4498 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO.

12, DECEMBER 2006

Study of 2-bit Antenna–Filter–Antenna Elements for

Reconfigurable Millimeter-Wave Lens Arrays
Chih-Chieh Cheng, Student Member, IEEE, and Abbas Abbaspour-Tamijani, Member, IEEE

Abstract—This paper presents a new reconfigurable an- eliminates the feed matrix and can overcome the scanning
tenna–filter–antenna (AFA) element based on slot antennas and degradations due to the phase aberration of the fixed arrays for
switchable resonators. This reconfigurable AFA can operate in off-axis feed positions. However, due to the large number of
four modes of operation as a three- or four-pole filter, and yields a
2-bit variable phase delay. As a result, the multimode AFA can be elements and small cell area in millimeter-wave arrays, the only
used as the building block of 2-bit adaptive lens arrays. This paper viable scenario for implementing the phase-shifting capability
details design, modeling, and miniaturization of the reconfigurable is resorting to fully integrated architectures.
AFA, and demonstrates its performance through preconfigured Implementation of quasi-optical array with built-in phase
prototypes. The proposed AFA has a loss of 1.4–1.6 dB measured shifters using solid-state and microelectromechanical systems
at 32 GHz in both three- and four-pole filter modes, and exhibits
a frequency response that is almost insensitive to the angle of (MEMS) technology has been a subject of research at least
incidence. Several proof-of-concept fixed lens arrays have been since the late 1980s, and has been addressed by a number of
also fabricated for output beams scanned to 0 , 15 , 30 , 45 , and researchers. Probably the first reported implementation of an
60 in the - and -plane. The measurement results show that integrated free-space beam-steering system can be found in a
the output beam can be scanned to 60 in both principle planes, paper by Lam et al. published in 1988 [6], demonstrating a
with a worst case sidelobe level of less than 11 dB and a scan
loss that hardly exceeds the theoretical limit. reflective phase-shifting grid of 1600 Schottky barrier diodes
with a maximum phase shift of 70 and 7-dB loss at 93 GHz.
Index Terms—Antenna–filter–antennas, beam steering, fre- The authors theorize the use multilayer grids for realizing larger
quency-selective surface (FSS), microelectromechanical systems
(MEMS) antennas, phase shifters, reconfigurable antennas.
phase shifts and one- or two-directional beam steerers. Later,
Sjogren et al. [7] demonstrated a reflective 8640 Schottky
diode grid with 60 flat amplitude phase shift and 3.5-dB
I. INTRODUCTION loss at 132 GHz, and for the first time reported the measured
performance of the grid for beam steering ( 16 scan width),
focusing ( 7-dB focusing gain), and polarization control
( 12-dB change in axial ratio). Reference [8] reports a grid
I N millimeter-wave frequencies (30–300 GHz), beam
forming is usually achieved by using antenna arrays with
free-space feeding schemes, commonly known as quasi-op-
with improved diode design that could achieve 130 reflective
phase shift and 2.7-dB loss at 62 GHz. The major limitations
tical systems. Space-feeding eliminates the loss and parasitic associated with the use of Schottky diodes are the large series
effects of the conventional (constrained) feed networks and can resistance, inadequate capacitive ratio, and dc power consump-
dramatically improve the radiation performance. Free-space tion. In this respect, MEMS switches present ideal substitutes
beam-forming arrays can be realized as transmission type (lens for the Schottky diodes for alleviating these limitations.
arrays) [1] or reflection type (reflect arrays) [2]. In both cases, The earliest conception of a reconfigurable array based on
the array elements are designed to compensate the spherical MEMS switches can be tracked to 1994 in a paper by Chiao and
phase error of an input wave generated by the low-gain feed Rutledge [9]. In this paper, the authors propose a quasi-optical
antenna and produce a directive output beam. Inexpensive transmittive beam steerer as a two-dimensional (2-D) array of
beam-steering systems can be implemented using fixed arrays switch-loaded rectangular (or rhombic) waveguides. The wave-
either by mechanical rotation of the array (in the case of reflect guide array is constructed using a stack of lapped silicon wafers
arrays) or through using multiple feed antennas (matrix) and an (slices), each containing an array of metallized micromachined
RF switch. These methods are extensively used in commercial holes (waveguide sections). DC contact MEMS switches are
radars and multibeam satellite communication antennas [3]–[5]. fabricated on SiO N membranes and are used to implement a
A fully electronic high-resolution scanning, however, re- switchable capacitive/inductive septum inside each waveguide
quires integration of phase-shifting devices within the array section. By selectively biasing the switches, a quantized phase
elements to form reconfigurable arrays. A reconfigurable array shift of 0 –360 can be obtained from a multiwafer structure.
Although interesting in concept, the system is next to impos-
sible to fabricate, at least due to the difficulties associated with
Manuscript received April 14, 2006; revised August 30, 2006. This work was three-dimensional (3-D) biasing and control, and stress control
supported by the National Science Foundation under Award ECS-0524805. and stiction in the membrane [10]. The early onset of grating
The authors are with the Department of Electrical Engineering, Arizona State lobes and surface wave modes due to that the large distance be-
University, Tempe, AZ 85287 USA (e-mail: chih-chieh.cheng@asu.edu; ab-
basa@asu.edu). tween elements also limits the scanning width [11]. In 1999,
Digital Object Identifier 10.1109/TMTT.2006.885993 Mazotta et al. [10] used a modified method, based on TEM
0018-9480/$20.00 © 2006 IEEE
CHENG AND ABBASPOUR-TAMIJANI: STUDY OF 2-bit AFA ELEMENTS FOR RECONFIGURABLE MILLIMETER-WAVE LENS ARRAYS 4499

waves and a series of metallic screens, also loaded with switch-

able reactive loads. The concept was verified for single layer ar-
rays at 3 GHz using discrete p-i-n diode switches, and at 5 GHz
using conductive tapes (to simulate MEMS switches in up and
down states). Steering angles of up to 20 and 12.5 and in-
sertion losses of 6 and 2 dB were measured for 3- and 5-GHz
arrays, respectively. A later study [12] demonstrated functions
such as focusing, scanning, and beam splitting using precon-
figured prototypes at 5 GHz. With a reported insertion loss of
2 dB for a 45 phase shift per grid, the insertion loss of a eight-
fold 3-bit 360 system is estimated to be 16 dB at only 5 GHz,
suggesting that multigrid techniques are not suitable for mil-
limeter-wave application.
In this paper, we investigate a new reconfigurable MEMS
lens array comprised of reconfigurable antenna–filter–antenna
(AFA) elements. AFAs are three-layer metallic structures
composed of receive and transmit antennas and intercon-
necting resonant circuits, and acts as filters with radiation Fig. 1. (a) AFA array structure based on two Rogers 5880 laminates and 3001
ports. Reference [11] describes a class of AFA elements based bonding film. (b) Three layers of the AFA element.
on microstrip antennas and coplanar waveguide (CPW) res-
onators and demonstrates their application for constructing
frequency-selective surfaces (FSSs). These AFA elements have
also been demonstrated in nonuniform array configurations
for implementing fixed lens arrays [13], [14]. To form a fixed
lens array, the AFA elements are stagger tuned to implement
a location-dependent phase-delay function. A lens array with
beam-forming capability can be formed as an array of recon-
figurable AFA elements. A multimode bandpass AFA element
composed of slot antennas and stripline resonators has been
demonstrated in [15]. This element is designed to toggle
between four different modes of operation using five series
switches built into the resonator layer. A reconfigurable AFA
of this type functions as a 2-bit filter/phase-shifter module
with radiative ports, and can be used as the building block of a
digital reconfigurable lens array. The simple switching scheme
and the confinement of the switches to the middle layer renders
this structure very suitable for fabrication as a self-packaged Fig. 2. Reconfigurable stripline middle-layer composed of line segments, ca-
monolithic array. pacitive gaps, and series switches.
In this paper, we detail the underlying concepts and design
methodology for the 2-bit AFA element reported in [15], and
present an improved design based on stepped-impedance res- The top and bottom metal layers contain the slot antennas that
onators and slot antennas [16]–[18]. The new design is con- function as the first and last resonators of the AFA. The middle
siderably more compact and dramatically improves the scan- layer accommodates the stripline resonators. An incident wave
ning capability. A complete circuit model is presented and used with proper polarization is received by the top slot antenna in the
for simulation and optimization of the AFA elements. The per- input side, passes through an active (switched on) stripline res-
formance of the proposed AFA is demonstrated experimentally onator sub-circuit, and reradiates from the bottom slot antenna
through fixed uniform arrays in the form of FSSs and lens-array on the output side with orthogonal polarization.
prototypes configured for beams at 0 , 15 , 30 , 45 , and 60 The topology of the middle layer of the AFA is presented in
in both - and -planes. Fig. 2, where transmission-line segments, switches, and cou-
pling capacitors are denoted by , , and , respectively.
II. RECONFIGURABLE AFA ELEMENTS Fig. 3 shows the resonator configurations in different modes of
operation. In each mode, subsets of the t-line segments are con-
A. Basic Concept figured through the active switches to form a resonant circuit
A reconfigurable AFA can be formed using fixed receive and between the top and bottom slot antennas. In modes 1 and 2
transmit antennas and a reconfigurable resonator middle layer. [see Fig. 3(a) and (b)], the AFA element functions as a three-
Fig. 1 shows the AFA structure based on two layers of 381- m pole filter, as it consists of two resonant antennas and a single
-thick Roger’s 5880 microwave laminate ( , stripline resonator. Modes 3 and 4 [see Fig. 3(c) and (d)], on
) and three 18- m-thick layers of electroplated copper. the other hand, can be recognized as four-pole filters, as they
4500 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 12, DECEMBER 2006

where we have used for modes 1 and 2 and for

modes 3 and 4. The phase differences can be written as

(3)

which indicates that, in its four modes of operation, the reconfig-

urable AFA can provide all of the phase values required for 2-bit
phase shifting. Although the phase relationships in (3) are exact
only at the center frequency, simulation of the phase response
shows that they are valid within 10% for the entire passband of
the three- and four-pole filters (see Section II-B).

B. Design Method and Circuit Model

The advantage of utilizing slot antennas is their potential to
Fig. 3. Four modes of the operation of the AFA. (a) Mode1: S on, other
switches off, R and R are active and the rest of the resonators are inactive.
result in very low-loss arrays [19]. The slot lengths are designed
(b) Mode2: S on, other switches off, resonators R and R are active and the for resonance at the center of the operation band and the slot
rest of the resonators are inactive. (c) Mode3: S , S on, others switches off, widths are adjusted for the required value of radiation bandwidth
resonators R , R , R and R are active and the rest of the resonators are inac-
tive. (d) Mode4: S , S on, other switches off, resonators R , R , R and R
(equivalent to of the filter). The polarization rotation be-
are active and the rest of the resonators are inactive. Phase delays are indicated tween input and output is necessary for three reasons, which
for each mode. are: (1) to prevent the formation of transmission zeros as a re-
sult of direct coupling between the top and bottom antennas; (2)
to provide a mechanism for achieving 1-bit phase shift through
each contain a pair of capacitively coupled (through or ) selecting the direction of the rotation; and (3) to block the dis-
stripline resonators and the antennas. turbance caused by the spillovers of the feed antenna. The t-line
From the above description, it is evident that a 1-bit phase segments in the middle layer (Fig. 2) are positioned so as to
control (0 or 180 ) can be readily achieved by inverting the di- achieve the required value of coupling with the slots. The cou-
rection of the polarization rotation through switching between pling coefficient can be controlled by the length of the portion of
modes 1 and 2 or 3 and 4. We now show that a second bit of the stripline that is exposed to the slot antenna and the distance
phase control (an additional 90 ) is attainable by switching from of the coupling region from the center of the slots. The topology
mode 1 to mode 3 or from mode 2 to mode 4. First, let us re- of the stripline structure is derived based on circuit concepts, but
member from basic filter theory that a lossless bandpass filter fine tuning of the layout heavily relies on full-wave finite-ele-
presents a purely reactive behavior at dc, resulting in ment method (FEM) simulations. This is primarily due to the
. Since the transmission coefficients in modes 1 and 2 and presence of mutual coupling and the critical tradeoffs involving
modes 3 and 4 are 180 out-of-phase, we take the liberty of in- the inter-modal isolations and geometrical compactness. How-
dexing the modes so that ever, understanding the parasitic coupling mechanisms and an
insightful handling of the layout parameters can streamline the
layout optimization process.
Circuit models prove invaluable in understanding the design
(1) tradeoffs, and evaluating the effects of parasitics. Switches that
cannot be easily included in the electromagnetic model may also
where denotes the AFA transmission coefficient in mode be readily incorporated into the circuit model. Notional circuit
. Also, we notice that for an -pole filter (with no trans- models for three- and four-pole AFA topologies are given in
mission zeros), the total variation of the phase of the transmis- [15]. A complete circuit model of the multimode AFA can be
sion between dc and the upper rejection band is equal to formed as shown in Fig. 4, where the slot antennas are modeled
. The phase variation between dc and center frequency by parallel RLC circuits and the stripline middle layer is mod-
is half of this value, i.e., . Combining this with (1), eled by t-line segments. Transformers represent the coupling be-
we can write tween antennas and resonators, and capacitors model the cou-
pling gaps between the stripline resonators used in four-pole
configurations. Switches are modeled by capacitors in the
off state and by resistors in the on state (Fig. 5). Parasitic
capacitors and model the gap in the stripline where
the switches are embedded. The model parameters can be de-
(2) termined by FEM simulations of the complete geometry and/or
CHENG AND ABBASPOUR-TAMIJANI: STUDY OF 2-bit AFA ELEMENTS FOR RECONFIGURABLE MILLIMETER-WAVE LENS ARRAYS 4501

Fig. 4. Complete circuit model of the 2-bit reconfigurable AFA.

Fig. 6. Simulated frequency response of AFA for in different modes of opera-

tion. (a) Amplitude. (b) Phase.

Fig. 5. Model of switches in: (a) off state and (b) on state.
2, and by 0.2–0.7 dB in modes 3 and 4. It was found that the
off-state capacitor can cause a noticeable distortion in the
TABLE I
MODEL PARAMETERS FOR THE RECONFIGURABLE AFA
frequency response, which is more pronounced in the three-pole
modes of operation. However, this effect maybe compensated
by minor adjustments in the lengths of the t-line segments for
values of up to 10 fF. These values of and are at-
tainable using typical high-isolation MEMS cantilever switches
[20], [21].

C. Measurement Results
To verify the design and simulation method, uniform arrays of
the proposed AFA were fabricated in three- and four-pole con-
figurations using a standard printed circuit board (PCB) process.
partial structures. Table I shows the values of the model param- The periodic arrays of this type may be considered as FSS struc-
eters for the AFA element of Fig. 2. and are typical tures and can be easily characterized using the method described
values chosen to represent a small cantilever dc contact MEMS in [11]. The measurement setup consists of an Agilent 8510C
switch similar to the one reported [20]. vector network analyzer and two hard horns [22], which act as
Fig. 6 presents the simulated frequency response of the transitions between the coaxial input/output and planar wave-
32-GHz AFA in its different modes of operation. FEM simu- fronts. A free-space thru-reflect-line (TRL) calibration and time
lations are performed for normal incidence. Periodic boundary gating are applied to eliminate the effects of cables, connectors,
conditions are used to emulate the array environment and to ac- and hard horns and the residual errors of the higher order modes.
count for the effects of mutual coupling. Switches are replaced The measured transmission and reflection coefficients for
by perfect conductor strips in the on state and by 75- m gaps normal incidence have been given in [15] for three- and
in the off state. Circuit model simulations are also given for four-pole FSS structures. The normal incidence responses are
comparison. and are set to zero to comply with the quite similar to the simulated results of Fig. 6, except for the
FEM simulation. insertion loss of that is nearly 1 dB higher in both cases. The
The effect of switch imperfections can be easily evaluated performance of these FSS structures, however, is very sensitive
using the circuit model. Simulations show that for to angle of incidence and quickly deteriorates for oblique inci-
, the insertion loss increases by 0.1–0.4 dB in modes 1 and dence. Fig. 7 shows the transmission response of the four-pole
4502 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 12, DECEMBER 2006

Fig. 7. Measured transmission coefficient of the four-pole FSS for different

angles of incidences.
Fig. 8. Layout of the compact AFA element with stepped-impedance res-
onators.

FSS for different angles of incidence. It is observed that scan-

ning by only 30 drastically distorts the frequency response
and introduces a transmission zero at 34 GHz. This situation guided mode is minimized. With the current AFA array, how-
can become very problematic in large-aperture lens arrays with ever, there is not a distinction between - and -plane scans
small values of , and even for large values of can due to the polarization rotation between input and output. An
limit the scan width. In Section III, we propose an improved incident wave in the -plane generates a transmitted wave in
AFA design that can mitigate this difficulty. the -plane and vice versa so that the resonance always occurs
at least on one side of the array. In the lens array configuration,
however, only one side of the array sees a plane wave and obeys
III. COMPACT STEPPED-IMPEDANCE AFA ELEMENT Floquet’s theorem. As a result, the transmission zero is present
when the lens is configured for an -plane scan, but not when
A. Floquet-Mode Analysis it is configured for an -plane scan. This conclusion complies
Deterioration of the frequency response for oblique incidence with the results reported in [15] for 2-bit lens-array prototypes.
can be explained using Floquet’s theory [23]. When one of the
Floquet modes (i.e., the modes of the periodic array) coincides
B. Improved AFA Element Using Stepped-Impedance
with a guided mode of the structure, a resonance phenomenon
Resonators
occurs that manifests in the form of a transmission zero. In mul-
tilayer structures the guided modes are the surface waves. In the Besides using a low substrate, the onset of the Floquet
current case, where the dielectric structure is confined between mode resonance can only be deterred by reducing the grid length
two metallic sheets, the guided modes are those of the resulting through using smaller unit cells [24]. The AFA element of Fig. 2
parallel plate waveguide. The frequency of the lowest order res- can be considerably miniaturized by using stepped-impedance
onance can be calculated from concepts to reduce the length of stripline resonators and slot
antennas. For the slot antennas, miniaturization is achieved by
reducing the slot width in the middle region and increasing the
(4) width in the ends [18]. For the stripline resonators, the resonant
length can be reduced by widening the lines at the open ends
where is the speed of light, is the periodicity, is the relative and reducing their width in the middle [17]. In both cases, these
permittivity of the substrate, and is the incidence angle. The modification increase the effective values of capacitance and
lowest order mode can be excited by an incident wave scanned inductance in the predominantly capacitive and predominantly
in either - or -planes. inductive regions, respectively.
Equation (4) can be viewed as a relationship between the The layout of the modified AFA element is shown in Fig. 8.
lowest transmission zero of the AFA frequency response and This compact element can reduce the cell area by 50% and by
the scan angle. For the AFA element of Fig. 2 with mm 30%. Using mm and in (4), the transmis-
and , the transmission zero for 30 incidence is calcu- sion zero is calculated at 38 GHz, which is with a large margin
lated at 33.1 GHz, which is within 3% of the measured value above the frequency band of operation. As a result, the AFA
(see Fig. 7). The error is believed to be due to the tolerance of array is expected to show a much better performance for oblique
the dielectric constant. incidence. Fig. 9 shows the measured frequency response of
In single-polarized structures, the Floquet mode resonances the compact AFA for incident waves at 0 , 15 , 30 , and 45 .
may not be encountered for structures excited by incidence in The improved design shows an extremely stable amplitude re-
the -plane, as the coupling between the Floquet mode and the sponse in both three- and four-pole configurations. The phase
CHENG AND ABBASPOUR-TAMIJANI: STUDY OF 2-bit AFA ELEMENTS FOR RECONFIGURABLE MILLIMETER-WAVE LENS ARRAYS 4503

Fig. 9. Measured frequency response of the compact AFA in three- and four- Fig. 10. Map of the state of the AFA elements in the adaptive lens array for
pole configurations for different angles of incidence. (a) Amplitude. (b) Phase. different positions of the output beam.

response is also quite consistent in the three-pole mode, but it input and output sides, a single set of array prototypes can be
shows nearly 40 variation in the four-pole configuration. used to characterize beam steering in both - and -planes.
1021 AFA elements are arranged on a rectangular grid to form
IV. -BAND ADAPTIVE LENS ARRAY a circular array with diameter of 12 cm and a total effective area
The phase offsets existing between the different modes of of 104 cm . Fig. 10 shows the modal arrangement of the AFA
operation of the reconfigurable AFA can be utilized to gen- elements for different beam angles.
erate a 2-bit adaptive lens array. Elements in the lens array are Fig. 11 shows the measured radiation patterns for arrays with
configured to compensate for the spherical phase delay of the beams scanned in the -plane. Simulated results are also in-
input wavefront and generate a phase distribution corresponding cluded for comparison. These simulations are based on the sim-
to the desired output wavefront. For a single beam output, the plistic approach described in [14]. The measured patterns show
output phase will be a 2-bit approximation of a planar phase an overall good agreement with the simulations. The discrep-
distribution. The state of each AFA element in the array can be ancy in the location of the main beam is within 10 and is be-
calculated based on the location of the element in the array, focal lieved to be mainly due to the human errors in the placement and
distance, output phase, and operation frequency. In a real adap- orientation of the arrays (as the lens prototypes must be replaced
tive lens array, the decision on the states of the element at for each measurement). The measured patterns for the -plane
coordinates is made dynamically using the following scan are given in Fig. 12. The simulation results are identical to
equation for the mode index : the previous case, as the simulation method cannot differentiate
the - and -plane scans.
Some important data related to the radiation performances for
(5) different beam positions are summarized in Table II. The scan
loss at 60 is nearly 4 dB in the -plane, which is only 1 dB
where is the focal distance, is the free-space wavenumber, more than the theoretical cosine scan loss of an ideal aperture.
and is the desired output phase. indicates Besides the additional phase errors that might be introduced due
equality in modules of 360 and within an error of 45. to the nonideal operation of the AFA elements at 60 , the ele-
To verify the capability of the AFA elements for producing ment pattern is believed to contribute to the scan loss. Scan loss
adaptive lens arrays, five 32-GHz lens arrays were fabricated in the -plane is 6 dB for a 60 scan, which is in perfect agree-
with the AFA elements configured to produce output beams at ment with the theoretical value, taking into account the cosine
0 , 15 , 30 , 45 , and 60 from a spherical input wave ema- scan loss of the aperture and the cosine pattern of the short slot
nating at a focal distance of 12 cm. By exchanging the role of antennas. The lower value of gain in the 0 scan compared to 15
4504 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 12, DECEMBER 2006

Fig. 12. Measured radiation pattern of the lens array with the beam scanned in
Fig. 11. Measured radiation pattern of the lens array with the beam scanned in the H -plane. (a) 0 . (b) 15 . (c) 30 . (d) 45 . (e) 60 scan.
the E -plane. (a) 0 . (b) 15 . (c) 30 . (d) 45 . (e) 60 scan.

TABLE II
SCANNING PERFORMANCE
is counterintuitive. Part of this discrepancy may be attributed to
the misalignment of the main beam of antenna under test and
the measurement plane. It is also possible that the lower gain of
the 0 scan case is caused by the edge diffraction from the array
boundary, which can have a subtractive effect in the boresight.
The measured polarization ratio is better than 20 dB in all of the
studied cases. The discrepancy between gain and polarization
ratio in - and -planes at zero scan is believed to be due to
the measurement errors.
It is also interesting to investigate the efficiency of the pro- is the loss of the AFA elements. These two components can be
posed lens array. The theoretical aperture directivity for the recognized as the design-specific loss of the adaptive lens-array
aperture area of 104 cm is equal to 31.75 dBi at 32 GHz. The structure, collectively amounting to 2.25 dB. By assuming an in-
maximum gain of the lens array is 26.5 dBi, measured for the crease of nearly 0.55 dB corresponding to switch resistance of
-plane scan of 15 . There is a good reason to believe that this 1 (averaged for three- and four-pole modes, see Section II-B),
is close to the actual gain for the 0 scan should the effect of this loss component is expected to remain less than 3 dB. The re-
edge diffraction and misalignment be eliminated from the mea- maining 2.45-dB loss is related to effect of the 16-dB feed horn
surements. A systematic power analysis using the simulation used for the measurements. This loss can be reduced to approx-
method of [14] has been used to determine different components imately 0.6–0.8 dB through using an optimally designed 4 4
of the loss. The result of this analysis is summarized in Table III. focal plane array.
The spherical taper loss refers to the effect of the aperture taper As the AFA elements are primarily bandpass filters, the adap-
caused by the longer distance and off-boresight angle of edge el- tive lens array exhibits a bandpass frequency response. Fig. 13
ements relative to the feed. This effect is shared by all planar lens presents the simulated gain of the array for 0 scan. The ac-
arrays. Aperture phase-error loss reflects the effect of the quan- tual measured frequency response of the AFA elements has been
tization error of the 2-bit phase shifters, and the insertion loss used in this simulation. The result is a frequency response that
CHENG AND ABBASPOUR-TAMIJANI: STUDY OF 2-bit AFA ELEMENTS FOR RECONFIGURABLE MILLIMETER-WAVE LENS ARRAYS 4505

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4506 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 12, DECEMBER 2006

Chih-Chieh Cheng (S’06) received the B.S. degree Abbas Abbaspour-Tamijani (S’00–M’04) received
in aerospace engineering (with a minor in electrical the B.S. and M.S. degrees from The University of
engineering) from National Cheng Kung Univer- Tehran, Tehran, Iran, in 1994 and 1997, respec-
sity, Taiwan, R.O.C., in 2001, the M.S. degree in tively, and the Ph.D. degree from The University
electrical engineering from the University of Wis- of Michigan at Ann Arbor, in 2003, all in electrical
consin–Madison, in 2004, and is currently working engineering.
toward the Ph.D. degree in electrical engineering at From 1996 to 1999, he was an Antenna and RF
Arizona State University, Tempe. Engineer in industry. In 2004, he was a Research
During the summers of 2003 and 2004, he was Fellow with the Radiation Laboratory, The Uni-
an Intern for 3eTI, Washington, DC, and Media Tek, versity of Michigan at Ann Arbor. He is currently
Hsinchu, Taiwan, R.O.C. His research interest is an Assistant Professor of electrical engineering
millimeter-wave beam steering using MEMS fabrication techniques. with Arizona State University, Tempe. His research interests include RF
MEMS technology and applications, reconfigurable and intelligent front-end
electronics, integrated antennas, and biomedical application of microwaves.
Dr. Abbaspour-Tamijani is a member of the IEEE Microwave Theory and
Techniques, Antennas and Propagation, and Engineering in Medicine and Bi-
ology societies.