Session 3A2
Microwave and Millimeter Wave Circuits and Devices,
CAD
Adaptive RF Power Amplifier Tuned with Ferroelectric BST Varactor
Yulan Zhang, Thottam S. Kalkur, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Practical Use of the Kramers-Kronig Relation at Microwave Frequencies. Application to Photonic Like
Lines and Left Handed Materials
Jérôme Lucas, Emmanuel Géron, Thierry Ditchi, Stephane Holé, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Coaxial Quasi-elliptic Filter Using a Suspended Resonator and Vertically Stacked Coaxial Lines
Aline Jaimes-Vera, Ignacio Llamas-Garro, Alonso Corona-Chavez, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Asymmetric Microstrip Right/Left-handed Line Coupler with Variable Coupling Ratio
Emmanuel Géron, Thierry Ditchi, Jérôme Lucas, Stephane Holé, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Directional Coupler Using Back-to-back Microstrip Lines and Common Defected Ground Window
Structures
Jongsik Lim, Jaehoon Lee, Jun Lee, Bokyun Kim, Yongchae Jeong, Sang-Min Han, Dal Ahn, . . . .
Multi-mode Cavities for a High-gradient Two-beam Particle Accelerator Structure
Y. Jiang, S. V. Kuzikov, S. Yu. Kazakov, Jay L. Hirshfield, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Dual-band Wilkinson Power Divider Utilizing EBG Structure
Hsin-Hao Chen, Yi-Hsin Pang, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Large Scale Measurement of Microwave Electric Field Using Infrared Thermography and Electromagnetic
Simulation
Daniel Prost, F. Issac, P. Reulet, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Study of a Coplanar Zeroth-order Resonator on YIG Thin Film
Aziza Zermane, Bruno Sauviac, Bernard Bayard, Abdelmadjid Benghalia, . . . . . . . . . . . . . . . . . . . . . . . . . .
631
632
633
634
635
636
637
638
639
640
632 Progress In Electromagnetics Research Symposium Abstracts, Marrakesh, Morocco, Mar. 20–23, 2011
Adaptive RF Power Amplifier Tuned with Ferroelectric BST
Varactor
Yulan Zhang and T. S. Kalkur
Microelectronics Research Laboratories
Department of Electrical and Computer Engineering
University of Colorado at Colorado Springs
CO 80933-7150, USA
Abstract— Recent advancements in wireless communication systems necessitate improvements
in system functionality and performance with reduced cost and size. Present communication
systems use fixed band width amplifiers, antennas and filters which increases the need for large RF
components. The development of tunable capacitors using ferroelectrics gives us the opportunity
to develop tunable RF blacks. By changing the applied voltage to these capacitors the band width
of the components can be changed significantly. In this paper, we will discuss the fabrication
and characterization of ferroelectric thin film BST (Barium Strontium Titanate) capacitor for
RF applications. BST capacitors operating in the paraelectric region offer a tenability above 50%
within an applied voltage of ±5 Volts up to 10 GHz. We have measured the distortion in these
tunable capacitors using parallel resonant circuit approach. We will also present the design and
characterization of an adaptive matching network which is made of thin-film Barium-StrontiumTitanate (Ba0.7 Sr0.3 TiO3 (BST)) for a class A RF amplifier. A gain of 14.479 dB has been
achieved. The maximum output power load performance with both input and output matching
networks of tunable amplifier is improved compared to fixed-impedance amplifier. Control bias
variation of 4 V results in about 5.8 dB gain difference at 900 MHz. It provides the adaptation
for frequency bands of 600, 700, 800 and 900 MHz and different power levels.
REFERENCES
1. Zhang, Y. and T. S. Kalkur, “Analysis of distortion in ferroelectric varactors,” Journal IEEE
Transactions on Ultrasonics and Ferroelectrics, Vol. 57, No. 6, 2010.
