Enhanced Bandwidth Compact Hybrid Rat-Race Coupler for 5G Dual
Band Applications
IULIA ANDREEA MOCANU
Department of Telecommunications,
National University of Science and Technology Politehnica Bucharest,
Splaiul Independentei nr. 313, Bucharest,
ROMANIA
Abstract: - A compact hybrid rat-race coupler with dual-band behavior at 2.4 GHz, respectively at 5.2 GHz is
presented. The transmission lines used for the design consist of three impedance inverter symmetrical unit cells
with complementary behavior. The implementation with real lumped elements shows a very good agreement
between the ideal case and the real one. The simulations for the real implementation of the return and isolation
losses are around 40 dB, while the insertion and coupling losses are around 3.5 dB at both frequencies. The
phase difference at the output ports shows an imbalance of ±1o from the ideal case.
Key-Words: - Rat-race coupler, hybrid coupler, impedance inverter unit cells, dual-band, differential coupler,
artificial transmission lines, 5G communications.
Received: May 21, 2024. Revised: October 23, 2024. Accepted: November 19, 2024. Published: December 31, 2024.
1 Introduction
Hybrid rat-race couplers are very common in the
microwave domain. They are used to divide power
and ensure a phase difference of ±180o between the
output signals. Their main drawbacks are the fact
they work for only one frequency, and they have a
relatively narrow bandwidth, [1], [2].
On the other hand, nowadays the trend in
telecommunications is to use multi-band devices
with improved performances and reduced
dimensions, [3], [4]. To achieve these goals with
microwave circuits, new types of materials are
introduced. It is the case of metamaterial
transmission lines, also known as Left-Handed
transmission lines (LH TLs) which are created by
chaining a certain number of unit cells with a length
much smaller than a quarter of the wavelength, [5].
There are several types of such lines, but the
ones that are mostly used in applications are the
Composite Right Left-Handed (CRLH) [6] and Dual
Composite Right Left-Handed (D-CRLH) [7]. As
the names suggest they exhibit both Right Handed
and Left Handed properties which allows them to be
used for dual-band devices: branch line couplers [8],
[9], rat race couplers [10], [11], power dividers [12],
[13], diplexers [14], [15] in various technologies:
microstrip, stripline, coplanar, lumped [16], [17],
[18], [19]. Also, they have dual behavior: the CRLH
lines show a bandpass characteristic, while the D-
CRLH lines show a stopband one [20], [21]. When
designing such transmission lines, it is very
important to consider if the working frequencies are
in the bandwidth which assures propagation,
otherwise, the number of cells must be increased
[2], [7]. Sometimes this is not a viable solution
because both the losses and dimensions will
increase as well.
To overcome these drawbacks, we present in
this paper miniaturized CRLH and D-CRLH
transmission lines designed to work for two
arbitrary frequencies as impedance inverters and
have enhanced bandwidth.
2 Dual Band Artificial Transmission
Lines
It is known that the conventional rat-race coupler
consists of three identical λ/4 transmission lines and
one 3λ/4 line, where λ is the wavelength
corresponding to a frequency imposed by the
application. It means that the first type of line
introduces a 90-phase difference, while the second
type introduces a 270o/-90o phase difference at the
imposed frequency. As shown, the classical
transmission lines are single-band components, and
consequently, the coupler which is designed with
these lines is a single-band component as well.
In this paper, we aim to transform the classical
single-band component into a dual-band one, by
replacing the classical transmission lines with dual-
band ones, such as Composite Right Left-Handed
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.28
Iulia Andreea Mocanu
E-ISSN: 2224-266X
283
Volume 23, 2024
(CRLH) and Dual Composite Right Left-Handed
(D-CRLH). In this paper the first transmission line
is replaced by a new dual-band D-CRLH TL which
introduces a phase shift of ±90o for two arbitrary
frequencies and the second line is replaced by a new
dual-band CRLH TL which introduces a phase shift
of 90o at the two working frequencies.
Each artificial transmission line consists of an
odd number of unit cells and each unit cell
introduces a phase shift of ±90o/ 90o.
