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Dual-Band Branch-Line Hybrid with Distinct PowerDivision Ratio Over the Two Bands
Karun Rawat, Meenakshi Rawat, Mohammad S. Hashmi, Fadhel M. Ghannouchi
Department of Electrical and Computer Engineering, University of Calgary,T2N1N4 Calgary, Alberta, Canada
Received 15 October 2011; accepted 14 March 2012
ABSTRACT: This article presents a novel methodology for the design of transmission line-
based dual-band branch-line hybrid with distinct power division over any two specified fre-
quencies. These distinct power divisions at specified frequencies are achieved while keeping
the quadrature relation intact at both the frequencies. To demonstrate the effectiveness of the
proposed technique, a prototype of dual-band uneven branch-line hybrid operating at 1960
and 3500 MHz has been designed for use in Wideband Code Division Multiple Access
(WCDMA) and Worldwide Interoperability for Microwave Access (WiMax) applications. The
designed hybrid possesses equal power division in the WCDMA band and 3-dB unequal
power division in the WiMax band. VC 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE
00:000–000, 2012.
Keywords: dual-band/dual-impedance quarter-wave transformers; uneven power division; stub-
loaded line; dual-band; branch-line hybrid; microstrip; couplers; WiMax; WCDMA
I. INTRODUCTION
Dual band transmission line circuits are very useful in
high power reconfigurable transmitters due to their high
power handling capability as well as cost effectiveness.
Among these, dual-band branch-line hybrids are often
used in the design of dual-band circuits such as Doherty
power amplifiers (DPAs) [1–4]. These applications have
led to proposal of various topologies of dual-band hybrids
using transmission line sections [5–13].
Among various methodologies, most common
approach used in the design of dual-band component is to
replace each branch in a conventional single-band design
with a 2-port dispersive structure. These dispersive struc-
tures possess specific image impedance and phase charac-
teristic which corresponds to the required values of the
characteristic impedance and electric lengths at the respec-
tive two frequencies [7, 8]. There are two common techni-
ques to achieve dual-band quarter-wave operation from a
transmission line. In the first method, known as T-type, a
transmission line segment is loaded with a shunt suscep-
tance at the center [7, 13]; whereas the second method,
known as Pi-type, involves a transmission line segment
loaded with shunt sucseptance at its ends [8–12].
In common practice, dual-band hybrids designed using
T-type and Pi-type structures provide the same power di-
vision ratio at both frequencies and therefore find limited
usefulness in applications such as dual-band DPA, that
may require different power division ratios at the two fre-
quencies of operation [2–4, 14–16]. To overcome these
limitations and to achieve different power division ratios
at the two specified band, there have been proposed modi-
fications in dual-band hybrid design techniques such as
stub-loaded stepped impedance transformers [9, 10].
This article presents a novel technique to design a
dual-band hybrid with uneven power division ratio at two
frequencies in which each branch of a conventional
branch-line hybrid is replaced with a transmission line
loaded with multisection stub. Such loaded structure emu-
lates a quarter-wave transformer that has two different
characteristic impedances but the same electric lengths of
690� at the two frequencies.
A conventional Pi-type and T-type stub-loaded struc-
ture can also be used to design dual-band/dual-impedance
transformers as described in Refs. [4, 17]. However, it has
also been mentioned in Refs. [4, 17] that in common prac-
tice, to ensure such dual-band operation, a simultaneous
solution must be sought for the design parameters of the
loaded transmission lines and the open or short circuit
transmission line stubs realizing the required shunt suscep-
tance value [4, 17]. As in dual-band/dual-impedance
Correspondence to: K. Rawat; e-mail: [email protected]
VC 2012 Wiley Periodicals, Inc.
DOI 10.1002/mmce.20655Published online in Wiley Online Library
(wileyonlinelibrary.com).
1
transformer, the 90� electric length is desired along with
two different characteristic impedance at two frequencies,
sometimes, this methodology results in the physically
unrealizable solutions [17]. Commonly, these solutions are
in terms of the design parameters (characteristic imped-
ance and electric length) of the open and short circuit
transmission line stubs realizing the shunt susceptance, for
a given design parameters of a loaded line [17]. For
example, a very high value of characteristic impedance
results in narrow transmission lines, presenting difficulties
during fabrication [7, 8, 17]. The technique presented in
this article provides an analytical solution of the design of
dual-band/dual-characteristic impedance transformer utiliz-
ing the multisection stub loaded architecture instead of
open and short circuit transmission line stubs. In principle,
the presented technique can realize any values of suscep-
tance at the two specified frequencies provided these
selected frequencies are uncorrelated [3, 4, 17].
