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Abstract—A multibeam beam-forming network (BFN) for
generating 2-D multibeam array antenna (MAA) is proposed
using single-layer substrate integrated waveguide (SIW) tech-
nology. Firstly, a new topology for building 16 × 16 BFNs is pro-
posed, which successfully transform the traditional topology from
a 3-D configuration to a 2-D (or uniplanar) one. Two major chal-
lenges are tackled during this transformation, namely, the pla-
narization of basic components and the reduction of excessive
intersections between multiple paths. To this end, a novel design
of eight-port hybrid couplers, as critical components of this BFN,
is developed to transform a 3-D to a 2-D structure. Furthermore, a
new design of eight-port crossover, which can address four path
intersections simultaneously, is proposed to reduce the total
number of path intersections from 16 to only 4. The proposed
topology for 16 × 16 BFNs allow all the basic components, in-
cluding eight-port hybrid couplers, eight-port crossovers and
phase shifters, to be placed within a single-layer configuration.
Fed by the proposed uniplanar 16 × 16 BFN, a 2-D MAA with 16
(4 × 4) beams, which is capable of switching the beams in both
elevation and azimuth directions, is realized. Compared with
previous 2-D Butler matrix (BM) designs using multi-layer tech-
nology, it is for the first time that a uniplanar design of 16 × 16
BFN is proposed and realized, which significantly simplifies the
design and fabrication complexity.
Index Terms—Beam-forming network (BFN), 2-D multibeam
array antenna (MAA), 2-D Butler matrix (BM), substrate inte-
grated waveguide (SIW), eight-port crossover, eight-port hybrid
coupler, phase shifter, uniplanar configuration.
I. INTRODUCTION
EAM-FORMING networks (BFNs) form critical parts of
multibeam array antennas (MAAs), as they provide the
Manuscript received ** **, 2019. This work was supported in part by Na-
tional Natural Science Foundation of China (No. 61971098 and No.
U19A2055), in part by the Fundamental Research Funds for the Central Uni-
versities (No. ZYGX2018J037), and in part by National Science and Tech-
nology Specific Projects of China (No. 2018ZX03001001-004). (Corre-
sponding author: Yong-Ling Ban).
J.-W. Lian is with the School of Electronic Science and Engineering, Uni-
versity of Electronic Science and Technology of China, Chengdu 611731,
China, and also with the Global Big Data Technologies Centre, University of
Technology Sydney, Ultimo, NSW 2007, Australia.
Y.-L. Ban is with the School of Electronic Science and Engineering, Uni-
versity of Electronic Science and Technology of China, Chengdu 611731,
China (e-mail: byl@uestc.edu.cn).
H. Zhu and Y. J. Guo are with the Global Big Data Technologies Centre,
University of Technology Sydney, Ultimo, NSW 2007, Australia.
desired phase and amplitude distribution for generating multi-
ple beams [1]. Usually, there are two different types of
multibeam BFNs, namely circuit-type BFNs [2]-[6] and
lens-type BFNs [7]-[10], the former one being more popular
due to their balanced phase and amplitude distribution.
Most multibeam BFNs reported in the literature are for
one-dimensional (1-D) antenna arrays. For example, a
four-way Butler matrix (BM) can generate four beams in one
plane. For most applications in wireless communication and
sensing, a two-dimensional (2-D) antenna array would be re-
quired. However, realizing a 2-D multibeam BFN is a challenge
due to the complicated interconnections. It typically results in a
three-dimensional (3-D) configuration, which is bulky, difficult
to fabricate, and tends to be lossy. Therefore, it is highly de-
sirable to industry and academically important to develop pla-
nar or uniplanar multibeam BFNs to support multibeam an-
tennas.
A conventional topology of a 2-D multibeam BFN is com-
posed of two stacks of sub-BFNs, arranged in orthogonal di-
rections. Such a topology has been demonstrated in [11]-[14].
In [11], the 2-D lens is made up of two piles of lenses; one is the
vertical lens and the other is the horizontal lens. In [12] and [13],
Chen et al. and Hsieh et al. designed 8 four-way BMs and then
placed them in orthogonal planes to build 2-D BMs. A similar
topology is verified by Ren et al. in [14] by using three-way
Nolen matrices instead of four-way BMs. It should be pointed
out that some connectors are required between two stacks of
sub-BFNs and this is one of the most important reasons why
traditional 2-D multibeam BFNs are of bulky size and hard to
be implemented into planar designs.
In recent years, more attention has been paid to the planar
design of 2-D BFNs, especially with the emergence of the
substrate integrated waveguide (SIW) technology. To avoid
confusion, single- and multi-layer designs are referred to uni-
planar and quasi-planar designs in this paper, respectively. A 4
× 4 BFN generating 4 (2 × 2) beams can be realized by modi-
fying a traditional four-way BM with four inputs and four
outputs [15]-[16]. Since the number of components in such a 4
× 4 BFN is limited, it can be realized in a single layer, or a
uniplanar configuration. Four-way BMs have also been modi-
fied to realize other functions, like dual polarization [17], cav-
ity-backed feeding [18], and low sidelobe level [19].
