Phased Array Antenna Limitations for
Ultra-Wideband Focusing
Payam Nayeri, Atef Z. Elsherbeni, and Randy Haupt
Dept. of Electrical Engineering and Computer Science
Colorado School of Mines
Golden, CO, USA
pnayeri@mines.edu, aelsherb@mines.edu, rhaupt@mines.edu
I. INTRODUCTION
Microwave energy can be concentrated into a small spot in
the near field by focusing the antenna [1]. Many different types
of antennas, such as reflectors, lenses, and arrays [2, 3], can be
focused, but arrays have the highest degree of design freedom,
and as such, have received the most attention. Focused antenna
arrays have been applied, in medicine, radar, and imaging
systems [4, 5], many of which require a wide operating
bandwidth [6, 7]. In this paper we present the basic properties
of UWB focused phased array antennas, and delineate the
limits of these systems. We show that the use of time-delay
units addresses the limitations in focused gain bandwidth, and
yield perfect focusing across the band. For the validation of this
concept, a UWB focused Vivaldi antenna array is designed and
its focusing capabilities are demonstrated.
II. FOCUSED UWB LINEAR ARRAYS
To demonstrate the focusing properties of UWB array
antennas, we first study a linear array of isotropic radiators
placed along the x-axis. The radiated electric fields of this array
[8] in the x-z plane can be computed using
N
E ( x, z ) = ¦ a n e
n =1
jϕ n
e
− jkRn
4π Rn
(1)
where k is the wavenumber, an and ijn are the amplitude and
phase weighting of the elements, and Rn is radial length from
the source to the observation point based on the local
coordinates of each element which is given by
(2)
To focus the radiated power of the antenna array, the
radiated waves from all elements of the array should add up in
phase at the desired focusing point. Thus at a focusing distance
F along the z-direction, the required phase shift for each
element is obtained using
2
ϕn =
2π f F + x′n
c
2
(3)
,
where f is the design frequency.
Consider a 10 element linear array with an element spacing
of 15 mm and a Dolph-Tschebyscheff taper with a sidelobe
level of -25 dB. The phase shifts are computed at 7 GHz using
(3), to produce a focused beam at F = 100mm. The amplitude
and phase of the electric filed in the x-z plane is given in Fig. 1,
where it can be seen that the focal point is exactly located at z =
100 mm. Note that the peak magnitude of the electric field is
closer to the aperture of the array, however the location of the
focal point is observed in the phase plot.
t
200
200
0.04
100
0.02
z (mm)
Index Terms—Focused array, phased array, time-delay, UWB,
Vivaldi.
2
2
R n = ( x − x ′n ) + z .
z (mm)
Abstract—The fundamentals of ultra-wideband (UWB) focused
phased array antennas are reviewed, and some basic limitations
are outlined. It is shown that when phase shifters are used within
the architecture of the array, the focal point moves as a function
of frequency, which degrades the focusing performance of the
antenna. To mitigate these limitations, time-delay units are
proposed, and it is revealed that perfect focusing across a wide
bandwidth can be achieved by this approach. To validate this
concept, an UWB Vivaldi focused antenna array using time
delays is designed which demonstrates good focusing capability
across the UWB spectrum.
100
0
100
-100
0
-100
0
x (mm)
100
0
0
-100
0
x (mm)
100
(a)
(b)
Fig. 1. Electric fields of the array at 7 GHz: (a) amplitude, (b) phase.
For narrowband applications, the array focusing scheme
outlined here can easily be implemented with a phased array
system. UWB focusing however is a far greater challenge. In
particular, the focal point of the array should remain fixed at all
frequencies across the band. Unfortunately, the focal point
moves as a function of frequency. For example, the phase of
the electric fields at the lowest and highest frequencies in the
band is given in Fig. 2. It can be seen that the focal point moves
towards the aperture at lower frequencies, and moves away
from the aperture at higher frequencies.
The solution to this problem is to use time-delay units, as
opposed to phase shifters. The required time-delay that
produces a focused beam is given by
‹,(((
tn =
III. AN UWB FOCUSED VIVALDI ANTENNA ARRAY
2
(4)
.
c
For the same linear array, the phase of the electric fields at the
two off-center frequencies when time-delay units are used is
given in Fig. 3, where it can be seen that a fixed focal point is
maintained at both frequencies.
200
100
100
0
z (mm)
z (mm)
200
100
100
0
-100
-100
0
-100
0
x (mm)
0
100
-100
0
x (mm)
100
(a)
(b)
Fig. 2. Phase of the electric fields for the 10 element focused linear array using
phase shifters: (a) 4 GHz, (b) 10 GHz.
