HAL Id: hal-02865294
https://hal-univ-rennes1.archives-ouvertes.fr/hal-02865294
Submitted on 12 Jun 2020
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entic research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diusion de documents
scientiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
Analysis of Circularly-Polarized CTS Arrays
M. del Mastro, F.F. Manzillo, D. Gonzalez-Ovejero, M. Smierzchalski, P.
Pouliguen, P. Potier, R. Sauleau, M. Ettorre
To cite this version:
M. del Mastro, F.F. Manzillo, D. Gonzalez-Ovejero, M. Smierzchalski, P. Pouliguen, et al.. Analysis
of Circularly-Polarized CTS Arrays. IEEE Transactions on Antennas and Propagation, Institute of
Electrical and Electronics Engineers, 2020, 68 (6), pp.4571-4582. �10.1109/TAP.2020.2972438�. �hal-
02865294�
ACCEPTED MANUSCRIPT
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TAP.2020.2972438, IEEE
Transactions on Antennas and Propagation
1
Analysis of Circularly-Polarized CTS Arrays
Michele Del Mastro, Francesco Foglia Manzillo, Member, IEEE, David Gonz
´
alez-Ovejero, Senior Member, IEEE,
Maciej
´
Smierzchalski, Philippe Pouliguen, Patrick Potier, Ronan Sauleau, Fellow, IEEE, and Mauro Ettorre,
Senior Member, IEEE
Abstract—This paper presents an efficient analysis method for
a novel continuous transverse stub (CTS) antenna. As opposed to
state-of-the-art CTS antenna designs, the proposed architecture
achieves circular polarization using a single CTS array and
without any polarization converter. The structure consists of long
radiating slots/stubs fed by over-moded parallel-plate waveguides.
More precisely, the transverse electromagnetic (TEM) mode and
the first transverse electric (TE
1
) mode of the feeding waveguides
are used to generate a circularly-polarized field. The array is
analyzed using a spectral mode-matching method. First, the
active reflection coefficient of the infinite array is derived in
closed form. A windowing approach is then adopted to compute
the radiation patterns of finite-size arrays. Numerical results
obtained with this method are in excellent agreement with full-
wave simulations, carried out with a commercial software. The
performance of this class of CTS antennas has been investigated
using the developed model. It is theoretically demonstrated that
the proposed array can be designed to attain an axial-ratio (AR)
lower than 3 dB over a 52.9% relative bandwidth at broadside.
Furthermore, the active input reflection coefficient is lower than
-10 dB over a 40.8% relative bandwidth when the array steers its
main beam at θ
0
= 45
◦
. This solution is an attractive candidate
for next generation satellite communication terminals.
Index Terms—Continuous transverse stub array, circular po-
larization, oversized parallel-plate waveguides.
I. INTRODUCTION
T
HE growth of satellite communication (Satcom) applica-
tions in Ka-band has boosted the development of novel
antenna solutions with wide-band performance, wide-angle
scanning capabilities, and low-form factor [1]. Continuous
transverse stub (CTS) arrays have received particular attention
from the community due to their low profile and wideband
performance [2]–[4]. They consist of arrays of stubs or open-
ended parallel-plate waveguides (PPWs), which radiate in free
space and may be fed either in series or in parallel. A series-
fed CTS array [5] comprises stubs, finite in height, placed on
the upper plate of a PPW. The beam is spatially steered by
varying the angle of incidence of the wave launched into the
Manuscript received on December 11, 2018; revised on September 09,
2019; published on January 24, 2020. “This work was supported by the
Direction G
´
en
´
erale de l’Armement and by Brittany Region, France.
M. Del Mastro, D. Gonz
´
alez-Ovejero, R. Sauleau, and M. Ettorre
are with Univ. Rennes, CNRS, IETR (Institut d’
´
Electronique et de
T
´
el
´
ecommunication de Rennes) - UMR 6164, F-35000 Rennes, France (e-
mail: michele.delmastro@univ-rennes1.fr).
F. Foglia Manzillo is with CEA-Leti, MINATEC Campus, 38054 Grenoble,
France and also with Universit
´
e Grenoble Alpes, 621 av. Centrale, 38400 Saint
Martin-d’H
´
eres, France.
M.
´
Smierzchalski are with CEA-LETI, MINATEC Campus, 38054 Greno-
ble, France.
P. Pouliguen is with the Strategy Directorate, Direction G
´
en
´
erale de
l’Armement, 75509 Paris, France.
