Phase Array Scan Theory

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 58, NO. 2, FEBRUARY 2010 1

A Novel Geometrical Technique for DeterminingOptimal Array Antenna Lattice Configuration

Srinivasa Rao Zinka, Il-Bong Jeong, Jong-Hoon Chun, Jeong-Phill Kim, Member, IEEE,

AbstractWe present a new 2D geometrical technique fordetermining optimal element arrangement for planar, phasedarray antennas with specified scan limits. This geometricaltechnique is not limited to conical or pyramidal scanning, butcan be extended to any scan type that can be represented withan analytical equation. In addition, simple equations are givenfor two very important scanning types, conical and pyramidal.These equations provide deeper understanding and simplergraphical solutions than other pure graphical techniques. Thispaper discusses optimal array arrangement from the viewpointof general lattice, which itself includes a hexagonal lattice as itssubset. An important practical system, where this technique wasfound to be useful, is the N -face phased array antenna providingscanning throughout a hemisphere. Simple equations are givenfor determining the maximum off-axis scan and tilt angles of eachface with respect to the zenith. Finally, the lattice arrangementof each face is decided by the new design technique.

Index TermsPhased arrays, grating lobes, conical scan,pyramidal scan, n-face array, hemispherical coverage

I. INTRODUCTION

ACOMPREHENSIVE analysis of grating lobe appearancein planar, phased array antennas with different possiblescanning specifications is presented. Although the conceptof grating lobes and optimal planar array arrangement iswell understood graphically [1][5], a complete analyticaltechnique has not yet been performed. The basic conceptbehind the geometrical design technique presented in thispaper is that almost all types of scan specifications can bemapped onto kxky domain as a single ellipse or a combinationof multiple ellipses. In addition, the technique discussed in thispaper is generalized to include all types of planar array latticesand provides simple expressions for instructive graphical plots.

One main application of this new design technique is deter-mining the optimal lattice configurations for N -face phasedarrays to cover an entire hemisphere. A brief comparisonbetween two different hemispherical sectorizations is givenin section IV. Although there are many parameters to betaken into consideration, the maximum off-axis scan angle(max) is usually chosen as the main criterion for decidingthe number of faces (N) and tilt angle (T ). After decidingN and T , the scan sectors are transformed from the earthscoordinates (x, y, z) to the array coordinates (x, y, z). Then,

Manuscript received March 19, 2009; revised May 27, 2009. The workreported in this paper was sponsored by Samsung Thales Co., Ltd., Kangnam-gu, Seoul, under Contract STC-C-07-032.

S. R. Zinka, I. B. Jeong, and J. P. Kim are with school of Electrical andElectronic Engineering, Chung-Ang University, Seoul 156-756, Korea. E-mail:[email protected], [email protected]

J. H. Chun is with Research and Development Center, Samsung Thales,Korea. E-mail: [email protected]

(a)

(b)Fig. 1. (a) A general array lattice and (b) corresponding grating lobe locationsin sine space.

the presented geometrical technique can be used to analyze thesine space of each individual array face.

II. BASIC THEORYIt can be shown [6] that for a general two-dimensional

lattice structure described in Fig. 1(a), grating lobes occur inthe kxky domain (sine space) at

(kxg)p = kx0 +2ppi

a

(kyg)p,q = ky0 +2qpi

b[

(kxg)p kx0tan

](1)


where p, q = 0,1,2, .Since by definition, kx = k0 sin cos and ky =

k0 sin sin, radiating far fields are confined to the circulardisk

(k2x + k

2y

)1/2 k0, often known as visible space. Theremaining kxky space, described as invisible space, is relatedto the stored energy in the near field, which is analogous tothe phenomenon of evanescent modes in a waveguide. Usually,an antenna engineer intends to avoid the appearance of all thegrating lobes (except for the p = q = 0, main lobe case)within the visible space.

