Design and performance of airborne radomes:a review

G.A.E. Crone, B.Sc, (Eng), Ph.D., A.W. Rudge, Ph.D., C.Eng., Sen. Mem. I.E.E.E., F.I.E.E., andG.N. Taylor, M.A., Ph.D., D.I.C.

Indexing terms: Aerospace facilities and techniques, Radomes

Abstract: The ever increasing demands on the performance of airborne antennas place comparable demandson the design of the enclosing randome to ensure minimal degradation of the antenna radiation pattern.Radomes for airborne application can be separated into three main categories: large aircraft radomes ofeither the nose-cone or under-fuselage type, small aircraft radomes often flush mounted to the airframe andmissile radomes. The geometry of the radome, being largely determined by aerodynamic considerations,often leads to severe degradation of the electrical performance of any enclosed antenna. Rain erosion andheating of the radome surface also constrain the electrical design by limiting the choice of material andbuilds. For large airborne radomes, the enclosed antenna may be required to exhibit both low angular aber-rations and small sidelobe degradations. Radomes for these applications may also be required to operate ineither a dual-, broad- or multiband role. Metallic or dielectric bodies, such as lightning conductors, the pitottube and pitot-static pressure tubes, either within or on the radome surface, also present potential sourcesof electromagnetic degradation. Missile radomes share most of these effects, but to varying degrees because

. of their relatively smaller size and different operational constraints. The paper reviews the electromagneticdesign and analysis of such radomes, examines the sources of degradation of the enclosed-antenna radiationpattern and discusses the design requirements with reference to the operational environment.

1 Introduction

The rapid growth in the use of the electromagnetic spectrumfor both civil and military applications over the last fewdecades has led to a growing pressure for improvements inthe performance of electromagnetic sensors. Antenna systemsoffering lower sidelobes, multiple frequencies, dual polaris-ations, improved tracking and wider bandwidths are of particu-lar importance in this respect and are receiving considerableattention [ 1 ] . Airborne antennas are almost invariablyenclosed by a radome whose transmission characteristics cannegate, or at least seriously degrade, the improved antennaperformance. The electromagentic characteristics of theradome are a key factor in the overall performance of anyradiating or receiving system, but airbome-radome design isoften dominated by other factors, such as the aerodynamicsand structural requirements of the airframe. In this area,advances in the performance of high-speed aircraft have ledto even greater demands on the nonelectromagnetic propertiesof the radome. In any meaningful review of airborne-radomedesign, the electromagnetic aspects cannot be consideredin isolation from the other factors which impinge stronglyon the shape of the radome and the choice of dielectricmaterials which can be used in its construction.

Radomes for airborne applications will be considered herein three main categories. The first is the class of aero-dynamically shaped radomes which are large with, respect tothe operating wavelength and which typically form the noseor tail cone of the aircraft, or which are realised either asunder-fuselage 'bubbles' or as rotating appendages which arecommonly referred to as 'rotodomes' [2,3]. The secondcategory is that of missile radomes, which must also be aero-dynamic but with an additional facility to withstand muchhigher accelerations and velocities and with dimensions whichare not necessarily very large with respect to the wave-length. Finally, the third category comprises small radome

Paper 16S2F, first received 8th July and in revised form 20th August1981Dr. Rudge is, and Dr. Crone was formerly, with ERA TechnologyLtd., Cleeve Road, Leatherhead KT22 75A, England. Dr. Crone is nowwith the European Space Research & Technology Centre, Domeinweg,Noordwijk, Netherlands. Mr. Taylor is with the Royal Signals & RadarEstablishment, St. Andrews Road, Great Malvern WR14.3PS, England

covers which are either flush mounted or sited on the leadingor trailing edges of a wing or tail fin.

Airborne radar antennas are required to operate withminimum angular aberrations (boresight errors) and lowcopolar and crosspolar sidelobes. The specifications for mod-ern systems are becoming increasingly demanding in theserespects, and the degree of performance degradation intro-duced by the radome is likely to be critical in many appli-cations. The fundamental requirement for a good aerodynamicshape will often complicate the electromagnetic design prob-lem, and the choice of dielectric materials will be constrainedby requirements for structural strength, low weight, thermalstability and rain-erosion resistance. The radome performancemay also be compromised by the scattering of electromagenticwaves from metallic pitot tubes and lightning protectionstrips outside the radome and dielectric pressure tubes withinit.

Missile radomes share most of the design problems of thelarger aircraft radomes, but in this case the choice of materialsis further restricted by the higher accelerations and terminalvelocities which are involved and the resultant increase inthermal shock and rain erosion effects. Boresight error, theangular deviation of boresight from its position in the absenceof the radome, and its rate of change with the seeker antennalook angle (i.e. boresight error slope) can seriously impairthe performance of a guided weapon by limiting its usefulvelocity and manoeuvrability. The electromagnetic analysisof missile radomes is complicated by their very pointedshapes and the fact that the curvature dimensions are notlarge with respect to the operating wavelength.

As a consequence of electronic warfare, the use of smallradome covers is increasing significantly. The geometriesand locations of radomes of this type are dominated by avariety of factors, almost all of which are outside of thecontrol of the radome designer. The outer surfaces of suchcovers must follow the contours of the aircraft and are oftenlocated in environments which have been described as structur-ally difficult and electromagnetically hideous. The smallradome cover is often employed to enclose a broadbandantenna, and thus its electromagnetic performance must bemaintained over wide frequency ranges. Rain erosion canrepresent a very severe problem for such radome covers,particularly for those which present a relatively blunt surfaceto the forward direction.

IEEPROC, Vol. 128, Pt. F, No. 7, DECEMBER 1981 0143-7070/81/070451 +14 $01.50/0 451

2 Radome wall configurations

Ideally, the radome wall must offer structural strength andrigidity with electromagnetic transparency over the operatingfrequency bands. There are three basic types of wall construc-tion which are commonly employed:

(a) thin wall(b) half-wavelength thick (A/2) or multiples thereof(c) sandwich or multilayer.