For the proof of concept an uneven branch-line hybrid
has been designed to operate at 1960 and 3500 MHz, for
WCDMA and WiMAx applications. The hybrid provides
equal-power division in the first frequency, whereas a 3-dB
unequal power division is targeted in the second frequency.
The design methodology is described in Section II, the experi-
ment and design considerations are presented in Section III.
Section IV describes the (electromagnetic) Electromagnetic
(EM) simulated and measured performance of the designed
branch-line hybrid. Section V presents the conclusion.
II. DESIGN METHODOLOGY
Figure 1 shows schematic of the proposed hybrid which
utilizes the transmission line loaded with dual-band multi-
section stubs at two edges.
For any arbitrary power division a, the required value
of characteristic impedances of a branch-line coupler is
given as [9, 10, 18]:
ZT;Aðf Þ ¼Z0
a11þa1
� �0:5
@f1
Z0a2
1þa2
� �0:5
@f2
8><>: (1a)
ZT;Bðf Þ ¼ Z0 a1ð Þ0:5 @f1Z0 a2ð Þ0:5 @f2
�(1b)
where ZT,A and ZT,B are the characteristic impedances of the
branches and a1 and a2 are the respective power division ratio
(PA/PB) between port 2 and port 3 in Figure 1 at f1 and f2.Z0 is the reference impedances of 50 X terminating the
ports. In this article, the design example has an equal power
division at f1 and a 3-dB unequal power division at f2 hencethe values of a1 and a2 are chosen as 1 and 0.5, respec-
tively. The corresponding required values of ZT,A(f1) and
ZT,A(f2) are calculated as 35.35 and 28.87 X, respectivelyusing Eq. (1a). Similarly, the values of ZT,B(f1) and ZT,B(f2)are obtained as 50 and 35.35 X using Eq. (1b).
The design methodology is divided into two sections.
The first section is related to the design of stub loaded 2-
port structure. In this section, the design parameters of the
stub loaded 2-port structure of Figure 1b are retrieved by
solving its corresponding ABCD matrix. The second sec-
tion deals with the realization of the multisection stubs
which load the transmission line section in Figure 1b.
A. Stub Loaded 2-Port StructureIn general, for a stub-loaded structure as shown in Figure
1b, if we consider BS(f) as the shunt susceptance loading
Figure 1 Dual-band hybrid architecture (a) overall schematic, (b) schematic of single branch, and (c) equivalent of stub-loaded structure.
[Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
2 Rawat et al.
International Journal of RF and Microwave Computer-Aided Engineering/Vol. 000, No. 000, Month 2012
the transmission line, the ABCD parameter of the stub
loaded structure is given by [8]:
A B
C D
� �
¼ coshS � BSZS sinhS jZS sinhSj sinhSZS
1 � Z2SB
2S þ 2BSZS coths
� �coshS � BSZS sinhS
" #
(2)
The Pi-type structure of Figure 1b is equivalent to a
transmission line of the characteristic impedance ZT and
electric length hT as shown in Figure 1c. Thus, the expres-
sion for the ABCD matrix of the Pi-type structure of Fig-
ure 1b can be used to obtain respective overall electric
length and the characteristic impedance as:
cosðhTÞ ¼ Aþ D
2¼ cos hs � BSZS sin hs (3)
ZT ¼ffiffiffiffiB
C
r¼ ZS
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1
1� Z2SB
2S þ 2ZSBS cot hs
s(4)
where ZS is the characteristic impedance of a series line
of electric length, hS, loaded by a susceptance of BS, as
shown in Figure 1b. Referring to the condition of a 90�
transformer in Eq. (3), we have:
BS ¼ 1
ZS tan hs(5)
Inserting Eq. (5) in Eq. (4) gives another condition:
ZT ¼ Zs sin hs (6)
For the structure in Figure 1b, Eqs. (5) and (6) together
guarantee the overall 90� electric length.
