EP1195847A2 - Multi-resonant, high-impedance surfaces containing loaded-loop frequency selective surfaces - Google Patents

Abstract

An antenna system and an artificial magnetic conductor (300) include afrequency selective surface having a frequency dependent permeabilityµ_1z in adirection normal to the frequency dependent surface, a conductive ground plane(806), and a rodded media (808) disposed between the frequency selective surfaceand the conductive ground plane.

Description

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation in part of application serial number 09/678, 128 filed October 4, 2000 and commonly assigned with the present application.

BACKGROUND

The present invention relates generally to high-impedance surfaces. Moreparticularly, the present invention relates to a multi-resonant, high-impedanceelectromagnetic surface.

A high impedance surface is a lossless, reactive surface whose equivalentsurface impedance,Z_s =E_tan /H_tan, approximates an open circuit and which inhibitsthe flow of equivalent tangential electric surface current, thereby approximating azero tangential magnetic field,H_tan ≈ 0.E_tan andH_tan are the electric andmagnetic fields, respectively, tangential to the surface. High impedance surfaceshave been used in various antenna applications. These applications range fromcorrugated horns which are specially designed to offer equal E and H plane halfpower beamwidths to traveling wave antennas in planar or cylindrical form.However, in these applications, the corrugations or troughs are made of metalwhere the depth of the corrugations is one quarter of a free space wavelength, λ/4,where λ is the wavelength at the frequency of interest. At high microwavefrequencies, λ/4 is a small dimension, but at ultra-high frequencies (UHF, 300MHz to 1 GHz), or even at low microwave frequencies (1-3 GHz), λ/4 can bequite large. For antenna applications in these frequency ranges, an electrically-thin(λ/100 to λ/50 thick) and physically thin high impedance surface is desired.

One example of a thin high-impedance surface is disclosed in D.Sievenpiper, "High-impedance electromagnetic surfaces," Ph.D. dissertation,UCLA electrical engineering department, filed January 1999, and in PCT Patent Application number PCT/US99/06884. Thishigh impedance surface 100 isshown in FIG. 1. The high-impedance surface 100 includes a lowerpermittivityspacer layer 104 and a capacitive frequency selective surface (FSS) 102 formed onametal backplane 106.Metal vias 108 extend through thespacer layer 104, andconnect the metal backplane to the metal patches of the FSS layer. The thicknessh of thehigh impedance surface 100 is much less than λ/4 at resonance, andtypically on the order of λ/50, as indicated in FIG. 1.

The FSS 102 of the prior arthigh impedance surface 100 is a periodic arrayofmetal patches 110 which are edge coupled to form an effective sheetcapacitance. This is referred to as a capacitive frequency selective surface (FSS).Eachmetal patch 110 defines a unit cell which extends through the thickness ofthehigh impedance surface 100. Eachpatch 110 is connected to themetalbackplane 106, which forms a ground plane, by means of a metal via 108, whichcan be plated through holes. The periodic array ofmetal vias 108 has been knownin the prior art as a rodded media, so these vias are sometimes referred to as rodsor posts. Thespacer layer 104 through which thevias 108 pass is a relatively lowpermittivity dielectric typical of many printed circuit board substrates. Thespacerlayer 104 is the region occupied by thevias 108 and the low permittivitydielectric. The spacer layer is typically 10 to 100 times thicker than theFSS layer102. Also, the dimensions of a unit cell in the prior art high-impedance surfaceare much smaller than λ at the fundamental resonance. The period is typicallybetween λ/40 and λ/12.

A frequency selective surface is a two-dimensional array of periodicallyarranged elements which may be etched on, or embedded within, one or multiplelayers of dielectric laminates. Such elements may be either conductive dipoles,patches, loops, or even slots. As a thin periodic structure, it is often referred to asa periodic surface.

Frequency selective surfaces have historically found applications in out-of-bandradar cross section reduction for antennas on military airborne and navalplatforms. Frequency selective surfaces are also used as dichroic subreflectors in dual-band Cassegrain reflector antenna systems. In this application, thesubreflector is transparent at frequency band f₁ and opaque or reflective atfrequency band f₂. This allows one to place the feed horn for band f₁ at the focalpoint for the main reflector, and another feed horn operating at f₂ at the Cassegrainfocal point. One can achieve a significant weight and volume savings over usingtwo conventional reflector antennas, which is critical for space-based platforms.

The prior art high-impedance surface 100 provides many advantages. Thesurface is constructed with relatively inexpensive printed circuit technology andcan be made much lighter than a corrugated metal waveguide, which is typicallymachined from a block of aluminum. In printed circuit form, the prior art high-impedancesurface can be 10 to 100 times less expensive for the same frequencyof operation. Furthermore, the prior art surface offers a high surface impedancefor both x and y components of tangential electric field, which is not possible witha corrugated waveguide. Corrugated waveguides offer a high surface impedancefor one polarization of electric field only. According to the coordinate conventionused herein, a surface lies in the xy plane and the z-axis is normal or perpendicularto the surface. Further, the prior art high-impedance surface provides a substantialadvantage in its height reduction over a corrugated metal waveguide, and may beless than one-tenth the thickness of an air-filled corrugated metal waveguide.

A high-impedance surface is important because it offers a boundarycondition which permits wire antennas conducting electric currents to be wellmatched and to radiate efficiently when the wires are placed in very closeproximity to this surface (e.g., less than λ/100 away). The opposite is true if thesame wire antenna is placed very close to a metal or perfect electric conductor(PEC) surface. The wire antenna/PEC surface combination will not radiateefficiently due to a very severe impedance mismatch. The radiation pattern fromthe antenna on a high-impedance surface is confined to the upper half space, andthe performance is unaffected even if the high-impedance surface is placed on topof another metal surface. Accordingly, an electrically-thin, efficient antenna is very appealing for countless wireless devices and skin-embedded antennaapplications.

FIG. 2 illustrates electrical properties of the prior art high-impedancesurface. FIG. 2(a) illustrates a plane wave normally incident upon the prior arthigh-impedance surface 100. Let the reflection coefficient referenced to thesurface be denoted by Γ. The physical structure shown in FIG. 2(a) has anequivalent transverse electro-magnetic mode transmission line shown in FIG. 2(b).The capacitive FSS 102 (FIG. 1) is modeled as a shunt capacitance C and thespacer layer 104 is modeled as a transmission line of lengthh which is terminatedin a short circuit corresponding to thebackplane 106. Figure 2(c) shows a Smithchart in which the short is transformed into the stub impedanceZ_stub just belowtheFSS layer 102. The admittance of this stub line is added to the capacitivesusceptance to create a high impedanceZ_in at the outer surface. Note that theZ_inlocus on the Smith Chart in FIG. 2(c) will always be found on the unit circle sinceour model is ideal and lossless. So Γ has an amplitude of unity.