The properties and design formulas for the various types ofwall geometry have been given by Cady etal. [4], and typicalperformances have been illustrated in many review articles[5, 6] . Some basic wall constructions are illustrated in Fig. 1.

ram erosionlayer

Fig. 1 Radome wall constructions

a Thin wallb Halfwavec A-sandwichd Multilayer

The thin-wall radome, usually less than 0.02 X thick, isseldom used in airborne applications owing to its low mechan-ical strength. Halfwave walls find application for small-to-medium size radomes and most missile radomes employ thisdesign. With this configuration, reflectionless transmission isachieved at a 'typical' angle of incidence by constructivecancellation of reflected energy from each of the two air-dielectric interfaces. Reasonable transparency can be main-tained over a relatively large range of incidence angles, makingit a useful design for nose radomes, since with highly taperedshapes the incidence angle may vary from 30° to 80° betweenthe tip and the base. Fig. 2 shows a typical frequency responseof such a design for one polarisation. It is fairly narrowband,and multiple-halfwave structures are even more so. Halfwavewall structures are often too heavy for very large aircraftradomes, for which a sandwich configuration is generallypreferred.

halfwave radome E = 4 0.75cm

2 4 6 8 10 12 14 16

frequency, GHz

Fig. 2 Transmission properties of halfwave thickness radome

af- = angle of incidence

Three-layer sandwich structures have relatively thin innerand outer skins of the same thickness and permittivity witha thicker core. The A- and B-sandwiches have cores with,respectively, lower and higher permittivities than the skins.The B-sandwich is analogous to a bloomed optical lens, withthe quarter-wavelength skins acting as reflectionless coatings.

Unfortunately, the core usually has to be so dense as toincur a severe weight penalty, and airborne applications arethus uncommon. The A-sandwich, on the other hand, iswidely used. This design can be made broadband and hasreasonable performance over a range of incidence angles(see Fig. 3).

skin 1mm E =

core 6mm E = 1.5

4 6 8 10 12 14 16

frequency , GHz

Fig. 3 Transmission properties of an A-sandwich radome

a,- = angle of incidence

Many variations on the basic sandwich structures exist.For example, two A-sandwiches may be placed back to backto produce the so-called C-sandwich, which has good perform-ance at high incidence angles. Alternatively, the dielectricmay be inductively loaded with very thin wires to modify itstransmission properties [5,7—9]. In this way, the perform-ance of an electrically thin randome may be achieved froma physically thick structure. An example of such loading isshown in Figs. 4A and B, where a GRP laminate 0.1 X thick isloaded to achieve a performance equivalent to laminate0.02 X thick in the same material. Alternatively, multibandor broadband transmission can be achieved [9, 10].

parallel incidence plane

dielectric sheet

embedded wire grating

wiresielectric sheet

perpendicularincidence plane

Zo C

Fig. 4A Wire loaded dielectric sheet and simplified transmission-line analogy

— 100°/

Z 90

I 80

1 70

S 60uc 5 0

perpendicular with wires

parallel withoutwires \

V--'

perpendicularwithout wires

10c 20° 30° 40" 50° 60° 70° 80°

Fig. 4B Theoretical transmission efficiency for a dielectric sheet(e = 4, d/ \ = 0.1) with and without inductive matching

452 IEEPROC, Vol. 128, Pt. F, No. 7, DECEMBER 1981

At frequencies where a true halfwave structure is tooheavy, a somewhat lighter equivalent structure may beachieved by loading the core of an A-sandwich with particlesof metals or high permittivity dielectric [11].

It is also useful to use gradient walls, in which the thicknessor permittivity of the wall is made a function of position(and thus of antenna pointing angle). This technique providesreduced reflections at high angles of incidence by means ofequalisation of the insertion phase delay, and was used for thispurpose in the US E-3A airborne surveillance radar antennasystem [3]. Feldman and Rulf have recently described thedesign features of this radome, which employs the 'rotodome'concept where the radome rotates with the scaning antenna[12].

3 General characteristics of aircraft and missile radomes

Fig. 5 shows a schematic diagram of a typical axially sym-metric aircraft nose-cone radome enclosing a scanning antennasystem. The passage of the electromagnetic field through thedielectric wall of the radome can lead to transmission lossand distortion of the antenna radiation pattern characteristics.These undesirable effects can be minimised for a fixed positionof the antenna and dielectric interface, but the design processis made more difficult when, as shown in Fig. 5, the wallgeometry, as presented to the antenna, varies with the antennapointing angle.

lightning conductors

pitot

Fig. 5 Problem areas in airborne radomes

For an airborne radar antenna, the most important aber-rations are those associated with boresight error, boresighterror slope and the degradation of the antenna sidelobes.To minimise these undesirable effects, the transmission lossand the variation of the insertion phase delay (IPD) as theelectromagnetic wave passes through the radome must bemade small, and polarisation must be made independentover a wide range of incident angles and antenna pointingangles.

Clearly from an electromagnetic viewpoint, a sphericalradome with a centrally located antenna represents the opti-mum configuration, but aerodynamic considerations maydemand a more tapered structure. Practical designs are usuallycircularly symmetric with surfaces such as cones, ogives andparabolas finding common application. In some instances,

other profiles such as Von Karmann or Sears Hack are used,with nonaxially symmetric configurations finding someapplication, such as the 'shark nose' radome employed on theUS F-5 advanced fighter aircraft [13]. The departure fromaxial symmetry is likely to complicate the radome design, butit must be remembered that from the electromagnetic view-point it is the symmetry, or lack of it, as seen by the antennawhich is the important factor. An outwardly asymmetricradome may, in fact, offer a more uniform dielectric interfaceto the enclosed antenna system over its scanning range.

In Fig. 5, the principal sources of radiation pattern degra-dation introduced by a large airborne radome are indicated.In addition to the aberrations resulting from the asymmetryof the dielectric interface presented to the antenna, there areother major contributors. For example, under certain con-ditions, the geometry of the inner air-dielectric interface canresult in the reflected energy forming a semicollimated beamat a wide angle from the antenna boresight. This reflectedbeam, which is often termed the 'flash lobe', can seriouslydegrade the overall sidelobe performance of the radar system.Large radomes often require some form of lightning protec-tion, and this may take the form of metallic strips or closelyspaced studs on the skin of the outer dielectric layer. Thepresence of these strips can result in electromagnetic scatteringwhich will again degrade the antenna sidelobe performance.The metallic pitot-head boom, which is generally sited at theapex of a nose-cone radome, can be a major source of electro-magnetic scattering, a situation that would still prevail evenfor a dielectric pitot tube. The pressure tubes, which may bemetal or plastic, and which run from the head on the insideof the radome, will also have undesirable sidelobe and aber-ration effects.

