Symposium, Vol. 2, pp , Jul. works must be obtained from the IEE

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1 NAOSITE: Nagasa Unverst's Ac Ttle Author(s) Ctaton Analss of arbtrarl shaped del Taguch, Mtsuo; Masuda, Mtsuhro; Kaumasa roc. of IEEE Antennas and ro Smposum, Vol., pp , Jul Issue Date -7 URL Rght (c) IEEE. ersonal use of ths permsson to reprnt/republsh th purposes or for creatng new collec servers or lsts, or to reuse an c wors must be obtaned from the IEE Ths document s downloaded

2 Analss of Arbtrarl Shaped Delectrc Lens Antenna Mtsuo TAGUCHI Mtsuhro MASUDA* Hdea SHIMODA** Kaumasa TANAKA Dept. of Electrcal & Electronc Eng., Nagasa Unverst -4 Buno-mach, Nagasa-sh, 85-85, Japan ** Telecom Technolog Development Center, TDK Co. -5-7, Hgash-Ohwada, Ichawa-sh, Chba, 7-6 Japan Introducton The collson warnng radar nstalled on the vehcle has been watched attenton as the net safet drvng support sstem n Japan. An electroncall scanned MMWantenna, a mcrostrp antenna and a delectrc lens antenna have been proposed for ths applcaton []. The lens antenna has sutable characterstcs such as narrow beamwdth, low sdelobes, and scannng capablt for the collson warnng radar. In ths paper, the ra tracng method s proposed to anale an arbtrarl shaped delectrc lens antenna. Theoretcal analss Fgure shows the delectrc lens antenna and the coordnate sstem for the ra tracng method. Let the source pont on the prmar radator be (,, ). The equvalent electrc and magnetc currents J (, ) and M (, ) are assumed on the source pont., and are the unt vectors of the Cartesan coordnate sstem. The flat nner surface of lens s S and the outer surface of lens s S and the reference plane of lens antenna s S. The ponts of the ra on S, S, Sare defned as (,, ), (,, ), (,, ), respectvel. Snell's law s epressed as follows: snθ = sn θ () where and are the propagaton constants wthn the outsde and nsde regon of lens, and θ and θ are the ncdent and the refractve angles, respectvel. Applng Eq. () to the ra tracng method, the ponts, and on S, S, and S can be obtaned straghtforwardl []. Fresnel s transmsson coeffcents of parallel and perpendcular polaraton are gven b the followng epressons, respectvel []. µ ncosθ TT M = () µ n cos θ+µ n sn θ T T E where n s the refractve nde of lens. cos n sn µ cosθ = () µ θ+µ θ //$. (c) IEEE

3 n µ ( ) ( ) ε j σ ω = = (4) µ ε σ ω B usng Eqs. () - (4), the ncdent electrc feld on s epressed as follows. E = + + ψ (5) ( E E E ) n E J (, ) = ( )( ) (, ) 4πR j E ( ) ( ) ( ) ( ) ( ), = jωµ J, + M, (7) 4π R R j E (, ) = ( )( ) J (, ) ( ) M (, ) (8) π 4 R R ep ( jr ) j (6) ψ= (9) The electrc feld on the reference plane S s obtaned as, R = ( E ) + E + E ψ { } ep{ j( R+ R + R) } E () (, ) = (, ) + (, ) + (, ) E K E K E K E, =,,or R R R R =, R =, R = K, K, K denote the varables defned b the normal vectors and the transmsson coeffcents at the ponts and. The transmsson coeffcent at each pont depends on the mode of ncdent ra. The radated feld s calculated b the surface ntegral on the reference plane S Replacng the coordnate orgn to the pont of ntersecton of S and the -as, the electrc feld s epressed b E(, r θ, ) = { jωµψ ( ) + ( ) ψ+ ( ) ψ } ds 4π n H n E n E S () ep( jr ) = D( θ, ) r j D( θ, ) = { E ( ) ( ) } { ( ), cos + E, sn θ E, cosθsn 4π S () E ( ) } { ( )}, cosθcos ep j snθcos+ snθsn ds Numercal and epermental results Fgure shows an eample of delectrc lens antenna and ts prmar radator. The lens s made of ABS resn. The dameter, the central thcness and the focal dstance of lens are h=6mm, T=mm, and F=45mm, respectvel. The nner surface s flat and the outer conve surface s rotatonall smmetrc wth respect to the -as. The relatve permttvt of ABS resn s.64 at the frequenc of 76.5 GH. The ()

4 geometr of lens antenna s desgned b usng the optcal desgn software CODE V [4]. The prmar radator s the concal horn antenna fed b the rectangular wavegude. The aperture plane of concal horn s located on the = plane. The se of wavegude s.54.7mm. The dameter of the aperture of concal horn s 6mm. The concal horn antenna s ected b the domnant TE mode of rectangular wavegude [5]. Fgure shows the electrc feld radaton patterns of lens antenna. The dstance between the lens and the aperture of horn s equal to the focal dstance of lens. Fgure 4 shows the calculated electrc feld radaton patterns for dfferent. Concluson The ra tracng method has proposed to anale the arbtrarl shaped delectrc lens antenna. Although the reflecton loss s consdered n the calculaton, the multple reflectons wthn the lens are not consdered. As an eample of numercal calculaton, the radaton patterns of the delectrc lens antenna fed b the concal horn antenna have been shown. References [] K. Nshawa: Antennas and propagaton for ITS (Intellgent Transport Sstem), roc. of Communcaton Socet Conf. of IEICE, TB--6, Oct. 998 (n Japanese). [] T. Kusaawa: Lens optcs Theor and practcal program, Toa Unverst ublshng, pp.-, 85-86, 98-, 988 (n Japanese). [] Insttute of Electroncs and Communcaton Engneers of Japan: Antenna engneerng handboo, pp.-, 98 (n Japanese). [4] [5] C. Balans: Antenna theor Analss and desgn, Chapter, John Wle & Sons, 98. S (,, ),,,,,, r, θ, S S ncdent ra S n E θ normal θ ref E transmttng ra ncdent ra S n E θ normal ref E θ 4 transmttng ra Fgure. Coordnate sstem for ra tracng method.

5 delectrc lens concal horn h T Fgure. Delectrc lens antenna. relatve power (db) measured calculated relatve power (db) measured calculated (a) E-plane patterns (b) H-plane patterns Fgure. Electrc feld radaton patterns of delectrc lens antenna. (h=6mm, T=mm, F=45mm, =45mm) relatve power (db) =45mm - =5mm - =4mm relatve power (db) (a) E-plane patterns (b) H-plane patterns Fgure 4. Electrc feld radaton patterns of delectrc lens antenna. (h=6mm, T=mm, F=45mm) =45mm - =5mm - =4mm