Analysis and Design of Ultra-Wideband 3-Way Bagley Power Divider Using Tapered Lines Transformers

Abstract

An ultra-wideband (UWB) modified 3-way Bagley polygon power divider (BPD) that operates over a frequency range of 2–16 GHz is presented. To achieve the UWB operation, the conventional quarter-wave transformers in the BPD are substituted by two tapered line transformers. For verification purposes, the proposed divider is simulated, fabricated, and measured. The agreement between the full-wave simulation results and the measurement ones validates the design procedure.

Full text

Hindawi Publishing Corporation
International Journal of Microwave Science and Technology
Volume 2012, Article ID 197416, 6pages
doi:10.1155/2012/197416
Research Article
Analysis and Design of Ultra-Wideband 3-Way Bagley Power
Divider Using Tapered Lines Transformers
Khair Al Shamaileh,1Abdullah Qaroot,2Nihad Dib,3
Abdelfattah Sheta,4and Majeed A. Alkanhal4
1Waseela for Integrated Telecommunication Solutions, P.O. Box 962487, Amman 11196, Jordan
2Electrical Engineering Department, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia
3Electrical Engineering Department, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan
4Electrical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia
Correspondence should be addressed to Khair Al Shamaileh, khair.shamaileh@waseela-net.com
Received 26 October 2011; Accepted 11 April 2012
Academic Editor: Walter De Raedt
Copyright © 2012 Khair Al Shamaileh et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
An ultra-wideband (UWB) modified 3-way Bagley polygon power divider (BPD) that operates over a frequency range of 2–16 GHz
is presented. To achieve the UWB operation, the conventional quarter-wave transformers in the BPD are substituted by two tapered
line transformers. For verification purposes, the proposed divider is simulated, fabricated, and measured. The agreement between
the full-wave simulation results and the measurement ones validates the design procedure.
1. Introduction
Recently, the need for microwave components that have the
capability of operating over a wide range of frequencies
has motivated many researchers. Thus, many papers that
investigate the ultra-wide operation for different microwave
devices such as the Wilkinson power dividers (WPDs),
branch line couplers (BLCs), and antennas were proposed.
In [1], an UWB directional coupler that operates over a
frequency range of 3.1–10.6 GHz was presented. To realize
such an UWB coupler, two elliptically shaped microstrip
lines, which are broadside coupled through an elliptically
shaped slot, were used. In [2], a similar approach was used
to design a slot-coupled multisection quadrature hybrid
coupler for UWB applications. A novel approach for the
design of UWB 3 dB couplers, out-of-phase equal-split
power dividers, omnidirectional monopole antennas, and
directional tapered slot antennas was proposed in [3]. In [4],
a novel UWB WPD with modifications on the traditional
divider by adding an extra open stub on each branch
was proposed. In [5], an UWB WPD that consists of two
branches of impedance transformers, each one consisting
of two sections of transmission lines with different charac-
teristic impedances and different lengths, was proposed. A
modified UWB WPD formed by implementing one delta
stub on each branch was proposed in [6]. In [7], and based
on the theory presented in [8],aWPDthatoperatesovera
frequency range of 2–10.2 GHz was designed by substituting
its conventional quarter-wave arms by tapered lines. Three
resistors were added along the tapered lines to achieve an
acceptable isolation between the output ports.
One of the power dividers, which has been a new area
of research, is the Bagley polygon power divider (BPD)
[9–17]. Compared to other power dividers, such as the
Wilkinson power divider, Bagley polygon power divider does
not use lumped elements, such as resistors, and can be
easily extended to any number of output ports. However,
the output ports for such dividers are not matched, and
the isolation between them is not as good as that of the
Wilkinson power divider. In [9], reduced size 3-way and 5-
way Bagley power dividers (BPDs), using open stubs, were
presented. In [10], an optimum design of a modified 3-
way Bagley rectangular power divider was investigated. In
[11,12], a general design of compact multiway dividers based

2 International Journal of Microwave Science and Technology
1 2 3 4 5 6 7 8
35
40
45
50
55
60
65
70
75
Return loss (dB)
Value of B
Figure 1: The obtained input return loss (in dB) versus Bfor Zs=100 Ωand Zl=33.333 Ω.
Port 4 Port 3 Port 2
Port 1
ZhZh
Zm
Zm
λ/4
Z0
Z0Z0
Z0
lh
(a)
Port 1
Zh
Zm
λ/4
2Z0
2Z0
Z0
lh
Zl
(b)
Figure 2: Schematic diagram of the 3-way BPD and its equivalent circuit.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
30
40
50
60
70
80
90
100
Tapered impedance (Ohms)
z/d
B=1.5
B=3.5
B=5.5
B=7.5
Figure 3: The tapered impedance variation for different values of
B.
00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
1.5
Width (mm)
B=7.5
B=5.5
B=3.5
B=1.5
z/d
−1.5
−1
−0.5
Figure 4: The tapered line width variation for different values of B.
on BPDs was introduced. In [13],acompactdual-frequency
3-way BPD using composite right-/left-handed (CRLH)