Thus, for different characteristic impedance at two dif-
ferent frequencies, Eqs. (5) and (6) can be written as:
ZTðf Þ ¼ ZS sin hSð Þ @f1ZS sin nhSð Þ @f2
�(7)
BSðf Þ ¼ ZS tan hSð Þð Þ�1 @f1ZS tan nhSð Þð Þ�1 @f2
�(8)
where, n is the frequency ratio f2/f1.If ZT(f1) and ZT(f2) are the two required characteristic
impedances at two frequencies f1 and f2, respectively, andtheir ratio is denoted by j, one can deduce following
expression from Eq. (7):
j ¼ ZT f2ð ÞZT f1ð Þ ¼
sin nhSð Þsin hSð Þ
(9)
The ratio of two sine functions can be solved graphi-
cally or analytically as given in appendix to obtain hS for
a required value of impedance ratio j.Figure 2 give range of the impedance ratios that can
be achieved by choosing different values of hS for a given
frequency ratio n for this topology.
Using Figure 2, the value of hS is obtained for a given
value of n and j. This value hS along with the known values
of ZT(f) and n are then used in Eq. (7) to obtain the corre-
sponding value of ZS. These values of ZS and hS once final-
ized according to Eq. (7), the corresponding required values
of BS(f) at the two frequencies can be obtained from Eq. (8),
hence guaranteeing the simultaneous existence of Eqs. (7)
and (8).
Figure 2 Range of the impedance ratio ZT2/ ZT1 obtained from proposed methodology for various frequency ratios n. [Color figure can
be viewed in the online issue, which is available at wileyonlinelibrary.com.]
Dual-Band/Dual-Impedance 90� Transformer in Hybrid Coupler Design 3
International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce
It is worth mentioning that the shunt susceptance and
series transmission line parameters are obtained by solving
Eqs. (7) and (8) simultaneously, but the susceptance val-
ues are realized using multisection stubs independent of
the design of loaded transmission line.
B. Multisection Stub DesignFigure 3 shows multisection stub that provides different
susceptance values at its input for two distinct frequen-
cies. The design of multisection stub can be divided in
two sections, as shown in Figure 3a, where the first step
is the realization of the required susceptance, BS(f2), at theinput, which is accomplished as in section 1 of Figure 3a.
Here, f1 is the lower frequency between f1 and f2. InFigure 3a, section 1 is depicted as a transmission line
short circuit at one end at node A. This short circuit is
realized by a 90� open circuit transmission line designed
at f2, and hence, section 1 can be realized as shown in
Figure 3b. Once the short circuit at node A is realized by
open circuit transmission line of quarter-wave length
at frequency f2, adding any further section beyond this
point will not affect the input admittance at frequency f2.Thus, section 2 is designed as an admittance that, when
terminating section 1 at node A, emulates susceptance
BS(f1) at the input of section 1. This terminating admit-
tance is denoted as YB(f1) in Figure 3a that can be further
realized by either an open or short circuit transmission
line.
For designing section 1 in Figure 3a, if the designer
chooses a certain realizable value of characteristic imped-
ance ZC1, to achieve the desired input admittance values
of jBS(f2), the electric length hC1 can be calculated as:
hC1ðf2Þ ¼ tan�1 �1
ZC1BSðf2Þ �
(10)
where BS(f2) can be positive or negative depending on the
required susceptance value. The value obtained for hC1 is
considered at f2, to calculate the physical length. Referring
to Figure 3b, once the short circuit at node A is realized
by open circuit transmission line of quarter-wave length at
frequency f2, the value of susceptance YB can be synthe-
sized for frequency f1. This requires synthesis of admittan-
ces YA(f1) and YC(f1), as shown in Figure 3a such that
YBðf1Þ ¼ YAðf1Þ � YCðf1Þ (11)
where, YC(f1) is the admittance at the input of the 90�
transformer in Figure 3b at f1 and is given as:
YCðf1Þ ¼ j1
ZC;OCtan
p2
f1f2
�(12)
However, YA(f1) can be synthesized by de-embedding
section 1, with a known value of BS(f1). This can be
obtained using a standard transmission line impedance
equation as follows:
YAðf1Þ ¼ j
ZC1
ZC1BSðf1Þ � tan hC1 f2ð Þ f1f2� �
1þ ZC1BSðf1Þ tan hC1 f2ð Þ f1f2� �
24
35 (13)
where BS(f1) can be positive or negative depending on the
imaginary value of the required susceptance to be seen at
the input of the multisection stub at frequency f1.
