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Abstract—In practice, the broadband feeding network on the
back side of an antenna can have a non-negligible effect on the
antenna’s back-radiation due to the feeding network’s radiation
contribution. Thus, a back-radiation cancellation scheme is
proposed by co-designing the antenna and its feeding network to
solve this problem. The antenna and its feeding network can be
viewed as a two-element array. Their radiation towards the
antenna's backward direction can cancel each other when both
have equal amplitude and opposite phases along the back direction.
A differential fed dielectric resonator antenna (DRA) through a
Rat-race coupler ( hybrid coupler) and a T-shaped
broadband differential feeding network are compared and
analyzed to verify the proposed scheme. In addition, a DRA
array with a T-shaped broadband differential feeding network in
a previous work (where the feeding network’s radiation effect on
the back side was overlooked) is used for experimental validation
of the proposed scheme. Simulations and measurements
demonstrate significant back-radiation suppression than the ideal
differential feeding network.
Index Terms—backward radiation suppression, feeding
network, dielectric resonator antennas (DRAs), phase center.
I. INTRODUCTION
HE feeding network is an integral part of an antenna [1],
[2]. A lossy feeding network can decrease the antenna
efficiency and deteriorate the radiation patterns due to the
dielectric loss, ohmic loss, and parasitic radiation of the feeding
network [3]. Microstrip, stripline, and waveguide feeding
configurations are widely employed in the feeding network
design of various antennas or arrays. Microstrip feeding
networks are commonly used at lower microwave frequencies
for compactness, easy integration, and low cost.
Dielectric resonator antennas (DRAs) have been widely
employed in various applications over the past few decades [4]-
[8]. However, the high backward radiation is an inherent
demerit for the DRA. Many efforts have been made to suppress
the backward radiation of the DRAs. Nevertheless, they mainly
This work was supported by the National Key Research and Development
Program of China under Grant 2020YFA0709800. (Corresponding author:
Xiaoming Chen).
S. Song, X. Chen, and J. Li are with the School of Information and
Communications Engineering, Xi’an Jiaotong University, Xi’an 710049, China
(email: xiaoming.chen@mail.xjtu.edu.cn).
focus on designing and optimizing antenna structures and pay
less attention to the feeding network effect, particularly when it
does not contribute to the antenna’s primary beam side.
However, when the feeding network is located on the opposite
side of the antenna and contributes to the back radiation side of
the antenna, it has a drastic effect on the back radiation that
could drastically increase the back radiation, such as the narrow
slot excitation, which should be blocked by a reflector to reduce
its effect [9]. Also, a printed circuit feeding network on the back
side could increase the back radiation of the antenna. Such a
case is usually overlooked. This article considers this case and
analyzes the feeding networks’ effects on back radiation. A
back-radiation cancellation scheme is proposed by co-
designing the antenna and its feeding network
Usually, feeding networks are designed to radiate as less as
possible to maintain the radiation patterns of antennas. Unlike
the previous works, this work shows that the backward
radiation can be significantly suppressed by properly designing
the antenna and its feeding network to make their backward
radiations equal in amplitude yet out-of-phase. A differentially
fed DRA [10] with a T-shaped broadband differential feeding
network [11] is used to validate the proposed design concept.
Note that the DRA was previously presented in [10], where the
large front-to-back ratio (FBR) is explained as it was due to the
magnetoelectric property of the DRA together with the small
decoupling ground; the feeding network’s radiation was
overlooked. Here, the focus is on the overlooked feeding
network’s radiation. The superior FBR performance of the
proposed scheme, compared with the ideal feeding network
(with no radiation) case, is further explained. More importantly,
an effective back radiation suppression scheme is proposed
accordingly. It is worth mentioning that the proposed scheme is
independent of the types of antennas and feeding networks, and
can be applied to magnetoelectric dipole (ME-dipole) antennas
for further FBR enhancement. Simulations and measurements
demonstrate the effectiveness of the proposed scheme.
A. A. Kishk is with the Department of Electrical and Computer Engineering,
Concordia University, Montreal, QC H3G 1M8, Canada (email:
kishk@encs.concordia.ca).