Fig. 1(b) shows the visible space and the grating lobe spacesplaced according to (1) in the kxky domain. Assuming thatV 1 represents the domain of the specified main lobe scanpositions, the closed loops G1 G6 represent contours ofall the possible nearest grating lobe scan positions. From Fig.1(b), it can be observed that all the grating lobe contours arejust touching the visible space circle, except for G2 and G5.Thus, for the given scan specification V 1, the array latticearrangement shown in Fig. 1(a) is not optimal. In this paper,optimal array arrangement is defined as the configuration thatmaximizes the arrays unit cell area (ab). In other words,an optimal configuration minimizes the number of elementsneeded in a given array aperture. To achieve this optimal arraylattice configuration, Fig. 1(b) should be modified accordingto the following description.

1) All the left-hand side grating lobe contours should bemoved upward and the right-hand side contours down-ward.

2) After an optimal skew with respect to the ky axis, bothleft-hand side and right-hand side grating lobe contoursshould be moved horizontally toward each other, so thatall would just touch the visible space circle.

3) If V 1 is symmetric with respect to both the kx andthe ky axes, then the contours G2, G3, G5 and G6will be at the same distance from the kx axis forthe optimal array lattice configuration. This optimalarray element arrangement is a hexagonal array lattice( = tan1

(2ba

)).

However, it should be mentioned that a hexagonal lattice maybe the optimal lattice even if V 1 is asymmetric with respect tothe kx or ky axes. To substantiate this statement, one exampleof trapezoidal scanning is provided in section IV.

From the above discussion, it is clear that to analyze thekxky domain for grating lobe appearance, V 1 should beevaluated for a given set of scan specifications. In [3][5],V 1 is obtained using pure graphical techniques. Althoughpure graphical techniques are simple and straightforward,they do not provide much information about the scanningprocedure. Thus, in this paper a new geometrical technique ispresented, which provides in-depth understanding and a mucheasier graphical solution. To explain this technique, two veryimportant and general scan options are considered in the nextsection.

III. MAPPING OF GENERAL SCAN SPECIFICATIONS ONTOTHE (kx, ky) DOMAIN

Two of the most important scan types are the conicaland pyramidal scans. A complete analysis of these two scan

(a)

(b)Fig. 2. Conical scanning: (a) geometry of the elliptical conical sector and(b) mapped scan region in sine space.

options is presented in this section. The conical sector to bescanned is assumed to be an elliptical cone. Even though anelliptical conical scan does not have much practical signifi-cance, the theory is nevertheless the same as for the circularconical scan. The second scan option, the pyramidal scan, isdescribed as scanning a polyhedral sector that has a polygon asits base and triangles with a common vertex (origin) for faces.Any practical scan specification can be expressed as either aconical or a pyramidal scan or as a combination of the two.

A. Conical ScanningFig. 2(a) shows an elliptical conical scan region with scan

limits 2x and 2y in the x and y directions, respectively.It is further assumed that the conical region is symmetricwith respect to the z axis. Without loss of generality, a plane(z = 1) with an elliptical boundary and perpendicular to z axiscan be mapped onto the kxky plane. Any point P , lying onthe boundary of this elliptical surface as shown in Fig. 2(a),is given by

(x, y, z)P = (r cos, r sin, 1) (2)where

r =TxTy

T 2y cos2 + T 2x sin

2

Tx = tan (x)


Fig. 3. Sine space corresponding to circular conical scan

Ty = tan (y) (3)

It is shown in Appendix A that mapping of this ellipticalcontour onto the kxky plane is given by(

kxk0 sin x

)2+

(ky

k0 sin y

)2= 1 (4)

The mapped region in the kxky plane, V 1, given by (4), isshown in Fig. 2(b). The elliptical boundary of this regionmakes it difficult to obtain an analytical solution for theoptimal array configuration.