International Journal of Microwave Science and Technology 3
0.43
39.96
2.67
(a)
0 2 4 6 8 10 12 14 16
0
5
Frequency (GHz)
Magnitude (dB)
−5
−10
−15
−20
−25
−3 0
−35
−45
−40
−50
S11
S21
(b)
Figure 5: (a) The designed UWB tapered line transformer (dimensions are in mm). (b) The input port matching parameter S11 and the
transmission loss parameter S21.
7.38
9.5
38.18
10
2.67
1.5
3.73
0.42
18.22
Figure 6:ThelayoutoftheproposedUWB3-wayBPD(dimensions
are in mm).
transmission lines was implemented. Recently, and based on
the generalized 3-way Bagley polygon power divider, dual-
passband filter section was presented in [14]. Moreover,
compact 5-way BPD for dual-band (or wide-band) operation
was proposed in [15]. Dual-band modified 3-way BPDs
based on substituting the quarter-wave sections of the
conventional design by their equivalent dual-band matching
networks were presented in [16]. Very recently, multiband
miniaturized 3-way and 5-way BPDs were proposed in [17].
It should be mentioned here that all of the BPDs investigated
in [9–17] have an odd number of output ports. In [18], a
novel approach for the design of modified BPDs with even
number of output ports was proposed.
In this paper, an UWB modified 3-way BPD that operates
over the frequency range of 2–16 GHz is presented. To have
such a divider, the quarter-wave sections are substituted by
their equivalent UWB tapered lines. The designed UWB
divider is simulated using two full-wave EM simulators.
Moreover, the divider is fabricated and measured, and the
simulation and measurement results are in a good agree-
ment.
2. Tapered Line Design
According to [7,8], the maximum input return loss (in dB)
for a given tapered line that is used in order to match a
source impedance Zsto a load impedance Zlis given by the
following equation:


RLinput

max
=−20 logtanhB
sinh B(0.21723)lnZl
Zs,
(1)
where Bis a predefined design parameter used to determine
the tapered line curve. Figure 1shows the effect of increasing
Bon the obtained input return loss.
As seen from Figure 1, larger values of Bresult in lower
reflection at the input port. However, increasing Bwill
demand wider tapered line width and longer length.
After choosing the value of Bin order to achieve a desired
input return loss, the exponential tapered line characteristic
impedance is calculated using the following equations [7,8]:
lnZ(z)
Zs=0.5ln
Zl
Zs1+GB,2
z
d−0.5,(2a)
where
G(B,ξ)=
B
sinh Bξ
0
I0B1−ξ2dξ.(2b)
It should be mentioned here that Z(z)in(2a) represents
the characteristic impedance of the tapered line at point z,
and I0(x) represents the modified zero-order Bessel function.
The tapered line length dis a predefined variable chosen
appropriately to achieve the desired maximum return loss.

4 International Journal of Microwave Science and Technology
02 4 6 8 10 12 14 16
Frequency (GHz)
Magnitude (dB)
−5
−10
−15
−20
−25
−3 0
−35
−45
−40
−50
S11: IE3D
S11: HFSS
(a)
0 2 4 6 8 10 12 14 16
Frequency (GHz)
Magnitude (dB)
−4.4
−4.6
−4.8
−5
−5.2
−5.4
−5.6
−5.8
−6.2
−6
S21: IE3D
S21: HFSS
(b)
0 2 4 6 8 10 12 14 16
Frequency (GHz)
Magnitude (dB)
−3.5
−4.5
−5.5
−4
−5
−6
S31: IE3D
S31: HFSS
(c)
Figure 7: Simulated scattering parameters for the designed UWB BPD.
3. UWB 3-Way BPD Design
In this section, the design of a modified UWB 3-way BPD
is presented. Figure 2(a) shows the schematic diagram of
the 3-way modified BPD [11]. Noting that this divider
is symmetric around its center line, an equivalent circuit
(looking from port 1 to the right or left side) can be drawn as
shown in Figure 2(b).
Referring to the equivalent circuit, it can be easily realized
that choosing Zh=2Z0makes the design of this BPD
independent of the length lh. In this case, the characteristic
impedance (Zm)ofthequarterwavesectionisZm=
(2Z0)Zl,whereZl=2Z0/3. This gives
Zm=(2Z0)
√3.(2)
Thus, each quarter-wave section matches a load impedance
of Zl=2Z0/3 to a source impedance of Zs=2Z0, resulting
in a perfect match at port 1 (the input port) and equal
split power division to the three output ports. As noted in
the Introduction, the BPD does not contain any lumped
elements, and it can be easily extended to any number of
output ports.
Now, considering a characteristic impedance of 50 Ω, the
values of Zsand Zlare 100 Ωand 33.333 Ω,respectively.
These values will be incorporated in the tapered line design
equations given in (1)and(2a). Then, the resulting tapered
line will replace each conventional quarter-wave transmis-
sion line transformers in the BPD presented in Figure 2
in order to obtain an UWB operation. Figure 3shows the
variation of the tapered impedance for different values of
B, which can be translated into microstrip width variation
as shown in Figure 4. It is worth mentioning here that the
substrate used in order to obtain the tapered line width for
all cases is Duroid RT5870 with a relative permittivity εr=
2.33, a thickness of 0.508 mm, and a loss tangent of 0.0012.
It can be seen from Figures 3and 4that larger values of
Bresult in a wider microstrip line width. In our design, B
is chosen to be 5.5, which corresponds to a maximum input
return loss of 56.44 dB. The length of the designed tapered
line is set to 40 mm, which is about 1.48 times the length of
the conventional transmission line transformer at the lower