The CRLH unit cell consists of an inductor,
with inductance LR in series with a capacitor, of
capacitance CL, placed in the longitudinal branch,
respectively of an inductor, with inductance LL in
parallel with a capacitor of capacitance CR, placed in
the transversal branch.
The D-CRLH unit cell, consists of other lumped
components placed in a dual configuration: a
parallel connection between LR and CL in the
longitudinal branch and a series connection between
LL and CR in the transversal branch. The constitutive
parameters given by LR, CR, LL and CL depend on
the two arbitrary frequencies, , and the
characteristic impedance, . The computational
relations for one CRLH unit cell are [22]:
(1)
(2)
(3)
; (4)
respectively for one D-CRLH unit cell, [23]:
(5)
(6)
(7)
; (8)
where 𝑍𝑐 is the characteristic impedance of the
transmission line and 𝑘 = 𝜔2𝜔1
⁄ represents the
ratio between the two angular working frequencies.
If we want the power to be divided equally by
the rat-race coupler, then the characteristic
impedance for all transmission lines is set to
ZC=70.71 Ω. Also, the microwave frequencies are
chosen from 5G standards: f1=2.4 GHz, respectively
f2=5.2 GHz. In these conditions we compute using
relations (1)-(4) and (5)-(8) the values for the
constitutive lumped elements of one CRLH unit
cell: LR=4.0192 nH, CL=0.5049 pF, LL=2.5249 nH,
CR=0.8038 pF., respectively for one D-CRLH unit
cell: LL=4.0192 nH, CR=0.5049 pF, LR=2.5249 nH,
CL=0.8038 pF.
As we want to increase the bandwidth of the
artificial transmission line, three-unit cells instead of
one will be chosen for the design.
The scheme of the ideal CRLH transmission
line is presented in Figure 1 and its performances
obtained after simulation with Ansoft Designer SV
are given in Figure 2 and Figure 3. Markers are
placed in both figures at the imposed frequencies to
measure the values of the simulated parameters.
Fig. 1: The ideal inverter CRLH transmission line
with three cells
Fig. 2: Return loss, S11, and insertion loss, S21 for the
ideal inverter CRLH transmission line with three
cells
1
2
C
Z
;
1
1
1
c
R
Z
k
L
;
11
1c
LZk
k
C
;
.
1
1
1
1c
RZk
C
1
1
c
L
Z
k
k
L
;
1
1
1
c
L
Z
k
L
;
11
1c
RZk
k
C
;
.
1
1
1
1c
LZk
C
1
1
c
R
Z
k
k
L
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.28
Iulia Andreea Mocanu
E-ISSN: 2224-266X
284
Volume 23, 2024
Fig. 3: Phase difference for the ideal inverter CRLH
transmission line with three cells
Figure 2 shows that port 1 is perfectly matched
(there are no reflections at port 1 and the whole
power at port 1 is transferred to port 2, the output
port), so the return loss is very high, ideally infinite
at the two imposed frequencies: -83.53 dB,
respectively -76.91 dB. Also, in Figure 2 we
observe that the insertion loss is 0 dB, at both
imposed frequencies, showing we have full transfer
from the input port to the output port, as in the
theoretical model.
Nevertheless, Figure 3 shows that the phase
difference is -89.99o for the first frequency,
respectively 90.03o for the second frequency in
comparison to -90o, respectively 90o in the
theoretical case.
Next, a comparison between the results obtained
for a CRLH transmission line with one unit cell,
three-unit cells and five-unit cells is carried. The
algorithm to design the lines in all three cases is
similar to the one presented previously. Based on
the simulations in the ideal case and imposing a
variation of the insertion loss of 0.2 dB in the ideal
case, the values for the bandwidth are given in Table
1.
Table 1. The bandwidth-BW for the ideal CRLH
transmission lines with one-unit cell, three-unit
cells, and five-unit cells
Operating central
frequency
f1=2.4 GHz
f2=5.2 GHz
One unit cell TL BW
[GHz]
0.51
1.12
Three-unit cells TL
BW [GHz]
0.76
1.41
Five-unit cells TL
BW [GHz]
0.5
1.02
So, the results from Table 1 show that the
largest bandwidth is obtained for three unit-cells
transmission line, and this one will be implemented
using real components.