Co-design of Dielectric Resonator Antenna and
T-shaped Microstrip Feeding Network for Back-
Radiation Suppression
Simin Song, Xiaoming Chen, Senior Member, IEEE, Jianxing Li, Member, IEEE, and Ahmed A.
Kishk, Life Fellow, IEEE
T
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Fig. 1. Antenna and its feeding network positioned along the z-axis.
(a) (b)
(c)
Fig. 2. (a) Differential fed DRA with
= 20, = 7.0, = 17.5,
= 8.3, = 26.6, = 28.5, = 21.7,
= 5.4, and
= 120.0 (unit:
mm) [10]. (b) Rat-race coupler with = 10.0, = 1.7, = 3.1, = 15.0,
= 10.3, = 15.0, = 21.8, and
= 13.1 (unit: mm). (c) T-shaped
broadband differential feeding network with (for = 10.0) = 22.7, =
16.5, = 15.0, = 10.4, = 53.0, = 5.0, = 4.0, = 10.0, =
4.0, = 1.8, and = 1.0 (unit: mm).
II. ANALYSIS AND DESIGN EXAMPLES
A. Back-Radiation Cancellation Scheme
The electric field component radiated by an antenna in the far
zone can be written as,
(1)
where
is a unit vector. and represent
amplitude and phase patterns, respectively. The phase center is
a reference point that minimizes ’s variations with
respect to and
[12]. Ideally, the phase center is the
reference point that achieves equi-phase far-field radiation of
the antenna. However, in practice, the phase center is not unique
but depends on the view range of the radiation pattern, radiation
plane cut, and frequency of operation [13]. Thus, the phase
center is better defined by the position where the phase variation
is sufficiently small within a defined solid angle over the main
lobe [14]-[16]. Analytical approaches for determining the
precise phase center positions can be applied to typical antennas
with well-defined far-field expressions like dipoles and horn
antennas [17]-[19]. For instance, the phase center was
considered to be the center of the radius of curvature of the
(a) (b)
Fig. 3. Radiation patterns of only the Rat-race coupler (3-dB hybrid
coupler) and the T-shaped differential feeding networks at 3.5 GHz in (a) E-
plane (yz-plane) and (b) H-plane (xz-plane).
(a) (b)
Fig. 4. Normalized radiation patterns of the DRAs fed by different feeding
networks at 3.5 GHz in (a) E-plane (yz-plane) and (b) H-plane (xz-plane).
aperture phase front [14], [17]. Additionally, it can be
determined by plotting the phase variations in the far field [18].
An alternative approach was to calculate the amplitude and
phase evolution of a radiation beam using the Gaussian beam
mode analysis [19]. In addition, several numerical methods
have been proposed for phase center calculation [20]-[23]. A
general approach was to use an iterative procedure to maximize
the phase efficiency via measured phase patterns [20]-[22].
Another procedure was based on the power measurements
without any requirement of radiation pattern’s phase
information [23]. The phase center of an antenna can also be
determined via the far-field radiation characteristics of the
antenna and a weighing factor derived from the amplitude
pattern [24]. Also, in [15], [16], optimization is used to find the
phase center point that maximizes the phase efficiency.
The antenna and its feeding network can be regarded as a
two-element array, where elements are located at their
respective phase centers (cf. Fig. 1). The main feeding network
radiates in the side of the back radiation of the antenna.
The backward field ( ) of the antenna is determined
by the far-field and the feeding network fields with a
phase difference between them. The back radiation can be
reduced when the phase difference between the antenna back
radiation and its feeding network radiation is between and
Furthermore, a back-radiation null can be achieved if the
phase difference is with = at . It is usually
required that the feeding network radiation be as small as
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possible to avoid affecting the radiation characteristics of the
TABLE I
RADIATION CHARACTERISTICS OF DIFFERENT FEEDING NETWORKS
Feeding
network
Backward
realized
gain (dBi)
Backward
E-field
(r=1m)
(V/m)
Phase center
(mm)
Phase
difference
()
Ideal
differential
-9.5
(0,0,14.2)
N.A.
