A Novel N-Port Series Divider Using Infinite Wavelength Phenomena
Anthony Lai, Kevin M.K.H. Leong, and Tatsuo Itoh
Department of Electrical Engineering, University of California, Los Angeles,
405 Hilgard Avenue, Los Angeles, CA 90095-1594. Email: antlai@ee.ucla.edu
Abstract— A novel N -port series divider based on a
composite right/left-handed (CRLH) transmission line (TL)
supporting a wave with an infinite wavelength is presented.
This novel divider evenly divides power in phase to an infinite
number of ports at its infinite wave frequency. In addition,
it is shown that the novel series divider’s performance is
not dependent on the location of its output ports. The basic
operating principle is based on the fact that a CRLH TL
is able to support a wave with an infinite wavelength. As
a result, all points along the CRLH TL have the same
magnitude and phase. A 3-port series divider consisting of a
8 unit-cell CRLH TL is shown to exhibit 0.22 dB maximum
magnitude difference and 1.32◦ maximum phase difference
between output ports at its infinite wavelength frequency.
In addition, a 5-port series divider consisting of a 13 unitcell CRLH TL is fabricated and shown to exhibit 0.30 dB
maximum magnitude difference and 6.3◦ maximum phase
difference between output ports at its infinite wavelength
frequency. Both simulation and experimental results are
shown to support the authors’ claims.
Index Terms— Metamaterials, composite right/left-handed,
infinite wavelength, power divider, series-fed array.
I. I NTRODUCTION
Power dividers of various types are regularly used in
microwave applications such as signal dividing for amplifier chains, antenna array feeds, or distribution to subsystems. There are two classes of dividers, parallel or series, each having their own advantages and disadvantages
[1]. Both topologies are generally scalable to accommodate
an N number of divisions. This usually comes with added
complexity and larger size. Due to the parallel divider’s
fundamental three port shape, parallel divider based feed
networks are usually large in comparison to series divider
based feed networks [2]-[3]. Series dividers are usually
used over parallel dividers in applications where power
needs to be equally divided to a large number of elements
and where the physical area of the feed network is limited.
For example, series dividers can be used to feed antenna
arrays. In order to ensure that each antenna element with a
predefined element spacing is fed with an equal amplitude
and equal phase signal, a meander line is usually used
such that power can be tapped from the series feed line
at locations which are integer multiples of the guided
wavelength. This meander line adds complexity to the
series divider design and places spacing restrictions on the
antenna elements in the array.
Fig. 1.
Infinite wavelength N -port series divider, element spacing
(d1 , d2 , d3 , ...) and physical length (l) is arbitrary.
In this paper, a novel N -port series divider is demonstrated with no limitations on the number of ports or
the location of the ports along the divider for equal
amplitude and equal phase power division. This novel
series divider is based on a composite right/left-handed
(CRLH) transmission line (TL), which is able to support
an infinite wavelength at certain frequencies [4]-[5]. The
basic concept is illustrated in Fig. 1. The magnitude and
phase at all points along an arbitrary length of CRLH
TL supporting a wave with an infinite wavelength are
identical. The physical length of the divider or the position
of the power taps has no effect on the phase and power
balance between each output port. Furthermore, the divider
can be easily expanded to accommodate an N number of
ports. The design concept is validated by fabrication and
measurement of a 3-port and a 5-port divider with arbitrary
signal tap spacing.
II. T HEORY
As mentioned above, the novel N -port series divider is
based on the CRLH TL. By operating the CRLH TL at an
infinite wave frequency (β=0, ω6=0), an infinite wavelength
is supported on the CRLH TL. To achieve a standing wave
with an infinite wavelength, a CRLH TL resonator is used.
As a consequence, all points along the CRLH TL have the
same magnitude and phase.
A. CRLH TL Theory
A CRLH metamaterial is a practical implementation
of a LH material, which also includes unavoidable RH
effects [4]. By modeling the CRLH as a periodic cascade
of equivalent LC unit-cells consisting of a series LH
capacitance (CL ), a series RH inductance (LR ), a shunt
LH inductance (LL ), and a shunt RH capacitance (CR ), a
ω
−βc
an infinite wavelength independent of the TL’s physical
length, l. [5].
For both the open- or short-circuit CRLH TL, the infinite
wavelength condition depends only on CL , CR , LL , and
LR of the unit-cell and not on the number of cells (physical
length of the CRLH TL) [5]. The infinite wavelength
condition of the open-circuit CRLH TL resonator is determined by ωsh , while the infinite wavelength condition
of the short-circuited CRLH TL resonator is determined
by ωse [5]. Therefore, at the infinite wavelength frequency,
the series elements of the open-circuit CRLH TL resonator
appears to be short while the shunt elements of the shortcircuit CRLH TL resonator appears to be open.