The reflection coefficient Γ has a phase angle  which sweeps from 180°at DC, through 0° at the center of the high impedance band, and rotates intonegative angles at higher frequencies where it becomes asymptotic to -180°. Thisis illustrated in FIG. 2(d). Resonance is defined as that frequency correspondingto 0° reflection phase. Herein, the reflection phase bandwidth is defined as thatbandwidth between the frequencies corresponding to the +90° and -90° phases.This reflection phase bandwidth also corresponds to the range of frequencieswhere the magnitude of the surface reactance exceeds the impedance of free space:|X| ≥ η_o = 377 ohms.

A perfect magnetic conductor (PMC) is a mathematical boundary conditionwhereby the tangential magnetic field on this boundary is forced to be zero. It isthe electromagnetic dual to a perfect electric conductor (PEC) upon which thetangential electric field is defined to be zero. A PMC can be used as amathematical tool to create simpler but equivalent electromagnetic problems forslot antenna analysis. PMCs do not exist except as mathematical artifacts. However, the prior art high-impedance surface is a good approximation to a PMCover a limited band of frequencies defined by the +/-90° reflection phasebandwidth. So in recognition of its limited frequency bandwidth, the prior arthigh-impedance surface is referred to herein as an example of an artificialmagnetic conductor, or AMC.

The prior art high-impedance surface offers reflection phase resonances ata fundamental frequency, plus higher frequencies approximated by the conditionwhere the electrical thickness of the spacer layer,βh, in the high-impedancesurface 100 isnπ, where n is an integer. These higher frequency resonances areharmonically related and hence uncontrollable. If the prior art AMC is to be usedin a dual-band antenna application where the center frequencies are separated by afrequency range of, say 1.5:1, we would be forced to make a very thick AMC.Assuming a non-magnetic spacer layer (µ_D =1), the thicknessh must be h=λ/14to achieve at least a 50% fractional frequency bandwidth where both centerfrequencies would be contained in the reflection phase bandwidth. Alternatively,magnetic materials could be used to load the spacer layer, but this is a topic ofongoing research and nontrivial expense. Accordingly, there is a need for a classof AMCs which exhibit multiple reflection phase resonances, or multi-bandperformance, that are not harmonically related, but at frequencies which may beprescribed.

BRIEF SUMMARY

By way of introduction only, in a first aspect, an artificial magneticconductor includes a frequency selective surface having a frequency dependentpermeability µ_1z in a direction normal to the frequency dependent surface, aconductive ground plane, and a rodded medium disposed between the frequencyselective surface and the conductive ground plane.

In another aspect, an artificial magnetic conductor includes a conductiveground plane and a spacer layer disposed on the ground plane. One or more arraysof coplanar loops are resonant at two or more frequency bands, each loop having a similar shape and similar size. The one or more arrays of coplanar loops producea frequency dependent normal permeability µ_z.

In another aspect, a disclosed electrical apparatus includes a conductiveground plane and a dielectric layer perforated by conductive rods in electricalcontact with the conductive ground plane. The electrical apparatus furtherincludes a frequency selective surface (FSS) disposed on the dielectric layer. TheFSS includes a first layer of capacitively coupled loops resonant at a firstfrequency, a dielectric spacer layer and a second layer of capacitively coupledloops resonant at a second frequency. The frequency selective surface has afrequency dependent permeability in a direction substantially normal to thefrequency selectively surface.

The foregoing summary has been provided only by way of introduction.Nothing in this section should be taken as a limitation on the following claims,which define the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view of a prior art high impedance surface;

FIG. 2 illustrates a reflection phase model for the prior art high impedancesurface;

FIG. 3 is a diagram illustrating surface wave properties of an artificialmagnetic conductor;

FIG. 4 illustrates electromagnetic fields of a TE mode surface wavepropagating in the x direction in the artificial magnetic conductor of FIG. 3;

FIG. 5 illustrates electromagnetic fields of a TM mode surface wavepropagating in the x direction in the artificial magnetic conductor of FIG. 3;

FIG. 6 illustrates top and cross sectional views of a prior art highimpedance surface;

FIG. 7 presents a new effective media model for the prior art high-impedancesurface of FIG. 6;

FIG. 8 illustrates a first embodiment of an artificial magnetic conductor;

FIG. 9 illustrates a second, multiple layer embodiment of an artificialmagnetic conductor;

FIG. 10 is a cross sectional view of the artificial magnetic conductor ofFIG. 9;

FIG. 11 illustrates a first physical embodiment of a loop for an artificialmagnetic molecule;

FIG. 12 illustrates a multiple layer artificial magnetic conductor using theloop of FIG. 11(d);

FIG. 13 shows y-polarized electromagnetic simulation results for thenormal-incidence reflection phase of the artificial magnetic conductor illustratedin FIG. 12;

FIG. 14 shows y-polarized electromagnetic simulation results for thenormal-incidence reflection phase of the artificial magnetic conductor very similarto that illustrated in FIG. 12, except the gaps in the loops are now shorted together;

FIG. 15 shows the TEM mode equivalent circuits for the top layer, or FSSlayer, of a two layer artificial magnetic conductor of FIG. 8;

FIG. 16 illustrates the effective relative permittivity for a specific case of amulti-resonant FSS, and the corresponding reflection phase; for an AMC whichuses this FSS as its upper layer.

FIG. 17 shows an alternative embodiment for a frequency selective surfaceimplemented with square loops;

FIG. 18 shows measured reflection phase data for an x polarized electricfield normally incident on the AMC of FIG. 17;

FIG. 19 shows measured reflection phase data for ay polarized electricalfield normally incident on the AMC of FIG. 17;

FIG. 20 shows additional alternative embodiments for a frequency selectivesurface implemented with square loops;

FIG. 21 shows additional alternative embodiments for a frequency selectivesurface implemented with square loops;

FIG. 22 shows measured reflection phase data for anx polarized electricfield normally incident on the AMC of FIG. 21;

FIG. 23 shows measured reflection phase data for a y polarized electricalfield normally incident on the AMC of FIG. 21;

FIG. 24 illustrates another embodiment of a capacitive frequency selectivesurface structure consisting of a layer of loops closely spaced to a layer of patches;

FIG. 25 illustrates an alternative embodiment of a capacitive frequencyselective surface structure using hexagonal loops;

FIG. 26 illustrates an alternative embodiment of a capacitive frequencyselective surface structure using hexagonal loops;

FIG. 27 illustrates an alternative embodiment of a capacitive frequencyselective surface structure using hexagonal loops;

FIG. 28 illustrates an effective media model for an artificial magneticconductor;

FIG. 29 illustrates a prior art high impedance surface;

FIG. 30 illustrates Lorentz and Debye frequency responses for thecapacitance of an FSS used in a multi-resonant AMC;

FIG. 31 illustrates an artificial magnetic conductor including a multiplelayer frequency selective surface; and

FIG. 32 illustrates a top view of the multiple-layer frequency selectivesurface of FIG. 31.