Fig. 6 shows a representative boresight error characteristicof an axially symmetric radome, while Fig. 7 provides an

antenna look angle

Fig. 6 Representative boresight error characteristic

-20

CD

^ - 3 0

£-50

< 36° >

Fig. 7 Radome-induced sidelobe modifications

angle

antenna aloneradome-induced modifications

IEEPROC, Vol. 128, Pt. F, No. 7, DECEMBER 1981 453

example of the undesirable sidelobe modifications introducedby a typical aircraft nose-cone radome [14]. In Fig. 8, thelevel and position of a 'flash lobe' is shown for various antennapointing angles within a conical radome.

-30r

-A0

-50

-60

J90

angle, deg180

Fig. 8 Radome flash

The high structural strength and low weight requirementsof large airborne radomes will generally dictate the type ofwall construction and limit the range of materials which canbe adopted. The radome must maintain its electrical andmechanical properties over a temperature range which isstrongly influenced by kinetic effects and will thereforedepend largely on the maximum speed of the aircraft.

For slower vehicles, such as long-range surveillance aircraft,the nose cones can be more blunt, but in these cases thewide-angle sidelobe specifications are likely to be moredemanding. To provide the necessary full azimuthal coverage,radomes for surveillance applications can be sited in pairs,fore and aft on the aircraft, as in the UK Nimrod AirborneEarly Warning system [3], or as a single installation eitherabove or below the fuselage. The US long-range surveillancedesigns (e.g. AWACS and E2C) have favoured a single above-fuselage rotodome approach [2, 3] . This has the advantagethat the radome presents a constant dielectric interface to theantenna which can be optimised during the design process.However, the mechanical problems are increased in this casesince the complete rotodome structure must be rotated inthe airstream.

Small radome covers are tending to proliferate on modernaircraft mainly because of the needs of electronic warfare(EW). Such covers are fitted to many types of aircraft, butdesign problems are most severe with high-speed aircraft.EW antennas, and their radome covers, are required to operateover wide bandwidths, typically within the band 0.5—40 GHz.Siting these antennas is a major problem since they must

provide adequate angular coverage, but at prime sites on theaircraft the aerodynamic performance almost always takesprecedence. The radome designer is thus often faced withoddly shaped protuberances from tail fins and wing-leadingedges on which to base his 'flush-mounted' cover. The radomeouter geometry is governed by local airflow conditions, andthis may result in a shape which is far from optimum electri-cally. Kinetic and rain erosion effects can be a problem onfaster aircraft, demanding materials with stable propertiesover wide temperature range which are able to survive thevery severe forces imposed by high-velocity impact withwater droplets.

Missile radomes, while sharing many of the problemsassociated with larger radomes, are further complicated bythe need to withstand very high initial accelerations and highterminal velocities. These conditions imply kinetic tempera-ture rises of the order of 400° C during the first second offlight with terminal temperatures varying from 450° C atMach 3 to 1150° C at Mach 5. Only few materials are availablewhich permit the missile radome to maintain its structuralintegrity and its electrical parameters to the necessary closetolerances. Even for Mach 3 operation, a dielectric is requiredwith a permittivity which remains stable within 10% over atemperature range of perhaps 0—500° C with a loss tangentnot exceeding 0.01.

To reduce the stresses on nose-cone radomes at very highvelocities, the use of very tapered shapes is common. Thedielectric wall presented to the scanning antenna will thenvary dramatically with the antenna pointing direction, andlarge incidence angles between the electromagnetic waves andthe dielectric wall are unavoidable. In some lower-velocitymissiles, use is made of more hemispherically shaped radomesfronted by a metal nose spike. However, the nose spiketends to degrade the boresight error characteristics of themissile. For example, Fig. 9 shows a comparison between ahemispherical radome and an ogival radome (1:5:1 finenessratio) both with and without a nose spike [15]. It is note-worthy that, even with the spike, the hemispherical radomeoffers superior electrical performance to the ogive.

0.05

2 0

| 0.05

0.1

metal spike

I \ dielectric spike

I % s v \ ^ ^ x -x hemisphere

\

metal spike ~o- 1.5 ogive

10 30scan angle , deg

Fig. 9 Spike protected radomes

4 Radome riiaterials

It is evident that radome designs, in all three categories con-sidered here, are heavily influenced by the limited availabilityof materials which can maintain the required balance ofstructural and electromagnetic properties in the verydemanding airborne environment. Unfortunately, low dielec-tric constant and high mechanical strength are often mutuallyexclusive characteristics, requiring the radome designer tosettle for a compromise solution. The choice of material isvery much dependent on the role in which the vehicle isdeployed.

454 IEEPROC, Vol. 128, Pt. F, No. 7, DECEMBER 1981

For subsonic or low supersonic applications, glass-fibrereinforced plastics (GFRP) are widely used in either mono-lithic or sandwich configurations. GFRPs, when employed asskins for A-sandwich radomes, can offer low weight andrelatively low production costs, but these materials cannotwithstand high temperatures and for higher-velocity missileapplications the use of inorganic materials, such as glassceramics, has become common. The inorganic materials offerbetter temperature and rain erosion properties but result inradomes which are relatively heavy and expensive to fabricate.Some of the principal features of radome materials are brieflyreviewed in the following Sections.

4.1 Glass-fibre reinforced plastics (GFRP)Radome wall materials for large airborne radomes are usuallyrealised in the form of resins laminated with a reinforcementmaterial. Polyester and epoxy resins remain the most commonwith the occasional usage of other varieties. For high-temperature applications, polymide materials [17, 20], whosethermal characteristics have been known for many years, arereceiving attention. They possess structural and electricalstability at up to 500° F over protracted duty cycles withthe same having been achieved for very short-term exposuresup to 1200° F. These materials, together with polybutadieneresins (PBD), owing to their low dielectric constants comparedwith epoxy and polyester laminates, offer advantages inbroadband applications [20, 21].

Reinforcements applied to resins to enable them to with-stand the structural loads on an airborne radome differdepending on the application of the vehicle. In general, acompromise solution is required since in most cases reinforcedlaminates with very good mechanical properties possessinferior electrical characteristics and vice versa. These fibresare generally orientated in either a knitted, woven or filament-wound form [16] with the laminates being made by either a'wet lay up', injection moulding or vacuum impregnationtechnique. Press moulding is also suitable for small radomesbased on thermoplastic resins. Terylene, quartz, Kevlar,E-, D- and S-glass are the most common reinforcement fibres.For S-glass, structural strength is maintained up to tempera-tures of 650° C, with D-glass providing better electrical proper-ties at the expense of structural stability. Quartz fibre is agood reinforcement since it possesses good thermomechanicalproperties and has a dielectric constant close in value to manyof the recipient resin materials. However, it is costly to pro-duce.