Figure 3 Schematic of Multisection stubs used to realize susceptance values at two frequencies. [Color figure can be viewed in the
online issue, which is available at wileyonlinelibrary.com.]
4 Rawat et al.
International Journal of RF and Microwave Computer-Aided Engineering/Vol. 000, No. 000, Month 2012
The synthesized value of YB(f1) can be obtained using
Eqs. (12) and (13) in Eq. (11) and can be realized by an
open or short stub of characteristic impedance ZC2 and
electrical length hC2, which is represented as section 2 in
Figure 3a. If the designer chooses a certain realizable
value for the characteristic impedance of ZC2 for this stub,its electric length can be given by:
hC2ðf1Þ ¼tan�1 ZC2imag YBðf1Þð Þð Þ for open stub
tan�1 �1ZC2 imag YBðf1Þð Þ
� �for short stub
((14)
The choice of using an open or short stub and ZC2 in
Eq. (14) depends on the realizability of YB(f1) with a min-
imum stub length. The imaginary value of YB(f1) in Eq.
(14) can be positive or negative, depending on the calcu-
lated results in Eq. (11).
III. EXPERIMENT AND DESIGN CONSIDERATIONS
Photograph of a dual-band hybrid designed and fabricated
on RT5870 is given in Figure 4. This prototype is
designed for the equal-power division (a1 ¼ 1) at 1960
MHz and half power division (a2 ¼ 0.5) at 3500 MHz.
The overall dimensions are 2.8 � 3 inch2. The substrate
has dielectric constant of 2.33, height of 20 mil, and loss
tangent of 0.0012.
For a given frequency ratio of n ¼ 1.786, the value of
series transmission line of Figure 1b has been obtained
using design curve given in Figure 2. It is evident from
Figure 2 and sine series expansion given in appendix, that
the maximum value of the impedance ratio j given in Eq.
(9), which can be achieved with the proposed methodol-
ogy, is equal to n. Thus, for a particular frequency ratio, a
certain level of uneven power division (corresponding to
the value of a) can only be achieved with the proposed
methodology. Thus, it is an important design consideration
while deciding the feasibility of the given 2-port structure
for achieving a given value of power division a for a
given frequency ratio n. It is also worth mentioning that
while designing multisection stub of Figure 3a, there is no
such limitation that section 1 should always be designed
for f2. As the two frequencies are assumed to be
Figure 4 Photograph of fabricated circuit. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
TABLE I Design Parameters for the Dual-Band/Dual Impedance Transformers
Electrical Design Parameters
Value Physical
Design
Parameters
Value Calculated
(mm)
Value Optimized
(mm)
ZT,A ZT,B ZT,A ZT,B ZT,A ZT,B
ZS (X) 37.13 51.42 wS 2.25 1.4 2.22 1.46
hS @f1 (�) 72.21 76.51 lS 21.63 23.29 19.18 19.48
ZC1 (X) 50 50 wC1 1.47 1.47 1.47 1.47
ZC,OC (X) 50 50 wC,OC 1.47 1.47 1.47 1.47
ZC2 (X) 50 50 wC2 1.47 1.47 1.47 1.47
hC1@f2 (�) 42.56 44.15 lC1 7.24 7.51 6.9 8.33
hOC @f2 (�) 90 90 lOC 15.32 15.32 15.2 15.2
hC2 @f1 (�) 39.41 35.27 lC2 11.98 10.72 11.81 10.08
Dual-Band/Dual-Impedance 90� Transformer in Hybrid Coupler Design 5
International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce
uncorrelated, section 1 can also be designed for f1 rather
than f2, depending on the value of susceptance BS(f) to be
realized at a particular frequency. For such a case, f1 is
replaced by f2 and vice versa in the design equations
(10)–(14). The choice of designing section 1 at f1 or f2depends on the configuration resulting in the overall
smaller size of the dual-band stub. In the present design
case, where the value of BS(f2) is much closer to the short
circuit than that of BS(f1); therefore, section 1 is designed
to realize BS(f2) and section 2 is designed to realize
BS(f1), to achieve an overall smaller size of the multisec-
tion stub.