DETAILED DESCRIPTION OF THE PRESENTLY PREFERREDEMBODIMENTS

A planar, electrically-thin, anisotropic material is designed to be a high-impedancesurface to electromagnetic waves. It is a two-layer, periodic,magnetodielectric structure where each layer is engineered to have a specifictensor permittivity and permeability behavior with frequency. This structure hasthe properties of an artificial magnetic conductor over a limited frequency band orbands, whereby, near its resonant frequency, the reflection amplitude is near unityand the reflection phase at the surface lies between +/- 90 degrees. This engineeredmaterial also offers suppression of transverse electric (TE) and transverse magnetic (TM) mode surface waves over a band of frequencies near where itoperates as a high impedance surface. The high impedance surface providessubstantial improvements and advantages. Advantages include a description ofhow to optimize the material's effective media constituent parameters to offermultiple bands of high surface impedance. Advantages further include theintroduction of various embodiments of conducting loop structures into theengineered material to exhibit multiple reflection-phase resonant frequencies.Advantages still further include a creation of a high-impedance surface exhibitingmultiple reflection-phase resonant frequencies without resorting to additionalmagnetodielectric layers.

This high-impedance surface has numerous antenna applications wheresurface wave suppression is desired, and where physically thin, readily attachableantennas are desired. This includes internal antennas in radiotelephones and inprecision GPS antennas where mitigation of multipath signals near the horizon isdesired.

An artificial magnetic conductor (AMC) offers a band of high surfaceimpedance to plane waves, and a surface wave bandgap over which bound, guidedtransverse electric (TE) and transverse magnetic (TM) modes cannot propagate.TE and TM modes are surface waves moving transverse or across the surface ofthe AMC, in parallel with the plane of the AMC. The dominant TM mode is cutoff and the dominant TE mode is leaky in this bandgap. The bandgap is a band offrequencies over which the TE and TM modes will not propagate as bound modes.

FIG. 3 illustrates surface wave properties of anAMC 300 in proximity toan antenna orradiator 304. FIG. 3(a) is an ω-β diagram for the lowest order TMand TE surface wave modes which propagate on theAMC 300. Knowledge ofthe bandgap over which bound TE and TM waves cannot propagate is very criticalfor antenna applications of an AMC because it is the radiation from the unboundor leaky TE mode, excited by thewire antenna 304 and the inability to couple intothe TM mode that makes bent-wire monopoles, such as theantenna 304 on theAMC 300, a practical antenna element. The leaky TE mode occurs at frequenciesonly within the bandgap.

FIG. 3(b) is a cross sectional view of theAMC 300 showing TE wavesradiating from theAMC 300 as leaky waves. Leakage is illustrated by theexponentially increasing spacing between the arrows illustrating radiation from thesurface as the waves radiate power away from theAMC 300 near theantenna 304.Leakage of the surface wave dramatically reduces the diffracted energy from theedges of the AMC surface in antenna applications. The radiation pattern fromsmall AMC ground planes can therefore be substantially confined to onehemisphere, the hemisphere above the front or top surface of theAMC 300. Thefront or top surface is the surface proximate theantenna 304. The hemispherebelow or behind theAMC 300, below the rear or bottom surface of theAMC 300,is essentially shielded from radiation. The rear or bottom surface of theAMC 300is the surface away from theantenna 304.

FIG. 4 illustrates a TE surface wave mode on the artificialmagneticconductor 300 of FIG. 3. Similarly, FIG. 5 illustrates a TM surface wave mode ontheAMC 300 of FIG. 3. The coordinate axes in FIGS. 4 and 5, and as usedherein, place the surface of theAMC 300 in the xy plane. The z axis is normal tothe surface. The TE mode of FIG. 4 propagates in the x direction along with loopsof an associated magnetic field H. The amplitude of the x component of magneticfield H both above the surface and within the surface is shown by the graph inFIG. 4. FIG. 5 shows the TM mode propagating in the x direction, along withloops of an associated electric field E. The relative amplitude of the x componentof the electric field E is shown in the graph in FIG. 5.

The performance and operation of theAMC 300 will be described in termsof an effective media model. An effective media model allows transformation allof the fine, detailed, physical structure of an AMC's unit cell into that ofequivalent media defined only by the permittivity and permeability parameters.These parameters allow use of analytic methods to parametrically study wavepropagation on AMCs. Such analytic models lead to physical insights as to howand why AMCs work, and insights on how to improve them. They allow one to study an AMC in general terms, and then consider each physical embodiment as aspecific case of this general model. However, it is to be noted that such modelsrepresent only approximations of device and material performance and are notnecessarily precise calculations of that performance.

First, the effective media model for the prior art high-impedance surface ispresented. Consider a prior art high-impedance surface 100 comprised of a squarelattice ofsquare patches 110 as illustrated in FIG. 6. Eachpatch 110 has a metalvia 108 connecting it to thebackplane 106. The via 108 passes through aspacerlayer 102, whose isotropic host media parameters are ε_D and µ_D.

FIG. 7 presents a new effective media model for substantiallycharacterizing the prior art high-impedance surface of FIG. 6. Elements of thepermittivity tensor are given in FIG. 7. The parameter α is a ratio of areas,specifically the area of the cross section of the via 108, πd²/4, to the area of aunit cell,a² =A. Each unit cell has an area A and includes onepatch 110,measuringb xb in size, plus the space g in the x and y directions to anadjacentpatch 110, for a pitch or period ofa, and with a thickness equal to the thickness ofthehigh impedance surface 100, orh + δ in FIG. 6. Note that α is typically asmall number much less than unity, and usually below 1%.

In the cross sectional view of FIG. 6(b), thehigh impedance surface 100includes a first orupper region 602 and a second orlower region 604. Thelowerregion 604, denoted here asregion 2, is referred to as a rodded media. Transverseelectric and magnetic fields in thisregion 604 are only minimally influenced bythe presence of the vias orrods 108. The effective transverse permittivity, ε_2x andpermeability, µ_2x, are calculated as minor perturbations from the mediaparameters of the host dielectric. This is because the electric polarisability of acircular cylinder, πd² /2, is quite small for the thin metal rods whose diameter issmall relative to the perioda. Also note that effective transverse permittivity, ε_2x,and permeability , µ_2x , are constant with frequency. However, the normal, or z-directed,permittivity is highly dispersive or frequency dependent. A transverse electromagnetic (TEM) wave with a z-directed electric field traveling in a lateraldirection (x or y), in an infinite rodded medium, will see therodded media 102 asa high pass filter. The TEM wave will experience a cutoff frequency,∫_c, belowwhich ε_2z is negative, and above this cutoff frequency, ε_2z is positive andasymptotically approaches the host permittivity ε_D. This cutoff frequency isessentially given by

The reflection phase resonant frequency of the prior art high-impedance surface100 is found well below the cutoff frequency of therodded media 102, where ε_2zis quite negative.

Theupper region 602, denoted asregion 1, is a capacitive FSS. Thetransverse permittivity, ε_1x or ε_1y, is increased by the presence of the edgecoupledmetal patches 110 so that ε_1x = ε_1y >>1, typically between 10 and 100 fora single layer frequency selective surface such as the high-impedance surface 100.The effective sheet capacitance,C =ε_oε_1xt, is uniquely defined by the geometryof eachpatch 110, but ε_1x in the effective media model is somewhat arbitrary sincet is chosen arbitrarily. The variablet is not necessarily the thickness of thepatches, which is denoted as δ. However,t should be much less than thespacerlayer 604 heighth.