As mentioned before, elliptical scanning is rarely needed,unlike circular conical scanning. For circular conical scanning,x = y = max and (4) represents a circle:

k2x + k2y = k

20 sin

2(max) (5)

An analytical solution for circular conical scanning can bederived from Fig. 3. Centers of the grating lobe contours G1G3 are at distances d1d3, respectively, from the origin, whered1d3 are given as

d1 =

(2pi

b

)

d2 = 2pi

(1

b2+

1

a2 sin2 2ab tan

)1/2

d3 =

(2pi

a sin

)(6)

(a)

(b)Fig. 4. Rectangular pyramidal scanning: (a) geometry of the rectangularpyramidal sector and (b) mapped scan region in sine space.

From (6), for a given general lattice configuration, the maxi-mum off-axis scan angle, max, is given by

max = sin1

[min (d1, d2, d3) k0

k0

](7)

Thus, given the input parameters [a, b, ], max can be evalu-ated from (7).

B. Pyramidal ScanningConical scanning, described in the previous subsection, is

simple and gives an analytical solution for the optimal arrayconfiguration. However, in many practical applications thescan region is not conical, but pyramidal. To take advantageof the irregular shape of the pyramidal scan region, a newmapping technique is necessary. In this subsection, first the

(x, y, z)P =

(Tx, Tx tan, 1) , if 0 tan1(TyTx

)(Ty cot, Ty, 1) , if tan1

(TyTx

) 90

(8)

(kxky)pyramidal scan :

(

kxk0 sin x

)2+(kyk0

)2= 1, if 0 tan1

(TyTx

)(kxk0

)2+(

kyk0 sin y

)2= 1, if tan1

(TyTx

) 90

(9)


(a) Grating lobe regions in sine space (b) A more detailed representation of sine space

Fig. 5. Rectangular pyramidal scanning

(a) Geometry of the triangular pyramidal sector (b) Mapped scan region in sine space

Fig. 6. Triangular pyramidal scanning

rectangular pyramidal scanning procedure is described, afterwhich the results obtained for the rectangular pyramidal scanare extended for a more general pyramidal scan with apolygonal base.

Fig. 4(a) shows a rectangular pyramidal scan region, whichis symmetric with respect to the z axis and with scan limits2x and 2y in x and y directions, respectively. Again withoutloss of generality, a rectangular surface at (z = 1) and perpen-dicular to the z axis is mapped onto the kxky plane. Only theregion corresponding to 0 90 is mapped and theremaining map can be constructed from the symmetry. Anypoint P lying on the boundary of the rectangular surface canbe represented by (8), where Tx, Ty have the same meaningas defined by (3). Following a similar procedure given inAppendix A, mapping of the rectangular pyramidal sector ontothe kxky domain is given by (9). It is interesting to note thatthe corresponding contour represents an intersection of twomutually orthogonal ellipses centered at the origin, as shownin Fig. 4(b). A complete description of rectangular pyramidalscanning with the closest grating lobe regions G1 G6 isshown in Fig. 5(a). Because of the symmetry of the gratinglobe lattice, it is sufficient to analyze G1 G3, as shown

in Fig. 5(b). It can be observed that the optimal value of thearray lattice parameter b, bopt, is solely decided by the ellipseE1.

bopt =2pi

k0 [1 + sin (y)](10)

The other array lattice parameter, a, is controlled by twoellipses (E2 and E3) and two critical points (CP2 and CP3).In addition, the primary scanning region, V 1, is symmetricwith respect to both the kx and the ky axes. Thus, the optimalarray lattice for rectangular scanning is a hexagonal lattice.

