array with SIW guide. (a)
Simulated. (b) S
11
parameters.
In order to implement the antenna, it is necessary
to design a transition between microstrip lines (2
different layers) for obtaining a good bandwidth
and also easy to build, in figure 13(a) is shown
the proposed prototype with Rotman Lens, figure
13(b) shows a prototype with SIW guide, besides in
figure 14 are shown the measured radiation patterns
of multibeam antenna prototype.
5 Conclusion
Thanks to the design and simulation of the elements
of a Butler matrix as hybrid couplers, cross couplers
and phase shifters, we achieved obtaining a new
model to create a forming network beam, which
can serve for antenna array used in applications
WiFi. The developed model has the same properties
and characteristics of a conventional Butler matrix,
furthermore, it has succeeded reducing size up to
7.8cm x 7 cm; these dimensions represent only the
40% of a conventional design.
It was possible to design a beam forming network
using a Rotman lens for a frequency of 5.8
(a)
(b)
Figure 13: Photographs of the prototype multibeam
antenna. (a) Bottom view (Rotman lens). (b) Top view
(SIW slots array).
Figure 14: Measured radiation patterns in the prototype
multibeam antenna.
GHz, this design could be performed through two
types: based on conventional port and SIW guide
ports, these results has been demonstrated through
experimental procedures.
http://novasinergia.unach.edu.ec 65
Interest Conflict
Authors declare that there is no conflict of interest
in this research.
Acknowledgment
This work has been supported by the scholarship
at the Universidad Nacional de Chimborazo
in Ecuador, by the Spanish Ministry of
Economy and Competitiveness under the project
TEC2016-78028-C3-3-P, and the Generalitat
Valenciana with the project GV/2015/065.
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