The tensor elements for theupper layer 602 of the prior art high-impedancesurface 100 are constant values which do not change with frequency. That is, theyare non-dispersive. Furthermore, for theupper layer 602, the z component of thepermeability is inversely related to the transverse permittivity by µ_1z = 2/ε_1x.Once the sheet capacitance is defined, µ_1z is fixed.

It is useful to introduce the concept of an artificial magnetic molecule. Anartificial magnetic molecule (AMM) is an electrically small conductive loop which typically lies in one plane. Both the loop circumference and the loop diameter aremuch less than one free-space wavelength at the useful frequency of operation.The loops can be circular, square, hexagonal, or any polygonal shape, as only theloop area will affect the magnetic dipole moment. Typically, the loops are loadedwith series capacitors to force them to resonate at frequencies well below theirnatural resonant frequency

A three dimensional, regular array or lattice of AMMs is an artificialmaterial whose permeability can exhibit a Lorentz resonance, assuming nointentional losses are added. At a Lorentz resonant frequency, the permeability ofthe artificial material approaches infinity. Depending on where the loop resonanceis engineered, the array of molecules can behave as a bulk paramagnetic material(µ_r > 1) or as a diamagnetic material (µ_r < 1 ) in the direction normal to the loops.AMMs may be used to depress the normal permeability of the FSS layer,region 1,in AMCs. This in turn has a direct impact on the TE mode cutoff frequencies, andhence the surface wave bandgaps.

The prior art high impedance surface has a fundamental, or lowest,resonant frequency near∫_o = 1/(2πµDµohC), where the spacer layer iselectrically thin, (βh <<1 where β =µDµoεDεo). Higher order resonances arealso found, but at much higher frequencies where βh ≈nπ andn=1,2,3,... Then=1 higher order resonance is typically 5 to 50 times higher than the fundamentalresonance. Thus, a prior art high impedance surface designed to operate at lowmicrowave frequencies (1-3 GHz) will typically exhibit its next reflection phaseresonance in millimeter wave bands (above 30 GHz).

There is a need for an AMC which provides a second band or even multiplebands of high surface impedance whose resonant frequencies are all relativelyclosely spaced, within a ratio of about 2:1 or 3:1. This is needed, for example, formulti-band antenna applications. Furthermore, there is a need for an AMC withsufficient engineering degrees of freedom to allow the second and higherreflection phase resonances to be engineered or designated arbitrarily. Multiplereflection phase resonances are possible if more than two layers (4, 6, 8, etc.) are used in the fabrication of an AMC. However, this adds cost, weight, and thicknessrelative to the single resonant frequency design. Thus there is a need for a meansof achieving multiple resonances from a more economical two-layer design. Inaddition, there is a need for a means of assuring the existence of a bandgap forbound, guided, TE and TM mode surface waves for all of the high-impedancebands, and within the +/- 90° reflection phase bandwidths.

FIG. 8 illustrates an artificial magnetic conductor (AMC) 800. TheAMC800 includes anarray 802 that is in one embodiment a coplanar array of resonantloops or artificialmagnetic molecules 804 which are strongly capacitively coupledto each other, forming a capacitive frequency selective surface (FSS). Theresonant loops 804 in the illustrated embodiment are uniformly spaced and at aheighth above a solidconductive ground plane 806. An array of electrically short,conductive posts orvias 808 are attached to theground plane 806 only and have alengthh. Eachloop 804 includes a lumpedcapacitive load 810. The one or morelayers of artificial magnetic molecules (AMMs) or resonant loops of the artificialmagnetic conductor 800 create a frequency dependent permeability in thezdirection, normal to the surface of theAMC 800.

AnAMC 800 with a single layer of artificialmagnetic molecules 804 isshown in FIG. 8. In this embodiment, each loop and capacitor load aresubstantially identical so that all loops have substantially the same resonantfrequency. In alternative embodiments, loops having different characteristics maybe used. In physical realizations, due to manufacturing tolerances and othercauses, individual loops and their associated resonant frequencies will notnecessarily be identical.

AnAMC 900 with multiple layers of artificialmagnetic molecules 804 isshown in FIG. 9. FIG. 10 is a cross sectional view of the artificialmagneticconductor 900 of FIG. 9. TheAMC 900 includes afirst layer 902 ofloops 804resonant at a first frequency f₁. TheAMC 900 includes asecond layer 904 ofloops 804 resonant at a second frequency f₂. Eachloop 804 of thefirst layer 902of loops includes a lumpedcapacitive load C₁ 908. Eachloop 804 of thesecondlayer 904 of loops includes a lumpedcapacitive load C₂ 906. The lumped capacitances may be the same but need not be. In combination, thefirst layer 902ofloops 804 and thesecond layer 906 ofloops 904 form a frequency selectivesurface (FSS)layer 910 disposed on aspacer layer 912. In practical application,the low frequency limit of the transverse effective relative permittivity, ε_1x and ε_1y,for themultiple layer AMC 900 lies between 100 and 2000. Accordingly, strongcapacitive coupling is present betweenloops 902 and 904. A practical way toachieve this coupling is to print two layers of loops on opposite sides of an FSSdielectric layer as shown in FIG. 10. Other realizations may be chosen as well.

FIG. 11 illustrates a first physical embodiment of aloop 1100 for use in anartificial magnetic conductor such as theAMC 800 of FIG. 8. Conducting loopssuch asloop 1100 which form the artificial magnetic molecules can beimplemented in a variety of shapes such as square, rectangular, circular, triangular,hexagonal, etc. In the embodiment of FIG. 11, theloop 1100 is square in shape.Notches 1102 can be designed in the loops to increase the self inductance, whichlowers the resonant frequency of the AMMs.Notches 1102 andgaps 1104 canalso be introduced to engineer the performance of theloop 1100 to a particulardesired response. For example, the bands or resonance frequencies may be chosenby selecting a particular shape for theloop 1100. In general, agap 1104 cuts allthe way through a side of theloop 1100 from the center of theloop 1100 to theperiphery. In contrast, a notch cuts through only a portion of a side between thecenter and periphery of theloop 1100. FIG. 11 illustrates a selection of potentialsquare loop designs.

FIG. 12 illustrates a portion of a two layer artificial magnetic conductorwhose FSS layer uses a square loop of FIG. 11(d). Wide loops with relativelylarge surface area promote capacitive coupling between loops of adjacent layerswhen used in a two-layer overlapping AMC, as illustrated in FIG. 12. Anoverlapregion 1202 at thegap 1104 provides the series capacitive coupling required forloop resonance.

In one preferred embodiment, loops of the type illustrated in FIGS. 11 and12 are formed on surfaces of dielectric materials using conventional printed circuit board (PCB) manufacturing techniques. For example, a metallic layer is depositedon a surface of the PCB and subsequently patterned by chemical etching or othertechnique. Such processes provide precise control of sizes, spacing anduniformity of printed features.

