354 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 10, 2011
EM/Circuit Mixed Simulation Technique
for an Active Antenna
Georges Zakka El Nashef, F. Torrès, S. Mons, T. Reveyrand, Member, IEEE, T. Monédière,
E. Ngoya, Member, IEEE, and R. Quéré, Fellow, IEEE
Abstract—Today’s increase of functions, improvement of perfor-
mance, and cost reductions required on an active electronically
scanned array (AESA), associated to the limited amount of avail-
able areas and volumes to implement the equipment, drive an ap-
proach leading to directly connect power amplifiers (PAs) to the an-
tennas array without placing an isolator/circulator between them.
In this letter, an electromagnetic/radio frequency (EM/RF) circuit
mixed simulation technique will be theoretically introduced and
experimentally demonstrated on transmission (Tx) chains to deal
with the proposed challenge.
Index Terms—Active electronically scanned array (AESA),
behavioral model, electromagnetic (EM) macro-model, mutual
coupling, power amplifier (PA).
I. INTRODUCTION
T HE SIMULATION and analysis of a transmission (Tx)chain have to face two types of problems: electromag-
netic (EM) characterization of the transmitting antennas and rig-
orous radio frequency (RF) circuit approach. The combination
of these issues is commonly referred to as EM/RF circuit cosim-
ulation. In general, cosimulation can be seen in many appli-
cation areas as encompassing nonlinear circuit conception, an-
tenna design, and signal integrity analysis in a global approach.
In our case, cosimulation approach is used to study interactions
between PAs and antennas.
Active electronically scanned array (AESA) design con-
straints are very critical since greater performances are required
within less room or nonconvenient places to fit the equipment,
and this compactness leads to many problems, such as heat
dissipation, EM coupling, etc. More precisely, in our case,
short relative distance between the array’s antennas may result
in a high level of mutual coupling between antennas, leading
to large output loading mismatches [up to voltage standing
wave ratio VSWR 4:1 and more]. This mismatching
affects PA behavior, which in turn directly impacts the gain
and phase controls of each radiating element. Therefore, the
cosimulation approach is of great help to investigate the effects
of large output mismatching and high-level
mutual coupling between antennas on the system performance.
Manuscript received March 15, 2011; accepted April 03, 2011. Date of
publication April 11, 2011; date of current version May 09, 2011. This work
was realized within the framework of the “Lypsis Project” supported by
Elopsys (competitiveness cluster for high technologies—www.elopsys.fr) and
the French “Direction Générale des Entreprises.”
The authors are with the XLIM Laboratory, OSA/C2S2 Departments, UMR
CNRS 06172, University of Limoges, 87060 Limoges Cedex, France (e-mail:
georges.zakka-el-nashef@xlim.fr).
Digital Object Identifier 10.1109/LAWP.2011.2141972
However, such general approaches may require large and
complex simulations. Therefore, an alternative method is used
in this letter, the “mixed simulation approach.” It consists in
dividing and solving separately both the RF circuit model and
EM model, which can then be combined to produce a general
behavioral model for system approach, enabling an efficient
synthesis and optimization.
Due to space limitations and already published theoretical
works in [2] and [6], a brief summary of the two different
approaches (Sections II-A and II-B) will be presented. Those
approaches enable us to have simulation models of separated
blocks [antennas and power amplifiers (PAs)] to ensure that
overall performance will meet requirements in given worst-case
conditions. Then, a preliminary mixed simulation approach
combining both models is presented in Section II-C. An exper-
imental validation is described in Section III. Conclusions are
given in Section IV.
II. MIXED SIMULATION CONCEPTS: PA AND EM MODELS
A. PA Behavioral Model
In this letter, a PA is directly connected to an antenna, which
then presents an unknown load impedance to the PA. The mu-
tual coupling between antennas may induce strong variations in
both the real and imaginary part of the antenna input impedance.
Hence, without an isolator, the load presented to the PA will
vary and the PA characteristics will change and cause a signif-
icant signal distortion [1]. Therefore, an extended bilateral be-
havioral model was developed in [2], based on nonlinear scat-
tering functions [3], allowing to take into account large output
mismatches (VSWR up to 4:1). The developed model [2] uses
second-order Taylor expansion to improve robustness and ac-
curacy. The phase of the four waves ( and ) is normalized
such as becomes real. Thus, assuming that is negligible
compared to , and that the PA is working at the fundamental
frequency, the second-order Taylor development can be written
as follows:
(1)
where , , , , and
are the nonlinear scattering functions.
The PA model can be extracted from continuous-wave (CW)
measurements at the operating frequency, as described in [4].
The identification of nonlinear scattering functions defined in
(1) can be obtained from waves’ measurements for at least six
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