International Journal of Microwave Science and Technology 5
# 2
# 3
# 4
# 1
Figure 8: The photograph of the fabricated divider.
0 2 4 6 8 10 12 14 16
Frequency (GHz)
Magnitude (dB)
0
−5
−10
−15
−20
−25
−30
−35
−40
−45
−50
S11
S21
S31
Figure 9: Measured scattering parameters of the divider shown in
Figure 8.
frequency (2 GHz). However, such slight increase in the
circuitry size leads to obtaining the desired electrical perfor-
mance, especially the input port matching and transmission
parameters performances, not only at a single frequency, but
also over a considerable wide range of 2–16 GHz. Figure 5(a)
shows the designed tapered transformer that matches a
source impedance of 100 Ωto a load impedance of 33.333 Ω
along with its obtained input port matching parameter (S11)
and transmission loss parameter (S21) shown in Figure 5(b).
An input return loss better than 10 dB is obtained over a
frequency range of 2–16 GHz for the designed transformer.
Moreover, the transmission coefficient S21 equals to −0.2 dB
overtheentirefrequencyrange.Itisworthtopointouthere
that these results were obtained using the full-wave simulator
IE3D [19].
4. Simulation Results
Figure 6shows the layout of the designed UWB modified
3-way BPD. This proposed divider is simulated using two
different full-wave electromagnetics simulators: IE3D [19];
which solves Maxwell’s equations using the method of
moments (MoM), and HFSS [20]; which solves the same
equations using the finite element method. Figure 7shows
the obtained scattering parameters.
Figure 7(a) shows that an input return loss better than
10 dB is achieved over the frequency range of 2–16 GHz.
Moreover, the resulting transmission parameter S21 (which
is equals to S41 because of the symmetry of the structure) is
close to its theoretical value of −4.7 dB ±1 dB over the same
frequency range except for the increase in the losses at higher
frequencies. Such losses can be decreased through the use of
low-loss tangent substrates. The transmission parameter S31
is also close to its theoretical value (−4.7 dB ±0.8 dB) over
the frequency band 2–16 GHz. The discrepancies between
the results of the two simulators are thought to be due the
different technique each simulator follows to solve Maxwell’s
equations, and the way the structure was divided in the
meshing process during the simulations.
5. Measurement Results
The circuit layout shown in Figure 6is implemented on
the same substrate mentioned in Section 3(Duroid RT5870
with a relative permittivity εr=2.33 and a thickness of
0.508 mm). The extended por ts in the circuit layout have
been chosen to allow accurate S-parameter measurements
using universal test fixture (GigaLane) without soldering. A
photograph of the fabricated circuit is shown in Figure 8.
ThemeasurementshavebeenperformedusingAnritsu
37369C network analyzer. The measured results are shown
in Figure 9. The measured return loss is better than 10 dB
from2to16GHz.ThemeasuredS31 is almost flat, around
−5 dB, in the entire band. It changes at a few bands to
−6 dB and some others to −4.5 dB. On the other hand, the
measured S21 is approximately −5.6 ±0.7 dB from 2 GHz
to 12 GHz except at 4.8 GHz and 7 GHz, where it reaches
−7.2 dB. From 12.5 GHz to 16 GHz, S21 changes from −6dB
to −7 dB; except for a small notch at about 15 GHz at which
S21 is about −7.7 dB.
6. Conclusions
In this paper, an UWB 3-way BPD using tapered line trans-
formers was designed, simulated, fabricated, and measured.
Simulation results show a very good performance of the
designed divider over a frequency range of 2–16 GHz. Mea-
surement results show an acceptable performance with little
discrepancies from the simulation ones. These differences
could be mainly due to the fabrication process, as well as,
measurement errors.
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