Table 1 summarises the properties of some samplereinforced laminates. In this Table, the resin used is eitherpolyester or RP12, a proprietary brand manufactured byPlessey Materials [8]. Many of these materials possess severethermal limitations, rendering them unsuitable for applicationsat very high speeds. Quartz-reinforced polymide laminates[17—20], however, appear suitable for high-temperatureapplication with proposed usage in the manufacture of missileradomes [19]. Also, rain erosion has marked effects on most

GFRP materials often necessitating the use of an additionalprotective material over the outer surface of the radome.

The core materials of A-sandwich-type radomes typicallytake the form of either honeycomb structures or expandedresins or foams. For airborne applications, foams have theadvantage that a closed-cell structure can be obtained, and sopenetration by moisture can be avoided. Foams offer thepotential of a high strength/weight ratio, a low dielectricconstant (since the structure is largely air) and low loss.

A number of polyurethane rigid foams are available withvarious advantages and disadvantages. For example, Rohacell(PM1) has a good strength/weight ratio and dielectric constant,but it has an open-cell structure which makes it susceptibleto moisture pick-up. Clocell (PE2) has excellent electricalproperties and can be produced at low cost, but the materialis severely temperature limited and its mechanical strengthfails off rapidly at temperatures above 100° C. The PlesseyP10 foam has good strength/weight and dielectric propertiesand is a closed-celi structure with good antimoisture character-istics. Its electrical and chemical properties are stable totemperatures up to 150° C. However, this foam is friable andis therefore more sensitive to rain erosion effects.

Syntactic foams are currently receiving considerable atten-tion as an alternative to polyurethane foams. These foams areformed using small hollow glass microspheres and, since theirclosed-cell structure is inherent, their antimoisture propertiesshould be good, with dielectric constants of the order of 1.8.The dielectric constant is higher than that of polyurethanefoams, and in other respects the electrical and mechanicalproperties of these foams appear attractive. The rain erosionproperties will remain dependent on the skin materials and theuse of protective coatings, but the avoidance of friabilitycould be an improtant advantage. If this is achieved withoutincurring any other serious penalty, syntactic foams couldultimately supersede the polyurethane foams. •

4.2 Modified dielectric core materialsArtificial dielectric materials are lightweight core materialsfor use in sandwich radomes. By matching the core permit-tivity to that of the skins, the structure behaves electricallyas a solid GFRP panel but is lighter in weight [11]. Artificialdielectrics have been developed in which the required corepermittivity is obtained by incorporating small conductingelements in a suitable matrix material which is then dispersedover the open cells of a polyurethane reticulated mat. Thefinished material is impregnated with polyurethane foam togive the desired closed-cell structure, which can then be variedaccording to mechanical strength requirements. Thesematerials offer relative dielectric constants (er) in the rangeer = 2.0 to 4.5 with loss tangents in the range 0.01-0.05.They can be machined by sawing, turning or grinding and arethermally stable up to 150° C. At temperatures between220°—240° C, the materials can be formed to curved shapes,and, since they offer additional parameters which can beoptimised in a specific design, the artificial dielectric materials

Table 1: Details of sample laminates (RP12) at 9.45 GHz using two theoretical models employing linear and logarithmic mixture characteristics

Sample F5P12Terylene

RP12quartz

RP12Kevlar 49

RP12E-glass

RP12D-glass

Polyester/Kevlar 49

Polyester/E-glass

Density, gm/cm% fabric by weight% fabric by volumeCalculated e linearCalculated e logMeasured eMeasured tan 6Fabric eFabric density, gm/cm3

1.1951.946.82.762.752.800.0033.01.38

1.4957.939.33.002.952.980.0023.72.20

1.2252.744.5

. 3.203.123.240.0054.01.44

1.7566.045.04.163.784.190.0056.132.55

1.5668.35i:93.303.223.290.004

1.4259.342.23.163.083.120.004

4.02.16

1.2650.944.73.243.183.280.014.01.44

1.8465.247.14.354.034.430.016.132.55

IEEPROC, Vol. 128, Pt. F, No. 7, DECEMBER 1981 455

can provide a means of reducing aberrations through theradome.

The electrical properties of conical or ogive airborneA-sandwich radomes may be controlled by either introducingcorrecting wire grids or a controlled dielectric anisotropy intothe radome core. The transmission performance of these wallconstructions have been previously considered. In Fig. 10 [9],the effect is demonstrated of one such loaded core scheme onthe radiation pattern of a low gain antenna. The radome,designed for a much higher frequency, is wire loaded. Fig.10A shows the undisturbed radiation pattern with Figs. 10Band C demonstrating the degradations experienced in both theunloaded and loaded situation. The advantages of such adesign technique for dual-band operation is obvious.

OdB

90 60 30 0degrees

30 60 90

Fig. 10A Radiation pattern of monopulse antenna

OdB.

90 60 30 0 30antenna scan angle, deg

60 90

Fig. 10B Radiation pattern of antenna in presence of unmatchedradome

OdB

90 60 30 0 30antenna scan angle,deg

60 90

Fig. 10C Radiation pattern of antenna in presence of wire matchedradome

4.3 Missile radome materialsThe extreme thermal conditions arising from the high acceler-ations and terminal velocities of missile radomes has led tothe widescale use of relatively costly and difficult to fabricateinorganic materials, such as alumina, silica, and proprietarymaterials, such as Pyroceram 9606. However, with the recentadvent of noncharring ablative coatings, lighter weight andcheaper plastic radomes are receiving considerable attention atthe research and development level [23—27].

With current missile radomes, various forms of loadedalumina are used for velocities up to Mach 2. Patridge andWard [28] have provided a useful review of the glass ceramicmaterials commonly used for missile radomes. Those suitablefor supersonic velocities include Pyroceram 9606 [29, 30],slip-cast fused silica (SCFS) [31,32] and reaction-sinteredand hot-pressed silicon nitride [33,34], Table 2 [35] showstypical mechanical and electrical properties of these materials.