P. Potier is with the Information Superiority, Direction G
´
en
´
erale de
l’Armement, 35170 Bruz, France.
feeding PPW. On the other hand, standard parallel-fed CTS
arrays [6], [7] adopt long slots in a metallic plane fed by a
corporate network of mono-modal PPWs, supporting the TEM
mode. Such network typically excites with the same amplitude
and phase each slot. The parallel-fed architecture exhibits very
wide-band capabilities owing to the mutual coupling of the
slots [8].
However, the main drawback of CTS arrays is that, due
to their radiation mechanism, they are inherently linearly-
polarized. Circular-polarization (CP) has become an essential
feature for Satcom applications for enhancing the robustness
of the satellite communication links [9]. Existing solutions to
achieve CP typically rely on add-on linear-to-circular (LP-to-
CP) converters, placed in proximity of the radiating slots [10],
[11]. Nevertheless, the use of LP-to-CP converters impacts on
the overall size and thickness of the antenna system and, at
the same time, introduces additional losses.
A novel concept is here proposed for CTS arrays. The main
underlying idea is based on the bi-modal operation of the
antenna. Over-moded PPWs are employed to feed the radiating
elements. In particular, both the slots and PPWs should support
the fundamental TEM and the first transverse electric (TE
1
)
modes. The transverse electric fields of these two modes
are orthogonally-polarized and therefore, if properly excited,
are able to radiate a CP field. This novel CTS architecture
relies on a single radiating aperture, rather than on two
arrays geometrically-organized in an egg-crate configuration,
as recently proposed in [12]. Indeed, the radiating aperture in
[12] consists of orthogonally-oriented long slots, series-fed by
a corporate network of mono-modal PPWs. Thus, the radiation
mechanism of the CTS antenna that we propose may provide
CP fields resorting to a single aperture, which supports two
orthogonally-polarized modes.
An efficient numerical tool is crucial to explore the po-
tential of the structure described above. The proposed anal-
ysis method is based on a spectral mode-matching technique
(MMT). This numerical tool builds on the work in [13], ex-
tending it to over-moded CTS arrays. In particular, the model
provides a closed-form expression for the active impedance
of an infinite array excited by the TE
1
mode. The active
impedance under TEM mode operation is also accurately pre-
dicted for slots and PPWs supporting the two selected modes,
which also constitutes a futher new contribution with respect
to [13]. Furthermore, the radiation patterns of finite-size arrays
are derived using a windowing approach. Design guidelines are
also discussed for achieving a wideband impedance matching
and low axial-ratio (AR). Several examples are presented to
provide the reader with an useful deepening for different
design goals arising in practical applications. The insight pro-
ACCEPTED MANUSCRIPT
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TAP.2020.2972438, IEEE
Transactions on Antennas and Propagation
2
(a) Perspective view.
(b) Cross-sectional view taken along the xz-plane.
Fig. 1. Geometry of the problem. Only three dielectric slabs are shown for
the layered media for the sake of clarity.
vided by the proposed analysis is of considerable importance
on the study of the antenna’s potentialities and limitations. The
versatility of the tool to analyze the array under different and
precisely controlled excitations (single-mode, multimode) is
fundamental to perform fast and accurate parametric studies.
The impact of the array parameters on the antenna’s matching
and radiation performance are exhaustively displayed and
discussed, thus easing the design of a circularly-polarized
SatCom terminal antenna.
The paper is organized as follows. In Section II, the active
impedance of the radiating slots is derived for an infinite
circularly-polarized CTS array under both TEM and TE
1
mode operation. In Section III, numerical results are validated
by comparison with full-wave simulations. In Section IV,
radiation properties and AR performance for a finite-size array
are derived. In Section V, design guidelines are outlined.
Furthermore, Section VI shows a representative example of
a possible design in Ka-band. Finally, Section VII concludes
the paper.
II. ANALYTICAL MODEL
Fig. 1 shows the geometry of the problem under consider-
ation. An infinite array of slots on a ground plane is fed by
over-moded PPWs. The width of the slots is a and they are
infinitely-extended along the y-axis. In order to guarantee a bi-
modal behavior of the PPWs, we restrict our analysis to values
of a between λ/2 and λ, where λ is the operating wavelength
in the medium filling the PPWs. The inter-element spacing
along the x-axis is d. The PPWs are filled with a material
of permittivity
r1
. The modes are considered propagating
along the z-axis. The metallic parts are considered lossless
and, hence, modeled as perfect-electric conductor (PEC). The
slots radiate into a planar multi-layered medium. The number
of media can be arbitrarily chosen and their height is indicated
by h
q
with q ∈ N
+
. Each medium has permittivity
r,q+1
,
where q ∈ N
+
.