With the conceptual insight provided by the rectangularpyramidal scanning procedure, it is intuitive that the samebasic concept can be applied to any general pyramidal scan-ning. One simple example is shown in Fig. 6(a). The regionto be scanned is a pyramidal sector with a triangular basecoinciding with the plane (z = 1). The lines joining the originto the closest point on each side of the base are at the angles1, 2 and 3 with respect to the z axis. In addition, the linesjoining the shifted origin (A) to these closest points are atangles 1, 2 and 3 with respect to the x axis. For bettervisualization, only information related to face 3 is shown inFig. 6. From (9), it is clear that the mapping of the x or y


(a) Three-face array with only side-faces (b) Three equal far-field triangular pyramidal sectors

Fig. 7. Three-face array for hemishpere scan coverage

(a) Knittels sectorization (b) Kmetzo-Coreys sectorization

Fig. 8. Comparison between different types of sectorizations

contour onto the kxky domain is an ellipse. If a x contouris rotated along the z axis, its corresponding mapping alsorotates by the same angle in kxky domain. This phenomenoncan be explained by the basic idea behind mapping. Mappingof a region from the (x, y, z) domain onto the kxky domainis equivalent to projection of the corresponding contour onthe sphere x2 + y2 + z2 = k02 onto the (x, y) plane [1].Such projection does not change its shape, but just rotateswith the corresponding rotation of the x contour. Thus, asshown in Fig. 6(b), mapping of the triangular pyramidal sectoris nothing more than a combination of three ellipses, witheach ellipse rotated by a proper angle from the kx axis. Thisgeneral technique can be used to map any arbitrary pyramidalregion with a polygonal base onto the kxky domain. Theapplication of this technique for covering a hemisphericalregion is demonstrated in the next section.

IV. APPLICATION OF SCANNING THEORY FOR COVERINGA HEMISPHERE

One of the main applications of phased array antennas ishemispherical scan coverage. Phased arrays providing beamscanning throughout a hemisphere require three or more faces,as shown in Fig. 7. Many criteria, such as the scan reflectioncoefficient and the realized gain at maximum scan angle,should be taken into consideration before choosing the number

of faces. In this paper, no effort was made to determine thenumber of faces. Instead, the authors only attempt to explainthe new mapping technique for a given number of array faces.

It should be noted here that a hemisphere can be dividedin several ways. Three simple sectorizations are shown inFigs 7(b) and 8. A 3-face array and its far-field triangularpyramidal sectors are shown in Fig. 7. It is possible to reducethe maximum off-axis scan angle by increasing the numberof radiating side faces. Fig. 8 shows two sectorizations,each having a sector perpendicular to the zenith. These twosectorizations are exactly the same from the viewpoint of themaximum off-axis requirement (max) and the tilt angle ofeach face with respect to the zenith (T ). The main differenceis the path joining points P and R. Actually, there is an infinitenumber of possible paths joining these two points, but the moreobvious ones are PQR and PSR. A plane going through pathPQR would intersect the z axis at the origin, whereas a planegoing through path PSR would be parallel to the (x, y) planeand intersect the z axis at point W , as shown in Fig. 9. Thesesectorizations are named after their respective authors [2][4].The sectorization shown in Fig. 8(a) is optimal, and preferable,for the following reasons.

1) In the KmetzoCorey sectorization, the top face has toscan more regions, thus decreasing its correspondingunit cell area.


(a) Knittels sectorization (b) Kmetzo-Coreys sectorization

Fig. 9. A more detailed representation of the two sectorizations

(a) Geometry of the trapezoidal pyramidal sector (b) Mapped scan region in sine space

Fig. 10. Trapezoidal pyramidal scanning with respect to array coordinates

2) Knittels sectorization is much simpler with respect toeach set of the individual array coordinates.

Thus, to explain the theory proposed in this paper, Knit-tels sectorization was adapted. Before proceeding, simpleequations for evaluating T and max are given in the nextsubsection.

A. Tilt Angle and Maximum Off-axis Scan RequirementFor an N -face array with no face perpendicular to the

zenith (i.e., N triangular pyramidal sectors), the tilt angle andmaximum off-axis scan requirements are given by

(T )tr = (max)tr = tan1 (sec ()tr) (11)

where ()tr =(piN

).