For the lumped elements, Surface Mounted
Devices (SMDs) are chosen to have a high-quality
factor at high frequencies and low parasitic
elements. The selected packages are chip, 0603
type, with the following dimensions: length-
1.55±0.05 mm, width-0.85±0.05 mm, height-
0.45±0.05 mm (60 x 30 x 20 mil, in Imperial
System). The small-size chip passive components
help to minimize the overall circuit. The lumped
elements used to implement the coupler are AVX
Accu-L 0603 for inductors with a quality factor of
around 60 and tight tolerances of ±0.1 nH,
respectively AVX UQCS for capacitors, having a
quality factor of around 250. Another aspect to be
considered in the design is the fact that the
standardized values are far from the computed ones,
so, series and parallel groups are needed to achieve
overall values as close as possible to the computed
ones. The combinations for the CRLH transmission
line are given in Table 2.
The markers placed at the two working
frequencies to measure the values of the
transmission parameters show that the implemented
CRLH transmission line can be used to create the
coupler.
Table 2. Real components for the implementation of
the CRLH transmission lines
Lumped
elements
Ideal
case
Available components
LR/2 [nH]
4.0192
1.8 nH in series with 2.2
nH =4 nH
LR [nH]
8.0384
3.3 nH in series with 4.7
nH=8 nH
LL [nH]
2.5249
2.7 nH in parallel with 2.7
nH in series with 1.2 nH
=2.55 nH
2CL [pF]
0.50499
0.5 pF
CL [pF]
0.252495
0.2 pF in parallel with 0.1
pF in series with 0.1 pF
=0.25 pF
CR [pF]
0.8038
0.8 pF
After implementation, a simulation of the
performances is run with Ansoft Designer SV and
the results are given in Figure 4 and Figure 5.
When using real components, there can be
noticed the influence of the losses, especially for the
values of the insertion loss which is now -0.39 dB,
respectively -0.34 dB at the two frequencies instead
of the 0 dB in the ideal case. Also, because of the
losses and approximations, the return loss is -38.28
dB, respectively -45.39 dB for the two frequencies
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.28
Iulia Andreea Mocanu
E-ISSN: 2224-266X
285
Volume 23, 2024
and not -83.53 dB, respectively -76.91 dB as in the
ideal case. The phase difference remains very close
to the ideal 90o being -89.77o, respectively 92.38o,
thus allowing us to use this type of transmission line
for our further design.
Fig. 4: Return loss, S11, and insertion loss, S21 for the
implemented inverter CRLH transmission line with
three cells
Fig. 5: Phase difference for the implemented
inverter CRLH transmission line with three cells
The second type of transmission line is the D-
CRLH one made of three identical unit cells, as
presented in Figure 6. The results after simulation
with Ansoft Designer SV for the ideal case are
given in Figure 7 and Figure 8.
In Figure 7 one can see the stop-band behavior
of the D-CRLH transmission line, different from the
pass-band behavior of the CRLH transmission line
(Figure 2).
Figure 7 shows that port 1 is perfectly matched
(there are no reflections at port 1 and the whole
power at port 1 is transferred to port 2, the output
port), so the return loss is very high, ideally infinite
at the two imposed frequencies: -103.89 dB,
respectively -96.99 dB. Also, in Figure 7 we
observe that the insertion loss is 0 dB, at both
imposed frequencies, showing we have full transfer
from the input port to the output port, as in the
theoretical model. Nevertheless, Figure 8 shows that
the phase difference is 90.01o for the first frequency,
respectively -89.97o for the second frequency in
comparison to 90o, respectively -90o in the
theoretical case.
Fig. 6: The ideal inverter D-CRLH transmission line
with three cells
Fig. 7: Return loss, S11, and insertion loss, S21 for the
ideal inverter D-CRLH transmission line with three
cells
Fig. 8: Phase difference for the ideal inverter D-
CRLH transmission line with three cells
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.28
Iulia Andreea Mocanu
E-ISSN: 2224-266X
286
Volume 23, 2024
Next, a comparison between the results obtained
for a D-CRLH transmission line with one unit cell,
three-unit cells and five-unit cells is done. The
algorithm to design the lines in all three cases is like
the one presented previously. Based on the
simulations in the ideal case and imposing a
variation of the insertion loss of 0.2 dB in the ideal
case, the values for the bandwidth are given in Table
3.