By virtue of the equivalence theorem, a magnetic field
integral equation (MFIE) is derived to formulate the electro-
magnetic problem by enforcing the continuity of the tangential
component of the magnetic field on the slots:
ˆz × [H
i
(x, y, z) + H
r
(x, y, z) − H
t
(x, y, z)] |
on D
= 0 (1)
where D = {(x, y, z) ∈ R
3
: nd < x < a + nd with n ∈
Z, −∞ < y < +∞, z = 0}.
In (1), H
i
(x, y, z), H
r
(x, y, z), and H
t
(x, y, z) are, respec-
tively, the incident, reflected and transmitted magnetic field at
the discontinuity z = 0. A simple graphical representation of
the fields is shown in Fig. 1(b). The two incident fields are
given by
H
TEM
i
=
+∞
X
n=−∞
H
TEM
PPW
(x − nd, y)
Q
a
x −
a
2
− nd
e
−ik
x0
nd
(2)
H
TE
1
i
=
+∞
X
n=−∞
H
TE1
PPW
(x − nd, y)
Q
a
x −
a
2
− nd
e
−ik
x0
nd
(3)
when the array is excited by a TEM or a TE
1
mode, respec-
tively. In turn, the expressions for the reflected and transmitted
fields are
H
r
= −
+∞
X
n=−∞
H
PPW
(x − nd, y)
Q
a
x −
a
2
− nd
e
−ik
x0
nd
(4)
H
t
=
Z
R
2
G
t
HM
(x − x
0
, y − y
0
) M
t
(x
0
, y
0
) dx
0
dy
0
(5)
where
Q
a
(x)
= 1 for −a/2 < x < a/2 and null elsewhere,
k
x0
= k
0
sin θ
0
cos φ
0
with (θ
0
, φ
0
) the beam pointing direc-
tion, and M
t
(x, y, z) is the transverse magnetic distribution on
D and its expression can be found in [13]. Furthermore, G
t
HM
is the transverse dyadic Green’s function for the half-space
over the slots. The latter may be evaluated in the presence
of a layered medium using an equivalent transmission-line
model as in [14]. The extended forms of H
TEM
PPW
, H
TE
1
PPW
,
and H
PPW
in (2), (3), and (4), respectively, are provided in
[13]. It is important to notice that only the TEM and TE
1
mode
excitations are considered in (2) and (3) for the incident field
even if, since λ/2 < a < λ, the TM
1
mode can propagate
as well. Since possible mutual couplings between TEM and
TM
1
modes may occur along any eventual discontinuities, a
possible solution to cut-off the TM
1
mode relies on feeding the
slots with longitudinally-corrugated PPWs [21]–[25]. In the
following we will exclude the TM
1
mode to feed the structure.
By replacing (2) or (3), (4), and (5) in (1), a MFIE
is obtained. This equation can be approximately solved by
ACCEPTED MANUSCRIPT
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TAP.2020.2972438, IEEE
Transactions on Antennas and Propagation
3
truncating the series to 2M-1 PPW’s modes and 2N
f
+1
Floquet’s modes, and applying the Galerkin’s method to (1).
Two different linear problems arise for the two selected modes.
For each mode, the matrix-based form yields
Y
T E,T E
Y
T E,T M
Y
T M,T E
Y
T M,T M
V
TE
V
TM
=
I
01
I
02
(6)
where V
TE
=
V
T E
0
, V
T E
1
, . . . , V
T E
M−1
and V
TM
=
V
T M
1
, . . . , V
T M
M−1
are the scalar mode functions of TE and
TM modes in the PPWs, respectively. Depending on the
type of impinging field we consider (i.e., TEM (2) or TE
1
(3)), the known terms I
01
and I
02
take a different form. The
mathematical expression of the admittance matrix in (6) can
be found in [13].
A. Active admittance for TEM-excitation
For completeness, we report the main results for the TEM
mode given in [13]. The constant term in (6) is given by
I
01
=
iV
T EM
inc
√
aY
T E
0
0
.
.
.
0
, I
02
=
0
.
.
.