+βc
ωΓ2
ω0
ωΓ1
β
Fig. 2.
Dispersion diagram of an unbalanced CRLH TL [7].
CRLH TL can be realized. The fundamental characteristics
of the CRLH TL can be observed in its dispersion diagram
shown in Fig. 2.
At frequencies below the infinite wavelength point
(β=0), the fundamental mode of the CRLH structure is
LH and phase advance occurs (β<0). In contrast, in the
frequency range above the infinite wavelength point, the
fundamental mode of the CRLH structure is RH and phase
delay occurs (β>0). In general, the product CR LL and the
product CL LR of the CRLH TL are not equal (unbalanced)
and a stop-band appears between the LH and RH ranges
as depicted in Fig. 2. Therefore, the unbalanced CRLH TL
has two frequencies that can support an infinite wavelength
which are given by
ωsh = √
1
C R LL
and
ωse = √
1
.
C L LR
III. I MPLEMENTATION
In order to demonstrate the proposed idea, a 3-port, 8
unit-cell series divider and a 5-port, 13 unit-cell series
divider are implemented. In the case of the 3-port divider,
the output ports are evenly distributed, while for the 5port divider, the output ports are unevenly distributed. The
results of these two circuits confirm the proposed idea.
series interdigital capacitor
4.8 mm
9.9 mm
10.4 mm
shunt stub to ground
via (radius: 0.12 mm)
(1)
The CRLH TL supports a wave with an infinite wavelength at both ωΓ1 and ωΓ2 , where ωΓ1 =min(ωse , ωsh ) and
ωΓ2 =max(ωse , ωsh ). At both ωΓ1 and ωΓ2 the group velocity (vg =dω/dβ) is zero and the phase velocity (vp =ω/β)
is infinity. This unusual infinite wave phenomenon (β=0,
ω6=0) is a unique property of the CRLH TL and is not
possible in a purely RH or a purely LH TL.
(a)
(b)
Fig. 3. CRLH TL resonator. (a) Unit-cell details; width of fingers are
0.3 mm, width of stub is 1.0 mm, and gaps are all 0.2 mm. (b) 8 unit-cell
realization of resonator.
B. TL Resonator Theory
To realize the N -port series divider, a CRLH TL resonator is used in order to obtain a standing wave with
an infinite wavelength. A conventional (i.e. RH) open- or
short-circuit TL of physical length, l, can be used to realize
a parallel resonator with resonance condition described by
nπ
,
(2)
l
where βn is the phase constant of resonance mode n [5].
For the conventional TL resonator, n has to be a nonzero, positive integer. In the case of a CRLH TL resonator,
n can also be negative or even zero. From (2), a CRLH
TL resonator with n = 0, referred to as a zeroth order
resonator (ZOR), is able to support a standing wave with
βn =
Fig. 4.
E-field plots of CRLH TL at different resonant modes [5].
A. Design Methodology
An open-circuit CRLH TL resonator comparable to the
one presented in [5] is used to design the novel N -port
series divider. The unit-cell used to realize the CRLH TL
is depicted in Fig. 3(a). The interdigital capacitor provides
CR and the short stub provides LL [6]. The substrate used
is Rogers RT/Duroid 5880 with dielectric constant εr =2.2
and thickness h=1.57 mm. These dimensions are chosen to
create a CRLH TL with an infinite wavelength frequency
around 2.3∼2.4 GHz. Parameter extraction yields LC
values of CL =1.27 pF, CR =1.45 pF, LL =3.27 nH, and
LR =3.21 nH corresponding to fsh =2.31 GHz. Eight unitcells of Fig. 3(a) are cascaded to realize the CRLH TL
resonator shown in Fig. 3(b). Coupling capacitors with
values of 0.5 pF are used to increase the transferred power
since weak coupling is not of interest for the divider design. In addition, Method of Moment (MoM) simulations
are used to confirm Fig. 3(b)’s CRLH nature. A 2.28 GHz
and 2.32 GHz infinite wavelength frequency is obtained by
MoM and measurement, respectively. These results show
good agreement between the predicted resonant frequency
of 2.31 GHz and MoM/experimental results. In addition,
Fig. 4 shows the CRLH nature of the implemented CRLH
TL; at n=0 an infinite wave is supported and for n<0,
wavelength is proportional to frequency.
was chosen in order to connect SMA connectors to the 50Ω
output ports.