To design an 8 × 8 BFN producing 8 (2 × 4) beams, four 90º
couplers and two four-way BMs are required to provide eight
Uniplanar Beam-Forming Network Employing
Eight-Port Hybrid Couplers and Crossovers for 2-D
Multibeam Array Antennas
Ji-Wei Lian, Yong-Ling Ban, He Zhu, Member, IEEE, and Y. Jay Guo, Fellow, IEEE
B
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inputs and eight outputs; therefore the design difficulty in-
creases greatly, and one often resorts to multi-layer (qua-
si-planar) designs. Two examples of 8 × 8 BFNs deployed in
multi-layer SIW were realized in [20]-[21], both of which used
folded four-way BMs to reduce the overall size of the designs
and the overall configuration was composed of six-layer SIW.
Recently, such a topology was demonstrated in a uniplanar
design which required a large number of crossovers [22].
Compared with the above designs, a 2-D MAA with 16 (4 ×
4) beams is much more complicated and difficult to realize in
uniplanar configuration, because a 16 × 16 BFN with 16 inputs
and 16 outputs is required. Some different designs can be found
in the open literature [23]-[26]. All of these designed are real-
ized employing multi-layer SIW technology. Recently, a con-
cept of 2-D BM was proposed and a similar topology is realized
using waveguide technology [27]-[28]. The core concept of the
2-D BM is to combine the function of E-plane coupler and
H-plane coupler into a 2-D coupler to allocate the phase and
amplitude distribution at the same time. Such a concept helps
simplify the overall configuration because some of the neces-
sary components are integrated, although it does not contribute
a lot to the planarization and the reduction of the required in-
terconnections.
It should be noticed from [23]-[28] that a 16 × 16 BFN is not
easy to be integrated into a single layer or a uniplanar config-
uration, mainly because of the interconnections between two
sub-BFN sections. Taking the design in [24] for an example,
eight four-way BMs are required, half of which are E-plane
BMs and the rest are H-plane BMs. Between the E-plane sec-
tion and the H-plane section, overall 16 (4 × 4) interconnections
need to be dealt with. That is the reason why multi-layer SIW
technology is popular because it can help arrange the inter-
connections in separated layers to avoid too many intersections.
Unfortunately, multi-layer BFNs have a number of drawbacks
as follows: aligning different layers, particularly at high fre-
quencies; the losses caused by the transmission between sepa-
rated layers, and the fabrication complexity and high cost.
To tackle the above challenge, this paper presents a novel
uniplanar 16 × 16 BFN by using single-layer configuration. The
main contributions of this paper include the following. First, a
new topology for uniplanar 16 × 16 BFNs is proposed for the
first time. Second, a uniplanar eight-port hybrid coupler is
developed from a 3-D to a 2-D structure, corresponding to the
proposed topology for 16 × 16 BFNs. Third, a novel eight-port
crossover in SIW technology to address the path intersection
issue is reported, after introducing which, the number of the
intersections are dramatically reduced from 16 to merely 4.
Last but not the least, a single-layer SIW 16 × 16 BFN em-
ploying the proposed topology and eight-port components is
developed, based on which, 16 (4 × 4) beams are produced with
a simulated antenna array in High Frequency Structure Simu-
lator (HFSS).
The rest of the paper is organized as follows. The proposed
topology for uniplanar 16 × 16 BFNs is discussed in Section II,
based on which, the HFSS simulated model is shown in Section
III. The detailed design process is described in Section IV and
the experimental results are reported in Section V. Finally, a
brief conclusion is drawn in Section VI.
II. PROPOSED TOPOLOGY AND ITS REALIZATION
The traditional topology of the 2-D BM is displayed in Fig.
1(a) [27]. As is shown, there are eight blocks, denoting eight
2-D hybrid couplers. The whole 2-D BM is comprised of 16
input ports (or beam ports #B1-#B16) and 16 output ports (or
array ports #A1-#A16). Such a BFN can equally divide the
power into 16 output ports from any input with phase gradient
of ±45º, or ±135º along both x-axis and z-axis. With different
combinations, this BFN has 16 different phase states (φx, φz)
related to different inputs as follows.
(45º, 45º); (45º, 135º); (45º, –45º); (45º, –135º);
(–45º, 45º); (–45º, 135º); (–45º, –45º); (–45º, –135º);
(135º, 45º); (135º, 135º); (135º, –45º); (135º, –135º);
(–135º, 45º); (–135º, 135º); (–135º, –45º); (–135º, –135º).
For clarity, the 2-D hybrid couplers are divided into two
groups with different colors, four of which (CDEF) are in red
color and the other four (GHIJ) are in blue color. There are
overall 16 interconnections between these two sets of 2-D
hybrid couplers and this is the main reason why such a topology
is difficult to be integrated into a uniplanar form. It should be
mentioned that the intersections after the second set of the
couplers are removed to simplify the topology. The main
function of the removed intersections is to make sure the phase
difference between adjacent ports remain the same, which can
also be realized by rearranging the output ports. The arrange-
ments of the output ports before and after the removed inter-
section are shown in Fig. 1(b). In order not to change the phase
distribution, the output ports are arranged based on the dis-
(a)
(b)
Fig. 1. (a) Topology of the conventional 16 × 16 BFN. (b) Port rearrangement.
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tribution on the right in Fig. 1(b).
Based on Fig. 1(a), a new topology for uniplanar 16 × 16
BFNs is shown in Fig. 2(a). The first set of the 2-D hybrid
couplers (CDEF) are extracted and then placed in the four
corners of this topology while the other four (GHIJ) are placed
in the center. The couplers are connected to each other based on
their relationship in a 2-D BM. Phase shifters with different
value of phase shifting α1-α4 are introduced between couplers to
achieve desired phase distribution.