0
(7)
where V
T EM
inc
= 1 (V/
√
m) and Y
T E
0
= 1/ζ with ζ the intrin-
sic impedance of the medium inside the PPWs. By inverting
(6), the scalar mode functions V
T E
m=0,...,M−1
and V
T M
m=1,...,M−1
can be calculated and the fields on the aperture expressed in
a closed-form. The active admittance of the radiating slots
can be then derived. The mathematical expression of the
normalized active admittance is given by
¯
Y
T EM
act
= −
1
V
T E
0
√
a
2
Z
D
H
t
· M
*
t, TEM
dxdy (8)
M
t, TEM
= −
iV
T E
0
√
a
Q
a
x −
a
2
e
−k
y0
y
ˆy (9)
In (8), H
t
takes into account the contribution of all higher
order modes in the PPWs and the mutual coupling among
feeding waveguides (see (5)). In (9) M
t, TEM
considers only
the effect of the fundamental mode within the PPWs.
The extended form of the normalized active admittance (8)
is given in [13].
B. Active admittance for TE
1
-excitation
When the array is excited by a TE
1
mode, the incident fields
are expressed by (3). In this case, the known term of the linear
system (6) is given by
I
01
=
0
V
T E
1
inc
Y
T E
1
k
T E
1
π
√
2a
0
.
.
.
0
, I
02
=
iV
inc
Y
T E
1
k
T E
1
2k
y0
√
a
0
.
.
.
0
(10)
where V
T E
1
inc
= 1 V /
√
m, Y
T E
1
=
q
k
2
−
k
T E
1
2
/(ζk), and
k
T E
1
=
q
(π/a)
2
+ k
2
y0
with k
y0
= k
0
sin θ
0
sin φ
0
, whereas
k
0
and k are wave-numbers in free space and in the medium
inside the PPWs, respectively. In (10), the non-null entry of I
02
takes into account the coupling between TE and TM modes
which occurs when the antenna beam is steered in planes φ 6=
{0
◦
, 180
◦
}.
As for TEM mode, by solving (6) the scalar mode functions
V
T E
m=0,...,M−1
and V
T M
m=1,...,M−1
are found. The electromag-
netic field on the plane of the slots is therefore completely
determined. The active admittance can be then expressed as
¯
Y
T E
1
act
= −
1
V
T E
1
√
a
2
Z
D
H
t
· M
*
t, TE1
dxdy (11)
where
M
t, TE1
= M
x
t,T E
1
ˆx + M
y
t,T E
1
ˆy (12)
with
M
x
t,T E
1
= −
r
2
a
π
a
V
T E
1
e
−ik
y0
y
q
k
2
y0
+ (π/a)
2
+∞
X
n=−∞
sin
π
a
(x − nd)
×
Q
a
x −
a
2
− nd
e
−ik
x0
nd
(13)
M
y
t,T E
1
= −
r
2
a
ik
y0
V
T E
1
e
−ik
y0
y
q
k
2
y0
+ (π/a)
2
+∞
X
n=−∞
cos
π
a
(x − nd)
×
Q
a
x −
a
2
− nd
e
−ik
x0
nd
(14)
The complete expression the active admittance (11) is given
in Appendix A.
III. NUMERICAL RESULTS
The model presented in Section II allows to compute the
active impedance per unit length Z
act
= 1/
¯
Y
act
. The obtained
results have been extensively validated by using a commercial
full-wave simulator (i.e., CST STUDIO SUITE
®
[32]). The
simulation setup is shown in Fig. 2. A waveguide port is
used to launch the TEM and TE
1
modes into the radiating
slot, respectively. Furthemore, a Floquet’s port is considered
on the top of the air-box, placed above the radiating slot.
Unit-cell boundary conditions are enforced on the lateral
faces of the model. The reference plane of the derived active
Fig. 2. Simulation setup of the CTS array unit-cell. The structure is periodic
along x- and y-axes.
ACCEPTED MANUSCRIPT
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TAP.2020.2972438, IEEE
Transactions on Antennas and Propagation
4
0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
1.5
2
frequency/f
ma
x
ℜ{Z
act
/Z
T EM
}
CST
Proposed tool
(ǫ
r1
, ǫ
r2
) = (2, 4)
(ǫ
r1
, ǫ
r2
) = (2, 2)
(ǫ
r1
, ǫ
r2
) = (1, 1)
(a) Real part of the active impedance versus frequency.
0.5 0.6 0.7 0.8 0.9 1
−1
−0.5
0
0.5
1
frequency/f
ma
x
ℑ{Z
act
/Z
T EM
}
CST
Proposed tool
(ǫ
r1
, ǫ
r2
) = (2, 4)
(ǫ
r1
, ǫ
r2
) = (2, 2)
(ǫ
r1
, ǫ
r2
) = (1, 1)
(b) Imaginary part of the active impedance versus frequency.