2. Boeck, G., D. Pienkowski, R. Circa, M. Otte, B. Heyne, P. Rykaczwski, R. Wittman, and
R. Kakerow, “RF front end technology for reconfigurable mobile systems,” IEEE MTT-S
International, Vol. 2, 863, 2003.
Progress In Electromagnetics Research Symposium Abstracts, Marrakesh, Morocco, Mar. 20–23, 2011 633
Practical Use of the Kramers-Kronig Relation at Microwave
Frequencies. Application to Photonic Like Lines and Left Handed
Materials
J. Lucas1 , E. Géron1 , T. Ditchi2 , and S. Holé2
1
2
Laboratoire d’Electricité Général, ESPCI-Paris Tech, France
Laboratoire de Physique et d’Etude des Matériaux, UPMC Univ Paris 06, ESPCI-Paris Tech
CNRS UMR8213, France
Abstract— As early as 1914 Arnold Sommerfeld published two papers in Annalen der Physik
discussing the question of signal velocity in dispersive media. This work was at this time of
pure academic interest. Nowadays photonic crystals, and left handed materials are common
objects at microwave frequencies, and the questions raised by Arnold Sommerfeld, and addressed
by Léon Brillouin in his famous book of 19601 are practically encountered in everyday physics
at the laboratory. The famous well known second order differential equation known as the
wave equation is indeed not satisfied in dispersive medium such as photonic crystals and left
handed materials. Group velocities greater than the speed of light in vacuum and negative phase
velocities are encountered respectively in photonic crystals and left handed materials. These
phenomenons arise many questions especially insofar the theory of relativity is concerned and
promise many applications. A. Sommerfeld stated the problem considering the propagation of a
signal terminated on one side, and L. Brillouin carried out the calculus trying to find out a general
signal velocity. The results that can be obtained using this methodology which is equivalent to
considering the causality of a signal is more widely known particularly in optics through the
Kramers-Kronig relation. This relation has many applications and allows to link for instance
the imaginary part to the real part of the dielectrical constant of materials for instance. It is
also often used to explain the so-called anomalous dispersion phenomenon of light encountered
in some materials.
In this work, after a brief presentation of the implication of attenuation on the interpretation of
the group velocity, we demonstrate the use of the Kramers-Kronig relation for instance to obtain
the dispersion from an attenuation measurement at microwave frequencies in microstrip lines.
The measurements obtained using a Vector Network Analyser are compared to those calculated
from a single spectrum analyzer measurement on a photonic microwave crystal. We discuss at
this point the different nature of the attenuation required by causality, and the one due to the
losses in the media and how they interfere with each other. The method is also successfully
applied to periodical structures presenting evanescent waves as well as to left handed materials.
Finally we emphasize on the efficiency of the method to deal with causality and related pulse
reshaping considerations in a far more efficient way than transient or pulsed measurements or
considerations.
1 Wave
Propagation and group velocity, ACADEMIC PRESS INC.
634 Progress In Electromagnetics Research Symposium Abstracts, Marrakesh, Morocco, Mar. 20–23, 2011
Coaxial Quasi-elliptic Filter Using a Suspended Resonator and
Vertically Stacked Coaxial Lines
Aline Jaimes-Vera1 , Ignacio Llamas-Garro2 , and Alonso Corona-Chavez3
1
Signal Theory and Communications Department, Technical University of Catalonia
Barcelona 08034, Spain
2
Centre Tecnologic de Telecomunicacions de Catalunya, CTTC
Barcelona 08860, Spain
3
National Institute for Astrophysics, Optics and Electronics
Puebla 72840, México
Abstract— In this paper, pairs of air suspended coaxial resonators have been used to obtain
electric, magnetic and mixed couplings to produce a four pole quasi-elliptic, narrowband filter
at X-band. The filter is composed of two vertically stacked rectangular coaxial lines. One pair
of resonators is placed on the lower coaxial line and another pair is located on the upper line,
coupling between coaxial lines is achieved through an iris in the common coaxial ground plane.