Assuming the transmission matrices of the eight-port hybrid
coupler and the intersection portion are Th and Ti, respectively,
the transmission matrix TB of the whole 2-D BM can be written
as
B H i H
T T TT
(1a)
where
000
0 0 0
0 0 0
000
h
h
Hh
h
T
T
TT
T
(1b)
and
1
2
3
4
2
1
4
3
3
4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
j
j
j
j
j
j
j
j
j
ij
eeee
eeee
Tee
1
2
4
3
2
1
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
j
j
j
j
j
j
ee
eeee
(1c)
Because the eight-port hybrid coupler is capable of providing
equal amplitude and ±90º of phase difference in two orthog-
onal directions, its transmission matrix Th can be expressed as:
/2 / 2
/2 / 2
/2 / 2
/2 / 2
1
1
1
21
1
j j j
j j j
hj j j
j j j
e e e
e e e
Te e e
e e e
(1d)
It can be noticed that the main difference between Fig. 1(a)
and Fig. 2(a) is that the topology of this 16 × 16 BFN is trans-
formed from a 3-D configuration to a 2-D, which means all the
components are placed within the same plane. However, the
eight-port hybrid coupler is of 3-D configuration and it is not
suitable for the proposed 16 × 16 BFN. To overcome this issue,
a new eight-port hybrid coupler is developed, which success-
fully converts the 3-D configuration into a 2-D case. The details
of such eight-port hybrid couplers are elaborated in the next
section.
In Fig 2(a), there are excessive intersections and they will
greatly complicate the design, which is another challenge in
the uniplanar design. Usually, crossovers are introduced to
address the path intersections. For example in Fig. 2(a), one
crossover is placed in one intersection, making it too com-
plicated to design when the topology contains too many in-
tersections. To alleviate this issue, a modified topology is
proposed and shown in Fig. 2(b) by employing two eight-port
crossovers, which allows four paths crossing over at the same
intersection. Based on these two eight-port crossovers, the
total number of path intersections is reduced from 16 to only 4,
which remarkably simplifies the complexity of the proposed
uniplanar 16 × 16 BFN.
Based on the topology given in Fig. 2(b), a uniplanar 16 ×
16 BFN is designed in SIW technology, as shown in Fig. 3(a),
as well as the fabricated prototype in Fig. 3(b). This BFN is
designed at the center frequency of 10 GHz, and the used
substrate is F4B with a dielectric constant of 2.55 and a loss
tangent of 0.001 @ 10 GHz. The conductor layer is copper
with thickness of 0.035 mm, the conductivity of which is 5.8 ×
(a) (b)
Fig. 2. (a) Proposed topology of 16 × 16 BFN. (b) Proposed topology of 16 × 16 BFN with eight-port crossover.
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107 siemens/m. The overall dimension of this design is 22.0 λ
× 16.7 λ × 0.03 λ (660 mm × 500 mm × 1 mm), where λ is the
wavelength in free space. The detailed design procedures are
illustrated in the following Section.
III. DETAILED DESIGN
Based on the above concept, one can design a uniplanar 16 ×
16 BFN by employing 8 eight-port hybrid couplers, 2 eight-port
crossovers, 4 four-port crossovers, and 16 phase shifters with
four values. The design processes of these basic components
are elaborated as follows.
A. Eight-Port Hybrid Coupler
As mentioned above, the uniplanar eight-port hybrid coupler
is a critical component because it is the key to transform the
topology of the 16 × 16 BFN from Fig. 1(a) to Fig. 2(a), i.e.,
from a 3-D to a 2-D topology. The development of the uni-
planar eight-port hybrid coupler is shown in Fig. 4(a). Starting
with state 1, the hybrid coupler is of 3-D topology and it is not
suitable for uniplanar design. It is capable of providing equal
amplitude and ±90º of phase difference in two orthogonal di-
rections, whose output phases are summarized in Table I. The
transmission matrix of the 3-D hybrid coupler Th can be de-
composed and represented as:
11
11
1 0 0 0
00
0 0 1 0
100
0 1 0 0
2
0 0 0 1
hh
hhh
TT
TTT
(2a)
where
/2
1/2
1
1
j
hj
e
Te
(2b)
where Th1 is the transmission matrix of the 2-D four-port hybrid
coupler. Based on this, the 3-D eight-port hybrid coupler is
taken apart into four 2-D four-port hybrid couplers, which are
orthogonally placed. The last step is to unfold the topology in
State 2 and rearrange all the couplers in one plane, as shown in
state 3, thus resulting in a uniplanar structure.
Based on Fig. 4(a), a uniplanar eight-port hybrid coupler is
designed in SIW technology, as shown in Fig. 4(b). The input
ports are #1-#4 and the output ports are #5-#8. Here, eight
imaginary ports #1'-#8' are placed at the end of the coupling
region like [29] to theoretically analyze the performance. For a
dually symmetric eight-port hybrid coupler, the four-mode
(a)
(b)
Fig. 3. (a) Simulated model of the proposed 16 × 16 BFN. (b) Fabricated
prototype of the proposed 16 × 16 BFN.
(a)
(b)
Fig. 4. (a) Development and (b) simulated model of eight-port coupler.