Table I gives the electrical and physical design para-
meters of the design parameters of dual-band/dual-imped-
ance transformers used in Figure 1a calculated using the
proposed methodology of Section II.
IV. RESULTS AND DISCUSSION
The fabricated prototype has been measured using cali-
brated Vector Network analyzer. Figure 5 shows EM
simulated and measured results of return loss and isolation
of the fabricated branch-line hybrid. The measured return
losses are better than 10 dB over a band of 160 MHz
symmetrical around 1960 MHz frequency. The corre-
sponding isolation is around 15 dB over a band of 100
MHz symmetrical around 1960 MHz. Similarly the meas-
ured return loss is better than 10 dB over a band 120
MHz symmetrical around 3500 MHz. The corresponding
isolation is around 15 dB over a band of 100 MHz sym-
metrical around 3500 MHz. Because of some fabrication
error there is a slight frequency shift at both center fre-
quencies resulting into slightly lower bandwidth symmet-
ric around the two center frequencies of 1960 and 3500
MHz as shown in zoomed versions of graph in Figure 5.
Hence, if we ignore this symmetry about these center fre-
quencies, the first and second band has bandwidth of 200
MHz, where the return loss is around 10 dB.
Figure 5 Measured and EM simulated isolation and return loss of the fabricated branch-line hybrid. [Color figure can be viewed in the
online issue, which is available at wileyonlinelibrary.com.]
Figure 6 Measured and EM simulated insertion loss of the fab-
ricated branch-line hybrid. [Color figure can be viewed in the
online issue, which is available at wileyonlinelibrary.com.]
6 Rawat et al.
International Journal of RF and Microwave Computer-Aided Engineering/Vol. 000, No. 000, Month 2012
Similarly, the isolation is around 15 dB over a fre-
quency range of 120 and 180 MHz at the first and second
band of operation, respectively.
Figure 6 shows EM simulated and measured results of
insertion loss of the fabricated branch-line hybrid. The
equal power division is maintained with an error of 1 dB
over a frequency range of 120 MHz in the first band and
unequal 3 dB power division is maintained with 1 dB
error over a frequency range of 200 MHz in the second
band.
Figure 7 shows measured results of quadrature phase
relationship between split ports of the fabricated branch-
line hybrid.
Again, phase error of around 10� from the quadrature
relation has been achieved over the frequency range of
150 and 200 MHz in the first and second band, respec-
tively, as shown in Figure 7.
V. CONCLUSIONS
A dual-band/dual-impedance transformer has been real-
ized to design dual-band branch line hybrid with two
different power divisions at two frequencies of opera-
tion. The multisection stubs guarantees that any
required value of susceptance can be realized independ-
ent of series lines parameters and hence resulting into
robust solution. The electric design parameters calcu-
lated using the given formulae validate the proposed
methodology.
ACKNOWLEDGMENTS
The authors thank T. Bata for his technical assistance in
manufacturing the prototype. They also appreciate the valua-
ble support of the team of the iRadio Laboratory at the Uni-
versity of Calgary. This work was supported by the Alberta
Innovates Technology Future (AITF), The Natural Sciences
and Engineering Council of Canada, the Canada Research
Chair (CRC) Program.
APPENDIX
The ratio of Sine functions given in Eq. (9) can be
expresses as:
sin nhSð Þsin hSð Þ
� A0 þ A1h
2S þ A2h
4S þ A3h
6S þ A4h
8S
þ……Amh2mS (A1)
where; 0 < hS <2pn
Expanding sine series in each numerator and denomina-
tor of Eq. (A1) and rearranging
nhS � nhSð Þ33!
þ nhSð Þ55!
� nhSð Þ77!
þ :::
¼ A0 þ A1h2S þ A2h
4S þ ::::
� �hS � h3S
3!þ h5S
5!� h7S
7!:::
�(A2)
Figure 7 Measured quadrature phase performance of the fabricated hybrid. [Color figure can be viewed in the online issue, which is
available at wileyonlinelibrary.com.]
