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Asymmetric Microstrip Right/Left-handed Line Coupler with
Variable Coupling Ratio
E. Géron1 , T. Ditchi2 , J. Lucas1 , and S. Holé2
1
2
Laboratoire d’Electricité Général, ESPCI-ParisTech, France
Laboratoire de Physique et d’Etude des Matériaux, UPMC Univ Paris 06, ESPCI-ParisTech
CNRS UMR 8213, 10, rue Vauquelin, Paris 75005, France
Abstract— This work presents a microstrip coupler with a variable couling ratio taking advantage of structures presenting both LH and RH behaviour. After some considerations on the
LH line theory, the asymmetric RH/LH coupler is presented focusing on the parameters yielding
the coupling ratio and the frequency range. This type of couplers exhibits a high coupling ratio
though the gap between the two coupled lines is relatively large compared to the one of the
classical RH couplers. Furthermore, the frequency range of these couplers does not depend on
their length. Both simulations and measurements of the coupling ratio versus the number of cells
constituting the coupler are presented. From these results, we explain why such a structure is a
good way to realize a coupler presenting a variable ratio. Finally, the feasibility of electronically
controlled ratio couplers presenting a large bandwidth is discussed.
1. INTRODUCTION
Since the nineties, the feasibility of materials presenting simultaneously a negative permeability and
permittivity are demonstrated in built up macro-structures named metamaterials. A negative phase
velocity for the electromagnetic waves is observed in such structures. Consequently, the wave vector
~k, the electrical field vector E
~ and the magnetic field vector H
~ constitute an indirect trihedron.
Thus, such metamaterials are called Left Handed materials (LH) in opposition to the standard
Right Handed propagation (RH) [8]. The singularity of this negative phase velocity has triggered
a great interest and a lot of works have been carried out lately to develop these metamaterials in
1D, 2D and 3D structures.
As 2D and 3D structures are interesting optical and radiofrequency radiated applications [4, 5],
1D structures such as hybrid transmission lines are potentiality relevant for microwave circuit
applications [6, 12]. Symmetrical coupling structures using two LH coupled lines [3] or asymmetrical
structures using one LH line and one RH line coupled together [2] are excellent candidates to develop
new circuits for telecommunications.
In a great number of applications both a large coupling bandwidth and a high coupling ratio
are required. At high frequencies these electromagnetic couplers are often designed by closing up
two RH lines. The frequency range of such couplers is limited since it is directly dependent on
the length of the two lines in regard. In this case, the ratio between the coupled output and the
transmit output can only be adjusted by the gap between the two lines [7]. In some applications,
a variable coupling ratio is necessary.
This work presents a microstrip coupler with a variable coupling ratio. After some considerations
on the LH line theory, the asymmetric RH/LH coupler is presented focusing on the parameters
yielding the coupling ratio and the frequency range. We will present results on the coupling factor
function of the number of cells constituting the coupler. From these results, we explain why such
a structure is a good way to realize a coupler presenting a variable coupling ratio. Finally, the
feasibility of electronically controlled ratio couplers presenting a large bandwidth is discussed.
2. THEORETICAL APPROACH OF THE LH/RH COUPLER
A LH line is a 1D structure in which the roles of the capacitor and of the inductor have been
swapped compared to the elementary model of a conventional transmission line. As these RH lines
do not exist naturally, a LH line must be artificially realized using capacitors CL connected in series
and inductors LL connected to the ground. Such a line is in fact unrealisable because short RH
lines are necessary to connect the lumped components. The transmission line used in our prototype
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is therefore an hybrid RH/LH line [1]. This line exhibits a typical transmission response (Figure 2)
with the three following characteristic frequencies.
1
4π LL CL
1
√
=
2π CR LL dR
1
√
=
2π LR CL dR
fc1 =
fc2
fc3
√
s(2,1) dB
In these equations, CL and LL are lumped components inducing the LH behaviour. CR and LR
are the inductance and capacitance per unit length of the Right Handed lines model. The distance
dR is the length of RH line used to connect CL and LL .
The targeted applications are telecommunications systems in the 2.4 GHz ISM band. Thus, the
central frequency of the coupling range is chosen equal to fcoupling = 2.45 GHz. The circuit board is
realized with an ordinary FR4 substrate (²r = 4.3, h = 0.8 mm, copper35 µm, tan(δ) = 0.02) where
the wavelength of a RH microstrip line at the central frequency is λline = √L1 C /f = 70.34 mm.