200
100
100
0
-100
0
-100
0
x (mm)
z (mm)
z (mm)
200
100
100
-100
0
x (mm)
100
(a)
(b)
Fig. 3. Phase of the electric fields for the 10 element focused linear array using
time-delay units: (a) 4 GHz, (b) 10 GHz.
The magnitude of the electric field in the focal plane of the
array, i.e. z = 100 mm, is shown in Fig. 4, for both scenarios.
The peak of the electric field radiated by the phased array
varies with frequency. Time-delay units are focused at a
constant field magnitude at all frequencies across the band.
|Et| (V/m)
6
4 GHz
7 GHz
10 GHz
4
2
0
-150 -100
-50
|Et| (V/m)
6
0
0
-100
0
100
Vivaldi antenna arrays [9] have a VSWR smaller than 2 for
bandwidths of 10:1 or more, with nearly ideal element patterns
in all scan planes. Moreover, Vivaldi arrays are usually
constructed with printed circuit techniques which employ
stripline or microstrip input to the elements. As such they have
extensively been used in UWB phased array systems. Here we
study the focusing properties of a 4 element linear Vivaldi
antenna array using Ansys HFSS [10].
The antenna array is designed to operate in the UWB range
(3.1 to 10.6 GHz). The width of the Vivaldi element
corresponds directly to the element spacing of the array, thus it
was selected to be 13 mm (about 0.45Ȝ at 10.6 GHz). A
stripline is used to feed each element which is terminated in a
radial stub. The antenna is printed on two 62 mil layers of RT
Duroid 5880 substrate. The model of the antenna, along with
the simulated reflection magnitudes are given in Fig. 5, where
it can be seen that the antenna is matched at all ports (|Snn| < 10 dB) across the band.
0
50
x (mm)
(a)
100
Reflection Magnitude
2
F + xn′
|S11|
|S22|
|S33|
|S44|
-5
-10
-15
-20
-25
2
4
6
8
Frequency (GHz)
10
(a)
(b)
Fig. 5. A 4 element Vivaldi array antenna: (a) model configuration, (b)
simulated reflection magnitude.
This antenna is designed to focus the beam at a distance of
50 mm from the phase center of the array. The simulated
electric fields in the focal plane at 7 GHz are shown in Fig. 6.
Similar to the results in Fig. 1, the focal point can be clearly
observed in the phase plot. It is important to note that with this
design, due to the large length of the Vivaldi element, the
focusing is rather close to the physical aperture, however
focusing at further distances can easily be attained with a larger
number of elements in the array.
150
4 GHz
7 GHz
10 GHz
4
2
0
-150 -100
-50
0
50
100 150
x (mm)
(b)
Fig. 4. Magnitude of the electric field in the focal plane of the focused linear
array: (a) with phase shifters, (b) with time-delay units.
(a)
(b)
Fig. 6. The electric fields of the Vivaldi antenna array in the focal plane at 7
GHz: (a) magnitude of Ey, (b) phase of Ey.
To validate the proposed concept, the phase of the electric
fields in the focal plane of this focused Vivaldi array at the two
off-center frequencies when time-delay units are used is given
in Fig. 7. It can be seen that a fixed focal point is maintained at
both frequencies. Similar observations were made at other
frequencies across the band, indicating ultra-wideband focusing
characteristics for the array. It is important to point out here
that to mimic the time delay in the simulation model, the
corresponding phase at each frequency is computed and
assigned to the port excitation. In practice, this is realized by
time-delay units which are basically transmission lines that
provide the required time shift.
(a)
(b)
Fig. 7. Phase of the electric fields of the Vivaldi antenna array when time-delay
units are used: (a) 4 GHz, (b) 10 GHz.
IV. CONCLUSIONS
Some basic characteristics of UWB focused antenna arrays
are reviewed, and analytical studies are performed to
investigate the fundamental limitations of these system. It is
revealed that the use of phase-shifter units within the
architecture of the focusing array significantly reduces the
focusing capabilities of the system. Time-delay units are
proposed to mitigate this problem, and it is shown that perfect
focusing across the band of interest can be achieved by this
approach. To validate the concept, a Vivaldi antenna array is
designed which demonstrates good UWB focusing capability
using time delays. Experimental demonstration of UWB
focusing using timed-arrays, and in particular analysis of the
element dispersion and mutual coupling of the array elements,
will be conducted in the near future.
ACKNOWLEDGEMENT
The authors gratefully acknowledge the generous
contributions of Ansys Inc. and Intel Corporation to Colorado
School of Mines.
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