Table 3. The bandwidth-BW for the ideal D-CRLH
transmission lines with one-unit cell, three-unit
cells, and five-unit cells
Operating central
frequency
f1=2.4 GHz
f2=5.2 GHz
One unit cell TL BW
[GHz]
0.53
1.34
Three-unit cells TL
BW [GHz]
0.8
2.14
Five-unit cells TL
BW [GHz]
0.97
2.3
So, the results from Table 3 show that the
largest bandwidth is obtained for three unit-cells
transmission line, and this one will be implemented
using real components.
Also, if we compare the bandwidths for three-
cells CRLH and D-CRLH TLs, we can observe that
the largest bandwidth is obtained for D-CRLH line
and this justifies using it to replace three classical
lines rather than just one.
In Figure 8, by analyzing the values of the phase
difference at the two working frequencies given by
the two markers, one can see the dual behavior of
the D-CRLH line in comparison with the behavior
of the CRLH one. Again, we have a great agreement
between simulation and theory.
The next step, as in the case of the CRLH
transmission line, is to implement the line with real
available components. We also use AVX Accu-L
0603 for inductors and AVX UQCS for capacitors
with the same characteristics explained in the case
of the CRLH TL implementation. The series and
parallel combinations of components for the D-
CRLH transmission line are given in Table 4.
The results of the simulation with Ansoft
Designer SV are the ones in Figure 9 and Figure 10.
In Figure 9 there are placed markers at the two
working frequencies to measure the return loss and
insertion loss, meanwhile in Figure 10, the markers
are placed at the two frequencies to measure the
phase difference introduced by the real D-CRLH
transmission line.
Table 4. Real components for the implementation of
the D-CRLH transmission lines
Lumped
elements
Ideal
case
Available components
LR/2 [nH]
2.5249
2.7 nH in parallel with
2.7nH in series with 1.2
nH=2.55 nH
LR [nH]
5.0498
10 nH in parallel with 10
nH=5 nH
LL [nH]
4.0192
1.8 nH in series with 2.2 nH
=4 nH
2CL [pF]
0.8038
0.8 pF
CL [pF]
0.4019
0.4 pF
CR [pF]
0.50499
0.5 pF
When using real components, there can be
noticed the influence of the losses, especially for the
values of the insertion loss which is now -0.37 dB,
respectively -0.35 dB at the two frequencies instead
of the 0 dB in the ideal case. Also, because of the
losses and approximations, the return loss is -31.87
dB, respectively -35.31 dB for the two frequencies
and not -103.89 dB, respectively -96.99 dB as in the
ideal case.
Fig. 9: Return loss, S11, and insertion loss, S21 for the
implemented inverter D-CRLH transmission line
with three cells
Fig. 10: Phase difference for the implemented
inverter D-CRLH transmission line with three cells
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.28
Iulia Andreea Mocanu
E-ISSN: 2224-266X
287
Volume 23, 2024
The phase difference remains very close to the
ideal ±90o being 90.58o, respectively -87.47o, thus
allowing us to use this type of transmission line for
our further design.
The results obtained for the CRLH and D-
CRLH transmission lines implemented with real
components with a finite quality factor show that the
losses appear and affect both the return loss and the
insertion loss, but still the performances are as
expected.
3 Dual Band Differential Hybrid
Coupler
The differential hybrid coupler is implemented as
suggested previously in Chapter 2 with CRLH and
D-CRLH inverter transmission lines. As shown in
Figure 3 and Figure 8, the CRLH line introduces -
89.99o at 2.4GHz, respectively 90.03o at 5.2GHz, so
it acts as a 3λ/4 classical line but at two arbitrary
frequencies, while the D-CRLH line introduces
90.01o at 2.4GHz, respectively -89.97o at 5.2GHz,
so it acts as a λ/4 classical line but at two arbitrary
frequencies. These observations remain valid for the
real-case implementation of the transmission lines.
