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

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.

Index Terms—Focused array, phased array, time-delay, UWB, Vivaldi.

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

n n

jkRj

n R

eeazxE

nn

1 4),(

πϕ (1)

where k is the wavenumber, an and n 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

22)( zxxR nn +′−= . (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 22

c

xFf nn

′+=

πϕ (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.

-100 0 1000

100

200

x (mm)

z (m

m)

0

0.02

0.04

-100 0 100

0

100

200 t

x (mm)

z (m

m)

-100

0

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

.22

c

xFt nn

′+= (4)

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.

-100 0 1000

100

200

x (mm)

z (m

m)

-100

0

100

-100 0 1000

100

200

x (mm)

z (m

m)

-100

0

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.

-100 0 1000

100

200

x (mm)

z (m

m)

-100

0

100

-100 0 1000

100

200

x (mm)

z (m

m)

-100

0

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.

-150 -100 -50 0 50 100 1500

2

4

6

x (mm)

|Et| (

V/m

)

4 GHz7 GHz10 GHz

(a)

-150 -100 -50 0 50 100 1500

2

4

6

x (mm)

|Et| (

V/m

)

4 GHz7 GHz10 GHz

(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.

III. AN UWB FOCUSED VIVALDI ANTENNA ARRAY 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 0.45 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.

2 4 6 8 10-25

-20

-15

-10

-5

0

Frequency (GHz)

Ref

lect

ion

Mag

nitu

de

|S11

| |S22

| |S33

| |S44

|

(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.

(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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[10] High Frequency Structure Simulator, Ansys HFSS 2014, ANSYS Inc. Pittsburgh, PA 2014.