FIG. 13 and FIG. 14 show simulation results for the normal-incidencereflection phase of the AMC illustrated in FIG. 12. In both simulations, theincident electric field is y-polarized. In the simulation illustrated in FIG. 13,P=10.4mm, h=6mm, t=0.2mm, s=7.2mm, w=1.6mm, g2=0.4mm, ε_r1=ε_r2=3.38.FIG. 13 shows a fundamental resonance near 1.685 GHz, and a second resonancenear 2.8 GHz. In FIG. 14, when the gap in the loops is eliminated so that theloops are shorted and g2=0 in FIG. 12, then only one resonance is obtained. Thereason that theAMC 800 withgaps 1104 has a second resonance is that theeffective transverse permittivity of the frequency selective surface has becomefrequency dependent. A simple capacitive model is no longer adequate.

FIG. 15 shows equivalent circuits for portions of the artificialmagneticconductor 800 of FIG. 8. FIG. 15(a) illustrates the second Foster canonical formfor the input admittance of a one-port circuit, which is a general analytic model forthe effective transverse permittivity of complex frequency selective surface (FSS)structures. FIG. 15(b) gives an example of a specific equivalent circuit model foran FSS whereby two material or intrinsic resonances are assumed. FIG. 15(c)shows the TEM mode equivalent circuit for plane waves normally incident on atwo layer AMC, such asAMC 900 of FIG. 9. As noted above, the modelsdeveloped herein are useful for characterizing, understanding, designing andengineering devices such as the AMCs described and illustrated herein. Thesemodels represent approximations of actual device behavior.

Complex loop FSS structures, such as that shown in FIG. 12, have adispersive, or frequency dependent, effective transverse permittivity which can beproperly modeled using a more complex circuit model. Furthermore, analyticcircuit models for dispersive dielectric media can be extended in applicability tomodel the transverse permittivity of complex FSS structures. The second Foster canonical circuit for one-port networks, shown in FIG. 15(a), is a general casewhich should cover all electrically-thin FSS structures. Each branch manifests anintrinsic resonance of the FSS. For an FSS made from low loss materials, R_n isexpected to be very low, hence resonances are expected to be Lorentzian.

The effective sheet capacitance for the loop FSS shown in FIG. 12 has aLorentz resonance somewhere between 1.685 GHz and 2.8 GHz. In fact, if thetransverse permittivity of this FSS is modeled using only a three-branchadmittance circuit, as shown in FIG. 15(b), theε_1y curve 1602 shown in the uppergraph of FIG. 16 is obtained. Two FSS material resonances are evident near 2.25GHz and 3.2 GHz. The ε_1y curve 1604 is the transverse relative permittivityrequired to achieve resonance for the AMC, a zero degree reflection phase. Thiscurve 1604 is simply found by equating the capacitive reactance of the FSS,X_c = 1/(ωC) = 1/(ωε_1yε_ot), to the inductive reactance of the spacer layer,X_L = ωL = ωµ_2xµ_oh, and solving for transverse relative permittivity:
ε_1y = 1/(ω²µ_2xµ_oε_oht). Intersections of thecurve 1602 and thecurve 1604 definethe frequencies for reflection phase resonance. The reflection phase curve shownin the lower graph of FIG. 16 was computed using the transmission line modelshown in FIG. 15(c) in which the admittance of the FSS is placed in parallel withthe shorted transmission line of lengthh representing the spacer layer andbackplane. This circuit model predicts a dual resonance near 1.2 GHz and 2.75GHz, which are substantially the frequencies of intersection in theε_1y plot. Thusthe multiple resonant branches in the analytic circuit model for the FSS transversepermittivity can be used to explain the existence of multiple AMC phaseresonances. Any realizable FSS structure can be modeled accurately using asufficient number of shunt branches.

There are many additional square loop designs which may be implementedin FSS structures to yield a large transverse effective permittivity. More examplesare shown in FIGS. 17, 20 and 21 where loops of substantially identical size andsimilar shape are printed on opposite sides of a single dielectric layer FSS. Reflection phase results for x and y polarized electric fields applied to an AMC ofthe design shown in FIG. 17 are shown in FIGS. 18 and 19. In this design, P=400mils, g1=30 mils, g2=20 mils, r=40 mils, w=30 mils, t=8 mils, and h=60 mils.ε_r=3.38 in both FSS and spacer layers since this printed AMC is fabricated usingRogers R04003 substrate material. In the center of each loop, a via is fabricatedusing a 20 mil diameter plated through hole.

FIG. 18 shows measured reflection phase data for anx polarized electricfield normally incident on the AMC of FIG. 17. Resonant frequencies areobserved near 1.6 GHz and 3.45 GHz. Similarly, FIG. 19 shows measuredreflection phase data for a y polarized electric field normally incident on the AMCof FIG. 17. Resonant frequencies are observed near 1.4 GHz and 2.65 GHz.

In FIGS. 18 and 19, a dual resonant performance is clearly seen in thephase data. For the specific case fabricated, each polarization sees differentresonant frequencies. However, it is believed that the design has sufficientdegrees of freedom to make the resonance frequencies polarization independent.

FIG. 21 shows an additional alternative embodiment for a frequencyselective surface implemented with square loops. The illustrated loop design ofFIG. 21 has overlappingsquare loops 2100 on eachlayer 902, 904 withdeepnotches 2102 cut from thecenter 2104 toward each corner.Gaps 2106, 2108 arefound at the 4:30 position on the upper layer and at the 7:30 position on the lowerlayer respectively. This design was also fabricated, using h=60 mils and t=8 milsof Rogers R04003 (ε_r=3.38) as the spacer layer and FSS layer thicknessrespectively. AMC reflection phase for the x and y directed E field polarization isshown in FIGS. 22 and 23 respectively. Again, dual resonant frequencies areclearly seen.

An alternative type of dispersive capacitive FSS structure can be createdwhereloops 2402 are printed on the one side and notchedpatches 2404 are printedon the other side of a single dielectric layer FSS. An example is shown in FIG. 24.

In addition to the square loops illustrated in FIGS. 17, 20, 21 and 24,hexagonal loops can be printed in a variety of shapes that include notches which increase the loop self inductance. These notches may vary in number andposition, and they are not necessarily the same size in a given loop. Furthermore,loops printed on opposite sides of a dielectric layer can have different sizes andfeatures. There are a tremendous number of independent variables which uniquelydefine a multilayer loop FSS structure.

Six possibilities of hexagonal loop FSS designs are illustrated in FIGS. 25,26 and 27. In each of FIGS. 25, 26 and 27, afirst layer 902 of loops iscapacitively coupled with a second layer ofloops 904. The hexagonal loopspresented here are intended to be regular hexagons. Distorted hexagons could beimagined in this application, but their advantage is unknown at this time.