In order to make a comparison between the
ideal and real coupler, we have created the real
coupler with port 1 as the input port, port 2 as the
transmission port, port 3 as the isolated port, and
port 4 as the coupled port and the ideal coupler for
which port 5 is the input port, port 6 is the
transmission port, port 7 is the isolated port and port
8 is the coupled port. In Figure 11 there are given
the results of the return loss for the real and ideal
coupler, S11 and S55, and of the isolation loss for the
real and ideal coupler, S31 and S75.
Fig. 11: Return loss, for the real and ideal coupler,
S11 and S55, respectively the isolation loss for the
real and ideal coupler S31, respectively, S75
It can be seen that the ideal and real case exhibit
similar characteristics, the only difference is the
values of the parameters at the two working
frequencies. In the real case, the values for the
return loss are 32.21 dB , respectively 39.76 dB in
comparison to 88.03 dB , respectively 85.2 dB. For
the isolation loss, in the real case there have been
measured 41.42 dB, respectively 40.65 dB in
comparison to 94.77 dB, respectively 88.13 dB in
the ideal case. These values are smaller than in the
ideal case, because of the losses modeled by the
finite quality factor considered for the lumped
components. Also, the approximations done when
the implementation with real components was
carried out led to some small frequency shifts in the
case of the return loss, for the second bandwidth, so
that the best value is obtained for 5.25 GHz instead
of 5.2 GHz as imposed by design.
In Figure 12 there are given the results for the
insertion and coupling loss for the real and ideal
coupler case of the coupler (S21, respectively S65 and
S41, respectively S85).
Based on the data in Figure 12, we can
determine for real components that the insertion loss
and coupling loss are around 3.5 dB instead of 3 dB
as desired in the ideal case. This fact shows that the
losses play an important role, so high-quality
components are needed to implement the coupler.
Otherwise, we notice that the behavior of the
coupler even with real components is as expected in
the ideal case.
Fig. 12: Insertion loss for the real (S21) and ideal
coupler (S65) and coupling loss for the real (S41) and
real ideal (S85)
In Figure 13, there is depicted the phase
difference between the signals at the output ports in
the real and ideal coupler case.
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.28
Iulia Andreea Mocanu
E-ISSN: 2224-266X
288
Volume 23, 2024
Fig. 13: Phase difference between the signals at the
output ports in the real and ideal coupler case
implementation of the rat race coupler
For the real case, a phase difference of -181.04o,
respectively 178.88o is determined rather than -180o,
respectively 180o in the ideal case. This means that
the losses do not affect the phase difference between
signals at the output ports.
The data discussed previously are synthesized
below. For a better comparison between the results
obtained in the ideal case and the real one, the main
parameters are given in Table 5 at the two imposed
frequencies.
Table 5. The main parameters for real and ideal rat
race coupler
Operating
frequency
f1=2.4 GHz
f2=5.2 GHz
Type of coupler
Ideal
Real
Ideal
Real
Return loss [dB]
88.03
32.21
85.23
39.76
Isolation loss [dB]
94.77
41.42
88.13
40.65
Insertion loss [dB]
3.01
3.52
3.01
3.46
Coupling loss [dB]
3.01
3.59
3.01
3.52
Phase difference at
output ports [o]
-180
-181
180
178.9
The results from Table 5 show great agreement
between the ideal and real cases. The coupler’s
performances are similar at both frequencies and the
dual band behavior is demonstrated. As expected,
because of the approximations, the phase difference
at the output ports shows an imbalance of ±1o from
the ideal case.
The effect of the losses can be seen especially
for the insertion and coupling losses, so high-quality
components are needed when designing the coupler.
To evaluate the relative bandwidth, we impose
in the real case for the return and isolation losses to
be greater than 15 dB, BW15dB, and for the insertion
and coupling losses to have an imbalance of ±1.5
dB.
By imposing the threshold of 15 dB for the
return loss, we determine a frequency range between
2.58 GHz and 2.22 GHz, respectively between 5.51
GHz and 4.89 GHz, which means a relative
bandwidth of 15%, respectively 12% for both
central frequencies. Imposing the same threshold for
the isolation loss, we determine a frequency range
between 2.6 GHz and 2.2 GHz, respectively
between 5.6 GHz and 4.7 GHz, which means a
relative bandwidth of 16.6%, respectively 17.3% for
both central frequencies. For the coupling loss we
determine a bandwidth of 0.48 GHz, respectively
1.04 GHz, which corresponds to a relative
bandwidth of 20%, while the insertion loss shows a
bandwidth of 0.55 GHz, respectively 1.25 GHz,
which corresponds to a relative bandwidth of 24%.
