PIERS Proceedings, Stockholm, Sweden, Aug. 12–15, 2013
240
Design Considerations for a Low-frequency Vivaldi Array Element
A. Tibaldi1 , G. Virone2 , F. Perini3 , J. Monari3 , M. Z. Farooqui1 , M. Lumia2 ,
O. A. Peverini2 , G. Addamo2 , R. Tascone2 , and R. Orta1
1
Dipartimento di Elettronica e Telecomunicazioni (DET), Politecnico di Torino
Corso Duca degli Abruzzi 24, Torino 10129, Italy
2
Istituto di Elettronica e di Ingegneria dell’Informazione e delle Telecomunicazioni (IEIIT), Consiglio
National Research Council of Italy (CNR) c/o Politecnico di Torino
Corso Duca degli Abruzzi 24, Turin 10129, Italy
3
Istituto di Radioastronomia (IRA), Istituto Nazionale di Astrofisica (INAF)
Via Fiorentina 3513, Medicina (BO) 40059, Italy
Abstract— A cavity-backed Vivaldi antenna is suggested as dual-polarization array element for
the low-frequency instrument of the Square Kilometer Array (SKA) project. A design strategy
aimed at maximizing the sensitivity for such an array element is described. As an example, an
antenna was obtained, with a sensitivity higher than 10 cm2 /K in the operative bandwidth and
in the 45◦ sky coverage angle, for each polarization.
1. INTRODUCTION
The Square Kilometer Array (SKA) represents one of the most interesting new-generation radiotelescopes owing to its extreme sensitivity performance [1]. One of the main SKA subsystems is
the low-frequency Aperture Array (AA-low), which has to operate in the [70, 450] MHz band [2].
Several wide-band antenna systems have been studied within this framework: the spiral antenna [2],
the BLU-antenna [3], the log-periodic antenna [4]. Recently, a dual-polarization Vivaldi array
element has been proposed as a potential candidate for AA-low [5]. The main advantages of this
configuration are a single ended 50 Ω matching and a low cross-polarization in the principal planes,
owing to the symmetry of the antenna. Furthermore, the antenna is self-standing, does not require
either bulky dielectric parts or ground planes and can be manufactured in a gridded version [6].
2. DEVELOPMENT OF A CAVITY-BACKED VIVALDI CONFIGURATION
The first item of this work is the selection of a suitable geometry for the rear part of the antenna,
in order to enhance its performance in terms of front-to-back ratio (FBR). The starting structure
is the Vivaldi antenna with a circular back stub adopted in [5]; its FBR is presented in Figure 1,
as a black dashed line. This parameter can not be improved by introducing a ground plane behind
the antenna, because this would introduce an additional ripple in the curve, without significant
improvements (red dash-dotted line).
Front-to-Back Ratio
30
25
VivaldiStub
VivaldiGNDPlane
CavityBackedVivaldi
FBR (dB)
20
15
10
5
0
0.05
0.1
0.15
0.2
0.25
0.3
frequency (GHz)
0.35
0.4
0.45
Figure 1: Front-to-back ratio of Vivaldi with three back structures.
Progress In Electromagnetics Research Symposium Proceedings, Stockholm, Sweden, Aug. 12-15, 2013 241
(a)
(b)
Figure 2: Cavity-backed Vivaldi antenna. (a) Lateral view. (b) Front view.
On the contrary, recalling the TEM horn structures [7], the cavity-backed configuration represented in Figure 2 has been conceived. The feed point of the antenna is located at the junction of
the Vivaldi “wings” with the cavity. The design parameters of this structure are: The front width
of the non-blended antenna W , the aperture width A, the antenna length L, the blending radius
C, the base width Wb , the back cavity length Lb and the back cavity width Ab .
In Figure 1 it is possible to observe that the FBR curve of a non-optimized version of this
structure is almost monotone with improved values at higher frequencies. This structure has been
used as starting guess for the following design procedure.
3. DESIGN PROCEDURE
The AA-low instrument is a sparse random array, where the average embedded element pattern
is, as a first approximation, similar to the pattern of the single (isolated) element [8, 9]. In this
regard, the element design can be performed focusing on the sensitivity enhancement of the single
element [2]. The maximization of the worst-case sensitivity of the array element corresponds to
the minimization of the number of antennas needed to satisfy the SKA sensitivity specifications,
leading to a reduction of manufacturing costs.
The sensitivity S is defined as the ratio of the element effective area Aeff to its noise temperature
Tsys :
µ ¶
Aeff (r̂, f ) m2
S(r̂, f ) ,
(1)
Tsys (f )
K
where r̂ indicates the observation direction and f is the frequency. Aeff is calculated from the
radiation patterns, which are obtained using a full-wave simulator.
For what concerns the denominator, Tsys can be calculated as the sum of three contributions:
Tsys (f ) = Tant,sky (f ) + Tant,gnd (f ) + Trec (f )
(2)
Tant,sky (f ) and Tant,gnd (f ) quantify the noise contributions coming from the sky and from the
ground. These two quantities are evaluated by means of the Cortes model [10]. The measured
receiver noise temperature Trec (f ) is approximately 30 K in the whole band.
The structure should be designed in order to maximize the sensitivity in the 70–450 MHz band
within the 45◦ sky coverage from zenith (SC), for each polarization. This goal is achieved by
exploiting a synthetic representation of the sensitivity as a function of the geometrical parameters.