Dual-Band/Dual-Impedance 90� Transformer in Hybrid Coupler Design 7
International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce
Comparing each term of the same order of hS in Eq. (A2),
values of coefficients can be obtained as
A0 ¼ n; A1 ¼ n� n3
3!; A2 ¼ n5 � n
5!þ A1
3!; A3
¼ n� n7
7!� A1
5!þ A2
3!; A4 ¼ n9 � n
9!þ A1
7!� A2
5!þ A3
3!(A3)
As the coefficients corresponding to higher values of �Sin Eq. (A2) tend to vanish in a fast manner; the approxi-
mation up to eighth order in right hand side of Eq. (A1)
(four coefficient terms) can give sufficient accuracy in
calculating �S.
The polynomial expansion in Eq. (A1) with coefficient
given by Eq. (A3) can be used for solving �S for a
required value �. It has been used for plotting Figure 2.
REFERENCES
1. F.M. Ghannouchi, Power amplifier and transmitter architec-
tures for software defined radio systems, IEEE Circ Syst Mag
10 (2010), 44–55.
2. X. Li, W. Chen, Z. Zhang, Z. Feng, X. Tang, and K. Mouth-
aan, A Concurrent dual-band Doherty power amplifier, Proc.
of Asia Pacific Microwave Conf., Yokohama, Japan, 2010,
pp. 1–4.
3. P. Colantonio, F. Feudo, F. Giannini, R. Giofre, and L. Piazzon,
Design of a dual-band GaN Doherty amplifier, 18th Int. Conf. on
Microw. Radar and Wireless Comm. MIKON, Vilnius, Lithua-
nia, 2010, pp. 1–4.
4. K. Rawat, and F.M. Ghannouchi, Design methodology for
dual-band Doherty power amplifier with performance en-
hancement using dual-Band offset lines, IEEE Trans Indus
Electron (2011), DOI: 10.1109/TIE.2011.2176695.
5. H.-x. Xu, G.-m. Wang, P.-l. Chen, and T.-p. Li, Miniaturized
fractal-shaped branch-line coupler for dual-band application
based on composite right/left handed transmission Lines, J
Zhejiang Univ-Sci C (Computers & Electronics) 12, (2011),
766–773.
6. C. Caloz and T. Itoh, Electromagnetic metamaterials: Trans-
mission line theory and microwave applications, Wiley-Inter-
sience publication, NJ, 2006.
7. K. Rawat, F.M. Ghannouchi, M. Rawat, and M.S. Hashmi,
Analysis of frequency selective impedance loading of trans-
mission lines for dual band couplers, Int J Microw RF Com-
put Aided Eng 21 (2011), 325–335.
8. K.K.M. Cheng and F.L. Wong, A novel approach to the
design and implementation of dual-band compact planar 90�
branch-line coupler, IEEE Trans Microw Theory Tech 52
(2004), 2458–2463.
9. C.L. Hsu, C.W. Chang, and J. Tsai Kuo, Design of dual band
microstrip rat race coupler with circuit miniaturization, IEEE
MTT-S Int. Microwave Symp. Dig., Honolulu, Hawaii, 2007,
pp. 177–180.
10. C.L. Hsu, J. T. Kuo, and C.W. Chang, Miniaturized dual-
band hybrid couplers with arbitrary power division ratio,
IEEE Trans Microw Theory Tech 57 (2009), 149–156.
11. K.M. Cheng and F.L. Wong, Dual band rat-race coupler
design using tri- section branch-line, Electron Lett 43 (2007),
345–346.
12. S. Dwari and S. Sanyal, An arbitrary dual-band microstrip
hybrid-ring, Wiley Microwave Opt Lett 48 (2006), 840–842.
13. H. Zhang and K.J. Chen, A stub tapped branch-line coupler
for dual band operations, IEEE Microw Wireless Comp Lett
17 (2007), 106–108.
14. S. Bousnina, Maximizing efficiency and linearity, IEEE
Microw Mag 10 (2009), 99–107.
15. J. Kim, J. Cha, I. Kim, and B. Kim, Optimum operation of
asymmetrical-cells-based linear Doherty power amplifiers-
Uneven power drive and power matching, IEEE Trans
Microw Theory Tech 53 (2005), 1802–1809.
16. K.J. Cho, W.J. Kim, J.H. Kim, S.P. Stapleton, Linearity opti-
mization of a high power Doherty amplifier based on post-
distortion compensation, IEEE Microw Wireless Comp Lett
15 (2005), 748–750.