The resonator is suspended by short circuited stubs, and can be used to produce quasi-elliptic
function or linear phase responses.
The proposed structure is smaller in size compared to conventional coaxial-combline cavity filters [1], which are commonly used for mobile communication applications. The unloaded quality
factor of a single resonator was measured and has been found to fall in-between the high Q obtained through optimized conventional coaxial-combline cavities and interdigital or microstripcombline filters. This structure avoids the use of coupling probes [2], and also avoids the use of
extra cavities or small metal plates among the resonators to design quasi-elliptic filters [1, 3].
The filter has been designed with a center frequency of 9.1 GHz with a 4% fractional bandwidth
and presents a transmission zero at each side of the pass-band. The device is made of nine planar
copper layers which are machined, stacked and compressed together to form the two rectangular
coaxial lines that form the quasi-elliptic filter. The planar implementation allows scaling the
designs to the millimeter-wave frequency range, using micromachining [4]. Design methodology,
simulated and measured results for the proposed device will be presented.
REFERENCES
1. Wang, Y. and M. Yu, “True inline cross-coupled coaxial cavity filters,” IEEE Transactions on
Microwave Theory and Techniques, Vol. 57, No. 12, 2958–2965, Dec. 2009.
2. Wang, C. and K. A. Zaki, “Full-wave modeling of electric coupling probes in comb-line resonators and filters,” IEEE Transactions on Microwave Theory and Techniques, Vol. 48, No. 12,
2459–2464, Dec. 2000.
3. Cogollos, S., R. J. Cameron, R. R. Mansour, M. Yu, and V. E. Boria, “Synthesis and design
procedure for high performance waveguide filters based on nonresonanting nodes,” IEEE MTTS International Microwave Symposium Digest, 1297–1300, Honololu, Jun. 2007.
4. Lancaster, M. J., J. Zhou, M. Ke, Y. Wang, and K. Jiang, “Design and high performance of a
micromachined k-band rectangular coaxial cable,” IEEE Transactions on Microwave Theory
and Techniques, Vol. 55, No. 7, 1548–1553, Jul. 2007.
Progress In Electromagnetics Research Symposium Abstracts, Marrakesh, Morocco, Mar. 20–23, 2011 635
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— 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 propagation vector, the electrical field vector and the magnetic field vector
constitute an indirect trihedron. Thus such metamaterials are called Left Handed materials (LH)
in opposition to the standard Right Handed propagation (RH). 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. 1D structures such as hybrid transmission lines are potentiality relevant for microwave circuit applications. Symmetrical coupling
structures using two LH coupled lines or asymmetrical structures using one LH line and one RH
line coupled together are excellent candidates to develop new circuits for telecommunications such
as coupler to be used in frequency synthesizers for instance. 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. In some applications, a variable coupling ratio is necessary.
This work presents a microstrip coupler with a variable 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. 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 which makes it easier to build. Furthermore, the frequency range
of this kind of couplers does not depend on its 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.
