Compact wide-band Branch line Hybrids

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704 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 2, FEBRUARY 2006
Compact Wide-Band Branch-Line Hybrids
Young-Hoon Chun, Member, IEEE, and Jia-Sheng Hong, Senior Member, IEEE
Abstract—Wide-band branch-line couplers are designed and
tested. The proposed couplers feature compact size on a single cir-
cuit layer structure without via-holes. For the broad-band property
and cost effectiveness, we have designed a four-branch hybrid with
mixed distributed and lumped distributed elements. Analysis on
the equivalent circuits was performed carefully in order to obtain
a sufficient bandwidth with reduced design area. The fabricated
hybrids have the fractional bandwidth larger than 56% at the
center frequency of 2 GHz. They also show size reduction up to
55.2% compared with the conventional design method.
Index Terms—Branch-line, broad-band, couplers, hybrids,
lumped distributed elements, microstrip line, planar circuits.
I. INTRODUCTION
WIDE-BAND circuits are now in demand as wide-bandsystems such as ultra-wideband (UWB) become prac-
tical. In general, a wide-band circuit requires a large design
area or complicated structure such as a three-dimensional cou-
pling structure or wire-bonding connections. Modern communi-
cation systems also need various hybrids to enable digital data
transmit via microwave bands. Thus, several types of microwave
quadrature hybrids have been reported for the realization of
balanced circuits and matched attenuators and phase shifters
[1]–[4]. The branch-line coupler is one of the most popular hy-
brids for the convenience of design and implementation. It, how-
ever, has narrow-band characteristics and requires a large circuit
area. In order to reduce the size of branch-line hybrids, many
authors have suggested several solutions [3]–[7]. While lumped
or lumped distributed elements give us a chance to have a small
design area, they cannot enhance the bandwidth. Only the cas-
caded branch line can enlarge the bandwidth when we choose
it as a quadrature hybrid circuit. In fact, there are other circuits
for a broad-band hybrid, such as a Lange coupler, tandem cou-
pler, and so on. Although they show wide-band performances
with small sizes, most of them need multilayered or air-bridged
structures for tight coupling and signal routing (crossover) over
a wide frequency range. The requirement for air-bridges results
in more masks and fabrication processes, leading to more costs.
Moreover, these air-bridges would represent a bottleneck for
power handling and, hence, limit the applications of Lange and
tandem couplers. To this end, it would be desirable to develop
an alternative hybrid that can achieve a better tradeoff between
bandwidth, size, and power handling. This study stemmed from
Manuscript received July 10, 2005; revised September 12, 2005. This work
was supported in part by the U.K. Engineering and Physical Science Research
Council under Grant GR/S68910/01. The work of Y.-H Chun was supported by
the Korea Research Foundation under a Postdoctoral Fellowship Program.
The authors are with the Department of Electrical, Electronic, and Computer
Engineering, Heriot-Watt University, Edinburgh EH14 4AS, U.K. (e-mail:
younghoon@ieee.org; j.hong@hw.ac.uk).
Digital Object Identifier 10.1109/TMTT.2005.862657
Fig. 1. Size reduction scheme using lumped distributed elements.
(a) Conventional transmission line. (b) Equivalent transmission line with
a series transmission line and two open stubs. (c) Equivalent lumped-element
model for calculating the cutoff frequency.
our recent development of high-power RF microelectromechan-
ical systems (MEMS) switches for which 90 -hybrids with high
power-handling capability are needed for designing high power
single-pole–double-throw (SPDT) switches.
The loaded line is a popular method to reduce the size of
transmission-line circuits such as branch-line and ring hybrids,
which is important for planar integrated circuits [5]–[7]. The
results using a loaded line show good efficiency with regard to
size reduction. Nevertheless, more consideration of analysis and
design for wide-band applications is required. In [8], we have
shown a highly miniaturized branch-line hybrid, as well as its
simple analysis.
In this paper, we further propose a novel design of a cascaded
branch-line coupler, which has four branch lines using lumped
distributed elements. The desired 90 hybrid should have a good
performance such as return loss and isolation better than 20 dB
over 55% or wider bandwidth, and a small size on a single-layer
circuit without using any air-bridges. The investigation has led
to the design of the proposed hybrids. For our design, we use an
approach based on circuit models. Since an equivalent circuit
may make the bandwidth shrink in general, and it can be critical
when it is used for broad-band designs, we take into account the
frequency responses of the equivalent circuit used and decide a
proper configuration for broad-band circuits. Furthermore, the
simulated and measured results of the proposed hybrids are also
presented.