Similarly, T and max for an N -face array with one facebeing perpendicular to the zenith (i.e., (N 1) trapezoidalpyramidal sectors and one regular polygonal pyramidal sector)are given by

(T )tp = cos1

1

1 cos2 ()tp sin2 ()tp

sin2 ()tp

(max)tp = cos1(sin (T )tp cos ()tp

)(12)

where ()tp =(

piN1

).

Expressions given by (12) can be derived either by coor-dinate transformations [4] or by simply using the followingconditions.

MR = MR

MR = 2 radius sin(

(max)tp2

)(13)

where points M,R and R are depicted in Fig. 9(a). Inaddition, without loss of generality, the radius of the far-fieldsphere can be assumed as 1.

B. Scan Specifications with respect to Array CoordinatesOnce T and max are determined, scan specifications with

respect to the earth coordinate system should be transformedto an array coordinate system. An equivalent (but not exactlysame) representation of a trapezoidal pyramidal scan (Fig.9(a)) is shown in Fig. 10(a). Scan specifications with respectto the array coordinate system are derived in Appendix B andthey are given by

(2)tp = tan1

tan (T )tp

(m)2tp + 1

(2)tp = tan1

(1

(m)tp

)(14)


Fig. 11. 2D top view of (z = 1)-plane (Fig. 10(a))

where

(m)tp =

tan (T )tp tan

((T )tp

2

)

tan2 (max)tp tan2(

(T )tp2

) (15)

Only scan specifications corresponding to contour RR aregiven in (14). Remaining parameters can be evaluated intu-itively from Fig. 10(a). Mapping of this trapezoidal pyramidalsector onto the kxky space is done using the theory describedin the previous section and shown in Fig. 10(b).

Following a similar procedure, scan specifications corre-sponding to a triangular pyramidal scan (Fig. 7(b)) are givenby

(2)tr = tan1

tan (max)tr

(m)2tr + 1

(2)tr = tan1

( 1(m)tr

)(16)

where

(m)tr = tan (max)tr + cot (max)tr

tan2 (max)tr cot2 (max)tr

(17)

C. ExampleTo demonstrate the new geometrical design technique, a

5-face array was considered. The sectorization for a 5-facearray is shown in Fig. 9(a). The tilt angle of each side facewith respect to the zenith (T ) and the maximum off-axisscan angle (max) were determined from (12). Their valueswere 74.46 and 47.06, respectively. From Fig. 9(a), it isevident that the array lattice configuration of the side face isdifferent to that of the top face. Thus, mapping of each faceis done separately as shown in Fig. 11. In addition, in Table I,these results were compared with the results obtained from thecircular conical scan assumption (i.e., the irregular shape of thescan region is not taken advantage of). By taking the irregularshape of the scan region into consideration, unit cell areasobtained for the top and side faces were, respectively, 10%and 8% larger than for the circular conical scan. Even thoughV 1 is asymmetric with respect to the kx axis for the side face,

(a)

(b)Fig. 12. Hemisphere scan coverage by 5-face array: (a) sine space corre-sponding to the side faces and (b) sine space corresponding to the top face.

TABLE ILATTICE CONFIGURATIONS OBTAINED BY DIFFERENT SCAN SECTOR

ASSUMPTIONS

scan sector a b top-face rectangular pyramid 0.677 0.623 61.48

side-faces trapezoidal pyramid 0.667 0.623 61.84all faces circular cone 0.667 0.577 59.97

from Fig. 11(a) it is clear that the optimal array configuration isa hexagonal lattice. Similar analysis can be performed for anyarbitrary multiface array with specified conical or pyramidalscan sectors.

V. CONCLUSIONA 2D geometrical technique has been developed for de-

termining the optimal array configuration of planar-phasedarray antennas. The basic theory for mapping different typesof scan regions onto sine space has been presented. Todemonstrate the proposed technique, a multiface array antennafor hemispherical coverage was considered. Simple equationswere given to evaluate T and max of each array face.In addition, the theoretical analysis for transforming scan


specifications from earth coordinates to array coordinates hasbeen presented. Finally, the technique presented in this paperwas applied to analyze a 5-face array antenna for the optimalarray geometries. The geometrical technique presented in thispaper provides deeper understanding and simpler graphicalsolutions than other pure graphical techniques. In addition, thisgeometrical technique is not limited to conical or pyramidalscanning, but can be extended to any scan type that can berepresented with an analytical equation.