Pyroceram 9606, a magnesium-aluminium silicate com-pound has excellent thermal shock and rain erosion propertiesfor moderately high velocities, but, with the demand forweapon velocities approaching Mach 5, a material with betterenvironmental performance is required. In response to thisdemand, Corning has recently developed two new compo-sitions which are predominantly cordierite but contain differ-ent amounts of secondary phase such as cristobolite andmagnesium titanate. Hallse et al. [29] have shown that onesuch material called Pyroceram 9603 offers improved thermalperformance with only a marginal increase in electrical loss.

The simple manufacturing process of slip-cast fused silica[31] together with its good thermal shock resistance renderit an attractive material for this application. Its poor rainerosion performance, however, necessitates the inclusion ofa rain erosion tip, usually made of metal. This inclusionobviously has an effect on the boresight error performanceof the radome similar to that already discussed for a nosespike obscuration.

Silicon nitride, also a strong candidate for high-temperatureapplications, is manufactured by hot pressing or reaction

. sintering. It is a very good material from both a mechanicaland thermally stable point of view, but its very high pro-duction costs may prohibit its widespread application. Plastic-radomes must be protected from aerothermal and rain erosioneffects by the use of ablation and rain erosion layers. Fibrereinforced fluorocarbons such as Duroid 5870 [28],reinforced tetrafluorethylene (Teflon) Avcoat 8027—29, a castepoxy polyurethene, a fluoroelastomer and a particle loadedTeflon, are typical examples of ablative materials. In general,fibre reinforced Teflon offers both good thermal and rainerosion protection at elevated velocities, whereas the particlereinforced Avcoat offers less protection.

Both ceramic and ablative plastic radomes will exhibitsome variations in their electrical performance during flight.For ceramics, the temperature dependence of permittivityand loss tangent, together with the thermal expansion of thewall material [36,37], can have significant effects on theboresight error profile. Fig. 11A shows the variation of tem-perature, permittivity with loss angle 8 with normaliseddisplacement yjt through the wall of a Pyroceram 9606 VonKarmann radome halfway through its flight, at its axial mid-point. Fig. 1 IB demonstrates that large axial temperaturegradients exist over the missile surface, where axial station isthe axial displacement in inches of an observation pointfrom the radome tip.

For ablatively coated radomes, surface recession will alsohave an effect on their electrical performance. Crowe [26]has demonstrated these effects for an Avcoat 8029 ablatersupported on an epoxy/glass substrate. This showed that theboresight error performance was retained over typical flight

456 IEEPROC, Vol. 128, Pt. F, No. 7, DECEMBER 1981

Table 2: Radome material properties

Material Elasticmodulus(106 psi)RT 1500°F

Expansioncoefficient(10-6/°F)RT 1500°F

Thermalconductivity(Btu/fth°F)RT 1500°F

Dielectricconstant

RT 1500° F

Losstangent

RT 1500°F

Maximumusetemperature(°R)

Bendingstrength

(psi)

HPSNp = 3.2g/cm3

RSSNp = 2.4g/cm3

SCFSp = 1.926g/cm3

Pyroceram 9606p = 2.6g/cm3

43.5

15.0

8

16.5

43.5

15.0

10

16.8

1.77

1.1

0.45

2.5

1.77

2.05

0.175

3.0

12.1

5.4

0.31

2.2

9.0

4.05

0.40

1.74

7.59

5.56

3.4

5.515

8.55

6.1

3.5

5.805

0.00275

0.005(?)

0.0014

0.0003

0.0065

0.005(?)

0.002

0.01

3870

3870

3600

2930

58000

20000

4000

22 500

recession cycles, whereas transmission loss increased signifi-cantly after only 10 mils of recession probably due to a buildup of char residue on the surface.

0.7n

c 0.65-

0.6J

" 5.7-,

S 5.6^

••fi 5.5-J

elevated temperature e |

room temperature e4.646 (fortified layer)

4.646

5700 0.2 0.4 0.6

y/t0.8 1.0

Fig. 11A Temperature, dielectric constant and loss tangent variationthrough radome wall

600

D

ot, 500a.E

400

Fig. 11B

5 10 15 20 25axial station # in

External surface temperature against axial station

4.4 Rain erosionThe provision of adequate protection from rain erosionrepresents a major challenge in the design of high-performance

;radomes. Rain erosion is defined as the damage sustained byaircraft materials or components in collision with precipitationand has been observed in aviation for over 30 years. It remainsa key factor for radomes on vehicles whose operational speedcan exceed 250 mile/h (112m/s) in rain. Radomes are requiredto last for at least 500 flying hours in mixed weather, and it isunfortunate that materials which can best meet these require-ments tend to have poor electrical characteristics. Rain erosionis particularly marked for small radome covers, which maypresent a relatively blunt face to the direction of motion, andconsiderable difficulties have been encountered in the designof such covers for modern high-speed aircraft [38].

For example, for frequencies in the 2—18GHz band it ispossible to design either a glass-fibre reinforced plastic (GFRP)sandwich which is electrically satisfactory but which fails athigh speed in heavy rain, or an erosion-resistant mouldedthermoplastic radome with high insertion loss. The combi-

nation of low losses and erosion resistance over broad band-widths is difficult to realise. The angle of impact of the drop-lets is a key parameter. Broadside impact represents the worstcase, and damage falls off rapidly with increasing incidenceangle. Blunt forward-facing radomes are thus a much greaterproblem in this respect than the tapered nose-cone type. Suchradomes mounted in forward-facing locations on tail fins areparticularly vulnerable.

Resistance to rain erosion damage depends on a multiplicityof factors, such as type of material, surface finish, shape andspeed [38—41]. Inorganic ceramic materials, often employedin missile radomes, generally have good erosion resistance,although at high Mach numbers one candidate, slip-cast fusedsilica (SCFS) [42], may prove to be inadequate, requiringthe inclusion of a metallic rain erosion tip or in some casesan electrically more suitable silicon nitride tip.