Rat-race
coupler
-12.4
1.2
(-22.4, 26.9, 2.2)
50.5
T-shaped
(=4 mm)
-17.4
0.6
(-6.7, 29.7, -19.6)
142.1
T-shaped
(=7 mm)
-16.4
(-0.8, 32.8, -17.8)
134.5
T-shaped
(=10 mm)
-13.7
(6.2, 30.5, -16.9)
130.8
antenna. However, it is shown here that properly designing the
antenna and its feeding network for their back radiation at
is equal in magnitude but out-of-phase to minimize their
summation within the antenna bandwidth. In this sense, the
feeding network’s radiation does not need to be made as small
as possible.
B. Two Types of Microstrip Feeding Networks
To demonstrate the theoretical analysis of the back-radiation
cancellation, DRAs (recently proposed in [10]) with two kinds
of microstrip feeding networks are designed and simulated as
an example. Fig. 2(a) shows two probes differentially fed the
proposed DRA on a small ground plane with detailed
dimensions.
Two different microstrip feeding networks with an operating
band of 3-4 GHz are designed for differential excitation of the
DRA. The circuit configurations of these two feeding networks
are presented in Figs. 2(b) and (c), respectively. One is the Rat-
race coupler (3-dB ring hybrid coupler) [25], which has a
simple structure without additional matching components
compared with other couplers like the Magic Tee. The other is
the T-shaped broadband phase shifter [11], [26] cascaded to a
Wilkson power splitter. For the T-shaped phase shifter, the
phase shift value is mainly determined by the widths of the main
line and the open stub ( and ). The design parameters of
the feeding networks are listed in the caption of Figs. 2(b) and
(c). The radiation patterns of the Rat-race coupler and the T-
shaped broadband differential feeding networks with different
at center frequency are depicted in Fig. 3. Note that the
length of the main microstrip line is reduced for increased
for the opposite phase output. is up to 10 mm for
demonstration of the proposed scheme, and more parameters
need to be considered for wider . Larger radiation of the
feeding network can be seen for wider , since the T-shaped
phase shifter can be view as a radiating element whose radiation
increases by increasing . In addition, the Rat-race coupler
has the largest back radiation compared to the T-shaped
broadband feeding networks.
The normalized radiation patterns of the DRAs, together with
the feeding mentioned above networks at the center frequency,
are shown in Fig. 4. Note that the DRA with an ideal differential
feeding network is used as a benchmark. As can be seen,
compared with the benchmark, the Rat-race coupler feeding
Fig. 5. Differential fed conventional DRA with
= 23.2, = 6.0, = 20.0,
= 7.8, and
= 120.0 (unit: mm).
(a) (b)
Fig. 6. Normalized radiation patterns of the conventional DRA fed by different
feeding networks at 3.5 GHz in (a) E-plane (yz-plane) and (b) H-plane (xz-
plane).
network causes higher backward radiation of the antenna,
whereas that with the T-shaped differential feeding networks
are suppressed. Furthermore, the backward radiation of the
antenna (with the T-shaped feeding network) decreases by
increasing .
The gains of the DRAs fed by the T-shaped differential
feeding networks are dBi, whereas that with the Rat-
race coupler causes an average 1.9 dB gain drop compared with
the ideal differential feeding network due to the larger losses.
Moreover, the peak total radiation efficiencies of the antennas
with the T-shaped feeding networks and the Rat-race coupler
are 95% and 72%, respectively.
The backward radiation characteristics and phase centers of
the DRA and the feeding networks are listed in TABLE I. The
phase center is calculated by the full-wave simulation software
CST Microwave Studio. The phase center of the DRA is 0.2
(where is the free-space wavelength at the center frequency)
above the large ground plane, whereas the phase centers of the
feeding networks are near or below the ground plane. Ideally,
the electromagnetic waves of the antenna element and the
feeding network traveling along the backward direction can be
the same in magnitude and out-of-phase. Specifically, the phase
difference between the antenna and the Rat-race hybrid coupler
in the negative z-axis is , leading to an increase in
backward radiation. On the other hand, the phase difference
between the antenna and the T-shaped broadband differential
feeding network with varied ranges from to
along the negative z-axis, leading to reduced back radiation. It
can also be seen that for wider , the radiation of the T-shaped
feeding network is stronger and closer to the antenna's back
radiation. Thus, a wider leads to back radiation suppression.