(d1=19.60, d2=9.40, d3=5.10, d4=5.10, d5=25.90, d6=14.2. Unit: mm)
TABLE I
PHASE DISTRIBUTION OF EIGHT-PORT HYBRID COUPLER
Phase
Input port
#1
#2
#3
#4
#5
#6
180
90
90
0
90
180
0
90
#7
#8
90
0
180
90
0
90
90
180
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decomposition method can be utilized to analyze the
S-parameters [30] as follows:
11 11 11 11
11 4
ee oo eo oe
S S S S
S
(3a)
11 11 11 11
21 4
ee oo eo oe
S S S S
S
(3b)
11 11 11 11
31 4
ee oo eo oe
S S S S
S
(3c)
11 11 11 11
41 4
ee oo eo oe
S S S S
S
(3d)
21 21 21 21
51 4
ee oo eo oe
S S S S
S
(3e)
21 21 21 21
61 4
ee oo eo oe
S S S S
S
(3f)
21 21 21 21
71 4
ee oo eo oe
S S S S
S
(3g)
21 21 21 21
81 4
ee oo eo oe
S S S S
S
(3h)
where ee oo eo and oe are short for the even-even, odd-odd,
even-odd, and odd-even mode, respectively. Excited by these
four different modes, the E-field distribution is plotted in Fig. 5.
It can be noticed that TE10 mode is stimulated when the
boundary condition is set as PMC and TE20 for PEC. Assuming
the input signal is α, the reflection coefficient for the bend is
j
e
, and the transmission coefficient for the bend is
j
e
,
the reflected signal and the transmission signal for the odd-odd
mode are
20 1
2
jjd
ee
and
20 1
2j j d
ee
, respec-
tively, where β20 is the phase constant of the TE20 mode and d1
is the length of the coupling region. Therefore,
20 1
2
11 jjd
oo
S e e
and
20 1
2
21 j j d
oo
S e e
.
Similarly, the results of the other three modes can be ob-
tained and the all results are summarized as below.
20 1
2
11 jjd
oo
S e e
(4a)
20 1
2
21 j j d
oo
S e e
(4b)
10 1
2
11 jjd
eo
S e e
(4c)
10 20 1
()
21 j j d
eo
S e e
(4d)
20 1
2
11 jjd
oe
S e e
(4e)
20 10 1
()
21 j j d
oe
S e e
(4f)
10 1
2
11 jjd
ee
S e e
(4g)
10 1
2
21 j j d
ee
S e e
(4h)
Substituting the results of (4a)-(4h) into (3a)-(3h), the ex-
pressions for S11-S81 can be obtained.
For the traditional four-port hybrid coupler design, the fol-
lowing condition is satisfied:
20 10 1
()
2
d
(5)
For an ideal bend, there are ρ=0 and τ=1. Based on these
results, the following relations can be found:
S11=S21=S31=S41=0 (6a)
10 20 1
()
51 1
2j j d
S e e
(6b)
10 20 1
()
61 1
2j j d
S je e
(6c)
10 20 1
()
71 1
2j j d
S je e
(6d)
10 20 1
()
81 1
2j j d
S e e
(6e)
Since this is a dually symmetric coupler, the S-parameters
for the other seven ports are also composed of these seven
factors. By choosing appropriate phase reference
(
10 20 1
()j j d
ee
), the S-matrix of this eight-port hybrid coupler
is depicted as follows.
OA
SAO
(7a)
where
/2 / 2
/2 / 2
/2 / 2
/2 / 2
1
1
1
21
1
j j j
j j j
j j j
j j j
e e e
e e e
Ae e e
e e e
(7b)
and O is the 4 × 4 zero matrix. Compared the results in (7b)
with that in (1d), it can be found that the transmission matrix of
the proposed eight-port hybrid coupler meets the phase and
amplitude requirements, i.e., to provide equal amplitude and
±90º of phase difference in two orthogonal directions.
To test its property, the HFSS simulated results of this SIW
eight-port hybrid coupler are shown in Fig. 6 including the
Fig. 5. E-field distribution at four different modes.
(a) (b)
Fig. 6. Simulated (a) S-parameters and (b) phase of the eight-port coupler.
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S-parameters and the phase performance. Within the target
frequency range (9.5-10.5 GHz), it is observed that the isolation
and reflection coefficients are lower than ‒15 dB. The trans-
mission coefficients vary from ‒6.6 dB to‒6.2 dB, and the
phase error is within ±3º.
B. Eight-Port Crossover
According to Fig. 2 (a) and (b), the eight-port crossover is
critical in reducing the number of intersections, thus simplify-
ing the design and making the uniplanar design easier. In the
open literature, most of the crossovers are four-port compo-
nents and can only address one path intersection [31]-[34]. To
deal with multiple intersections in multi-path BFNs, cascaded
crossovers are usually the solution, which would greatly in-
crease the design complexity and introduce more loss. To re-
place cascaded crossovers, crossovers with six ports or even
eight ports can help simplify the design. In the open literature,
there are limited crossover designs with more than four ports. In
[35], Lin et al. proposed a three-way crossover using three
different cavity modes. Such a method is not feasible for SIW
because it requires six ports along three directions. Two
six-port crossovers are realized in microstrip technology in
[36]-[37] and the design in [37] is further developed to an
eight-port crossover [38]. Such designs, however, are also not
suitable for SIW because they are based on impedance match-
ing theory.