636 Progress In Electromagnetics Research Symposium Abstracts, Marrakesh, Morocco, Mar. 20–23, 2011
A Directional Coupler Using Back-to-back Microstrip Lines and
Common Defected Ground Window Structures
Jongsik Lim1 , Jaehoon Lee1 , Jun Lee1 , Bokyun Kim1 , Yongchae Jeong2 ,
Sang-Min Han1 , and Dal Ahn1
1
2
Soonchunhyang University, Republic of Korea
Chonbuk National University, Republic of Korea
Abstract— A new directional coupler structure using defected ground window structures between back-to-back microstrip lines is described in this paper. Directional couplers have been
designed and fabricated conventionally with planar substrate structures such as microstrip line
(Fig. 1) and striplines. Even though a few three-dimensional (3-D) directional couplers have
been proposed previously as extremely exceptional cases, but the required costs are too expensive because semiconductor fabrication processes should be provided for fabrication. In order to
overcome the cost problem and propose a new solution for 3-D directional couplers with cheap
microstrip lines, the authors propose a directional coupler, which consists of back-to-back microstrip lines and a defected ground window structure on the common ground plane. The side
view of Fig. 2 shows the structure of back-to-back microstrip lines with the common ground
plane. If the line from port1 to port 2 is placed on the top plane, while the other one from port 3
to port 4 bottom plane, and if the long rectangular area called defected ground window structure
(DGWS) is removed on the ground plane with a good alignment for the coupling section, a 3-D
directional coupler is designed with cheap microstrip structure as shown in Fig. 3. It is noted
that the coupling coefficient depends on not only the line width and dielectric media as general
cases, but also the dimensions of DGWS strongly. Fig. 4 shows the S-parameters of the proposed
directional coupler when the dielectric constant and thickness of the microstrip substrate are 2.2
and 31 mils, respectively. In Fig. 4, the coupling coefficient (S41 ) in this case is 15 dB with an
excellent isolation property (S31 ). The advantages of the proposed coupler structures are; 1)
reduced size 2) improved directivity than conventional design, 3) coupling coefficients are also
controlled by the dimensions of DGWS, 4) more flexible design, 5) possibility for providing better
density of integration because additional high frequency circuits can be realized on both sides of
microstrip line, and so on.
Figure 1.
Figure 2.
Figure 3.
Figure 4.
ACKNOWLEDGMENT
This work was supported by the National Research Foundation of Korea Grant funded by the
Korean Government (MEST) (KRF-2009-220-D00074).
Progress In Electromagnetics Research Symposium Abstracts, Marrakesh, Morocco, Mar. 20–23, 2011 637
Multi-mode Cavities for a High-gradient Two-beam Particle
Accelerator Structure
Y. Jiang1 , S. V. Kuzikov2, 3 , S. Yu. Kazakov2, 4 , and J. L. Hirshfield1, 2
1
Department of Physics, Yale University, New Haven, CT 06520, USA
2
Omega-P, Inc., New Haven, CT 06510, USA
3
Institute of Applied Physics, RAS, Nizhny Novgorod 603950, Russia
4
Fermi National Accelerator Laboratory, Batavio, IL 60510, USA
Abstract— A novel class of microwave cavities is described that have eigenmode spectra that
are harmonically related. A structure embodying a chain of such cavities could be the basis for
a two-beam, high-gradient, particle accelerator [1]. Versions of the structure could be used for
acceleration of beams of electrons, positrons, muons, protons, or heavier ions; with either electron
or proton drive beams. Excitation of the cavities in several harmonically-related eigenmodes can
be such that RF fields reach their peak values only during small portions of each basic RF period.
This feature could help raise breakdown and pulse heating thresholds. In this configuration, no
transfer elements are needed to couple RF energy from the drive beam to the accelerated beam,
since both beams traverse the same cavities. Purposeful cavity de-tuning is used to provide much
smaller deceleration for a high-current drive beam, than acceleration for a low-current accelerated
beam, i.e., to provide a high transformer ratio. A self-consistent theory based on elementary
circuit concepts is presented to calculate idealized acceleration gradient, transformer ratio, and
efficiency for energy transfer from the drive beam to the accelerated beam, for either parallel or
anti-parallel motion of the beams. The theory has been cast in dimensionless quantities so as to
facilitate optimization with respect to efficiency, acceleration gradient, or transformer ratio; and
to illuminate the interdependence of these parameters. Means for dramatically shortening the
structure fill time for the cavities are also described.
ACKNOWLEDGMENT
Research sponsored by Office of High Energy Physics, US Department of Energy.
REFERENCES
1. Kazakov, S. Y., S. V. Kuzikov, Y. Jiang, and J. L. Hirshfield, Phys. Rev. ST Accel. Beams,
Vol. 13, 071303, 2010.