It is worth mentioning that the radiation of the feeding network
should not be as small as possible. Instead, it should be designed
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(a) (b)
(c)
Fig. 7. Photos of (a) the rightmost array element of the fabricated 14 DRA
array, (b) the feeding network at the array’s backside, and (c) the testing
environment.
(a) (b)
Fig. 8. Simulated responses of the T-shaped feeding network. (a) S-parameters.
(b) Phase difference between Port2 and Port3.
in conjunction with the antenna to achieve back-radiation
cancellation.
To further verify the proposed scheme, the T-shaped
differential feeding network [cf. Fig. 2(c)] is applied to a
conventional DRA differentially fed by a pair of probes, as
shown in Fig. 5. The detailed dimensions of the DRA are listed
in the caption of Fig. 5.
The radiation patterns of the conventional DRA with an ideal
differential feeding network and the T-shaped network are
depicted in Fig. 6. The T-shaped network exhibits an opposite
effect compared with the phenomenon mentioned above,
causing higher backward radiation compared with the
benchmark. The phase centers of the conventional DRA and the
T-shaped feeding network are 0.38 and 0.2 below the large
ground plane, respectively. The phase difference between the
DRA and T-shaped differential feeding network is along
the negative z-axis. The electromagnetic waves of the DRA and
the feeding network in the back direction are superimposed to
some extent, leading to an increase in the backward radiation of
the antenna. Note that the T-shaped feeding network has an
opposite effect for different antenna elements. Thus, it is
necessary to jointly design the antenna and its feeding network
for back-radiation suppression.
C. Experimental Validation
To experimentally demonstrate the effectiveness of the
(a) (b)
Fig. 9. Normalized simulated and measured radiation patterns of the DRA array
with a T-shaped differential feeding network at 3.5 GHz in (a) E-plane (yz-
plane) and (b) H-plane (xz-plane) of Antenna 1.
proposed scheme, a DRA array fed by a T-shaped differential
feed network with 0.5 inter-element spacing [10] is used as
an example (cf. Fig. 7). The DRA is made of ceramic dielectric
blocks with 9.8 relative permittivity and 0.002 tangential loss.
The feeding network is printed on a 0.813-mm thick Rogers
RO4003C substrate (with a relative permittivity of 3.55 and a
loss tangent of 0.0027), and the width of the open stub () is
10 mm. The simulated responses of the T-shaped differential
feeding network are depicted in Fig. 8. As can be seen, the
phase difference varies from to within the
operating band 3-4 GHz, indicating good performance.
The radiation characteristics are measured in a multi-probe
anechoic chamber. Simulated and measured radiation patterns
of Antenna 1 (i.e., the rightmost array element) at 3.5 GHz are
plotted in Fig. 9. Other antenna elements exhibit similar
radiation patterns and are omitted here for brevity.
Compared with the ideal differential feeding network, the
simulated and measured backward radiations for co-
polarizations of the DRAs fed by the T-shaped feeding
networks are reduced by 5.8 dB and 5.7 dB, respectively (which
was overlooked in the previous work). The cross-polarizations
are negligible (< -23 dB). The simulated and measured gains
are dBi and dBi, respectively. Good
agreement between measurement and simulation verifies the
effectiveness of the proposed scheme.
III. CONCLUSION
A back-radiation suppression scheme has been proposed.
The backward radiations from the radiation element and the
feeding network could cancel each other by properly designing
the antenna and its feeding network. DRAs fed by different
microstrip differential feeding networks have been compared
and analyzed for verification. The T-shaped broadband
differential feed network with closer amplitude and opposite
phase can significantly reduce the back radiation of the DRA.
A prototype of a DRA array with a T-shaped feeding network
has been used for experimental demonstration. Noticeable
back-radiation suppression has been observed compared with
the ideal differential feed network. The proposed scheme’s
effectiveness has been verified by simulation and measurement.
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Sim S11
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