Rain erosion has an effect both on the aerothermal andelectrical properties of the radome [43]. For an SCFS radomewith a silicon nitride tip, little reduction in transmitted poweris detected, whereas quite significant increases in boresighterror result. Fig. 12 illustrates increases in the error in the

increase in boresight error, mrad

a b

Fig. 12 Increase in boresight error due to erosion against scan angle

a In E planeb In H plane

180

150

| 120

0.

| 90a

° 60

I JO

polyurethane

velocity-500 miles / h , simulatedrainfall 1 in / h, substrate-glass -epoxy laminate

neoprene

0 5 10 15 20 30 35cooting thickness , mils

Fig. 13 Comparison of rain erosion performance of polyurethane andneoprene using rotating-arm apparatus

IEEPROC, Vol. 128, Pt. F, No. 7, DECEMBER 1981 457

principal planes of the antenna radiation pattern. Theboresight error was measured both before and after exposureof the radome to a Mach 1 rain field. Surface erosion of theSCFS varied from 0.2 to 0.1 mm with no erosion of the tip.In general, the rain erosion resistance of reinforced plasticmaterials is poor, necessitating the addition of an elastomericcoat to afford the requisite protection. A 0.25 mm coatingof thick neoprene rubber applied to a GFRP radome cansignificantly extend its eiosiion life. More effective protectionis given by fluoroelastomers [44] and polyurethane [45]coating, with Fig. 13 showing the improved performance ofthe latter over neoprene at subsonic velocities.

The most widely used coating, material is polyurethane,which must be applied in numerous thin coatings, each ofwhich must be allowed to cure before the next is applied.The number of coats provided is a compromise betweenimproved protection and the degradation of the dielectricproperties of the radome. The application process is timeconsuming and expensive. In-service repair of damage isvirtually impossible and complete stripping of the coat isusually necessary prior to recoating. It is sometimes alsorequired that the coatings be slightly conductive to avoid thebuild up of static electrical charge, or that they be white toresist flash effects, these requirements being difficult toreconcile with each other.

Sandwich structures are particularly prone to rain erosionbecause of delamination effects. The problem occurs, fordifferent reasons, with both foam and honeycomb cores.Since the problem occurs beneath the surface, the use ofcoating will offer only partial protection.

5 Radome obscurations

The electromagnetic design of an airborne radome is con-strained by the availability of suitable dielectric materials andthe other conditions imposed by the airborne environment.In addition, the electromagnetic performance which can berealised can be seriously limited by aberrations arising frommetallic or dielectric obscurations within, or exterior to, theradome. On missile radomes, the obscuration may arise froma rain erosion tip or a metallic nose spike, but the problem is

radome wall

nose spike internalearthing

Si conductors

to airflame

Fig. 14A Internally earthed nose spike

stud wall

to airframe

earthingconductor

even more severe with large aircraft radomes where the pitotboom, pitot tubes and lightning protection schemes canseriously degrade the radome performance.

The possibility of relocating the pitot boom is an obviousone, and this solution has been adopted in some US aircraftdesigns. The lightning protection strips represent a less trac-table problem. The need for such protection is obvious in thatlightning can strike through the radome and attach itself tothe metallic components within. If the radome wall is punc-tured in the process, then this will cause serious damage,resulting at best in the loss of the sensor functions and atworst in the loss of the aircraft. Since the presence of a light-ning protection scheme appears unavoidable, and its impactupon the radome electromagnetic performance can be signifi-cant, it will be constructive to summarise some of the schemescommonly employed.

A number of protection schemes have been reported inthe literature [41-49] and these can be classified into twogroups according to whether the earthing system adopted isinternal or external to the radome. Fig. 14A shows an intern-ally connected nose-spike connected to the airframe byheavy duty conductors, orientated to minimise radar degra-dation. As a protection scheme, this type of system has noserious defects except where the lightning strikes the internalconductors directly. The internally earthed studs shown inFig. 14B are similarly connected to internal conductors and

;operate in the same way. This system offers the advantagethat the distributed attachment points minimise the possibilityof a direct strike to the internal conductors. The major draw-back of this design is the risk of moisture pick-up on theradome wall, which will degrade the electromagnetic trans-mission performance.

Fig. 15A shows an externally earthed 'cage of strips'system. The conductors are either made of foil or are moresubstantial metal strips. The foil system is not adequate

short thick^ or foil conductorshielding the antenna

to airframe

long thick conductorshielding antenna andearthing pitot

Fig. 15A External foil or conducting strips

metallic studs ^ 2.5mm diameter~0.25mm gaps

to airframe

short segmentedstrip

radome

long segmented stripalso to earth pitot (note :only with plastic air pipesand high-resistanceheater wires)

Internally earthed studs Fig. 15B External segmented strip

IEEPROC, Vol. 128, Pt. F, No. 7, DECEMBER 1981

under multistrike conditions, where more substantial conduc-tors are required. Button strip (Fig. 15B) is a similar system,but here the conductor comprises metal discs on a GFRPsubstrate. This system can only be used in short lengths,thus limiting its application. This latter system offers betterradar transparency than the former. The effects of these twoprotection schemes on the sidelobe performance of a typicalantenna are shown in Figs. 16A and 16B. The effects areclearly not insignificant.

-20

CO

•5" - 3 0

1(D

a-40

>0 -45

.|j . . , $ iJ/LA' '"J*"1 '' • ''''^''ii'l fll 1

'! /

liI :i1

\/l 1I/1 '

A

11|

90 angle, deg

co - 4 0•D

fc-50

a .a>

180 angle, deg 90

Fig. 16 Effect of lightning protection schemes on sidelobe per-formance

a Spiral coilb Cage of strips

clean radomemodifications due to lightning protection

Electromagnetic analysis of obscurations such as the pitotboom and lightning protection schemes have not been dealtwith extensively in the literature. In cases where the body islarge compared with wavelength, it may be considered as aform of aperture blockage and its effect computed by rep-resentation as an equivalent source of the same magnitudebut opposite in phase to the incident radiation. For bodieswith all dimensions much less than a wavelength, the obscur-ations may usually be ignored. The problem arises in thesituation where the body is of the order of a wavelength. Inthese cases [47], a semiempirical method has been usedwhere the modified equivalent source is obtained by measuringthe diffraction pattern of the obstacle.

It has been proposed elsewhere [50] to adopt either aninduced field ratio technique [41] or a finite elementapproach in the solution of these problems, but no detailed•results are as yet available and it is clear that much workremains to be done in this area.

6 Radome analysis techniques

Over the past few decades, simple ray-tracing techniqueshave been the dominant technique in the analysis of randome-enclosed antennas, and these methods are both well estab-lished and well understood. In the transmit formulation,electromagnetic energy is assumed to propagate in a directionnormal to the radiating aperture to the inner surface of the

radome. At each point of incidence, the curved surface isapproximated by an infinite flat slab, the incident radiationresolved into vector components parallel and perpendicularto the plane of incidence and the requisite plane-wave trans-mission coefficients applied. Transformation to the far fieldmay then be effected by either tracing through to a secondaryaperture plane exterior to the radome, where integration ofthe tangential fields over this region yields the far-field pat-tern, or by performing an integration of tangential fieldsover the radome surface.