2. Kuzikov, S. V., S. Y. Kazakov, Y. Jiang, and J. L. Hirshfield, Phys. Rev. Lett., Vol. 104,
214801, 2010.
638 Progress In Electromagnetics Research Symposium Abstracts, Marrakesh, Morocco, Mar. 20–23, 2011
A Dual-band Wilkinson Power Divider Utilizing EBG Structure
Hsin-Hao Chen and Yi-Hsin Pang
Department of Electrical Engineering, National University of Kaohsiung, Taiwan, R.O.C.
Abstract— This paper presents a novel dual-band Wilkinson power divider which utilizes
the electromagnetic band-gap (EBG) structure. The conventional Wilkinson power divider is
composed of two transmission lines, each of which the characteristic impedance is 70.7 Ω. A
lump resistor of resistance = 100 Ω is connected between the output ports for good isolation.
In addition, the electrical length of each transmission line could be θ = nπ/2, n = 1, 3, 5, . . ..
The Wilkinson power divider inherently possesses the multiband characteristics. However, odd
harmonics of the fundamental frequency are required. Utilizing the EBG structure, a lower
operated frequency could be acquired. Fig. 1 shows the relationships between frequency and
phase constant β for a microstrip line with and without the EBG structure, respectively. For
the microstrip line with the EBG structure, a band-gap is presented and the phase constant
β increases nonlinearly with frequency. At a lower frequency f1 , the electrical length of the
microstrip line with the EBG structure is designed to be θ = π/2. By adjusting the size of the
EBG structure, the electrical length of the microstrip line would be θ = 3π/2 at the desired
second frequency f2 which is less than 3f1 due to the rapid change of β near the band-gap. The
required dual-band operation is then achieved. In this work, a dual-band Wilkinson power divider
was designed and simulated using the full-wave simulator Agilent Momentum. The power divider
has been fabricated on an FR4 printed circuit board (PCB) of thickness h = 1.6 mm, relative
permittivity εr = 4.33 and loss tangent tan δ = 0.022, and would be measured for verification.
Figure 1: Dispersion diagrams of a microstrip line with and without the EBG structure, respectively.
Progress In Electromagnetics Research Symposium Abstracts, Marrakesh, Morocco, Mar. 20–23, 2011 639
Large Scale Measurement of Microwave Electric Field Using
Infrared Thermography and Electromagnetic Simulation
D. Prost, F. Issac, and P. Reulet
ONERA — The French Aerospace Lab, 2 avenue E. Belin, Toulouse, France
Abstract— We present an original method for measuring the microwave electric field and
achieving large scale field cartography. This is based on the use of a conductive and thermoemissive thin film of large dimensions, where induced currents due to incident field are responsible
for ohmic losses and therefore create thermal heating. This heating is recorded by an infrared
camera. The obtained thermal frame is obviously directly linked to the electromagnetic energy
dissipated inside the film. This frame can be used qualitatively, for example to detect field leakage
near electromagnetic junctions or to get antenna near field patterns, as it has been used for many
years at French Aerospace Lab ONERA. To get a quantitative field evaluation, a calibration is
necessary and needs a field sensor.
However, with the help of simulation we are able to get quantitative information, like field
amplitude or even component values of the field, making the film become an electric field sensor.
The simulation work addresses both electromagnetism, through EFIE computation of the electric
field, and thermal finite elements simulation, to get the temperature frame on the film. The
computed frame is compared to the recorded image and an iterative process is launched to get
acceptable matching of the two temperature cartographies. The correct electric field is assumed
to be the heating source whose thermal simulation gives compatible with measurement results,
taking into account the perturbation on the field due to the film itself. Moreover, through the use
of anisotropic films, components of the field can be obtained using the same method, providing
a complete picture of the microwave incident field.