In this paper, a new eight-port crossover in SIW technology
is proposed, as shown in Fig. 7. Different from the traditional
design, eight power dividers are introduced between input ports
and the formed circular cavity. Since this eight-port crossover
is dually symmetric, only the result of port #1 is analyzed and
the results for other seven ports are similar. After applying the
power dividers, each input port is divided into two virtual ports
(#1 to #1' and #1''). Since the TE10 mode is stimulated at the
input port, only z-component of the E-field exists within the
circular cavity. At port n' (n=2-7), the incident wave can be
expressed as
11
11
11
( , ) ( , ) ( , )
ˆ
( , ) ( , )
nn
n n n
jkr jkr
nn
E E E
E e E e z
(8)
where
1n
E
and
1n
E
are the incident field at port n' stimulated
by ports 1' and 1'', respectively; k is the wavenumber;
1n
r
(or
1n
r
) are the distance between port 1'(or 1'') and port n'.
Similarly, the incident field at port n'' can be represented by
11
11
11
( , ) ( , ) ( , )
ˆ
( , ) ( , )
nn
n n n
jkr jkr
nn
E E E
E e E e z
(9)
where
1( , )
n
E
and
1( , )
n
E
are the incident field at port
n'' stimulated by ports 1' and 1'', respectively; k is the wave-
number;
1n
r
(or
1n
r
) are the distant between port 1'(or 1'') and
port n''.
Fig. 7. Simulated model of the proposed eight-port crossover. (d7=14.00,
d8=4.00, d9=32.23, d10=38.84. Unit: mm)
(a)
(b)
(c)
Fig. 8. (a) Simulated E-field, (b) simulated results, and (c) parameter sweep of
eight-port crossover.
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The output field at port #n is the sum-field of two virtual
ports n' and n''.
( , ) ( , ) ( , )
n n n
E E E
(10)
Due to the symmetry, if and only if n=4, we have the fol-
lowing conditions
11nn
EE
(11a)
11nn
EE
(11b)
11nn
rr
(11c)
11nn
rr
(11d)
Under this condition,
( , )
n
E
and
( , )
n
E
have the same
amplitude and are in phase so that the field of port 4' and 4'' are
the same. For the other output ports (
4n
), the E-field does
not meet the condition (11) so that the field in dual virtual ports
of the output divider will be cancelled to some extent. Overall,
the introduced power dividers have two main functions. One is
to increase the transmission coefficient between opposite ports
and the other is to reduce the coupling between the input and
the isolated ports.
To further demonstrate the effect brought by the power di-
viders, the HFSS simulated E-field distributions of an
eight-port crossover with or without power dividers are pro-
vided in Fig. 8 (a) and (b), respectively. It can be observed that
this eight-port component functions as a crossover after intro-
ducing power dividers because most of the input energy goes
directly to the opposite output port.
The HFSS simulated S-parameters of the eight-port crosso-
ver with or without power dividers are depicted in Fig. 8(b).
Within the targeted frequency spectrum (9.5 GHz-10.5 GHz),
the isolation and reflection coefficients are both lower than ‒12
dB while the insertion loss is merely 0.43 dB at 10 GHz.
It should be noticed that some ripples appear in the results of
S-parameters and that is because of the emergence of the
higher-order mode, as shown in Fig. 8(c). The cavity of the
crossover can be viewed as an octagon confined by the aper-
tures of eight power dividers. The width of the aperture is 2*d7.
According to the geometrical characteristic of an octagon, the
dimension of the cavity d10 should be larger than d7*sec(3π/8)
in order to avoid overlap of adjacent ports. Such an overlarge
cavity can generate some higher-order modes, as indicated by
Fig. 8(c). One easy way to manipulate higher-order modes is to
adjust the parameter d8, which can help reduce the size of the
cavity. As is shown, the resonant frequencies of both the first
and second higher-order modes increase with a larger d8. By
choosing an appropriate value of d8, the higher-order mode can
be removed from the targeted frequency spectrum, i.e., 9.5 GHz
to 10.5 GHz. The final result of d8 in this design is 4.00 mm.
Such an eight-port crossover can be analyzed using the
four-mode decomposition technique as well according to
(3a)-(3h). Similar to the analysis conducted for the eight-port
hybrid coupler, two cuts are introduced in the diagonal lines of
the eight-port crossover to simplify the eight-port network into
a two-port circuit. Since it is not easy to express the reflection
and transmission coefficients under these four modes, we use
HFSS to extract these results as shown below.
11 0.13 0.93
oo
Sj
(12a)
21 0.25 0.03
oo
Sj
(12b)
11 0.26 0.92
eo
Sj
(12c)
21 0.10 0.04
eo
Sj
(12d)
11 0.47 0.85
oe
Sj
(12e)
21 0.10 0.04
oe
Sj
(12f)
11 0.36 0.90
ee
Sj
(12g)
21 0.02 0.01
ee
Sj
(12h)
Substituting these results into Equations (3a)-(3h), we have
11 0.06 0.02Sj
(13a)
21 0.11 0.03Sj
(13b)
31 0.01 0.01Sj
(13c)
41 0.31 0.9Sj
(13d)
Fig. 9. Simulated and calculated S-parameter.
(a)
(b)
Fig. 10. Simulated (a) model and (b) phase of phase shifters.
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8
51 0.11 0.03Sj
(13e)
61 0.07 0.01Sj
(13f)
71 0.07 0.01Sj
(13g)
81 0.01 0.02Sj
(13h)
The HFSS simulated S-parameters at 10 GHz are shown in
Fig. 9 together with the calculated results obtained from
(13a)-(13h). The HFSS simulated results in Fig. 9 are directly
extracted from HFSS results of the eight-port crossover. The
calculated results are obtained by converting the value in
(13a)-(13h) into decibel. It can be seen from Fig. 9 that the
calculated results agree well with the HFSS simulated coun-
terparts. Ideally, the S-matrix of the eight-port crossover can be
expressed as follows,
AO
SOA
(14a)
where
0 0 0 1
0 0 1 0
10 1 0 0
2
1 0 0 0
A
(14b)
C. Phase Shifter
To maintain the constant phase difference along two direc-
tions, the values of phase shifters are chosen as below.