II. ANALYSIS
Fig. 1 shows a conventional transmission line and its equiv-
alent circuit using lumped distributed elements. By applying
a matrix formulation, the -parameters of the equiva-
lent circuit shown in Fig. 1(b) can be deduced. Equating the
0018-9480/$20.00 © 2006 IEEE
CHUN AND HONG: COMPACT WIDE-BAND BRANCH-LINE HYBRIDS 705
-matrices for both the circuits shown in Fig. 1(a) and
(b) results in (1), shown at the bottom of this page, where
(2)
is the input admittance of the open stubs in Fig. 1(b). From (1),
two design equations can be derived as follows:
(3)
(4)
Note that we assume for our applications
and discussions, which makes in (3) always positive for a
capacitive loading. We can also estimate the cutoff frequency for
the low-pass filter-like structure in Fig. 1(b) and its equivalent
circuit in Fig. 1(c). Each parameter in Fig. 1(c) is defined as
follows [9]. Define a 3-dB cutoff frequency as follows:
(5)
We then obtain
(6)
where is the cutoff frequency of the equivalent circuit in
Fig. 1(b) and is, in general, a nominated operation frequency
at which the equivalent lumped elements and are deter-
mined. In our case, can be taken as the center frequency of
a coupler.
Equation (6) sets out the higher frequency or bandwidth limit
for the equivalent circuit, which depends on several design pa-
rameters. For wide-band operations, a larger ratio of is
desirable, which, however, will be a tradeoff with size reduc-
tion. Using (4) and (6), Fig. 2 plots the cutoff frequency and
the required characteristic impedance of series transmission
line against the ratio of the electrical length and for
given values of and . The ratio of and represents the
size reduction of the transmission line. Its lower value ensures
the compact design area. Fig. 2 indicates a guideline to choose
a unit section.
For a demonstration, we select a transmission line of Fig. 1(a)
with the characteristic impedance and the electrical
length as a unit line section. It can be replaced by an
equivalent distributed lumped element circuit in Fig. 1(b) with
the characteristic impedance of a series transmission line
and the cutoff frequency varying with the value of the electrical
length of a series transmission line . This is shown in Fig. 2(a).
Fig. 2(b) shows the ranges for and the cutoff frequency when
the electrical length of the unit line section is 45 .
For a broad-band circuit, we should choose a unit section with
the higher cutoff frequency. As shown in Fig. 2, a transmis-
sion line of Fig. 1(a) can hardly be converted into a single unit
section of Fig. 1(b) for wide-band operation. In order to have
more than 50% higher cutoff frequency, the maximum size re-
duction is approximately 10% when we look at Fig. 2(a). Com-
pared with this result, a equivalent transmission line, which
consists of two 45 unit sections, as shown in Fig. 2(b), has a
higher cutoff frequency than the case of using a single unit sec-
tionin Fig. 2(a). If the desirable size reduction is 50%, the ratio
of and should be approximately 0.5. For this condition, the
cutoff frequency can be improved from 0.8 to 1.5 when
the unit length is shortened from 90 to 45 , which is found in
Fig. 2(a) and (b). The cutoff frequency is, however, defined as
a 3-dB degrade frequency for a unit section such as (5). There-
fore, cascading unit sections shrink the bandwidth. For example,
while a unit section has the cutoff frequency of 7.7 GHz, the cas-
cade circuit with four unit sections has the cutoff frequency of
7.2 GHz. Moreover, the line impedance varies as the frequency
goes near the cutoff frequency.
Furthermore, the dimension of an open stub, as well as the
unit length of a series line, influences the cutoff frequency. It
arises from the frequency-dependent characteristic of a dis-
tributed element that has not only capacitive, but also inductive
characteristics while the analysis is performed for a capacitive
loaded line. The amplitude and phase responses of the reduced
lines with the same series line and different open stubs are
plotted in Fig. 3. As the impedance of an open stub decreases,
the cutoff frequency increased. This is because the length of
the open stub shrinks for a lower line impedance in order to
have a desired admittance given by (3) and, thus, a shorter
open-circuited stub with lower characteristic impedance leads
to a better approximation to a lumped-element capacitor over a
wide frequency range. For the case of using a 50- open stub,
the cutoff frequency can go down up to 80% of the calculated
cutoff frequency , and it can be enhanced by the use of a
short open stub (low-impedance line stub). The higher limit for
this value is close to the calculated value in (6), which is also
shown in Fig. 4.
From this condition, even if a 45 unit section could enhance
the performance rather than a 90 unit section, we need higher
cutoff frequency for wide-band applications, which require
more than 50% fractional bandwidth. As you can find in
Fig. 2(c), when we adopt a 30 line section for the unit section,
(1)
706 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 2, FEBRUARY 2006
Fig. 2. Z and the normalized cutoff frequency variations as a function of
� =�. (a) Z = 50 
 and � = 90 . (b) Z = 50 
 and � = 45 . (c) Z =
50 
 and � = 30 .
we can get a cutoff frequency ratio of 2.2, which
guarantees a wide-band operation in spite of degradation due
to cascading unit sections and adopting open stubs.