It is useful to define the goal function S̃:
S̃(f ) = min S(r̂, f )
r̂∈SC
(3)
As far as frequency is concerned, it should be noted that the operative conditions in the AA-low
band are not homogeneous. Indeed, in the lower part of this band, the sky noise contribution
is dominant. On the other hand, the most significant high-frequency noise contributions are the
PIERS Proceedings, Stockholm, Sweden, Aug. 12–15, 2013
242
remaining two. Therefore, S̃(f ) has been parametrized by means of its minimum values in three
sub-bands: B1 = 70–200 MHz, which is the sky-noise dominated band; B2 = 200–350 MHz, which
is a transition band; B3 = 350–450 MHz band, which is dominated by the receiver noise.
This representation of the goal function is very convenient for the evaluation of the effects of the
geometrical parameters; for example, S̃(f ) is showed in Figure 3 as a function of the length of the
Vivaldi antenna L and of its aperture width A. The white star markers identify the optimal values
for the B2 and B3 bands. From the figure it is also possible to observe that the design procedure,
in this case, is mainly driven by the higher band, where the sensitivity is generally low. Moreover,
the sensitivity in B1 appears to be almost independent of A and L.
The same procedure must be performed varying other couples of parameters, in order to complete
the design of the structure.
min(Aeff/Tsys) (cm2/K), f ∈ B2
min(Aeff/Tsys) (cm2/K), f ∈ B 3
6
6
7.2
6.3
7.2
7.5
6.6
6.6
6.9
7.2
2
900
5.7
6
400
800
7.2
1200
1000
L (mm)
1100
Figure 3: Minima of S̃(f ) in the three sub-bands.
solid: θ=0°; dashed : θ=45°, H plane; dash-dotted : θ=45°, E plane
40
S(0°)
S(45°)|H
35
S(45°)|E
30
2
S(θ,f) (cm /K)
25
20
15
10
5
0
50
100
150
200
4
3
450
7.5
6
7.5
6.9
7.5
7.2
7.5
6
7.5
A (mm)
6.6
7.2
6.6
6.9
6.3
A (mm)
7.8
5.7
1100
4.8
6.3
5.4
7.5
7.57.5
7.8
7.8
7.8
7.8
6
7.8
5.4
5.7
A (mm)
5.1
6.9
1000
L (mm)
6.6
900
250
300
350
7
6
7.5
400
800
7.8
1200
8
5
6.9
1100
500
8.1
6.9
6.3
7.8
1000
L (mm)
7.8
7.8
6.6
6.3
7.5
450
900
600
550
500
450
400
800
7.2
7.8
550
7.8
500
600
650
9
6.
600
550
650
700
6.6
650
6 6.3
700
6.3
700
10
9
750
7.2
750
6.9
750
3
6.6
800
5.7
7.8
800
6.3
min(Aeff/Tsys) (cm2/K), f ∈ B1
800
400
frequency (MHz)
Figure 4: Sensitivity goal function of the designed structure.
450
1
1200
0
Progress In Electromagnetics Research Symposium Proceedings, Stockholm, Sweden, Aug. 12-15, 2013 243
4. DESIGN RESULTS
The performance of a significant design example is discussed in this section. The main dimensions
of the designed antenna are 1.2 × 1.2 m2 footprint and 1.5 m height. Figure 4 shows the sensitivity
function S(r̂, f ) for ϑ = 0◦ and ϑ = 45◦ in the H-plane and in the E-plane; it is possible to
observe that S(r̂, f ) is higher than 10 cm2 /K in most situations. The effective area of the designed
antenna and the three noise temperature contributions are represented in Figure 5 and in Figure 6.
In particular, Figure 6 confirms that the main noise contribution for lower frequencies is the sky
one, while the receiver noise is dominant for higher frequencies. Moreover, the new configuration
exhibits a good symmetry of the pattern, which leads to high IXR values [11].
In Figure 7 it is possible to observe that the 50 Ω reflection coefficient is below −10 dB above
170 MHz.
4
4.5
x 10
4
7000
5000
Aeff(0°)
Aeff(0°)
Aeff(45°)|H
Aeff(45°)|H
Aeff(45°)|E
6000
Aeff(0°)
Aeff(45°)|H
4500
Aeff(45°)|E
Aeff(45°)|E
4000
3.5
5000
3500
2.5
2
Aeff(θ,f) (cm2)
Aeff(θ,f) (cm2)
Aeff(θ,f) (cm2)
3
4000
3000
3000
2500
2000
1.5
1500
2000
1
1000
1000
0.5
0
50
500
100
150
frequency (MHz)
0
200
200
250
300
frequency (MHz)
0
350
350
400
frequency (MHz)
450
Figure 5: Aeff (ϑ, f ) of the structure.
4000
3500
250
50
Tant,gnd
Tant,gnd
Tant,sky
Tant,sky
Trec
Trec
Tant,gnd
Tant,sky
45
Trec
200
40
3000
2500
2000
1500
Tsys(f) contributions (K)
Tsys(f) contributions (K)
Tsys(f) contributions (K)
35
150
100
30
25
20
15
1000
50
10
500
0
50
5
100
150
frequency (MHz)
200
0
200
250
300
frequency (MHz)
350
0
350
400
frequency (MHz)
Figure 6: Tsys (f ) contributions of the designed structure.
450
PIERS Proceedings, Stockholm, Sweden, Aug. 12–15, 2013
244
0
-5
S11 (dB)
-10
-15
-20
-25
-30
50
100
150
200
250
300
350
400
450
500
frequency (MHz)
Figure 7: Reflection coefficient of the designed structure.
5. CONCLUSION
A cavity-backed Vivaldi antenna has been proposed as array element for the SKA AA-low project.
A design procedure based on a full-wave simulator and the Cortes noise temperature model has
been developed and described. An effective organization of the sensitivity parametric analyses has
been proposed in order to define a suitable and exhaustive design strategy; it should be noted that
the same design procedure can be applied to other antenna structures.
In conclusion, the results obtained demonstrated that good performance can be achieved with
the Vivaldi element.
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