APPENDIX AMAPPING OF CONICAL SCAN REGION ONTO SINE SPACEThe locus of any point P on the contour of the elliptical scan

region as shown in Fig. 2(a) is given by (2). This expressionwas obtained using the following polar representation ofellipse. If an ellipse is expressed as(x

a

)2+(yb

)2= 1 (18)

then its polar form can be written as

(r, ) =

[(ab

b2 cos2 + a2 sin2

),

](19)

From (2) or by simply observing Fig. 2(a), it is evident that () = tan1 [r ()]

= tan1

TxTy

T 2y cos2 + T 2x sin

2

(20)

and from the fundamental definition of sine space

k2x + k2y = k

20 sin

2

(ky/kx) = tan (21)Substituting (20) into expressions given by (21) results in(

kxk0 sin x

)2+

(ky

k0 sin y

)2= 1 (22)

A similar procedure can be used to derive mapping equa-tions for a pyramidal scan region given by (9).

APPENDIX BSCAN SPECIFICATIONS WITH RESPECT TO ARRAY

COORDINATESA 2D top view of Fig. 10(a) is shown in Fig. 11. Applying

simple geometry, line RR can be written as

y = mx + tan(T ) (23)Similarly, a line going through the origin and perpendicular toRR (MB) is given by

y =1mx (24)

where

m = tan T tan ( T2 )

tan2 max tan2(T2

) (25)

The point of intersection of lines RR and MB is at a distanceD from the origin, where D is given by

D =tan Tm2 + 1

(26)

and from Fig. 10(a), it is evident thatD = tan 2 (27)

Therefore, from (26) and (27), 2 is given by

2 = tan1D = tan1

[tan Tm2 + 1

](28)

From (24) and (25), 2 is given by

2 = 6 AMB =

tan1

tan2 max tan2

(T2

)tan T tan

(T2

) (29)

Finally, two more important equations for graphical analysisare

6 AMR =pi

2 cos1

[tan

(T2

)tan max

]

6 AMR = pi2

+ cos1[

cot Ttan max

](30)

Similar equations can be derived for triangular pyramidalscan and are given by (16) and (17).

REFERENCES[1] W. H. V. Aulock, Properties of phased arrays, Proceedings of the IRE,

pp. 17151727, 1960.[2] G. H. Knittel, Choosing the number of faces of a phased-array antenna

for hemisphere scan coverage, IEEE Transactions on Antennas andPropagation, vol. AP-13, no. 6, pp. 878882, 1965.

[3] J. L. Kmetzo, An analytical approach to the coverage of a hemisphere byn planar phased arrays, IEEE Transactions on Antennas and Propagation,vol. AP-15, no. 3, pp. 367371, 1967.

[4] L. E. Corey, A graphical technique for determining optimal array antennageometry, IEEE Transactions on Antennas and Propagation, vol. AP-33,no. 7, pp. 719726, 1985.

[5] A. Jablon and A.Agarwal, Optimal number of array faces for activephased array radars, in Proc. IEEE Antennas Propagat. Symp., Monterey,CA, 2004, pp. 40964099.

[6] A. K. Bhattacharyya, Phased Array Antennas, Floquet analysis, Synthesis,BFNs, and Active Array Systems. Hoboken, NJ: John Willey, 2006.

Srinivasa Rao Zinka was born in Guntur, India, onApril 25, 1984. He received B.Tech degree in elec-tronics and communication engineering from Jawa-harlal Nehru Technological University, Hyderabad,in 2005 and M.Tech. degree in electrical engineeringfrom Indian Institute of Technology, Kanpur, in2007. He is currently pursuing his Ph.D. degree atChung-Ang University, Seoul.