17. K. Rawat and F.M. Ghannouchi, A novel dual-band matching
technique based on dual-characteristic impedance transformer
for dual-band power amplifier design, IET Microw Antennas
Propag 5 (2011), 1720–1729.
18. Y.B. Kim, H.T. Kim, K.S. Kim, J.S. Lim, and D. Ahn, A
branch line hybrid having arbitrary power division ratio and
port impedances, Proc. of Asia Pacific Microwave Conf.,
Yokohama, Japan, 2006, pp. 1–4.
BIOGRAPHIES
Karun Rawat (IEEE M’08, S’09)
received his B.E degree in electron-
ics and communication engineering
from Meerut University, UP, India,
in 2002. He is currently pursuing his
Ph.D. in the Department of Electrical
and Computer Engineering, Schulich
School of Engineering, University of
Calgary, Calgary, AB, Canada. He worked as scientist in
the Indian Space Research Organization (ISRO) from
2003 to 2007. After that, he joined the iRadio Laboratory
of the Schulich School of Engineering, University of Cal-
gary, where he has been working as a student research as-
sistant. He is the reviewer of several well-known journals,
and his current research interests are in the areas of
microwave active and passive circuit design and advanced
transmitter and receiver architecture for software defined
radio applications. His research involvement has resulted
in more than 20 publications in journals and conferences.
Due to his active research activities and publications, he
has been recipient of research production award for the
three consecutive years from 2009 to 2012 by Department
of Electrical and Computers Engineering at University of
Calgary.
8 Rawat et al.
International Journal of RF and Microwave Computer-Aided Engineering/Vol. 000, No. 000, Month 2012
Meenakshi Rawat (IEEE S’09)
received her B. Tech. degree in electri-
cal engineering from Govind Ballabh
Pant University of Agriculture and
Technology, Pantnagar, Uttaranchal,
India, in 2006. She is currently pursu-
ing her Ph.D. in the Department of
Electrical and Computer Engineering,
Schulich School of Engineering, University of Calgary, Cal-
gary, AB, Canada. She was associated with Telco Construc-
tion Equipment Co. Ltd., India, from 2006 to 2007 and Hin-
dustan Petroleum Corporation Limited (HPCL), India,
during 2007–2008. She is now working with the iRadio Lab
of the Schulich School of Engineering, University of Cal-
gary, as a student research assistant. She is also reviewer of
several well-known journals and her current research interest
is in the area of digital signal processing, neural networks,
and microwave active and passive circuit modeling.
Mohammad S. Hashmi (IEEE S’04–
M’09) received his B. Tech. degree
from Aligarh Muslim University,
India, in 2001, his M.S. degree from
the Darmstadt University of Technol-
ogy, Germany, in 2004, and his Ph.D.
degree from Cardiff University, UK,
in 2009. He subsequently worked as a
postdoctoral fellow at Cardiff University. Since September
2009, he has been a postdoctoral fellow with iRadio Lab,
University of Calgary, Canada. He also worked at PhilipsSemiconductors and Thales Electronics in Germany, duringwhich time he was involved in the field of RF circuits andsystems. His current research interests are the characteriza-tion and linearization of power amplifiers for mobile and sat-ellite applications, microwave active and passive circuits andnonlinear microwave instrumentation. Dr. Hashmi was the re-cipient of the 2008 Automatic Radio Frequency TechniquesGroup (ARFTG) Microwave Measurement Fellowship.
Fadhel M. Ghannouchi (IEEE S’84,
M’88, SM’93, FIEEE’ 07) is currently
a professor and iCORE/CRC Chair in
the Department of Electrical and
Computer Engineering of the Schulich
School of Engineering at the Univer-
sity of Calgary and Director of the
Intelligent RF Radio Laboratory. He
has held numerous invited positions at several academic
and research institutions in Europe, North America, and Ja-
pan. He has provided consulting services to a number of
microwave and wireless communications companies. His
research interests are in the areas of microwave instrumen-
tation and measurements, nonlinear modeling of microwave
devices and communications systems, design of power and
spectrum efficient microwave amplification systems and
design of intelligent RF transceivers and SDR radio sys-
tems for wireless and satellite communications. His
research activities have led to more than 450 publications
and 10 US patents (three pending).
Dual-Band/Dual-Impedance 90� Transformer in Hybrid Coupler Design 9
International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce