Two-dimensional beam steering using an electrically tunable impedance surface

Abstract

By covering a metal ground plane with a periodic surface texture, we can alter its electromagnetic properties. The impedance of this metasurface can be modeled as a parallel resonant circuit, with sheet inductance L, and sheet capacitance C. The reflection phase varies with frequency from +π to -π, and crosses through 0 at the LC resonance frequency, where the surface behaves as an artificial magnetic conductor. By incorporating varactor diodes into the texture, we have built a tunable impedance surface, in which an applied bias voltage controls the resonance frequency, and the reflection phase. We can program the surface to create a tunable phase gradient, which can electronically steer a reflected beam over +/- 40° in two dimensions, for both polarizations. We have also found that this type of resonant surface texture can provide greater bandwidth than conventional reflectarray structures. This new electronically steerable reflector offers a low-cost alternative to a conventional phased array.

Full text

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 51, NO. 10, OCTOBER 20032713
Two-Dimensional Beam Steering Using an
Electrically Tunable Impedance Surface
Daniel F. Sievenpiper, Member, IEEE, James H. Schaffner, Senior Member, IEEE, H. Jae Song, Member, IEEE,
Robert Y. Loo, Member, IEEE, and Gregory Tangonan, Member, IEEE
Abstract—By covering a metal ground plane with a periodic
surface texture, we can alter its electromagnetic properties. The
impedance of this metasurface can be modeled as a parallel res-
onant circuit, with sheet inductance ?, and sheet capacitance ?.
The reflection phase varies with frequency from ?
crossesthrough0attheLCresonancefrequency,wherethesurface
behaves as an artificial magnetic conductor. By incorporating var-
actor diodes into the texture, we have built a tunable impedance
surface, in which an applied bias voltage controls the resonance
frequency, and the reflection phase. We can program the surface
to create a tunable phase gradient, which can electronically steer
a reflected beam over ?
40 in two dimensions, for both po-
larizations. We have also found that this type of resonant surface
texture can provide greater bandwidth than conventional reflec-
tarray structures. This new electronically steerable reflector offers
a low-cost alternative to a conventional phased array.
to, and
Index Terms—Antenna arrays, grid arrays, high impedance
surfaces, impedance sheets, reconfigurable antennas, scanning
antennas, textured surfaces, tunable antennas.
I. INTRODUCTION
I
surfaces to perform a variety of functions. For example, specific
textures can be designed to change the surface impedance for
one or both polarizations, or to manipulate the propagation of
surface waves. The simplest examples are corrugated metal
sheets, often known as soft and hard surfaces. [1] These mate-
rials are typically built as a metal slab with quarter-wavelength
deep corrugations. They are usually analyzed by treating
the corrugations as quarter-wavelength transmission lines, in
which the short circuit at the bottom of each groove is trans-
formed into an open circuit at the top surface. This provides a
high-impedance boundary condition for electric fields polar-
ized perpendicular to the corrugations, and low-impedance for
electric fields parallel to the grooves. Soft and hard surfaces are
used in various applications such as manipulating the radiation
patterns of horn antennas, or controlling the edge diffraction of
reflectors. Further background on these and related structures
can be found in the literature on corrugated surfaces [2]–[6].
Similar structures have also been built in two dimensions, such
T is well-known that metal-dielectric composite textures
can be used to alter the electromagnetic properties of metal
Manuscript received September 30, 2002; revised January 22, 2003. This
work was supported in part by DARPA under Contract N6601-99-C-8635.
D. F. Sievenpiper, J. H. Schaffner, and H. J. Song are with HRL Laboratories
LLC, Malibu, CA 90265 USA.
R. Loo was with retired from HRL Laboratories LLC, Malibu, CA 90265
USA.HeisnowwithWirelessMEMSIncorporated,OakPark,CA91377USA.
G. Tangonan was with HRL Laboratories LLC, Malibu, CA 90265 USA. He
is now with the Ateneo de Manila University, Quezon City, Philippines.
Digital Object Identifier 10.1109/TAP.2003.817558
as two-dimensional (2-D) shorted waveguide arrays [7], or the
inverse structures, which are known as pin-bed surfaces [8].
These textured materials are typically one-quarter wavelength
thick in order to achieve a high-impedance boundary condition.
Recently, compact structures have been developed that can
alsoaltertheelectromagneticboundaryconditionofametalsur-
face,butwhicharemuchlessthanone-quarterwavelengththick.
The reduction in thickness is achieved by capacitive loading,
suchasbyusingcloselyspacedmushroom-shapedmetalprotru-
sions, or overlapping thumbtack-like structures [9], [10]. These
materials provide a high-impedance boundary condition (
) for both polarizations. They are sometimes known as
artificial magnetic conductors, because the tangential magnetic
field is zero at the surface, rather than the electric field, as with
an ordinary metal. In addition to their unusual reflection phase
properties, these materials have a surface wave bandgap, within
which they do not support bound surface waves of either TM
or TE polarization. However, they do support leaky TE waves,
which can be useful for certain applications. The surface wave
properties of these materials are described in greater detail else-
where [9], [10]. In the present paper, we are only interested in
their reflectionphase properties, which are the basisof our elec-
tronically steerable reflector.
Conventional high-impedance surfaces are typically con-
structed as printed circuit boards, where the bottom side is a
solid metal ground plane, and the top contains an array of small
(
) metal patches The plates are connected to the ground
plane by metal plated vias to form a continuous textured metal
structure. An example of such a material is shown in Fig. 1. It
can be considered as a 2-D version of the corrugated ground
plane, where the quarter-wavelength resonant corrugations
have been folded up into small resonant circuits, and distributed
on a 2-D lattice.
When the period is small compared to the wavelength of in-
terest,wemayanalyzethematerialasaneffectivemedium,with
its surface impedance defined by effective lumped-element cir-
cuit parameters that are determined by the geometry of the sur-
face texture. A wave impinging on the material causes electric
fields to span the narrow gaps between the neighboring metal
patches, and this can be described as a sheet capacitance
with units of [
]. As currents oscillate between
the neighboring patches, the conducting paths through the vias
and the ground plane provide a sheet inductance
of [Henrys/square]. These form a parallel resonant circuit that
dictatestheelectromagnetic behaviorofthematerial. Itssurface
impedance is given by
,
, with units
(1)
0018-926X/03$17.00 © 2003 IEEE

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2714IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 51, NO. 10, OCTOBER 2003
Fig. 1.
reflector. It is constructed as a printed circuit board, where metal plated vias
connect an array of plates on the top surface to a metal ground plane on the
bottom surface. The capacitance and inductance between the plates determine
the electromagnetic properties of the surface.
Resonant textured surface, that is the basis of our 2-D beam steering
The surface impedance becomes infinite at the resonance fre-
quency, which is
(2)
Fora normallyincidentwave,thereflectionphaseofthesurface
is
(3)
where
phase function is shown in Fig. 2.
Far below the resonance frequency, the surface reflects with
a phase shift of , just like an ordinary electric conductor. The
reflection phase decreases with higher frequencies, crossing
through 0 at resonance, where the surface behaves as an arti-
ficial magnetic conductor, and approaches
far above resonance. Applications for these surfaces include
low-profile antennas, in which radiating elements can lie
very close (
) to a high-impedance ground plane without
being shorted out. The effective image currents in an artificial
magnetic conductor are in-phase with the antenna current, and
thus reinforce the radiation, rather than canceling it as with an
electric conductor.
Theeffectivesurfaceimpedancemodelisnotstrictlyvalidfor
objects thatare muchcloser thana wavelength from thesurface.
However, we find that in practice, antennas can be built as close
as 1/100 wavelength from a properly designed textured surface
is theimpedance offreespace.Thisreflection
for frequencies
Fig. 2.
the resonance frequency, where the surface behaves as an artificial magnetic
conductor. By tuning the capacitance or inductance, we can shift this curve to
the left or right, thereby tuning the reflection phase for a fixed frequency.
Reflection phase of a resonant textured surface crosses through 0 at
with little more than reactive tuning at the feed point. The sepa-
rationlimitisdeterminedbytherequirementthatthecapacitance
between the antenna and the surface must be small compared to
the built-in surface capacitance, so as not to detune the surface.
II. TUNABLE IMPEDANCE SURFACE
The resonance frequency of a textured ground plane can be
tuned by adjusting the values of its effective circuit parameters
and . Because the reflection phase is determined by the fre-
quency of the incoming wave with respect to the resonance fre-
quency,suchasurfacecanperformasadistributedphaseshifter.
As the resonance frequency is swept from low to high, the curve
in Fig. 2 is shifted from right to left, so the reflection phase at
any fixed frequency varies from
is programmed as a function of position across the surface, it
can be used for beam steering. A linear gradient
will reflect a normally incident microwave beam to an angle in
the
- plane of
to . If the reflection phase
(4)
Other phase functions can be used for other tasks, such as a par-
abolic phase function for focusing. These concepts have been
demonstrated previously using arrays of various resonant ele-
mentsrangingfromdipolestopatches,andbeam-formingstruc-
tures employing this technique are commonly known as reflec-
tarrays [11]–[18]. Tunable reflectarrays using varactor diodes,
[19], [20] and related devices known as grid arrays [21], [22]
have also been built.
The resonance frequency and the reflection phase of a high-
impedance surface can be tuned by changing the capacitance,
the inductance, or both. However, the sheet inductance is given
by
(5)
where
the substrate. Without magnetically active materials, the induc-
tanceisprimarilydeterminedbythethickness,andisdifficultto
tune.Thecapacitanceiseasiertocontrolbychangingthegeom-
etry and arrangement of the metal plates, or by adding tunable
lumped capacitors. Reflective beam steering using a mechan-
ically tuned surface has already been demonstrated by adding
and arethemagneticpermeabilityandthethicknessof

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SIEVENPIPER et al.: 2-D BEAM STEERING2715
Fig. 3.
neighboring pairs of plates. Half of the plates are grounded, and the other half
are attached to control wires on the back of the surface. The diodes are oriented
in opposite directions in each alternate row.
Electrically tunable impedance surface, with varactor diodes between
a layer of movable tuning plates that overlap with a stationary
high-impedance surface [23]. Moving the tuning layer with re-
spect to the surface changes the resonance frequency, and ro-
tating thetuning layer with respect to the stationary surface pro-
duces a phase gradient, which steers a reflected beam.
In our electrically tunable impedance surface, the movable
plates are replaced with varactor diodes, as illustrated in Fig. 3.
Each unit cell in the periodic surface texture is connected
to its four neighbors by reverse-biased diodes. By changing
the voltage on the diodes, we adjust the capacitance between
neighboring cells, and tune the resonance frequency. In order
to supply the required voltage to all of the varactors, we
alternately bias half of the cells, and ground the other half
in a checkerboard pattern. At the center of each biased cell,
a metal via passes through a hole in the ground plane, and
connects to a control line located on a separate circuit layer on
the back of the surface. By controlling the varactors from the
back of the surface in this way, the bias lines do not interfere
with the microwave fields on the front side. The varactors are
oriented in opposite directions in each alternate row, so that
when a positive voltage is applied to control lines, all the diodes
are reverse-biased. By individually addressing each cell, the
reflection phase can be programmed as a function of position
across the surface.
Fig. 4.
a thin wire grid to a lattice of broad plates. In each case, the period was 1 cm,
and a 1-mm dielectric cube was placed at each edge to model the varactors. The
theoretical bandwidth for a high-impedance surface with a thickness of ?????
is shown as a dashed line.
Plot of the simulated bandwidth for various geometries, ranging from
III. BANDWIDTH OF REFLECTARRAYS
It is known that the geometry of the resonant elements can
have a significant effect on the performance of reflectarrays
[16], [17], so we examined the effect of the plate geometry
on the properties of our textured surface. For example, a thin
wire grid structure has a greater tuning range than a broad plate
structurebecauseithaslowerfixedcapacitance.Relateddevices
known as grid arrays have already demonstrated 1-D steering,
using a series of metal strips printed on a grounded substrate,
and connected by rows of varactors [21], [22].
We simulated a series of structures using Hewlett Packard
HighFrequencyStructure Simulator (HFSS).In modeling these
periodic surface textures, one unit cell is sufficient to determine
the reflection phase. Typically, the single unit cell is placed at
the end of a square TEM waveguide, which has electric bound-
aries on two opposing walls, and magnetic boundaries on the
othertwo walls. Awaveis excitedfrom a port atthe front end of
the waveguide, and the reflection phase from the surface at the
back end is recorded as a function of frequency. Although this
methodonlyprovidesthereflectionphasefornormalincidence,
it is sufficientfor examiningtrends in the reflection phase band-
widthwithchangesingeometry.Westudiedgeometriesranging
from simple squares to a narrow wire grid, shown in Fig. 4. For
everycase,thesubstratewas1.6-mm-thickRogersDuroid5880.
The lattice had a 1-cm period, and 1–mm dielectric cubes were
centered on the plate edges to simulate the varactor diodes. By
changing the dielectric constant in these small cubes, we could
tune the reflection phase as a function of frequency.
By narrowing the square plates to a grid of wires, the fixed
capacitance is reduced, and the tuning range is increased. How-
ever, the bandwidth is also diminished as shown in Fig. 5. We