Early work by Tricoles [52] uses ray tracing to analysean antenna enclosed in an infinitely extended dielectricwedge. Later papers [53, 54] use the technique to predictthe boresight error induced by a more realistic radome shape;an axially symmetric dielectric shell with both E- and //-planeradiation and boresight error characteristics being comparedwith measured results in Figs. 17A, B and C with good agree-ment around the main beam.

Cary [55] and Dowsett [56] applied the technique withparticular reference being given to the depolarisation effectscaused by radomes. Burks et al. [57] have applied the tech-nique in the receive formulation, where a ray-tracing pro-

or

-5

-10

I -15o

U 2 0 - 2angle j*.,deg

Fig. 17A E-plane pattern

x computed without radomemeasured without radome

o computed with radomemeasured with radome

-5

1-10

1 - 1 5

Fig. 17B

94 9? 90 88 86angle 0. ,deg

H-plane pattern

x computed without radomemeasured without radome

o computed with radomemeasured with radome

IEEPROC, Vol. 128, Pt. F, No. 7, DECEMBER 1981 459

cedure is employed to find the incident fields at the antennawith surface integration to obtain the receive voltages.

Many radome shapes, such as ogive and cone, lend them-selves to exact solution of the intersection of the ray trajec-tory with the surface, but others such as Von Karmann andSears Hack do not. Huddleston [58] has recently presenteda generalised ray-tracing method to analyse such geometries.

•DO

i - 2

0

- 1

- 2

-6 -A -2 0 2 4 6gimbal angle , deg

Fig. 17C Radome boresight error for halfwave wall (k = 5.4) withoutprotective layer

Upper curve, for if-plane, is for displacement of the receiving antennain a horizontal plane. This plane is parallel to the direction of the Evector. Lower curve is for //-plane, which is orthogonal to these planes.The curves are measured data. One of the measured curves was obtainedfor the radome in its normal position and the other after turning theradome upside down. Calculated data are shown the the closed dots

The aperture projection or ray-tracing techniques do notaccount for the amplitude and phase variations occurringin the antenna near field. In ray-tracing analysis, the field isassumed to propagate as a single plane wave and remainconfined to the cylinder whose cross-section is defined by theaperture. In reality, a divergence of the field occurs whichcan be calculated using more accurate analysis techniques.The former method is only valid where the surface of theradome lies totally in the paraxial region of the antennafield. This may be a valid approximation for more compli-cated, higher aspect ratio antennas such as slotted waveguidearrays or elliptical aperture reflectors, where points on theradome can be anywhere from the very near to far field ofthe antenna. In these situations, a technique must be appliedthat is valid for all space. The two commonly used methodsfor the prediction of the near field of aperture antennasare aperture field integration [59] and plane-wave spectrumanalysis [60]. Both techniques have been applied extensivelyto the analysis of circularly symmetric antennas, with thelatter technique proving to be computationally more efficientfor these cases.

Paris [61] used the aperture field technique to predictthe radiation pattern of a A\\ and 6X pyramidial hornenclosed in a multilayered airborne radome. The field incidenton the radome surface is assumed to be locally plane, andflat-slab transmission coefficients are applied yielding theexterior tangential field. This field is integrated over thesurface to yield the secondary pattern. Fig. 18 summarisesthe results from this study with E- and //-plane patternsbeing presented for an antenna look angle of 38°. Good corre-

lation is obtained between experiment and theory, both inthe main beam and in the sidelobe region.

Booker and Clemmow [62] demonstrated that any electro-magnetic field may be represented as an angular spectrum ofplane waves and defined the relationship between the apertureand radiation fields. A full exposition of the technique ispresented in Clemmow [63] with Wu and Rudduck [64]applying the technique to the antenna radome problem.They demonstrated its equivalence to, and computationalsurperiority over, aperture field techniques for the analysis ofcircularly symmetric antennas.

0 20 40 60 80 100a 9. deg

-400 20 40 60b 6 , deg

Fig. 18 Measured and calculated patterns for n = 30°

a if-planeb //-plane

measuredx calculated

Employing the plane-wave spectrum approach, the aperturefield of the enclosed antenna can be expressed in Cartesianco-ordinates as

E(x,y,0) = f(x,y)dx + g(x,y)d. 0)where dx,dy>dz are the unit vectors in the x,y and z direc-tions, respectively.

The plane-wave spectrum associated with each componentcan be obtained by taking the Fourier transformation of theaperture field components/and g as

Fx(Kx,Ky) = [J f(x,y)exp {+ j(Kxx + Kyy)}dxdyA

(2)

with a similar expression holding for Fy, and if we define acombined spectrum function F(K) as

F(K) = Fxdx + Fydy + Fzdz

where K, the propagation vector, is defined as

(3)

K = Kxdx + Kydy + Kzdz

then

Fz = -(KxFx+KyFy)/Kz

with expressions for the field at field point r being+ OO + OO

E(r) = J J F(K) exp (-jk • r)dkxdky—oo— oo

and+ 00+00

//(/•) = jj K/\F(K)exv(-jk-r)dkxdky

(4)

(5)

(6)

460 IEEPROC, Vol. 128, Pt. F, No. 7, DECEMBER 1981

The integrands of eqns. 5 and 6 can be recognised as planewaves and the fields at any point as an integration of a spec-trum of plane waves. In extending the formulation to radomeanalysis, each plane wave is resolved into components perpen-dicular and parallel to the plane of incidence of a flat-slabapproximation to the radome surface, and the respective aretransmission coefficients applied. The exterior field is givenby integration over the plane wave spectrum. Surface inte-gration is then used to yield the far field.

For circular symmetric distributions, the analysis is greatlysimplified as eqn. 2 can then be solved explicitly and thenear-field calculation of eqn. 6 reduces to a single integration.

The formulation of the near field for circularly symmetricapertures using this technique is particularly amenable to

solution using stationary phase techniques, as was demon-strated by Chen [65]. Anderson applied similar methods tothe dielectric flat slab [66].