In literature, other dual-band rat-race couplers
have been reported with different performances. In
[12], there is proposed a coupler designed using
stepped impedance stub lines, which has a relative
bandwidth for the insertion loss of 21% for the 2.4
GHz and 12% for 5.8 GHz, instead of 24% as in this
paper for similar frequencies.
The coupler presented in [24] is implemented
using differential bridged-T coils and for it there are
reported an input return loss of 24.2 dB and an
isolation loss of 38.2 dB at 2.45 GHz. At the second
frequency, 5.5 GHz, the input return loss is 17.3 dB,
whereas the isolation loss is 22.3 dB.
Another rat-race coupler is reported in [25] and
is designed using synthetic transmission lines. The
relative bandwidth for this coupler, determined by
imposing a 10 dB threshold for the isolation loss is
42 % for the 2.45 GHz and 4.27 % for 5.8 GHz.
The coupler proposed in this work has similar
performances at both frequencies and they are
mostly better than the ones reported in literature.
If we compare the results obtained in this study
to the ones from a classical single-band rat-race
coupler, implemented in microstrip technology, then
imposing the same conditions, we compute a
relative bandwidth for the coupler of around 30 %.
Even if the bandwidth is 10 % larger, the main
disadvantage is working at only one frequency.
Instead, the proposed coupler works for both
frequencies with similar performances and slightly
smaller bandwidths and improved performances
than the reported couplers in literature.
4 Conclusion
In this paper, we present a rat race coupler designed
using the novel Composite Right Left-Handed and
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.28
Iulia Andreea Mocanu
E-ISSN: 2224-266X
289
Volume 23, 2024
Dual Composite Right Left-Handed transmission
lines with enhanced bandwidth for dual-band
behavior at 2.4 GHz and 5.2 GHz. Their dual
behavior in frequency helps minimize the
dimensions but provides very good performances at
two microwave arbitrary frequencies, 2.4 GHz and
5.2 GHz.
To enhance the bandwidth, we considered for
each transmission line three-unit cells that act as
inverters. We have determined the bandwidth for
one-unit cell, three-unit cells, and five-unit cells
CRLH and D-CRLH transmission lines and we
concluded that the largest bandwidth with minimum
components is obtained for three-unit cells D-CRLH
transmission lines. This allows us to implement the
coupler in this topology to enhance the overall
bandwidth. The implementation is done with SMD
lumped components with high quality to reduce the
overall losses. Also, series and parallel groups are
needed to achieve equivalent values for the lumped
elements as close as possible to the computed ones.
This ensures very small shifts in frequency.
The newly proposed rat race coupler shows very
good agreement between the performances in the
ideal case and the real one. The return and coupling
losses are around 40 dB, while the insertion losses
are around 3.5 dB. Also, the phase imbalance is
around ±1o for both frequencies. We have obtained a
bandwidth of 24% for both frequencies for the
isolation loss and 20% for the return loss. These
performances are improved when compared to the
similar couplers reported in the literature.
References:
[1] C. Y. Pon, Hybrid-ring directional coupler for
arbitrary power division, IRE Trans. Microw.
Theory Tech., vol. MTT-9, pp.529 -535 1961,
doi: 10.1109/TMTT.1961.1125385
[2] C. Caloz, T. Itoh, Electromagnetic
Metamaterials: Transmission Line Theory and
Microwave Applications, John Wiley & Sons,
Inc., Hoboken, New Jersey, pp. 215-216,
2006.
[3] A. B. Shallah, F. Zubir, M. K. A. Rahim, N.
M. Jizat, A. Basit, M. Assaad, H. A. Majid, A
Miniaturized Metamaterial-Based Dual-Band
4×4 Butler Matrix with Enhanced Frequency
Ratio for Sub-6 GHz 5G Applications, in
IEEE Access, vol. 12, pp. 32320-32333, 2024,
doi: 10.1109/ACCESS.2024.3371027.