190
(15a)
245
(15b)
345
(15c)
40
(15d)
As shown in Fig. 10(a), the phase shifters are inserted between
the first set and the second set of couplers. The four output ports
are connected to four phase shifters, namely, α1, α2, α3, and α4.
For clarity, the main transmission paths of these four phase
shifters are represented by lines in different colors. When de-
signing the phase shifters, it should be pointed out that the
phase error is mainly caused by two factors: one is the different
distance between couplers and the other is the phase shifting
brought by the crossover. To compensate the phase error and to
design phase shifters with balanced phase shifting ability, some
meander lines are introduced. It is known that the phase shift in
SIW is dispersive and can be represented as a function of fre-
quency. This approach is based on the fact that the phase var-
ying tendency of changing the width and the length of SIW are
(a) (b) (c) (d)
Fig. 11. (a) Simulated reflection coefficients. (b) Measured reflection coefficients. (c) Simulated isolation coefficients. (d) Measured isolation coefficients.
(a) (b) (c) (d)
(e) (f) (g) (h)
Fig. 12. Simulated transmission coefficients for ports (a) #B1, (b) #B2, (c) #B3, and (d) #B4. Measured transmission coefficients for ports (e) #B1, (f) #B2, (g) #B3,
and (h) #B4.
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9
opposite; therefore, appropriate width and length of SIW can be
selected to cancel the phase error [39]. The meander line can
extend the equivalent length of the SIW. In part of the trans-
mission line, the width is altered to realize balanced phase shift.
The HFSS simulated results of these four phase shifters are
plotted in Fig. 10(b).
IV. PERFORMANCE AND DISCUSSION
All the components designed in the above Section can be
integrated into a single layer and fabricated using printed circuit
board technology. The S-parameter and phase measurement is
conducted by KEYSIGHT N5225A Network Analyzer.
A. BFN Performance
Since this design is of dually symmetric configurations, only
the results of exciting ports #B1-#B4 are provided here. The
HFSS simulated and measured reflection coefficients are
shown in Fig. 11 (a) and (b), while the isolation coefficients
counterparts in Fig. 11 (c) and (d), respectively. From 9.5 GHz
to 10.5 GHz, all the results are lower than ‒10 dB including the
HFSS simulated and measured results. The reflection and iso-
lation coefficients of the BFNs are decided by these coefficients
of the basic components. When designing eight-port hybrid
couplers, eight-port crossovers, four-port hybrid couplers, and
phase shifters, the reflection and isolation coefficients are op-
timized to be less than –10 dB, which contributes to the satis-
factory reflection loss and isolation loss of the entire BFN.
Fig. 12 shows the transmission coefficients. For an ideally
lossless BFN, the transmission coefficients should be ‒12 dB.
The HFSS simulated results for ports #B1-#B4 are provided in
Fig. 12 (a)-(d) while the measured results in Fig. (e)-(f). Most
of the HFSS simulated transmission coefficients vary from ‒12
dB to ‒16 dB. Taking port #B1 as an example, the insertion loss
of the entire BFN is 1.9 dB at 10 GHz, including dielectric loss
of 1.5 dB. Operating at 10 GHz, the conductor loss is negligible;
therefore the conductor layer is assigned as Perfect-E boundary
in HFSS to accelerate simulation and the conductor loss is not
included in the simulation. Overall, the measured results drop
by around 3 dB compared with the HFSS simulated case. It is
inferred that the increase of the dielectric loss tangent contrib-
utes to the reduction of the measured transmission coefficients.
To demonstrate this inference, a HFSS model of a SIW path
with length of 700 mm is built to test the loss property, whose
result is plotted in Fig. 13 (700 mm is the estimated length of
the practical transmission path from port #B1 to #A1). Oper-
ating at 10 GHz, the dielectric loss can add up to 4.0 dB when
the dielectric loss tangent increases to be 0.003.
The phase differences along y- and x-directions are plotted in
Fig. 14 and 15, respectively. According to Fig. 14, the HFSS
simulated phase differences for ports #B1-#B4 are 45º±15º, ‒
135º±17º, 45º±15º and ‒135º±14º at 10 GHz. Similarly, the
phase differences shown in Fig. 15 are 45º±5º, 45º±16º, ‒
135º±5º and ‒135º±11º for ports #B1-#B4, respectively. It can
be noticed that the measured phase errors increase compared
with HFSS simulated counterparts. The difference between
simulation and measurement may be attributed to several fac-
tors, including:
1) The inconstant dielectric loss tangent of the substrate;
2) Fabrication tolerance;
3) Installation error brought by inserting and soldering
SMA connectors;
4) The phase and amplitude fluctuation caused by the ca-
bles.
B. 2-D Multibeam Array Antenna Using the Uniplanar BFN
To use the designed BFN, one can design a 4 × 4 antenna
array and connect it with the BFN by using, for instance, cables
as demonstrated in [2] and [14]. For a planar rectangular array,
the beam angle (θ, φ) is calculated by [24],
1
tan yx
xy
d
d
(16a)
2
2
1
sin y
x
xy
kd kd
(16b)
where k is the propagation constant in free space, ϕx and dx
represent the progressive phase differences and the distances
between the adjacent antenna elements along x-direction. Sim-
ilarly, ϕy and dy are the counterparts along y-direction.