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2716IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 51, NO. 10, OCTOBER 2003
(a)
(b)
Fig. 5.
(a) In a thin wire grid structure the electric field is primarily concentrated
beneath the wires, which tends to reduce the bandwidth. (b) In a flat plate
structure the field is more evenly distributed throughout the surface.
Electric field within the substrate for two different plate geometries.
define the bandwidth of the resonance as the range where the
phase falls between
and
width is directly proportional to its usable instantaneous band-
width as a beam steering reflector, because a reflectarray with a
steeper phase curve is less able form a consistent phase profile
over a broad range of frequencies.
This dependence of the bandwidth on the plate geometry can
be explained by examining the electric fields within the surface
texture. The field inside the substrate is shown for two cases in
Fig. 5. For the narrow wire grid structure, the electric field is
primarily concentrated beneath the wires, while for the lattice
of square plates, it is more evenly distributed across the plate
edges. The field distribution within a resonant textured surface
affects its bandwidth in much the same way as for a small reso-
nant antenna, as first described by Wheeler and Chu [24]–[26].
A small antenna having a volume
bandwidth of
. This measure of band-
is limited to a maximum
(6)
Fig.6.
1cm,andthereare25?25cells.Thereare1125varactors,whichareaddressed
inrowsthroughtheribboncableattheleftedge.At4.5GHz,thesurfaceisabout
3.75-wavelengths wide.
Photographoftheelectronicallysteerablereflector.Thelatticeperiodis
where is the volume of a sphere having a radius of
(7)
known as the radian length. The bandwidth is further reduced
from this upper limit by the degree to which the fields do not
uniformly fill that volume, so an antenna with highly localized
fields tend to have narrower bandwidth. For a resonant textured
ground plane, the same rule may be applied, and structures with
uneven field distributions tend to have narrower bandwidths.
The theoreticalbandwidth for a high impedance surface is in-
dicated by a dashed line in Fig. 4. This bandwidth can be calcu-
lated as the frequency range where the magnitude of the surface
impedance is greater than the impedance of free space
(8)
We solve for
to yield the frequencies of the two band edges
(9)
The terms in
in
are typically small compared to the terms
, so we neglect them to obtain
(10)
where
(11)
For structures that are thin compared to the wavelength,
typically small compared to , so we can expand the square root
in (10), to approximate the fractional bandwidth as
is
(12)

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SIEVENPIPER et al.: 2-D BEAM STEERING 2717
(a)
(b)
Fig. 7.
solid lines correspond to a uniform voltage ranging from 9 to 20 V, which
provide a tuning range of 3.5 to 4.5 GHz. For the dashed lines, two different
voltages were applied to alternate rows, which doubles the effective period,
splittingtheresonanceintwo,andpushingtheupperresonancetonearly5GHz.
(a) Reflection phase and (b) the magnitude for various voltages. The
Using (2) and (5) we multiply the numerator and denominator
by
, and substitute forto obtain
(13)
where
quency. We recognize
Thus, the bandwidth
) resonant textured ground plane is limited by its thickness
divided by the radian length at resonance. It is further reduced
bythe degreetowhich thefieldsare localizedwithin thesurface
is the free space wavelength at the resonance fre-
as the radian length in (7) [24].
of a thin, () nonmagnetic, (
Fig. 8.
oriented at 45 to the horizon, and illuminated from below by a feed horn. The
surface and feed horn were rotated about the vertical axis, and the radiation
pattern was measured in the horizontal plane by a second receive horn.
Setup for measuring the radiation pattern of the tunable surface. It was
texture and do not uniformly fill its volume, as summarized by
the inequality
(14)
which can be viewed as the 2-D analog of (6), derived here for
a resonant textured surface.
One can further expect that any array of resonant elements
where the period is significantly greater than the size of the ele-
ments would suffer a similar reduction in bandwidth, compared
toadenselypackedlattice,duetotheunusedportionsofthesur-
face area where the fields are negligible. Indeed, similar trends
in bandwidth are seen for traditional reflectarrays [16], [17].
Furthermore, (14) only specifies the maximum inherent band-
width of the resonant surface. Its usable bandwidth as a beam
steering reflector is even less, because of the curvature of the
reflection phase function
(15)
andtheneedfor
phasediscontinuitiestosteertolargeangles.
IV. DESIGN AND CHARACTERIZATION
We built our tunable impedance surface as a lattice of square
plates with varactor diodes connecting between each adjacent
pair of plates, as shown in Fig. 6. The diodes are Micrometrics
silicon hyperabrupt varactors, model MHV500–19–1, which
have a usable capacitance range of roughly 0.2 to 0.8 pF. From
(2), we can expect a frequency tuning range of somewhat less
than2:1withthesevaractors.Thesurfaceis builtasa multilayer
circuit board, with three metal layers and two substrate layers.
The front metal layer contains the lattice of square plates, the
middle layer is the ground plane, and the back layer contains
the control lines that bias the varactors. The substrate layers
are both 1.6-mm-thick Rogers Duroid 5880, and were designed
with equal thickness to prevent warping of the substrate during
fabrication. The square metal plates are 9.2-mm wide, and the