FIG. 28 illustrates an effective media model for ahigh impedance surface2800. The general effective media model of FIG. 28 is applicable to highimpedance surfaces such as the prior arthigh impedance surface 100 of FIG. 1 andthe artificial magnetic conductor (AMC) 800 of FIG. 8. TheAMC 800 includestwo distinct electrically-thin layers, a frequency selective surface (FSS) 802 and aspacer layer 804. Eachlayer 802, 804 is a periodic structure with a unit cellrepeated periodically in both thex andy directions. The periods of eachlayer 802,804 are not necessarily equal or even related by an integer ratio, although theymay be in some embodiments. The period of each layer is much smaller than afree space wavelength λ at the frequency of analysis (λ/10 or smaller). Underthese circumstances, effective media models may be substituted for the detailedfine structure within each unit cell. As noted, the effective media model does notnecessarily characterize precisely the performance or attributes of a surface suchas theAMC 800 of FIG. 8 but merely models the performance for engineering andanalysis. Changes may be made to aspects of the effective media model withoutaltering the overall effectiveness of the model or the benefits obtained therefrom.

As will be described, thehigh impedance surface 2800 for theAMC 800 ofFIG. 8 is characterized by an effective media model which includes an upper layerand a lower layer, each layer having a unique tensor permittivity and tensorpermeability. Each layer's tensor permittivity and each layer's tensor permeability have non-zero elements on the main tensor diagonal only, with the x and y tensordirections being in-plane with each respective layer and the z tensor directionbeing normal to each layer. The result for theAMC 800 is an AMC resonant atmultiple resonance frequencies.

In the two-layer effective media model of FIG. 28, eachlayer 2802, 2804 isa bi-anisotropic media, meaning both permeability µ and permittivity ε are tensors.Further, eachlayer 2802, 2804 is uniaxial meaning two of the three main diagonalcomponents are equal, and off-diagonal elements are zero, in both µ and ε. Soeachlayer 2802, 2804 may be considered a bi-uniaxial media. The subscriptstandn denote the transverse (x andy directions) and normal (z direction)components.

Each of the twolayers 2802, 2804 in the bi-uniaxial effective media modelfor thehigh impedance surface 2800 has four material parameters: the transverseand normal permittivity, and the transverse and normal permeability. Given twolayers 2802, 2804, there are a total of eight material parameters required touniquely define this model. However, any given type of electromagnetic wavewill see only a limited subset of these eight parameters. For instance, uniformplane waves at normal incidence, which are a transverse electromagnetic (TEM)mode, are affected by only the transverse components of permittivity andpermeability. This means that the normal incidence reflection phase plots, whichreveal AMC resonance and high-impedance bandwidth, are a function of onlyε_1t,ε_2t, µ_1t, and µ_2t (and heightsh andt). This is summarized in Table 1 below.

Wave Type	Electric Field Sees	Magnetic Field Sees
TEM, normal incidence	ε1t ,ε2t	µ1t , µ2t
TE to x	ε1t, ε2t	µ1t , µ2t, µ1n , µ2n
TM to x	ε1t , ε2t , ε1n, ε2n	µ1t , µ2t

A transverse electric (TE) surface wave propagating on thehigh impedancesurface 2800 has a field structure shown in FIG. 4. By definition, the electric field(E field) is transverse to the direction of wave propagation, the +x direction. It isalso parallel to the surface. So the electric field sees only transverse permittivities.However, the magnetic field (H field) lines form loops in thexz plane whichencircle the E field lines. So the H field sees both transverse and normalpermeabilities.

The transverse magnetic (TM) surface wave has a field structure shown inFIG. 5. Note that, for TM waves, the role of the E and H fields is reversed relativeto the TE surface waves. For TM modes, the H field is transverse to the directionof propagation, and the E field lines (in thexz plane) encircle the H field. So theTM mode electric field sees both transverse and normal permittivities.

The following conclusions may be drawn from the general effective mediamodel of FIG. 28. First, ε_1n andε_2n are fundamental parameters which permitindependent control of the TM modes, and hence the dominant TM mode cutofffrequency. Second, µ_1n and µ_2n are fundamental parameters which permitindependent control of the TE modes, and hence the dominant TE mode cutofffrequency.

One way to distinguish between prior arthigh impedance surface 100 ofFIG. 1 and an AMC such as AMC 800 (FIG. 8) or AMC 900 (FIG. 9, FIG. 10) isby examining the differences in the elements of theµ_i andε_i tensors. FIG. 29shows a prior arthigh impedance surface 100 whose frequencyselective surface102 is a coplanar layer of square conductive patches of size b x b, separated by agap of dimension g.. In thehigh impedance surface 100, ε_D is the relativepermittivity of the background or host dielectric media in thespacer layer 104, µ_Dis the relative permeability of this background media in thespacer layer 104, andα is the ratio of cross sectional area of each rod or post to the area A of the unitcell in the rodded media orspacer layer 104. The relative permittivityε_avg = 1+ε_D / 2 is the average of the relative dielectric constants of air and the background media in thespacer layer 104.C denotes the fixed FSS sheetcapacitance.

The permittivity tensor for both the high-impedance surface 100 and theAMCs 800, 900 is uniaxial, orε_ix =ε_iy =ε_it ≠ε_iz = ε_in ;i=1, 2 with the same beingtrue for the permeability tensor. Thehigh impedance surface 100 has a squarelattice of both rods and square patches, each having the same period. Therefore,unit cell areaA = (g +b)². Also, α= (πd²/4)/A, whered is the diameter of therods or posts. The dimensions of the rods or posts are very small relative to thewavelength at the resonance frequencies. The rods or posts may be realized byany suitable physical embodiment, such as plated-through holes or vias in aconventional printed circuit board or by wires inserted through a foam. Anytechnique for creating a forest of vertical conductors (i.e., parallel to the z axis),each conductor being electrically coupled with the ground plane, may be used.The conductors or rods may be circular in cross section or may be flat strips of anycross section whose dimensions are small with respect to the wavelength λ in thehost medium or dielectric of the spacer layer. In this context, small dimensions forthe rods are generally in the range of λ/1000 to λ/25.

In some embodiments, theAMC 800 has transverse permittivity in the ytensor direction substantially equal to the transverse permittivity in the x tensordirection. This yields an isotropic high impedance surface in which the impedancealong the y axis is substantially equal to the impedance along the x axis. Inalternative embodiments, the transverse permittivity in the y tensor direction doesnot equal the transverse permittivity in the x tensor direction to produce ananisotropic high impedance surface, meaning the impedances along the two inplaneaxes are not equal. Examples of the latter are shown in Figures 17 and 21.

Effective media models for substantially modelling both thehighimpedance surface 100 and anAMC 800, 900 are listed in Table 2. Two of thetensor elements are distinctly different in theAMC 800, 900 relative to the priorart high-impedance surface 100. These are the transverse permittivity ε_1x, ε_1y andthe normal permeability µ_1z, both of the upper layer or frequency selective surface. The model for the lower layer or spacer layer is the same in both thehighimpedance surface 100 and theAMC 800, 900.