R R
The hybrid line consists in a sequence of the elementary cells presented Figure 1 connected in
series. Each cell is composed of two capacitors 2CL = 2.4 pF serially connected, separated by a self
LL = 5.1 nH connected in parallel to the ground. The two RH line sections usedpto connect these
components are d2R = 2.35 mm length and their characteristic impedance is Z0 = LR /CR = 71 Ω.
The parameters of the RH lines are CR = 82 pF · m−1 and LR = 410 nH · m−1 . Using these
parameters the 3 characteristic frequencies are fc1 = 1 GHz, fc3 = 3.34 GHz, fc2 = 3.63 GHz. This
structure is equivalent to a line assuming that the cell length dr is small compared to the wave
length in the microstrip wave guide. The RH/LH material can be considered as homogeneous for a
λ
dimension dr lower than 10
. The full elementary length of a cell is dr = 5 mm. As the wave length
λ
of microstrip line at this frequency on such substrate is λline = 70.34 mm, we have dr ≈ 14
and the
λ
condition d ≤ 10 is respected.
The hybrid line presents two typical bandpass filter behaviours. Between fc1 and fc3 , it has
been demonstrated that the phase velocity is negative while it is positive beyond fc2 .
The coupler is composed of a succession of cells containing lumped components to induce left
behaviour as explained above and two small classical RH couplers as illustrated in Figure 3.
In such a coupler, measurements and simulations of the Poynting vector show a backward
propagation of the power in the hybrid line (port 2 to 3) when it is classically forward in the
standard RH line (port 1 to 4). This forward/backward propagation yields a greater power transfer
between the two lines [10] even if the gap between the two lines of the coupler is large. 3D
electromagnetic simulations show that the coupling effect is the result of a vortex-like interface
mode between the hybrid RH/LH and the classical RH line.
frequency (GHz)
Figure 1: The hybrid RH/LH transmission line cell.
Figure 2: The combined RH/LH transmission line.
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1
4
3
2
top
Figure 3: The elementary hybrid coupler cell.
Figure 4: Layout of the hybrid coupler composed of
10 cells.
As explained in [9, 10], the coupling effect between the RH line and the hybrid line is noticeable
when the hybrid line exhibits its LH characteristic. According to simulations [11], the coupling
effect occurs as expected between the RH line sections of the hybrid line that are close to the RH
line. The coupling ratio is enhanced by the combination of the right and left handed behaviours
of the hybrid line allowing to achieve a high ratio for the power coupling with a small number of
cells. In [3], the authors have studied the coupling ratio as a function of the gap between the two
lines showing a strong coupling effect compared to that of a classical RH/RH coupler even for a
large gap. This characteristic is very interesting in this coupler design because it reduces one of
the constraint. As the coupling effect is clearly due to the LH behaviour of the hybrid RH/LH
line, its frequency bandwidth is defined by the characteristic frequencies controlled by the lumped
capacitors and the inductor of the elementary cell of the line. Finally the bandwidth does not
depend on the number of elementary cells of the structure but only on their length. Consequently,
this work is focused on the relation between the number of cells and the coupling ratio. Indeed,
we intend to introduce some electronic switches in the structure to modify the number of coupled
cells thus driving the coupling ratio.
3. THE COUPLING RATIO AS A FUNCTION OF THE NUMBER OF CELLS
For an application in the frequency range of telecommunications systems in the 2.4 GHz ISM band,
the central frequency of the coupling range defined at fcoupling = 2.45 GHz is pertinent. As explained
before, the LH line can be assimilated to an homogeneous LH material.
In order to study coupling ratio as a function of the number of cells, a simple hybrid RH/LH
microstrip line coupler composed of 10 cells (Figure 4) was realized. In [11], the input port is
located on the LH line. In the coupler studied in this work, the input and the transmit ports
(port 1 and 4) have been chosen on the RH microstrip line while the coupled port (#2) and the
isolated port (#3) are on the LH/RH line. With such a choice it is possible to leave some of the
last cells disconnected while maintaining the transmit power way. It is important to note that each
cell is symmetric (Figure 3). As specified for the hybrid RH/LH line, the 2 capacitors of each cell
are equal to 2.4 pF which leads to an equivalent capacitor CL = 1.2 pF, the inductor is equal to
L = 5.1 nF and the two RH section lines used for the coupling effect of the hybrid line are 2.3 mm
long. The coupling gap is set to s = 300 µm.