From the results in this section, we can assume that unit el-
ement with the length of 12.5 (for a size reduction factor of
and the impedance of an open stub of less than
50 make the fractional bandwidth more than 50%.
Fig. 3. Block diagram of: (a) a miniaturized transmission line and its
characteristics with different open stubs. (b) Amplitude responses. (c) Phase
responses.
III. DESIGN OF WIDE-BAND HYBRIDS
With the results in Section II, we can start to design hybrids
with wide bandwidth—more than 50%. Initially, we followed
a design method described in [10], and designed a cascaded
branch-line coupler, which has four branch lines to achieve a
fractional bandwidth of 60%, as shown in Fig. 5(a). The design
parameters can be found as follows:
This design, however, occupies a large circuit area. In order
to reduce the area, we adopted lumped distributed elements, as
CHUN AND HONG: COMPACT WIDE-BAND BRANCH-LINE HYBRIDS 707
Fig. 4. Comparison of frequency responses between distributed model in
Fig. 1(b) (solid lines) and lumped-element model in Fig. 1(c) (symbolized
lines) when the line impedance of the open stub is 15 
.
Fig. 5. Conventional branch-line hybrid with four branch lines. (a) Schematic
diagram. (b) Designed prototype hybrid.
shown in Fig. 1. We should consider frequency responses for the
equivalent circuit over a wide frequency range because it would
be used in a broad-band circuit.
Thus we chose to be 30 for the broad-band property, and
to be 12.5 for the size reduction and implementation of the high
characteristic impedance of . Once is determined, and
can be calculated by (3) and (4). The dimensions for an open
stub can also be determined by (2) and the layout conditions. We
designed the initial values for a unit section, which operates as
a transmission line with as follows:
S
We can choose one of the parameters of open stubs in Table I
with the susceptance of S. In this case, we decide
TABLE I
CHOICE OF OPEN STUB
Fig. 6. Simulation result of a prototype branch-line hybrid, which adopts ideal
transmission-line elements with the calculation results from the Section III.
the parameters as follows because its cutoff frequency will be
high enough and its dimension is practical to implement:
At the same time, we can design the 58- line as well by the
identical method. Its design parameters are as follows:
S
Other four high impedance lines with and
will maintain their parameters because the
impedance of a series line for an equivalent circuit is too high
to implement for a meaningful size reduction. Fig. 6 shows the
simulation result for the parameters that are calculated here.
All the elements in this simulation are ideal transmission lines.
IV. SIMULATED AND MEASURED RESULTS
For experimental demonstration, two hybrids were con-
structed using a dielectric substrate with a relative dielectric
708 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 2, FEBRUARY 2006
Fig. 7. Fabricated hybrids. (a) Type A: each open-stub is rearranged for
size reduction. (b) Type B: high-impedance lines are meandered for further
reduction.
Fig. 8. Simulated and measured S-parameters of the hybrids: (a) type A and
(b) type B. (Solid lines—simulated results, symbols—measured results.)
constant of 3.05 and a thickness of 1.54 mm. The two quadra-
ture hybrids operated at the center frequency of 2 GHz were
designed using the design parameters that were determined
in Section III. We have performed both circuit modeled sim-
ulation and electromagnetic (EM) simulation using Agilent
ADS. The lumped distributed elements make the frequency
responses different from the prototype hybrid, which consists
of conventional transmission lines. In order to achieve a good
Fig. 9. Measured phase difference between two quadrature outputs for hybrids
of types A and B.
TABLE II
SUMMARY OF PERFORMANCES FOR HYBRIDS
frequency response, optimization was performed using Agilent
ADS.
The fabricated hybrids are shown in Fig. 7. Type A in Fig. 7(a)
has open stubs, which are arranged to reduce the circuit area. The
further size reduction can be achieved by meandering the high-
impedance lines. The resultant coupler is shown in Fig. 7(b) as
type B design.
Scattering parameter measurements were performed using an
Agilent 8753 D network analyzer over the frequency range from
1 to 3 GHz. Fig. 8 gives the simulated and measured responses
of the hybrids in which the fractional band width were found
to be over 55%. Furthermore, the phase unbalance between two
quadrature outputs of less than 3 over the operating bandwidth
was observed in Fig. 9. Comparing modeled and measured re-
sults reveals a very good agreement. It was believed that the
little discrepancy between simulated and measured results is
mainly caused by the junction discontinuities and the tolerance
in fabrications.
Table II shows a comparison of the bandwidth and the circuit
areas occupied by the conventional hybrid design and those pro-
posed in this paper. The size of the proposed branch-line coupler
is from 44.8% to 54.0% of a conventional design, while the frac-
tional bandwidth was similar to conventional hybrids. This level
of size reduction is expected to be achievable for other frequen-
cies and substrates.