To test the simulated and calculated performance of a 2-D
MAA fed by the proposed BFN, a 4 × 4 patch array is designed
using HFSS. The output amplitude and phase generated by the
BFN is used to excite such an array, as shown in Fig. 16 (a).
The distance between adjacent antennas is set as half
Fig. 13. Dielectric loss of different loss tangent.
TABLE II
PREDICTED PERFORMANCE OF 2-D MAA WITH SIMULATED OR MEASURED
RESULTS OF THE PROPOSED BFN
Gain (dBi)
Simulated (GHz)
Measured (GHz)
9.5
10.0
10.5
9.5
10.0
10.5
#B1
14.9
15.2
14.3
11.9
12.1
11.7
#B2
13.7
14.0
13.4
8.8
10.7
9.6
#B3
13.5
13.7
12.8
9.7
10.6
10.2
#B4
11.8
12.6
12.1
8.3
8.8
8.1
Efficiency
Simulated (GHz)
Measured (GHz)
9.5
10.0
9.5
10.0
9.5
10.0
#B1
61%
63%
56%
33%
33%
31%
#B2
59%
62%
60%
27%
31%
26%
#B3
61%
63%
55%
25%
30%
28%
#B4
53%
61%
59%
28%
27%
24%
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wavelength in free space. The produced radiation patterns are
displayed in Fig. 16 (b). To evaluate the difference between
simulation and measurement, both HFSS simulated and meas-
ured results from Figs. 12-14 are used to feed the model in Fig.
16 (a), and the predicted performance of 2-D MAA with sim-
ulated and measured results of the proposed BFN is summa-
rized in Table II. The efficiency is defined as gain over di-
rectivity of the 2-D MAA. It is observed that gains calculated
from measured results are lower than those from HFSS simu-
lated results by around 3dB, which results from the reduced
transmission coefficients in measurement.
Table III lists the properties of the proposed design and some
similar designs in the open literature. The traditional method to
realize 2-D BFNs is to utilize multiple 1-D BFNs and combine
them in orthogonal planes. For example in [14], two stacks of
Nolen matrices are applied to design 2-D multibeam. In recent
year, 1-D coupler was developed to 2-D one; therefore, the
traditional 1-D BM can be extended to 2-D one as well
[27]-[28]. It can be found from Table III that most of the pub-
lished literatures pay attention to the quasi-planar designs of
2-D BFNs with resorting to multi-layer SIW technology [20],
[23]-[24]. None of these designs has successfully realized the
2-D BFN into a uniplanar configuration due to the fact that 2-D
BFN is of 3-D topology. Compared with previous designs, this
(a) (b) (c) (d)
(e) (f) (g) (h)
Fig. 14. Simulated phase difference along y-direction for ports (a) #B1, (b) #B2, (c) #B3, and (d) #B4. Measured phase difference along y-direction for ports (e)
#B1, (f) #B2, (g) #B3, and (h) #B4.
(a) (b) (c) (d)
(e) (f) (g) (h)
Fig. 15. Simulated phase difference along x-direction for ports (a) #B1, (b) #B2, (c) #B3, and (d) #B4. Measured phase difference along x-direction for ports (e)
#B1, (f) #B2, (g) #B3, and (h) #B4.
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paper has managed to realize the uniplanar realization of 16 ×
16 BFN. The key step is to propose a new uniplanar topology
and build it using novel designs of multi-port couplers and
crossovers, allowing for generating 16 (4 × 4) beams. As a
result, this paper successfully integrates a complicated 16 × 16
BFN into a single-layer (or uniplanar) design, as observed from
Table III.
V. CONCLUSION
In this paper, a uniplanar BFN with 16 inputs and 16 outputs
allowing for generating 16 (4 × 4) beams is proposed. To
overcome the bulky size and design difficulty in traditional 16
× 16 BFNs, a new topology which turns the 3-D into 2-D con-
figuration and integrates all the basic components into a single
layer is proposed. Based on the proposed topology, the
eight-port hybrid coupler, as a critical component of this BFN,
is unfolded and developed into a uniplanar design by combin-
ing four four-port couplers in a cruciform. Furthermore, an
improved topology is presented to reduce the excessive inter-
sections of 16 × 16 BFN by using eight-port crossover, which
can address four path intersections at the same time. After
designing couplers, crossovers, and phase shifters, all of these
components are integrated into a uniplanar configuration. The
complete BFN can generate phase gradient of ±45º and ±135º
in both of the x- and y-directions and thus can be used to pro-
duce 2-D multibeam scanning in both elevation and azimuth
directions. Compared with previous designs, the proposed 16 ×
16 BFN has realized uniplanar configuration for the first time,
which greatly reduce the complexity in designing and fabri-
cating 16 × 16 BFN. The design is particularly suited for lower
frequencies where losses in the dielectric and conductor etc can
be better controlled.
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COMPARISON WITH OTHER DESIGNS
Ref.
Frequency
Transmission
Configuration
Layers
Planarity
Beam
Size (λ3)
Amplitude/Phase
error
[14]
5.8 GHz
Microstrip
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1
uniplanar
2*4
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[23]
60 GHz
SIW
8 Butler matrices
5
quasi-planar
4*4
30.0*30.0*0.7
N.A.