In Table 2,Y(ω) is an admittance function written in the second Fostercanonical form for a one port circuit:

This admittance functionY(ω) is related to the sheet capacitance(C = ε_1tε_ot) of theFSS 802 of theAMC 800, 900 by the relationY =jωC. Thehigh impedance surface 100 has an FSS capacitance which is frequencyindependent. However, theAMC 800, 900 has anFSS 802 whose capacitancecontains inductive elements in such a way that the sheet capacitance undergoesone or more Lorentz resonances at prescribed frequencies. Such resonances areaccomplished by integrating into theFSS 802 the physical features of resonantloop structures, also referred to as artificial magnetic molecules. As the frequency of operation is increased, the capacitance of theFSS 802 will undergo a series ofabrupt changes in total capacitance.

FIG. 30 illustrates sheet capacitance for the frequencyselective surface 802of theAMC 800 of FIG. 8 and theAMC 900 of FIG. 9. FIG. 30(a) shows that thecapacitance of theFSS 802 is frequency dependent. FIG 30(b) shows a Debyeresponse obtained from a lossy FSS where R_n is significant. In FIG. 30, two FSSresonances (ω_n =1/LnCn,N=2) are defined. The drop in capacitance acrosseach resonant frequency is equal toC_n, the capacitance in each shunt branch ofY(ω). Although the regions of rapidly changing capacitance around a Lorentzresonance may be used to advantage in narrowband antenna requirements, someembodiments may make use of the more slowly varying regions, or plateaus,between resonances. This FSS capacitance is used to tune the inductance of thespacer layer 804, which is a constant, to achieve a resonance in the reflectioncoefficient phase for theAMC 800, 900. This multi-valued FSS capacitance as afunction of frequency is the mechanism by which multiple bands of high surfaceimpedance are achieved for theAMC 800, 900.

In contrast, the two-layerhigh impedance surface 100 will offer reflectionphase resonances at a fundamental frequency, plus higher frequencies near wherethe electrical thickness of the bottom layer isnπ and n is an integer. These higherfrequency resonances are approximately harmonically related, and henceuncontrollable.

A second difference in the tensor effective media properties for thehighimpedance surface 100 andAMC 800 is in the normal permeability componentµ_1n. Thehigh impedance surface 100 has a constant µ_1n, whereas theAMC 800,900 is designed to have a frequency dependent µ_1n. The impedance functionZ(ω)can be written in the first Foster canonical form for a one-port circuit.

This impedance function is sufficient to accurately describe the normalpermeability of theFSS 802 in anAMC 800, 900 regardless of the number andorientation of uniquely resonant artificial magnetic molecules.

The prior art high-impedance surface 100, whoseFSS 102 is composed ofmetal patches, has a lower bound for µ_1n. This lower bound is inversely related tothe transverse permittivity according to the approximate relation µ_1n ≈ 2/ε_1t.Regardless of the FSS sheet capacitance, µ_1n is anchored at this value for the priorart high-impedance surface 100. However, a normal permeability which is lowerthan µ_1n = 2/ε_1t is needed to cut off the guided bound TE mode in all of the high-impedancebands of a multi-band AMC such asAMC 800 andAMC 900.

The overlapping loops used in theFSS 802 of theAMC 800, 900 allowindependent control of the normal permeability. Normal permeabilities may bechosen so that surface wave suppression occurs over some and possibly all of the+/- 90° reflection phase bandwidths in a multi-band AMC such asAMC 800 andAMC 900. The illustrated embodiment uses arrays of overlapping loops as theFSS layer 802, or in conjunction with a capacitive FSS layer, tuned individually orin multiplicity with a capacitance. This capacitance may be the self capacitance ofthe loops, the capacitance offered by adjacent layers, or the capacitance of externalcapacitors attached to the FSS. such as chip capacitors. The loops and capacitanceare tuned so as to obtain a series of Lorentz resonances across the desired bands ofoperation. Just as in the case of the resonant FSS transverse permittivity, theresonances of the artificial magnetic molecules affords the designer a series ofstaircase steps of progressively dropping normal permeability. Again, the regionof rapidly changing normal permeability around the resonances may be used toadvantage in narrowband operations. However, the illustrated embodiment usesplateaus of extended depressed normal permeability to suppress the onset ofguided bound TE surface waves within the desired bands of high-impedanceoperation.

In summary, the purpose of the resonance in the effective transversepermittivities ε_1t is to provide multiple bands of high surface impedance. The purpose of the resonances in the normal permeability µ_1n is to depress its value soas to prevent the onset of TE modes inside the desired bands of high impedanceoperation.

In some applications, an artificial magnetic conductor having more thantwo layers of loops separated by more than a single dielectric layer may provideimportant performance advantages. FIG. 31 illustrates an artificialmagneticconductor 3100 including a multiple layer frequency selective surface (FSS) 3102.TheAMC 3100 further includes aconductive ground plane 3104 and a roddedmedia forming aspacer layer 3106 disposed between theFSS 3102 and theconductive ground plane 3104. TheFSS 3102 has a frequency dependentpermeability µ_1z in a direction normal to the frequencydependent surface 3102.Exemplary dimensions and coordinate axes are shown in FIG. 31.

TheFSS 3102 includes three arrays of substantially coplanar artificialmagnetic molecules. The artificial magnetic molecules are preferablyimplemented as overlapping capacitively coupled loops. In the embodiment ofFIG. 31, theFSS 3102 includes afirst array 3112, asecond array 3114 and athirdarray 3116 of artificial magnetic molecules. Afirst dielectric layer 3118 separatesthefirst array 3112 of artificial magnetic molecules from thesecond array 3114 ofartificial magnetic molecules.

Thearrays 3112, 3114, 3116 are shown as being coplanar in respectiveplanes. This arrangement is particularly well suited to manufacture usingconventional printed circuit board (PCB) manufacturing techniques of depositing ametallic layer on a PCB surface and etching with a chemical or other process. Inother embodiments, other manufacturing techniques, some of which will producearrays of artificial magnetic molecules which are not substantially coplanar, maybe substituted.

Also, theAMC 3100 includes threelayers 3112, 3114, 3116 of loopsseparated by twodielectric layers 3118, 3120. In other embodiments, othercombinations of layers of loops and dielectric layers may be used. In general, a FSS in accordance with the disclosed embodiments will includen layers of loopsandn-1 dielectric layers isolating the layers of loops.

Thespacer layer 3106 includesmetallic rods 3108 periodically positionedin a dielectric material. Preferably, each loop of each array ofloops 3112, 3114,3116 is associated with arod 3108 of thespacer layer 3106. Any suitablemanufacturing method, for example, as described above, may be used tomanufacture the rodded media of thespacer layer 3108.

FIG. 32 illustrates a top view of the multiple-layer frequencyselectivesurface 3102 of FIG. 31. FIG. 32 shows thefirst array 3112, thesecond array3114 and thethird array 3116 of the frequencyselective surface 3102. A portiononly of each array is visible to illustrate the layering of the respective arrays.