[4] Y. -H. Ji, C. -H. Chen and W. Wu,
Miniaturized Ku/Ka Dual-Band Rat-Race
Coupler With Dual Transmission Lines, 2023
16th UK-Europe-China Workshop on
Millimetre Waves and Terahertz Technologies
(UCMMT), Guangzhou, China, 2023, pp. 1-3,
doi: 10.1109/UCMMT58116.2023.10310486.
[5] C. Caloz, H. Okabe, T. Iwai, and T. Itoh,
Transmission line approach of left-handed
(LH) materials, USNC/URSI National Radio
Science Meeting, vol. 1, p. 39, San Antonio,
TX, June 2002.
[6] A. Lai, C. Christophe, and T. Itoh, Composite
right/left-handed transmission line
metamaterials, IEEE Microwave Magazine,
vol. 5, no. 3, pp. 34-50, September 2004, doi:
10.1109/TAP.2004.827249.
[7] Caloz, C., Dual Composite Right/Left-Handed
(D-CRLH) Transmission Line Metamaterial,
Microwave and Wireless Components Letters,
IEEE , vol.16, no.11, pp.585,587, Nov. 2006,
doi: 10.1109/LMWC.2006.884773.
[8] I.-H. Lin, C. Caloz, and T. Itoh, A branch line
coupler with two arbitrary operating
frequencies using left-handed transmission
lines, IEEE MTT-S Int. Microw. Symp. Dig.,
Philadelphia, PA, USA, vol. 1, pp. 325-328,
June 2003, doi:
10.1109/MWSYM.2003.1210944.
[9] R. M. Khattab and A. -A. T. Shalaby,
Metamaterial-Based Broadband Branch-Line
Coupler and its Application in a Balanced
Amplifier, 2021 International Conference on
Electronic Engineering (ICEEM), Menouf,
Egypt, 2021, pp. 1-7, doi:
10.1109/ICEEM52022.2021.9480615.
[10] K.-S. Chin, K.-M. Lin, Y.-H. Wei, T.-H.
Tseng and Y.-J. Yang, Compact dual-band
branch-line and rat-race couplers with
stepped-impedance-stub lines, IEEE Trans.
Microw. Theory Tech., vol. 58, no. 5,
pp.1213-1221, 2010, doi:
10.1109/TMTT.2010.2046064.
[11] Pei-Ling Chi; Tse-Yu Chen, Dual-Band Ring
Coupler Based on the Composite Right/Left-
Handed Folded Substrate-Integrated
Waveguide, Microwave and Wireless
Components Letters, IEEE, vol.24, no.5,
pp.330,332, May 2014, doi:
10.1109/LMWC.2014.2309087.
[12] T. Huang Taotao Huang, Linping Feng, Li
Geng, Haiwen Liu, Shao Yong Zheng, Sheng
Ye, Lina Zhang, and Hao Xu , Compact Dual-
Band Wilkinson Power Divider Design Using
Via-Free D-CRLH Resonators for Beidou
Navigation Satellite System, in IEEE
Transactions on Circuits and Systems II:
Express Briefs, vol. 69, no. 1, pp. 65-69, Jan.
2022, doi: 10.1109/TCSII.2021.3085093.
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.28
Iulia Andreea Mocanu
E-ISSN: 2224-266X
290
Volume 23, 2024
[13] Xue Ren; Kaijun Song; Maoyu Fan; Yu Zhu;
Bingkun Hu, Compact Dual-Band Gysel
Power Divider Based on Composite Right-
and Left-Handed Transmission Lines,
Microwave and Wireless Components Letters,
IEEE, On page(s): 82 - 84 Vol. 25, Issue: 2,
Feb. 2015, doi:
10.1109/LMWC.2014.2372481.
[14] Mansour, M.M.; Shalaby, A.-A.T.; El-Rabaie,
E.-S.M.; Messiha, N.W., Design and
simulation of microwave diplexer based on D-
CRLH metamaterials, Engineering and
Technology (ICET), 2014 International
Conference on Engineering and Technology
(ICET), Cairo, 2014, pp. 1-5, doi:
10.1109/ICEngTechnol.2014.7016782.