His current research interests are in the areas ofphased array antennas, frequency selective surfaces,microwave circuits and application of optimization

techniques for shaped beam synthesis. He is also involved in developing acomprehensive array design and analysis software.


Il-Bong Jeong was born in Gyeonggi, Korea, onFebruary 20, 1982. He received the B.S. degree inelectronic engineering from Chung-Ang University,Seoul, Korea, in 2008. He is currently pursuing hisM.S. degree at Chung-Ang University.

His recent research interests are in the areas ofphased array antennas and microwave circuits. Heis especially interested in optimized beam patternsynthesis and coupling compensation techniques forphased arrays. In addition, currently he is involvedin developing phased array antennas, where an

aperture-coupled microstrip patch is used as a radiator.

Jong-Hoon Chun was born in Busan, Korea, onMarch 5, 1959. He received the B.S. degree inelectronic engineering from Kyeongbook NationalUniversity, Daegu, Korea, in 1982, the M.S. degreein electrical engineering from Hanyang University,Seoul, Korea, in 1985 and the Ph.D. degree inelectrical engineering from KAIST, Daejeon, Korea,in 2000.

From 1985 to 2002, he was a research engineerin the Research and Development Center at LGInnotek, Korea, where he was involved with the

design of systems, transmitters, and receivers for various kinds of radars.Since 2004, he has been involved with radar system & subsystem design inthe Research and Development Center at Samsung Thales, Korea.

Dr. Chun is a member of the IEEE societies of Microwave Theory andTechniques and Aerospace and Electronic Systems.

Jeong-Phill Kim was born in Jeju, Korea, onNovember 2, 1964. He received the B.S. degreein electronic engineering from Seoul National Uni-versity, Seoul, Korea, in 1988, the M.S. and Ph.D.degrees in electrical engineering from Pohang Uni-versity of Science and Technology, Pohang, Korea,in 1990 and 1998, respectively. From 1990 to 2001,he was a research engineer in the Research andDevelopment Center at LG Innotek, Korea, where hewas involved with the design of antennas, transmit-ters, and receivers for various kinds of radar system.

Since 2001, he has been a faculty member with the School of Electrical andElectronic Engineering, Chung-Ang University, Seoul, Korea.

Dr. Kim has made contribution to the development of material constantsmeasurement setup for dielectric resonator. He also established efficientnetwork models of microstrip-to-slotline transition, slot-coupled microstriplines, microstrip-fed slot antenna, aperture-coupled microstrip patch antenna,and aperture-coupled cavity-fed microstrip patch antenna and coupler. Usingthese efficient network models, he has developed various kinds of novel slot-coupled microstrip circuits such as out-of-phase power dividers, multi-slotcouplers, magic-Ts, and filters. In addition, he was involved in developingphased array antennas, where an aperture-coupled microstrip patch and atapered slot were used as a radiator, and a microstrip meander-line ona ferrite substrate and coplanar waveguide on a thin film ferroelectric asa phase shifter. He also developed FDTD codes to simulate microwavecircuits and antennas. In addition, he was involved in developing a phasedarray antenna with microstrip patch radiator and PIN-diode phase shifter,and calibrating this antenna using the REV(rotating-element electric fieldvector) and MTE(measurement of two elements) methods. As well as, hedesigned an antenna with two fixed beams for direction finding application.His recent research interests include microstrip circuits and antennas, dielectricresonator antennas, mutual coupling phenomena in phased array antenna,numerical modeling and analysis, microwave measurements, and wirelesscommunication and sensor systems such as repeater and random noise radar.

Dr. Kim is a member of the IEEE societies of Microwave Theory and Tech-niques, Antennas and Propagation, and Aerospace and Electronic Systems.

Phase Array Scan Theory

Documents

Transcript of Phase Array Scan Theory