640 Progress In Electromagnetics Research Symposium Abstracts, Marrakesh, Morocco, Mar. 20–23, 2011
Numerical Study of a Coplanar Zeroth-order Resonator on YIG
Thin Film
Aziza Zermane1, 2, 3 , Bruno Sauviac1, 2 , Bernard Bayard1, 2 , and Abdelmadjid Benghalia3
1
Université de Saint-Etienne, F42023, France
TELECOM Saint-Etienne, école associée de l’Institut TELECOM, DIOM
EA 3523, F-42023, 25 rue Dr. Rémy Annino, Saint-Etienne 42000, France
3
Laboratoire LHS, Université Mentouri de Constantine
Route d’Ain EL Bey 25000 Constantine, Algérie
2
Abstract— The objective of this work is to study numerically the behaviour of a coplanar
composite right-left handed zeroth order resonator (CRLH ZOR) realized on a YIG (Yttrium
Iron Garnet) thin film. We are focusing on the effects on the resonant frequency when changing
the magnetic bias and the thickness of the YIG. This study presents for the first time a tunable
CRLH ZOR with a coplanar structure on YIG thin film. The length of the proposed design
(device) is 5.2 mm, which is very small compared to a traditional half wave resonator. The
proposed resonator is designed to be tuned over the 5–6 GHz frequency band; insertion loss is
lower than 1 dB and return loss is better than 10 dB.
The concept of the Composite Right-Handed Transmission Line (line with traditional propagation) and Left-Handed Transmission Line (line having a negative phase velocity) was proposed
by UCLA group [1]. Recently, ferrite materials have been used in metamaterials and in meta-line
too. Tsutsumi and Abdalla proposed a nonreciprocal left-handed transmission line in microstrip
and in coplanar waveguide configurations respectively over the ferrite substrate (thick layer) [2, 3].
Zeroth order resonator (ZOR) is one of the novel applications of LHMs (Left-handed materials).
The interest lies in the fact that the resonant frequency is independent from the physical length of
the resonator. Due to metamaterials properties, negative and zero resonances are possible. The
zeroth-order CRLH resonance (`/λg = 0, m = 0) is particularly unique and interesting [4], since
it has infinite guided wave-length at a specific frequency. The proposed resonator is realised in
coplanar waveguide configuration constructed using an interdigital capacitor (IDC) and a shortcircuited stub inductor (SSI).
Our objective is to prove that it is possible to make a tunable CRLH ZOR with a 15 µm ferrite
film only. The ferrite substrate has a relative dielectric permittivity close to 15, a saturation
magnetization equal to Ms = 1780 Gauss and a ferromagnetic resonance (FMR) line width
∆H = 20 Oe. It is supposed to be saturated and the internal bias field is supposed to be uniform.
In this work our magnetic layer is magnetized in a direction perpendicular to the propagation
direction.
Figure 1: Example of Tuned response of the ZOR with ferrite.
REFERENCES
1. Caloz, C., A. Sanada, and T. Itoh, “Microwave circuits based on negative refraction index
material structures,” 33rd European Microwave Conference, Munich 2003.
Progress In Electromagnetics Research Symposium Abstracts, Marrakesh, Morocco, Mar. 20–23, 2011 641
2. Tsutsumi, M. and T. Ueda, “Nonreciprocal left-handed microstrip lines using ferrite substrate,”
IEEE MTT-S Int. Microwave Sym. Dig., Vol. 1, 249–252, 2004,
3. Abdalla, M. and Z. Hu, “A nonreciprocal left handed coplanar waveguide on ferrite substrate
with only shunt inductive load,” Proceeding of Metamaterials, October 2007.
4. Sanada, A., C. Caloz, and T. Itoh, “Novel zeroth-order resonance in composite right/lefthanded transmission line resonators,” Asia Pacific Microwave Conference, 2003.
642 Progress In Electromagnetics Research Symposium Abstracts, Marrakesh, Morocco, Mar. 20–23, 2011