[15] H. Y. Zeng , G. M. Wang , D. Z. Wei and Y.
W. Wang, Planar diplexer using composite
right-.left-handed transmission line under
balanced condition, Electron. Lett., vol. 48,
no. 2, pp.104-106, 2012, doi:
10.1049/el.2011.2763.
[16] Colin, Daniel Decle; Hu, Zhirun, Uniplanar
metamaterial based dual composite right-/-left
handed (D-CRLH) microstrip line for
microwave circuit applications, Microwave
Conference (APMC), 2014 Asia-Pacific,
Sendai, Japan, 2014, pp.211,213, 4-7 Nov.
2014.
[17] Choi, J.H.; Wu, C.-T.M.; Hanseung Lee; Itoh,
T., Vialess composite right/left-handed
stripline and its applications for broadband 3-
dB and tunable couplers, European
Microwave Conference (EuMC), 2014, Rome,
Italy, 44th , vol., no., pp.315,318, 6-9 Oct.
2014, doi: 10.1109/EuMC.2014.6986433.
[18] Shih-Chia Chiu; Chien-Pai Lai; Shih-Yuan
Chen, Compact CRLH CPW Antennas Using
Novel Termination Circuits for Dual-Band
Operation at Zeroth-Order Series and Shunt
Resonances, IEEE Transactions on Antennas
and Propagation, vol.61, no.3, pp.1071,1080,
March 2013, doi:
10.1109/TAP.2012.2227102.
[19] H. -C. Lu, Y. -L. Kuo, P. -S. Huang and Y. -
L. Chang, Dual-band CRLH branch-line
coupler in LTCC by lump elements with
parasite control, 2010 IEEE MTT-S
International Microwave Symposium,
Anaheim, CA, USA, 2010, pp. 393-396, doi:
10.1109/MWSYM.2010.5517669.
[20] A. Sanada, C. Caloz, and T. Itoh,
Characteristics of the Composite Right/Left-
Handed Transmission Lines, IEEE Microwave
and Wireless Components Letter, Vol. 14,
No.2, Feb. 2004, doi:
10.1109/LMWC.2003.822563.
[21] Wang, Y., Yoon, K.-C. and Lee, J.-C. (2014),
A compact transmission line with dual-band
filter characteristics using a CRLH
metamaterial, Microw. Opt. Technol. Lett.,
56: 2150–2153, doi: 10.1002/mop.28546.
[22] I.A. Mocanu, Gh. Sajin, Dual band branch-
line coupler using novel CRLH transmission
lines, Metamaterials '2012: The Sixth
International Congress on Advanced
Electromagnetic Materials in Microwaves and
Optics, St. Petersburg, Russia, pp. 306-309,
September 2012.
[23] I.A. Mocanu and T. Petrescu, Dual band
Wilkinson power divider with artificial
transmission lines for mobile TV
services, 2014 11th International Symposium
on Electronics and Telecommunications
(ISETC), Timisoara, Romania, 2014, pp. 1-4,
doi: 10.1109/ISETC.2014.7010746.
[24] Y. -S. Lin, Y. -R. Liu and C. -H. Chan, Novel
Miniature Dual-Band Rat-Race Coupler With
Arbitrary Power Division Ratios Using
Differential Bridged-T Coils, in IEEE
Transactions on Microwave Theory and
Techniques, vol. 69, no. 1, pp. 590-602, Jan.
2021, doi: 10.1109/TMTT.2020.3035287.
[25] Chen, C.-.C., Sim, C.Y.D. and Wu, Y..-J.,
Miniaturised dual-band rat-race coupler with
harmonic suppression using synthetic
transmission line, Electron. Lett., 52: 1784-
1786, 2016, doi: 10.1049/el.2016.2154.
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.28
Iulia Andreea Mocanu
E-ISSN: 2224-266X
291
Volume 23, 2024
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
This work was supported by a grant from the
National Program for Research of the National
Association of Technical Universities - GNAC
ARUT 2023.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.28
Iulia Andreea Mocanu
E-ISSN: 2224-266X
292
Volume 23, 2024