The analysis of realistic two-dimensional aperture antennasby the application of plane-wave-spectrum surface-integration(PWS-SI) techniques can represent a formidable numericalproblem. The scale of the numerical problem may be greatlyreduced by replacing the continuous-spectrum representationof eqn. 5 by a discrete one, together with truncating thesummation within the visible spectrum. Green [67] postulatedthis method, but without full experimental verification. Workperformed at ERA [50] applied the discrete PWS-SI techniqueto an elliptical offset reflector antenna enclosed in a radome.Fig. 19 shows near-field results for x and y polarised field

-6 -A -2 0 2 U 6radial d isplacement r/h

-6 -A -2 0 2 U. radial displacement r

-7

- 8 - - -110°

- 8 -6 -U - 2 0 2 U 6radial displacement r/A - 8

d

-6 -U - 2 0 2 4rad ia l displacement r

--130'

r-2

-1

- 0

-2

- 3 «

A '•" 1

U. - 7 |

--8/

J

/ s/

Ifi

-

1/ V A '

i i i i i i

-

1i ,

8

phase

-

-

-

-

-

-

-

-

0°

-108

-20

-30°

-50*

-60°

-70°

-80°

-90°

-100

-110

Fig. 19 Near-field distribution of offset reflector antenna

a , 0Ex phase

0

a z = 0.0,

b z =

c z =

d z =

>=0°

2X, 0 = 0°Ex phase10 \ , 0=0°Ex phase30 X, 0=0°Ex phase

components over secondary aperture planes at distances 0,2, 10 and 30 X from the primary aperture in the plane ofoffset. The ripples in the pattern at z = 0 are due to truncationof the PWS within the visible spectrum. Fig. 20 shows thecomparison of the theoretically produced near-field result forthe same antenna with an experimental measurement showingexcellent agreement.

IEEPROC, Vol. 128, Pt. F, No. 7, DECEMBER 1981 461

Joy [68] has presented a more computationally efficientPWS analysis utilising an equivalent aperture formulation inconjunction with a fast Fourier transform algorithm. The PWSis first assessed by fast Fourier transformation of the aperture

separation

separation= 30A

azimuth"aperture

Fig. 20 Comparison of near-field calculations and measured patterns(15 XX 45 \ elliptical offset reflector antenna)

Separation z = 30 Xexperiment

• • theory (discrete) PWS

10 20 30scan angle, deg

50

Fig. 21A Boresight error against antenna azimuth scan angle usingthree-dimensional equivalent aperture plane-wave spectra analysis

field, and a grid is set up in the aperture from which eachplane wave of the spectrum is traced to the radome, wherethe appropriate plane-wave transmission coefficients areapplied. The radome is then removed and the weighted planewaves are traced back to the primary aperture, where theircontributions are added and a fast Fourier transform of theequivalent aperture distribution gives the radiation patternof the antenna radome. Fig. 21A shows the results obtainedusing this technique, where curves A, B and C demonstratethe slightly different results obtained by using, respectively,a flat-slab approximation, first ignoring and then includingthe ray displacement in passing through the dielectric, withcurve C representing the full representation of the curvedradome surface. Finally, Fig. 2IB demonstrates that compar-able results are obtained using a two-dimensional momentsmethod formulation for a radome-enclosed slot array.

7 Conclusions

The rapid growth of electromagnetic radiating and receivingsystems for airborne applications, in what is clearly a limitedfrequency spectrum, has resulted in a general requirement forincreased performance from a wide range of electromagneticsensors. The need for improved performance can be observedin both civil and military spheres, particularly in the areas ofcompatibility, avoidance of interference and jamming, radartracking accuracy and all aspects of electronic warfare.Antenna specifications calling for lower sidelobe radiation,reduced boresight errors, dual polarisations, wider andmultiple-frequency bandwidths, and generally more adaptableand flexible modes of operation are becoming commonplace.

For airborne systems, almost all the electromagneticsystems will be located behind radomes, and the need forimproved overall performance will require significant improve-ments in their electromagnetic properties. The paralleladvances being made in aircraft and missile performance onlyserve to compound the radome design problem, since higherspeeds will increase the thermal and structural stresses imposedon the radome and will give added emphasis to the alreadydominant aerodynamic requirements.

At the current state of the art in radome design, bothmaterials technology and electromagnetic design techniquesare being severely stretched by the levels of performancedemanded. Significant advances will be necessary in bothspheres if the radome is to avoid becoming the principallimiting factor in future airborne electronics systems.

8 Acknowledgments

The authors would like to thank J. Summers of the RoyalSignals & Radar Establishment and British AerospaceReinforced and Microwave Plastics Group for their help inthe preparation of this paper, and S. Gupta of ERA Tech-nology Ltd. for his technical input.

-1.520 30

scan angle , deg50

Fig. 21B Boresight error against antenna scan angle using two-dimensional method of moments analysis

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58 HUDDLESTON, G.K., and BALIUS, A.N.: 'A generalized raytracing method for single valued radome surfaces of revolution'.

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59 PARIS, D.T.: 'Digital computer analysis of aperture antennas',IEEE Trans., 1968, AP-16, pp. 262-264

60 RUDDUCK, R.C., WU, D.C.F., and INTIHAR, M.R.: 'Near fieldanalysis by plane wave spectrum approach' ibid., 1973, AP-21,pp. 231-234

61 PARIS, D.T.: 'Computer aided radome analysis', ibid., 1980,AP-28,pp. 7-15

62 BOOKER, H.G., and CLEMMOW, P.C.: The concept of an angularspectrum of plane waves', Proc. IEE, 1980, 97, pp. 11—17

63 CLEMMOW, P.C.: 'The plane wave spectrum representation ofelectromagnetic fields' (Pergammon Press, 1960)

64 WU, D.C.F., and RUDDUCK, R.C.: 'Applications of plane wave

spectrum representation to radome analysis', IEEE Trans., 1974,AP-22, pp. 497-500

65 CHEN, C.L.J.: 'The near field analysis of aperture and spiralantennas by the plane wave spectrum method'. Ph.D. thesis, OhioState, University, 1974

66 ANDERSON, I.: 'Basic studies of radome problems'. Ph.D. thesis,London University, 1969

67 GREEN, P.B.: 'Application of near field techniques to radome.analysis'. Proceedings of international symposium on antennasand propagation, Washington DC, 1978, pp. 61-64

68 JOY, E.B., WILSON, R.E., BALL, D.E., and JAMES, S.D.: 'Com-parison of radome electrical analysis techniques'. Proceedings of15th symposium on electromagnetic windows, Georgia Instituteof Technology, 1980, pp. 25-29

464 IEE PROC, Vol. 128, Pt. F, No. 7, DECEMBER 1981