In FIG. 32, each of thearrays 3112, 3114, 3116 includes substantiallyidentical hexagonal loops periodically spaced on theFSS 3102. Each loop isnotched to tailor the self-inductance of the loop and includes a gap to tailor theresonant frequency of the loop. The embodiment of FIGS. 31 and 32 is illustrativeonly. In other embodiments, different size and shape loops may be used alongwith different numbers of layers or arrays.

From the foregoing, it can be seen that the present embodiments provide avariety of high-impedance surfaces or artificial magnetic conductors which exhibitmultiple reflection phase resonances, or multi-band performance. The resonantfrequencies for high surface impedance are not harmonically related, but occur atfrequencies which may be designed or engineered. This is accomplished bydesigning the tensor permittivity of the upper layer to have a behavior withfrequency which exhibits one or more Lorentzian resonances.

While a particular embodiment of the present invention has been shownand described, modifications may be made. Other methods of making or usinganisotropic materials with negative axial permittivity and depressed axialpermeability, for the purpose of constructing multiband surface wave suppressingAMCs, such as by using artificial dielectric and magnetic materials, are extensionsof the embodiments described herein. Any such method can be used to advantageby a person ordinarily skilled in the art by following the description herein for the interrelationship between the Lorentz material resonances and the positions of thedesired operating bands. Accordingly, it is therefore intended in the appendedclaims to cover such changes and modifications which follow in the true spirit andscope of the invention.

Claims (17)

1. An antenna systemcharacterized by:

   an artificial magnetic conductor (AMC) (300) including

   a frequency selective surface having a frequency dependentpermeability µ_1z in a direction normal to the frequencydependent surface;

   a conductive ground plane (806) and

   a rodded media (808) disposed between the frequency selective surfaceand the conductive ground plane.
2. The antenna system of claim 1 furthercharacterized by:

   an antenna (304) in proximity to the AMC.
3. The antenna system of claim 2 wherein the frequency selective surfaceischaracterized by:

   a plurality of substantially identical periodically spaced loops (804)which are substantially coplanar and substantially uniformlyspaced a distanceh from the conductive ground plane.
4. The antenna system of 3 wherein the loopscharacterized by a lowfrequency limit of transverse effective relative permittivity ε_1x and ε_1y in the plane ofthe frequency selective surface in the range 100 to 2000.
5. The antenna system of claim 2 wherein the frequency selective surfaceischaracterized by a normal permeability µ_1z which exhibits one or more Lorentzmaterial resonances at particular frequencies.
6. The antenna system of claim 1 wherein the AMC is characterized to beresonant with a substantially zero degree reflection phase over two or more AMCresonant frequency bands and wherein the rodded media comprises a spacer layerincluding an array of metal posts extending through the spacer layer and wherein the afrequency selective surface (FSS) is disposed on the spacer layer, the frequencyselective surface, as an effective media, having one or more Lorentz resonances atpredetermined frequencies different from the two or more AMC resonant frequencybands.
7. An antenna systemcharacterized by:

   an artificial magnetic conductor (300) including

   a conductive ground plane (806),

   a spacer layer (808) disposed on the ground plane, and

   one or more arrays of coplanar loops (804) resonant at two or morefrequency bands, each loop having a similar shape and similarsize, the one or more arrays of coplanar loops producing afrequency dependent normal permeability µ_z; and

   an antenna (304) proximate the artificial magnetic conductor.
8. The antenna system of claim 7 wherein the one or more arrays ofcoplanar loops arecharacterized by:

   a first array (902) of loops regularly spaced a with a period P in a first plane;
      and

   a second array (904) of loops regularly spaced in a second plane.
9. The antenna system of claim 7 furthercharacterized by externalcapacitors to produce a series capacitance between adjacent loops.
10. The antenna system of claim 7 furthercharacterized by one or moredielectric layers separating each of the one or more arrays of coplanar loops.
11. An antenna systemcharacterized by:

    a conductive ground plane (806);

    a dielectric layer (912) perforated by conductive rods (808) in electricalcontact with the conductive ground plane;

    a frequency selective surface (910) disposed on the dielectric layer andincluding

    a first layer (902) of capacitively coupled loops resonant at a firstfrequency,

    a dielectric spacer layer, and

    a second layer (904) of capacitively coupled loops resonant at a secondfrequency, the frequency selective surface having a frequencydependent permeability in a direction substantially normal to thefrequency selectively surface; and

    an antenna (304) positioned proximate the frequency selective surface.
12. An artificial magnetic conductor (300) resonant with a substantiallyzero degree reflection phase over at least two resonant frequency bands, the artificialmagnetic conductorcharacterized by a frequency selective surface having a pluralityof Lorentz resonances in transverse permittivity at independent, non-harmonicallyrelated, predetermined frequencies different from the resonant frequency bands.
13. An artificial magnetic conductor (AMC) (300) resonant at multipleresonance frequencies, the AMCcharacterized by an effective media model, theeffective media modelcharacterized by:

    a first layer and a second layer, each layer having a layer tensor permittivityand a layer tensor permeability, each layer tensor permittivity and eachlayer tensor permeability having non-zero elements on a main diagonalonly, x and y tensor directions being in-plane with each respective layerand z tensor direction being normal to each layer.
14. The AMC of claim 13 wherein the effective media model is furthercharacterized by:

    a first layercharacterized by transverse permittivities in the y tensor directionand the x tensor direction which are variable with frequency and whichexhibit one or more Lorentz resonances.
15. The AMC of claim 14 wherein the transverse permittivity of the firstlayer is modeled by ε_1t =Y(ω) /jωε_ot whereY(ω) is an admittance function described byFoster's second canonical form for a one port circuit,

    

    wherej is the imaginary operator, ω is radian frequency,ε_o is the permittivity of freespace,C_∞ is the asymptotic limit on transverse capacitance of the first layer asω approaches an infinite value,L_o is the asymptotic limit on shunt inductance of themodel as ω approaches 0,R_n is a branch resistance,L_n is a branch inductance andC_n is a branch capacitance.
16. An artificial magnetic conductor (300) operable over at least a firsthigh-impedance frequency band and a second high-impedance frequency band as ahigh- impedance surface, the artificial magnetic conductor being defined by aneffective media modelcharacterized by:

    a spacer layer; and

    a frequency selective surface (FSS) disposed adjacent the spacer layer andhaving a transverse permittivity ε_1t defined by ε_1x = ε_1y =Y(ω) /jωε₀t,whereinY(ω) is a frequency dependent admittance function for thefrequency selective surface,j is the imaginary operator, ω corresponds to angular frequency, ε₀ is the permittivity of free space, and tcorresponds to thickness of the frequency selective surface.
17. The artificial magnetic conductor of claim 16 wherein the FSS layerhas a normal permeability µ_1z defined by µ_1z =Z(ω) /jωµ₀t, wherein Z(ω) is a frequencydependent impedance function,j is the imaginary operator, ω corresponds to angularfrequency, µ₀ is the permeability of free space, andt corresponds to thickness of thefrequency selective surface.

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