CHUN AND HONG: COMPACT WIDE-BAND BRANCH-LINE HYBRIDS 709
V. CONCLUSION
This paper has proposed a compact broad-band branch-line
hybrid and has analyzed it. Following a design process through
this analysis, we have designed and tested two typesof wide-
band hybrids. It is promising for high-power and wide-band ap-
plications with a single-layered structure. The measurement of
experimental demonstrators has demonstrated that the proposed
quadrature hybrid does have a broad bandwidth and small size.
This hybrid can be easily constructed by applying conventional
monolithic-microwave integrated-circuit (MMIC) techniques. It
could be an especially good choice for the application in which
the operating bandwidth increases and the handling power goes
higher. Furthermore, we hope that it helps to decrease the fabri-
cation costs and increase the yields because it consists of no ele-
ment that needs a multilayered or air-bridged structure. The ap-
plication of this type of hybrid to the development of high-power
RF MEMS SPDT switches is under consideration.
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Young-Hoon Chun (M’00) received the M.S.
and Ph.D. degrees in electronic engineering from
Sogang University, Seoul, Korea, in 1995 and 2000,
respectively.
From 2000 to 2005, he was with the research
staff of the Millimeter-Wave Innovation Technology
(MINT) Research Center, Dongguk University,
Seoul, Korea. In June 2004, he visited Heriot-Watt
University, Edinburgh, U.K. Since July 2005, he has
been a Research Associate with the Department of
Electrical, Electronic, and Computer Engineering,
Heriot-Watt University, Edinburgh, U.K. His research area includes microwave
active filters, RF MEMS, passive and active millimeter-wave devices, and
multifunctional integrated devices for RF front-ends.
Jia-Sheng Hong (M’94–SM’05) received the D.Phil.
degree in engineering science from the University of
Oxford, Oxford, U.K., in 1994. His doctoral disser-
tation concerned EM theory and applications.
In 1994, he joined the University of Birmingham,
where he was involved with microwave applications
of high-temperature superconductors, EM modeling,
and circuit optimization. In 2001, he joined the De-
partment of Electrical, Electronic, and Computer En-
gineering, Heriot-Watt University, Edinburgh, U.K.,
as a faculty member leading a team concerned with
research into advanced RF/microwave device technologies. He has authored and
coauthored over 100 journal and conference papers. He also authored Microstrip
Filters for RF/Microwave Applications (Wiley, 2001). His current interests in-
volve RF/microwave devices, such as antennas and filters, for wireless com-
munications and radar systems, as well as novel material and device technolo-
gies including RF MEMS, ferroelectric, and high-temperature superconducting
devices.
	toc
	Compact Wide-Band Branch-Line Hybrids
	Young-Hoon Chun, Member, IEEE, and Jia-Sheng Hong, Senior Member
	I. I NTRODUCTION
	Fig.€1. Size reduction scheme using lumped distributed elements.
	II. A NALYSIS
	Fig.€2. $Z_S$ and the normalized cutoff frequency variations as 
	Fig.€3. Block diagram of: (a) a miniaturized transmission line a
	III. D ESIGN OF W IDE -B AND H YBRIDS
	Fig.€4. Comparison of frequency responses between distributed mo
	Fig.€5. Conventional branch-line hybrid with four branch lines. 
	TABLE I C HOICE OF O PEN S TUB
	Fig.€6. Simulation result of a prototype branch-line hybrid, whi
	IV. S IMULATED AND M EASURED R ESULTS
	Fig.€7. Fabricated hybrids. (a) Type A: each open-stub is rearra
	Fig.€8. Simulated and measured $S$ -parameters of the hybrids: (
	Fig.€9. Measured phase difference between two quadrature outputs
	TABLE II S UMMARY OF P ERFORMANCES FOR H YBRIDS
	V. C ONCLUSION
	J. Lange, Interdigitated strip-line quadrature coupler, IEEE Tra
	G. Carchon, W. De Raedt, and B. Nauwelaers, Integration of CPW q
	D. P. Andrews and C. S. Aitchison, Wide-band lumped-element quad
	Y.-C. Chiang and C.-Y. Chen, Design of a wide-band lumped-elemen
	R. W. Vogel, Analysis and design of lumped- and lumped-distribut
	K. W. Eccleston and S. H. Ong, Compact planar microstripline bra
	H. Ghali and T. A. Moselhy, Miniaturized fractal rat-race, branc
	Y.-H. Chun and J.-S. Hong, Design of a compact broad-band branch
	J.-S. Hong and M. J. Lancaster, Microstrip Filters for RF/Microw
	M. Muracuchi, T. Yukitake, and Y. Naito, Optimum design of 3-dB