(a)
B. 3-Port Series Divider
4.8 mm
2
3
4.8 mm
4
1.4 mm
0.2 pF SMT
capacitor
25 mm
4.8 mm
1
1.5 pF SMT
capacitor
103 mm
Fig. 5.
Layout of 3-port series divider.
To demonstrate the novel series divider, the CRLH
TL resonator of Fig. 3(b) was modified as shown in
Fig. 5 in order to simultaneously maximize power to the
output ports and not to detrimentally affect the resonance
condition. Port 1 is used as the feed port and the other three
ports are output ports. A 1.5 pF coupling capacitor is used
at the feeding port to maximize the transferred power to
the output ports. As seen in Fig. 5, the output ports are
connected to the CRLH TL at the stub ends with 0.2 pF
capacitors. Currently, the only limitation on port location
is the size of the unit-cell used to realize the CRLH TL.
In the limit that the unit-cells are infinitesimally small, the
port locations can be truly arbitrary. A quarter-wave length
transformer was used for the output ports in order to match
the high impedance of the divider to the 50Ω output ports.
Three output ports were connected at the second, fourth,
and sixth unit-cells of the CRLH TL. This port distribution
(b)
Fig. 6. Simulation and experimental results for the 3-port divider of
Fig. 5. (a) Magnitude response. (b) Phase response.
Fig. 6(a) and Fig. 6(b) respectively show the output
ports’ magnitude and phase responses. The MoM results
were obtained from Ansoft Ensemble and the measured
results were obtained from an Agilent 8510C network analyzer. At f =2.37 GHz , the 3-port divider has the following
measured magnitude responses: |S11 |=-10.02 dB, |S21 |=6.64 dB, |S31 |=-6.42 dB, and |S41 |=-6.42 dB. In addition,
the corresponding measured phase responses at f =2.37
GHz are: S11 =-93.01◦ , S11 =-94.33◦ , and S11 =-93.07◦ .
The shift of the infinite wave frequency is attributed to
the coupling capacitors at the ports. The associated loss at
this frequency point due to radiation, capacitor, conductor,
and dielectric losses is -1.12 dB. The magnitude and
phase responses also show that the 3-port series divider’s
output ports are nearly equal from 2.34 GHz to 2.52 GHz,
corresponding to a 180 MHz bandwidth.
C. 5-Port Series Divider
2
3
5
4
6
0.2 pF SMT
capacitor
1
1.5 pF SMT
capacitor
161 mm
Fig. 7.
Layout of 5-port series divider.
In order to demonstrate that the novel divider presented
has no limitation on the number or location of output
ports, the 3-port series divider presented in Section III.B
is modified to create a 5-port series divider as shown in
Fig. 7.
The 5-port series divider of Fig. 7 is composed of 13
unit-cells and has five output ports unevenly distributed
along the CRLH TL. Port 1 is used as the feed port and
the other five ports are output ports. The experimental
magnitude and phase responses of the 5-port series divider
respectively shown in Fig. 8(a) and Fig. 8(b) confirm the
proposed idea presented in this paper. At f =2.37 GHz,
the 5-port divider has the following measured magnitude
responses: |S11 |=-10.39 dB, |S21 |=-8.32 dB, |S31 |=-8.56
dB, |S41 |=-8.48 dB, |S51 |=-8.31 dB, and |S61 |=-8.26 dB.
In addition, the corresponding measured phase responses
at f =2.37 GHz are: S21 =-96.04◦ , S31 =-100.17◦ , S41 =102.36◦ , S51 =-101.89◦ , and S61 =-100.59◦ . As mentioned
above, the shift in resonance frequency can be attributed
to the coupling capacitors. The associated loss at this
frequency point due to radiation, capacitor, conductor,
and dielectric losses is -0.90 dB. The magnitude and
phase responses also show that the 5-port series divider’s
output ports are nearly equal from 2.34 GHz to 2.40 GHz,
corresponding to a 60 MHz bandwidth.
IV. C ONCLUSION
A novel N -port series fed divider based on the infinite
wavelength characteristic of a CRLH TL is realized. Measurements of the 3-port and 5-port series dividers verify
that equal magnitude and equal phase can be achieved
without regards to the number or location of output ports.
The series divider demonstrated in this paper can be used
as a novel series fed array or for clock synchronization in
microwave systems.
ACKNOWLEDGMENT
This work is part of the MURI program ”Scalable
and Reconfigurable Electromagnetic Metamaterials and
Devices.”
(a)
(b)
Fig. 8.
Experimental results for the 5-port divider of Fig. 7 (a)
Magnitude response. (b) Phase response.
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