Fig. 3. Active impedance for TEM-mode excitation versus frequency along
the plane at φ = 90
◦
for θ
0
= 30
◦
. The parameters used in the simulation
are a = 0.5c/ (f
min
√
r1
), d = 1.07a, h = 0.5c/ (f
min
√
r2
), and
Z
T EM
= ζ.
parameters is located over the slot. The main parameters of
the structure are set as f
min
= f
T E
1
cut−off
, f
max
= 2f
min
,
and a = 0.5c/(f
min
√
r1
). These settings guarantee that only
the fundamental (i.e., TEM) and the first two higher order
modes (i.e., TE
1
and TM
1
) can propagate into the PPWs.
Furthermore, only one dielectric layer is considered over the
slots with an arbitrary height h
1
= 0.5c/(f
min
√
r2
). Finally,
the spatial periodicity of the array is d = 1.07a and the length
of the slot is d
y
= λ
max
/30. Note that CTS arrays are one-
dimensional periodic structure based on long slots. In this
case, such a very small periodicity along the slot is only used
to numerically-validate the proposed tool and avoid possible
artifacts due to periodicity along the slot using [32]. Several
combinations of
r1
and
r2
have been considered in order to
validate the numerical tool and provide some design guidelines
in various scenarios.
A. TEM-mode excitation
The TEM case is here considered since the results in [13]
were validated only for single-mode PPWs, i.e. for a < λ/2.
The number of Floquet’s modes required to get a stable
convergence is N
f
= 10, while the number of PPW’s modes
is M ≥ 5 both for the E-plane (i.e., φ = 0
◦
) and the
H-plane (i.e., φ = 90
◦
). The real and the imaginary parts
of the normalized active impedance versus frequency are
shown in Fig. 3 along the H-plane. An excellent agreement
is observed between the proposed tool and full-wave results.
0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
1.5
2
2.5
frequency/f
ma
x
ℜ{Z
act
/Z
T E
1
}
CST
Proposed tool
(ǫ
r1
, ǫ
r2
) = (1, 1)
(ǫ
r1
, ǫ
r2
) = (2, 1)
(ǫ
r1
, ǫ
r2
) = (2, 4)
(a) Real part of the active impedance versus frequency.
0.5 0.6 0.7 0.8 0.9 1
−1.5
−1
−0.5
0
0.5
1
frequency/f
ma
x
ℑ{Z
act
/Z
T E
1
}
CST
Proposed tool
(ǫ
r1
, ǫ
r2
) = (2, 1)
(ǫ
r1
, ǫ
r2
) = (2, 4)
(ǫ
r1
, ǫ
r2
) = (1, 1)
(b) Imaginary part of the active impedance versus frequency.
Fig. 4. Active impedance for TE
1
-mode excitation versus frequency along
the plane at φ = 0
◦
for θ
0
= 30
◦
. The parameters used in the simulation
are a = 0.5c/ (f
min
√
r1
), d = 1.07a, h = 0.5c/ (f
min
√
r2
), and
Z
T E
1
= 1/Y
T E
1
.
Similar results are obtained along the E-plane and are not
reported for the sake of brevity. Finally, it is important to
note that the active S-parameter corresponding to the case
r1
=
r2
= 1 is less than -10 dB over a 66.6% band along
the H-plane (i.e., for φ = 90
◦
) when the array is pointing at
θ
0
= 30
◦
.
B. TE
1
-mode excitation
In this subsection, we validate the active impedance cal-
culation for the TE
1
-excitation. Fig. 4 depicts the real and
imaginary parts of the normalized active impedance versus
frequency along the plane φ = 0
◦
. An excellent agreement is
observed also in this case between the proposed numerical tool
and full-wave results. One gets stable convergence for all the
cases in Fig. 3 considering M ≥ 8 and N
f
≥ 10. This method
has been validated for several combinations of
r1
and
r2
,
showing always an excellent agreement in comparison to full-
wave results. For the sake of completeness, Fig. 5 plots real
and imaginary parts of the active impedance, normalized to the
wave impedance Z
T E
1
= 1/Y
T E
1
of the TE
1
mode versus the
scan angles along the plane φ = 0
◦
at f
0
= (f
min
+ f
max
) /2.
Finally, we also report the active S-parameter S
act
=
(Z
act
− aZ
T E
1
)/(Z
act
+ aZ
T E
1
) along the E-plane (i.e.,
φ = 90
◦
) versus frequency (see Fig. 6(a)) and scan angles
θ
0
(see Fig. 6(b)). A stable convergence has been achieved by
considering M ≥ 10 PPW’s modes and N
f
= 10 Floquet’s
