Design of a Planar Slotted Waveguide Array Antenna for X-band ...

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JOURNAL OF THE KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE, VOL. 11, NO. 2, JUN. 2011portant to generate isolated slot admittance as a functionof slot length and the resonant length of the slot as afunction of its offset. For feed slots, the resonant lengthof the slot as a function of its tilt angle is also requiredforthe design of the array. A commercially available EMsimulation tool, HFSS, has been used to generate the basicslot data subsequently used in the array design. Inthe HFSS simulations for the shunt slot, the roundended 2.5 mm wide slot was created in a 1 mm thickbroadwall and admittance was recorded at a distance ofone-half the guide wavelength from the center of theslot; the waveguide was terminated in a short circuitplaced at a quarter-wave distance from the center of theslot. Slot length was varied and at each step of normalizedcomplex admittance, conductance (G/G r ) and susceptance(B/G r), was recorded and was normalized withresonant conductanceof the slot. The design curve thusgenerated is shown in Fig. 1. The real and imaginaryparts of the admittance are denoted as a h 1(y) and h 2(y),respectively, where y is the slot length normalized bythe resonant length, l/l r , which can be written as( , )Y x lG0( )= h ( y) + jh ( y) g( x)1 2The waveguide width and height are 21.5 mm and 5mm, respectively. Next, the slot offset is changed and ateach step, the slot resonant length is calculated wherethe imaginary component of the admittance was zero.The resulting resonant length of the slot as a functionof offset is shown in Fig. 2.We will denote the curve shown in Fig. 2 as v(x),where x is the offset of the slot from the center-line ofthe waveguide.Normalized resonant conductance, g ( x) = GrG0, ofthe isolated shunt slot as a function of offset is plottedFig. 2. Resonant length of the broadwall slot versus offset.in Fig. 3. The curve g(x) can be approximated as follows[7],2 æ p x ög ( x) = K sin ç ÷è a øa b 2 æ pb10 k0öK = 2.09 cos ç ÷b10 k0è 2 ø , (1)where a and b are the waveguide width and height respectively,and b10 is the propagation constant of TE 10mode and k0 = 2p l0.The coupling slot was also characterized in HFSS forits resonant resistance as a function of the tilt angle. Inthe simulation model, waveguide was terminated at thedistanceof the half-guided wavelength from the centerof the slot and resistance was recorded at the port locatedat thedistance of the half-guided wavelength fromFig. 1. Normalized admittance of isolated shunt slot versusslot length.Fig. 3. Normalized conductance of isolated shunt slot asa function of offset.98
BHATTI et al. : DESIGN OF A PLANAR SLOTTED WAVEGUIDE ARRAY ANTENNA FOR X-BAND RADAR APPLICATIONS( b / )( )( / l ) 3K = j k k b a3 10 0k0lmn- jk0R1- jk0R2æ z'ömn 1 e egmnrscos4lk lmn/ 4lmn/ k R k R0 mn0 î íì éù= òç÷ · ê + úè l ø l-0 ë 0 1 0 2 ûk0lrs- jk0Ré 1 ù æ z'örs e ïü+ ê1- ú · cosdz'rs ýdz'mn ,4lrs/ç04lk lrs/÷ë l òûk R- 0 rsè l0ø 0where R is the distance from the point Pmn( 0,0, z ¢mn )measured in local coordinates at the center of the mn thslot to the point Prs( 0,0, z ¢rs ) measured in local coordinatesat the center of the rs th slot. l mn and l rs representthe slot length of mn th and rs th , respectively.ïþFig. 4. Resonant length of the series coupling slot as afunction of tilt angle.the center of the slot. At each tilt angle, the slot lengthwas varied to make the imaginary component of the slotimpedance equal to zero. The resulting curve is shownin Fig. 4.Ⅲ. Planar Array Design ProcedureThe antenna design rests on the following designequation [2].YGamn0where,Kand,f1mn= K f1mn( )VVsmnm0 10( k k )1 20=j a l hG ( b / k)( ka)( kb)( 2 ) cos( 10 )2 2( p 2kl) - ( b k )p klmn b lmn æ p xmnö= -Ksin ç ÷ .è a ømn10(2)éR x x z zë2( mn pq ) ( mn pq )æzz öùç ÷ úèøûpq= - +mnê - + -k0 k0R 2 is the distance from P mn to the left end of the slotPrs( 0,0, - lrs) and R 1 is the distance from P mn to the rightend of the slot, Prs( 0,0, lrs ) and is given as,2 é( ) ( )zmnùR1= xmn - xpq + zmn zæpqlöê- + ç -kpq ÷ëè ú0 øû2 é( ) ( )zmnùR2= xmn - xpq + zmn zæpqlöê- + ç +kpq ÷ëè ú0 øûThe typical configuration of the two slots in an arrayis given in Fig. 5.In (3), MC mn is the mutual coupling term for the mn thslot, which incorporates interactions from all of the slotsin the array.The aperture distribution has been calculated by samplingthe continuous aperture at slot locations for the —25dB first sidelobe level.The planar array is depicted in Fig. 6. It consists ofa twelve branch waveguide witha feed waveguide placedZpq222In equation (2), V m is the mode voltage in the m thsbranch waveguide and Vmn is the slot voltage of themn th slot. Y is the active admittance of the mn th slot.YGamn0=amn2fmn ( xmn lmn)( )22 fmn xmn,lmn02 ,Y xmn lG( , )mn+ MCmn(3)x mnξ2l mnςR 2RR 12l pqxwWaveguide center lineVMC K g x l x lR S srsmn=3å å s mnrs mn mn rs rsr= 1 s= 1 Vmnrs ¹ mn( , , , )Z mnFig. 5. Two slots in a planar array.99
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