[24]
30 GHz
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8 Butler matrices
4
quasi-planar
4*4
16.5*4.5*0.2
2.4dB/10º
[27]
2.4 GHz
Microstrip
2-D Butler matrix
2
quasi-planar
4*4
1.6*1.6*0.004
1.2dB/7º
[28]
22 GHz
Waveguide
2-D Butler matrix
4
not planar
4*4
N.A.
N.A.
This
10 GHz
SIW
2-D Butler matrix
1
uniplanar
4*4
22.0*16.7 *0.03
2.6dB/17º
-90
-60
-30
0
30
60
90
-10
0
10
S
1
S
2
S
3
S
4
S
5
S
1
S
2
S
3
S
4
S
5
Radia
tio
n Pa
tte
rn (dB)
Theta (deg
)
(a) (b)
Fig. 16. (a) Simulated model of the 4 × 4 patch array. (b) Simulated pattern of the 4 × 4 patch array.
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Ji-Wei Lian was born in Guangdong, China, in 1992.
He received the B.S. degree in electronic science and
technology from Hunan University in 2015. He is
currently pursuing the Ph.D. degree in electromag-
netic field and microwave technology at the Univer-
sity Of Electronic Science and Technology of China
(UESTC), Chengdu, China.
Since 2018, he has been a Visiting Student with
the Global Big Data Technologies Centre, University
of Technology Sydney, Sydney, Australia. He has
authored/coauthored 20 papers in peer reviewed
international journals and conference proceedings. His current research inter-
ests include beam-forming networks and millimeter wave antenna arrays.
Mr. Lian is serving as a reviewer for several international journals, including
the IEEE Antennas and Wireless Propagation Letters, IEEE Access, and Mi-
crowave and Optical Technology Letters.
Yong-Ling Ban was born in Henan, China. He re-
ceived the B.S. degree in mathematics from Shandong
University in 2000, the M.S. degree in electromag-
netics from Peking University in 2003, and the Ph.D.
degree in microwave engineering from the University
of Electronic Science and Technology of China
(UESTC), Chengdu, China, in 2006.
In 2006, he joined the Xi’an Mechanical and Elec-
tric Information Institute as a Microwave Engineer. He
then joined Huawei Technologies Co., Ltd., Shenzhen,
China, where he designed and implemented various
terminal antennas for 15 data card and mobile phone
products customized from leading telecommunication industries like Voda-
fone. From 2010 to 2016, he was an Associate Professor with UESTC, where
he is currently a Professor. From 2014 to 2015, he was a Visiting Scholar with
Queen Mary University of London. His research interests include wideband
small antennas for 4G/5G handset devices, MIMO antenna, and millime-
ter-wave antenna array. He has authored 60 refereed journal and conference
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13
papers on these topics. He holds granted and pending Chinese and overseas
patents.
He Zhu (M’18) received the Bachelor and Master
degree from South China University of Technology,
Guangzhou, China, in 2011 and 2014, respectively,
and the Ph.D. degree in Electrical Engineering from
the School of ITEE, University of Queensland,
Brisbane, Australia, in 2017. He is currently a
Post-doctoral Research Fellow with Global Big Data
Technologies Centre (GBDTC), University of
Technology Sydney (UTS), Ultimo, NSW, Australia.
His research interests include development of passive
and tunable microwave and mm-wave devices, radio frequency integrated
circuits and systems, and beam-forming networks for antenna arrays.
Y. Jay Guo (Fellow’2014) received a Bachelor
Degree and a Master Degree from Xidian University
in 1982 and 1984, respectively, and a PhD Degree
from Xian Jiaotong University in 1987, all in China.
His research interest includes antennas, mm-wave
and THz communications and sensing systems as
well as big data technologies. He has published over
470 research papers including 250 journal papers,
most of which are in IEEE Transactions, and he holds
26 patents. He is a Fellow of the Australian Academy of Engineering and
Technology, a Fellow of IEEE and a Fellow of IET, and was a member of the
College of Experts of Australian Research Council (ARC, 2016-2018). He has
won a number of most prestigious Australian Engineering Excellence Awards
(2007, 2012) and CSIRO Chairman’s Medal (2007, 2012), and was named one
of the most influential engineers in Australia in 2014 and 2015, respectively.
Prof Guo is a Distinguished Professor and the Director of Global Big Data
Technologies Centre (GBDTC) at the University of Technology Sydney (UTS),
Australia. Prior to this appointment in 2014, he served as a Director in CSIRO
for over nine years. Before joining CSIRO, he held various senior technology
leadership positions in Fujitsu, Siemens and NEC in the U.K.
Prof Guo has chaired numerous international conferences and served as guest
editors for a number of IEEE publications. He is the Chair of International
Steering Committee, International Symposium on Antennas and Propagation
(ISAP). He was the International Advisory Committee Chair of IEEE
VTC2017, General Chair of ISAP2022, ISAP2015, iWAT2014 and
WPMC'2014, and TPC Chair of 2010 IEEE WCNC, and 2012 and 2007 IEEE
ISCIT. He served as Guest Editor of special issues on “Antennas for Satellite
Communications” and “Antennas and Propagation Aspects of 60-90GHz
Wireless Communications,” both in IEEE Transactions on Antennas and
Propagation, Special Issue on “Communications Challenges and Dynamics for
Unmanned Autonomous Vehicles,” IEEE Journal on Selected Areas in Com-
munications (JSAC), and Special Issue on “5G for Mission Critical Machine
Communications”, IEEE Network Magazine.