In order to validate the control of the coupling ratio by varying the number N of cells connected,
simulations and measurements were performed for various values of N .
Simulations were performed with the structure of the coupler presented Figure 4. Assuming
that the coupling effect which depends on LH behaviour is localized in the small RH couplers, it
is relevant to use microwave circuits simulator like ADS from Agilent Technologies instead of a 3D
electromagnetic simulator. The results are as accurate but obtained with a shorter computational
time. A good agreement between measurements and simulations validates this choice. Simulation
results are presented in Figure 5.
In a complementary way, measurements were performed with 1 up to 10 cells by populating
them with the lumped components one by one on the prototype presented in Figure 4. The 5 cells
measurement, for instance, was performed with all the capacitors and inductors of the 5 first cells
soldered leaving the remaining component footprints empty. Figure 6 presents the coupling ratio
and the transmit ratio of the coupler versus the frequency. Measurements were performed using an
HP8722ES network analyser. The bandwidth of the coupler is nearly as large as 500 MHz centered
at 2.45 GHz. This bandwidth is adequate for Ultra Wide Band Telecommunication applications.
374
Coupling ratio S21 (dB)
Transmission ratio S41 (dB)
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frequency (GHz)
frequency (GHz)
Coupling ratio S21 (dB)
Transmission ratio S41 (dB)
Figure 5: Coupling and transmission ratio simulated for 1 to 10 cells connected.
frequency (GHz)
frequency (GHz)
ratio (dB)
Figure 6: Coupling and transmission ratio for 1 to 10 cells populated.
connected cells
Figure 7: Coupling and transmit ratio at 2.45 GHz as a function of the number of component populated
cells.
Figure 7 presents on the same graph, at the central frequency, the growth of the coupling ratio
with the number of populated cells and its counterpart decrease of the transmit ratio. The graph
presents an asymptotic behaviour for more than 9 cells populated. It shows that the maximal
coupling that can be obtained is limited. The obtained coupling ratio goes from −15 dB (1 cell) up
to −3 dB (10 cells).
On can deduce from these measurements that the hybrid coupler presents some power losses
resulting of propagation along the 10 cells. This power losses are due to the FR4 substrate which
presents dielectric losses at the frequency used for the measurements.
4. FEASIBILITY OF AN ELECTRONIC CONTROLLED COUPLER
As shown by simulations and verified with measurements, it is clearly possible to modify the coupling ratio by modifying the number of cells involved in the coupling process. The problem consists
of implementing one or more electronic switches on the hybrid RH/LH line at high frequency while
changing as little as possible its characteristics. The LH behaviour of the line is very dependent
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on the RH section line necessary to integrate the switch, ie a PIN diode, its polarization and control circuit for instance. Inserting some RH additional section lines will modify the fc2 and fc3
characteristic frequencies. New simulations must then be performed to validate such structure.
Various switches can be used, preferentially MEMS switches or PIN diode switches. The isolation
provided by the electronic switch must be high enough to well control the coupling ratio. The
necessary minimum isolation has to be evaluated on the prototype with different active elements.
Standard RF PIN diodes exhibit a 10 dB isolation at 2 GHz which is enough to realize RF front-end
TX/RX switches. In the case of the coupler, such isolation seems to be just enough. A prototype is
being realized to test all these essential points for the validation of the coupler with an electronically
controlled coupling ratio.
The great overall length of such couplers can be invoked as a limiting factor for their industrial
use. Nevertheless, for typical industrial application where the maximal coupling ratio can be less
than −3 dB, a smaller number of cells is necessary which reduces drastically the length of the
coupler. The length of such couplers is therefore not the blocking factor to their industrial use.
5. CONCLUSION
The hybrid LH/RH line is a very efficient component to realize specific telecommunications circuits
using its Left Handed behaviour. When well dimensioned, the coupling ratio of such structure
can be modified by driving the number of cells of the coupler serially connected which has been
demonstrated by the performed simulations and measurements. We have discussed the feasibility
of electronically controling the number of cells: It essentially depends on the ability to maintain
the hybrid behaviour of the LH/RH line once the electronic switches have been introduced. To
definitively validate the feasibility of a driven power ratio coupler, a prototype with an electronic
switch is being investigated.
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